%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN439-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:06 AM UTC 2025
% Result : Unsatisfiable 1.41s 1.59s
% Output : Proof 2.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN439-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:35:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.41/1.59 % SZS status Unsatisfiable
% 1.41/1.59 % SZS output start Proof
% 1.41/1.59 tff(c2_1_type, type, (
% 1.41/1.59 c2_1: $i > $o)).
% 1.41/1.59 tff(a537_type, type, (
% 1.41/1.59 a537: $i)).
% 1.41/1.59 tff(c3_1_type, type, (
% 1.41/1.59 c3_1: $i > $o)).
% 1.41/1.59 tff(a545_type, type, (
% 1.41/1.59 a545: $i)).
% 1.41/1.59 tff(c0_1_type, type, (
% 1.41/1.59 c0_1: $i > $o)).
% 1.41/1.59 tff(a562_type, type, (
% 1.41/1.59 a562: $i)).
% 1.41/1.59 tff(hskp46_type, type, (
% 1.41/1.59 hskp46: $o)).
% 1.41/1.59 tff(c1_1_type, type, (
% 1.41/1.59 c1_1: $i > $o)).
% 1.41/1.59 tff(ndr1_0_type, type, (
% 1.41/1.59 ndr1_0: $o)).
% 1.41/1.59 tff(hskp4_type, type, (
% 1.41/1.59 hskp4: $o)).
% 1.41/1.59 tff(a586_type, type, (
% 1.41/1.59 a586: $i)).
% 1.41/1.59 tff(hskp27_type, type, (
% 1.41/1.59 hskp27: $o)).
% 1.41/1.59 tff(hskp6_type, type, (
% 1.41/1.59 hskp6: $o)).
% 1.41/1.59 tff(a548_type, type, (
% 1.41/1.59 a548: $i)).
% 1.41/1.59 tff(hskp33_type, type, (
% 1.41/1.59 hskp33: $o)).
% 1.41/1.59 tff(a582_type, type, (
% 1.41/1.59 a582: $i)).
% 1.41/1.59 tff(hskp19_type, type, (
% 1.41/1.59 hskp19: $o)).
% 1.41/1.59 tff(hskp50_type, type, (
% 1.41/1.59 hskp50: $o)).
% 1.41/1.59 tff(hskp25_type, type, (
% 1.41/1.59 hskp25: $o)).
% 1.41/1.59 tff(a556_type, type, (
% 1.41/1.59 a556: $i)).
% 1.41/1.59 tff(hskp42_type, type, (
% 1.41/1.59 hskp42: $o)).
% 1.41/1.59 tff(a590_type, type, (
% 1.41/1.59 a590: $i)).
% 1.41/1.59 tff(hskp0_type, type, (
% 1.41/1.59 hskp0: $o)).
% 1.41/1.59 tff(a547_type, type, (
% 1.41/1.59 a547: $i)).
% 1.41/1.59 tff(hskp38_type, type, (
% 1.41/1.59 hskp38: $o)).
% 1.41/1.59 tff(hskp34_type, type, (
% 1.41/1.59 hskp34: $o)).
% 1.41/1.59 tff(hskp39_type, type, (
% 1.41/1.59 hskp39: $o)).
% 1.41/1.59 tff(hskp37_type, type, (
% 1.41/1.59 hskp37: $o)).
% 1.41/1.59 tff(a544_type, type, (
% 1.41/1.59 a544: $i)).
% 1.41/1.59 tff(a573_type, type, (
% 1.41/1.59 a573: $i)).
% 1.41/1.59 tff(a569_type, type, (
% 1.41/1.59 a569: $i)).
% 1.41/1.59 tff(a552_type, type, (
% 1.41/1.59 a552: $i)).
% 1.41/1.59 tff(hskp8_type, type, (
% 1.41/1.59 hskp8: $o)).
% 1.41/1.59 tff(a589_type, type, (
% 1.41/1.59 a589: $i)).
% 1.41/1.59 tff(hskp28_type, type, (
% 1.41/1.59 hskp28: $o)).
% 1.41/1.59 tff(hskp15_type, type, (
% 1.41/1.59 hskp15: $o)).
% 1.41/1.59 tff(a574_type, type, (
% 1.41/1.59 a574: $i)).
% 1.41/1.59 tff(a554_type, type, (
% 1.41/1.59 a554: $i)).
% 1.41/1.59 tff(hskp9_type, type, (
% 1.41/1.59 hskp9: $o)).
% 1.41/1.59 tff(hskp31_type, type, (
% 1.41/1.59 hskp31: $o)).
% 1.41/1.59 tff(hskp52_type, type, (
% 1.41/1.59 hskp52: $o)).
% 1.41/1.59 tff(hskp40_type, type, (
% 1.41/1.59 hskp40: $o)).
% 1.41/1.59 tff(hskp41_type, type, (
% 1.41/1.59 hskp41: $o)).
% 1.41/1.59 tff(a555_type, type, (
% 1.41/1.59 a555: $i)).
% 1.41/1.59 tff(a549_type, type, (
% 1.41/1.59 a549: $i)).
% 1.41/1.59 tff(a571_type, type, (
% 1.41/1.59 a571: $i)).
% 1.41/1.59 tff(hskp17_type, type, (
% 1.41/1.59 hskp17: $o)).
% 1.41/1.59 tff(a551_type, type, (
% 1.41/1.59 a551: $i)).
% 1.41/1.59 tff(hskp18_type, type, (
% 1.41/1.59 hskp18: $o)).
% 1.41/1.59 tff(hskp16_type, type, (
% 1.41/1.59 hskp16: $o)).
% 1.41/1.59 tff(a570_type, type, (
% 1.41/1.59 a570: $i)).
% 1.41/1.59 tff(a572_type, type, (
% 1.41/1.59 a572: $i)).
% 1.41/1.59 tff(hskp7_type, type, (
% 1.41/1.59 hskp7: $o)).
% 1.41/1.59 tff(a550_type, type, (
% 1.41/1.59 a550: $i)).
% 1.41/1.59 tff(a535_type, type, (
% 1.41/1.59 a535: $i)).
% 1.41/1.59 tff(hskp45_type, type, (
% 1.41/1.59 hskp45: $o)).
% 1.41/1.59 tff(a561_type, type, (
% 1.41/1.59 a561: $i)).
% 1.41/1.59 tff(a567_type, type, (
% 1.41/1.59 a567: $i)).
% 1.41/1.59 tff(hskp14_type, type, (
% 1.41/1.59 hskp14: $o)).
% 1.41/1.59 tff(hskp1_type, type, (
% 1.41/1.59 hskp1: $o)).
% 1.41/1.59 tff(a539_type, type, (
% 1.41/1.59 a539: $i)).
% 1.41/1.59 tff(a540_type, type, (
% 1.41/1.59 a540: $i)).
% 1.41/1.59 tff(hskp2_type, type, (
% 1.41/1.59 hskp2: $o)).
% 1.41/1.59 tff(hskp26_type, type, (
% 1.41/1.59 hskp26: $o)).
% 1.41/1.59 tff(a584_type, type, (
% 1.41/1.59 a584: $i)).
% 1.41/1.59 tff(a583_type, type, (
% 1.41/1.59 a583: $i)).
% 1.41/1.59 tff(hskp51_type, type, (
% 1.41/1.59 hskp51: $o)).
% 1.41/1.59 tff(a536_type, type, (
% 1.41/1.59 a536: $i)).
% 1.41/1.59 tff(a581_type, type, (
% 1.41/1.59 a581: $i)).
% 1.41/1.59 tff(hskp24_type, type, (
% 1.41/1.59 hskp24: $o)).
% 1.41/1.59 tff(hskp43_type, type, (
% 1.41/1.59 hskp43: $o)).
% 1.41/1.59 tff(a568_type, type, (
% 1.41/1.59 a568: $i)).
% 1.41/1.59 tff(a557_type, type, (
% 1.41/1.59 a557: $i)).
% 1.41/1.59 tff(hskp49_type, type, (
% 1.41/1.59 hskp49: $o)).
% 1.41/1.59 tff(a538_type, type, (
% 1.41/1.59 a538: $i)).
% 1.41/1.59 tff(hskp35_type, type, (
% 1.41/1.59 hskp35: $o)).
% 1.41/1.59 tff(a591_type, type, (
% 1.41/1.59 a591: $i)).
% 1.41/1.59 tff(hskp30_type, type, (
% 1.41/1.59 hskp30: $o)).
% 1.41/1.59 tff(hskp29_type, type, (
% 1.41/1.59 hskp29: $o)).
% 1.41/1.59 tff(a596_type, type, (
% 1.41/1.59 a596: $i)).
% 1.41/1.59 tff(hskp32_type, type, (
% 1.41/1.59 hskp32: $o)).
% 1.41/1.59 tff(a564_type, type, (
% 1.41/1.59 a564: $i)).
% 1.41/1.59 tff(hskp47_type, type, (
% 1.41/1.59 hskp47: $o)).
% 1.41/1.59 tff(a546_type, type, (
% 1.41/1.59 a546: $i)).
% 1.41/1.59 tff(hskp5_type, type, (
% 1.41/1.59 hskp5: $o)).
% 1.41/1.59 tff(a563_type, type, (
% 1.41/1.59 a563: $i)).
% 1.41/1.59 tff(hskp12_type, type, (
% 1.41/1.59 hskp12: $o)).
% 1.41/1.59 tff(a558_type, type, (
% 1.41/1.59 a558: $i)).
% 1.41/1.59 tff(hskp10_type, type, (
% 1.41/1.59 hskp10: $o)).
% 1.41/1.59 tff(1,assumption,(c2_1(a537)), introduced(assumption)).
% 1.41/1.59 tff(2,assumption,(c3_1(a545)), introduced(assumption)).
% 1.41/1.59 tff(3,plain,
% 1.41/1.59 (^[V: $i, U: $i] : refl((hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(4,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[3])).
% 1.41/1.59 tff(5,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.59 inference(rewrite,[status(thm)],[])).
% 1.41/1.59 tff(6,plain,
% 1.41/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | hskp46) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp46))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp46) <=> (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | hskp46) <=> (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(7,plain,
% 1.41/1.59 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | hskp46) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[6])).
% 1.41/1.59 tff(8,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(V)) | hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause246')).
% 1.41/1.59 tff(9,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.41/1.59 tff(10,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.41/1.59 tff(11,plain,(
% 1.41/1.59 ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.59 inference(skolemize,[status(sab)],[10])).
% 1.41/1.59 tff(12,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[11, 4])).
% 1.41/1.59 tff(13,plain,
% 1.41/1.59 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(14,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[13])).
% 1.41/1.59 tff(15,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.59 inference(rewrite,[status(thm)],[])).
% 1.41/1.59 tff(16,plain,
% 1.41/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(17,plain,
% 1.41/1.59 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[16])).
% 1.41/1.59 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 1.41/1.59 tff(19,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.41/1.59 tff(20,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.41/1.59 tff(21,plain,(
% 1.41/1.59 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.59 inference(skolemize,[status(sab)],[20])).
% 1.41/1.59 tff(22,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.41/1.59 tff(23,assumption,(~hskp4), introduced(assumption)).
% 1.41/1.59 tff(24,assumption,(~c2_1(a548)), introduced(assumption)).
% 1.41/1.59 tff(25,plain,
% 1.41/1.59 (^[U: $i] : refl((hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(26,plain,
% 1.41/1.59 (![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[25])).
% 1.41/1.59 tff(27,plain,
% 1.41/1.59 (![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.41/1.59 inference(rewrite,[status(thm)],[])).
% 1.41/1.59 tff(28,plain,
% 1.41/1.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp19) | hskp50) <=> ((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp50))), rewrite(((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp50) <=> (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp19) | hskp50) <=> (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(29,plain,
% 1.41/1.59 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp19) | hskp50) <=> ![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[28])).
% 1.41/1.59 tff(30,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp19) | hskp50)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause220')).
% 1.41/1.59 tff(31,plain,
% 1.41/1.59 (![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.41/1.59 tff(32,plain,
% 1.41/1.59 (![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[31, 27])).
% 1.41/1.59 tff(33,plain,(
% 1.41/1.59 ![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.41/1.59 inference(skolemize,[status(sab)],[32])).
% 1.41/1.59 tff(34,plain,
% 1.41/1.59 (![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.41/1.59 tff(35,assumption,(~hskp33), introduced(assumption)).
% 1.41/1.59 tff(36,plain,
% 1.41/1.59 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(37,plain,
% 1.41/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[36])).
% 1.41/1.59 tff(38,plain,
% 1.41/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.41/1.59 inference(rewrite,[status(thm)],[])).
% 1.41/1.59 tff(39,plain,
% 1.41/1.59 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c3_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c3_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) | c1_1(W)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) | c1_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(40,plain,
% 1.41/1.59 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) | c1_1(W)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[39])).
% 1.41/1.59 tff(41,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c2_1(W)) | c3_1(W)) | c1_1(W)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause258')).
% 1.41/1.59 tff(42,plain,
% 1.41/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.41/1.59 tff(43,plain,
% 1.41/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.41/1.59 tff(44,plain,(
% 1.41/1.59 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.41/1.59 inference(skolemize,[status(sab)],[43])).
% 1.41/1.59 tff(45,plain,
% 1.41/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.41/1.59 tff(46,plain,
% 1.41/1.59 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(47,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[46])).
% 1.41/1.59 tff(48,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.41/1.59 inference(rewrite,[status(thm)],[])).
% 1.41/1.59 tff(49,plain,
% 1.41/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp25))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.41/1.59 inference(bind,[status(th)],[])).
% 1.41/1.59 tff(50,plain,
% 1.41/1.59 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.41/1.59 inference(quant_intro,[status(thm)],[49])).
% 1.41/1.59 tff(51,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause256')).
% 1.41/1.59 tff(52,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.41/1.59 tff(53,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.41/1.59 tff(54,plain,(
% 1.41/1.59 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.41/1.59 inference(skolemize,[status(sab)],[53])).
% 1.41/1.59 tff(55,plain,
% 1.41/1.59 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.41/1.59 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.41/1.59 tff(56,assumption,(~c0_1(a548)), introduced(assumption)).
% 1.41/1.59 tff(57,assumption,(~c1_1(a548)), introduced(assumption)).
% 1.41/1.59 tff(58,assumption,(~hskp38), introduced(assumption)).
% 1.41/1.59 tff(59,assumption,(hskp46), introduced(assumption)).
% 1.41/1.59 tff(60,plain,
% 1.41/1.59 (((~hskp46) | (~c0_1(a562))) <=> ((~hskp46) | (~c0_1(a562)))),
% 1.41/1.59 inference(rewrite,[status(thm)],[])).
% 1.41/1.59 tff(61,plain,
% 1.41/1.59 (((~c0_1(a562)) | (~hskp46)) <=> ((~hskp46) | (~c0_1(a562)))),
% 1.41/1.59 inference(rewrite,[status(thm)],[])).
% 1.41/1.59 tff(62,axiom,((~c0_1(a562)) | (~hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.41/1.60 tff(63,plain,
% 1.41/1.60 ((~hskp46) | (~c0_1(a562))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.41/1.60 tff(64,plain,
% 1.41/1.60 ((~hskp46) | (~c0_1(a562))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.41/1.60 tff(65,plain,
% 1.41/1.60 (~c0_1(a562)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[64, 59])).
% 1.41/1.60 tff(66,plain,
% 1.41/1.60 (^[V: $i, U: $i] : refl((hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(67,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[66])).
% 1.41/1.60 tff(68,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(69,plain,
% 1.41/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> (((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))))), rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp34) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp34))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp34) <=> (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp34) <=> (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(70,plain,
% 1.41/1.60 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp34) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[69])).
% 1.41/1.60 tff(71,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(V)) | c0_1(V)) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause250')).
% 1.41/1.60 tff(72,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.41/1.60 tff(73,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.41/1.60 tff(74,plain,(
% 1.41/1.60 ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(skolemize,[status(sab)],[73])).
% 1.41/1.60 tff(75,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.41/1.60 tff(76,plain,
% 1.41/1.60 (^[V: $i, U: $i] : refl((hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) <=> (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(77,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[76])).
% 1.41/1.60 tff(78,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(79,plain,
% 1.41/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))))), (((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V))), ((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V)))), (((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V))), (((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V)))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(V)) | hskp33) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) | hskp33))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) | hskp33) <=> (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(V)) | hskp33) <=> (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(80,plain,
% 1.41/1.60 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(V)) | hskp33) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[79])).
% 1.41/1.60 tff(81,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(V)) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause230')).
% 1.41/1.60 tff(82,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.41/1.60 tff(83,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[82, 78])).
% 1.41/1.60 tff(84,plain,(
% 1.41/1.60 ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.41/1.60 inference(skolemize,[status(sab)],[83])).
% 1.41/1.60 tff(85,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[84, 77])).
% 1.41/1.60 tff(86,assumption,(~c3_1(a586)), introduced(assumption)).
% 1.41/1.60 tff(87,assumption,(~c0_1(a586)), introduced(assumption)).
% 1.41/1.60 tff(88,assumption,(~c1_1(a586)), introduced(assumption)).
% 1.41/1.60 tff(89,plain,
% 1.41/1.60 (((~hskp27) | c1_1(a586)) <=> ((~hskp27) | c1_1(a586))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(90,axiom,((~hskp27) | c1_1(a586)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.41/1.60 tff(91,plain,
% 1.41/1.60 ((~hskp27) | c1_1(a586)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.41/1.60 tff(92,plain,
% 1.41/1.60 ((~hskp27) | c1_1(a586)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[91, 89])).
% 1.41/1.60 tff(93,plain,
% 1.41/1.60 ((~hskp27) | c1_1(a586)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[92, 89])).
% 1.41/1.60 tff(94,plain,
% 1.41/1.60 ((~hskp27) | c1_1(a586)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[93, 89])).
% 1.41/1.60 tff(95,plain,
% 1.41/1.60 ((~hskp27) | c1_1(a586)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[94, 89])).
% 1.41/1.60 tff(96,plain,
% 1.41/1.60 (~hskp27),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[95, 88])).
% 1.41/1.60 tff(97,assumption,(~c0_1(a545)), introduced(assumption)).
% 1.41/1.60 tff(98,assumption,(~hskp19), introduced(assumption)).
% 1.41/1.60 tff(99,plain,
% 1.41/1.60 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(100,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[99])).
% 1.41/1.60 tff(101,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(102,plain,
% 1.41/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) <=> (((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))))), rewrite((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(103,plain,
% 1.41/1.60 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[102])).
% 1.41/1.60 tff(104,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause236')).
% 1.41/1.60 tff(105,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.41/1.60 tff(106,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.41/1.60 tff(107,plain,(
% 1.41/1.60 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.60 inference(skolemize,[status(sab)],[106])).
% 1.41/1.60 tff(108,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[107, 100])).
% 1.41/1.60 tff(109,assumption,(~hskp15), introduced(assumption)).
% 1.41/1.60 tff(110,assumption,(~hskp50), introduced(assumption)).
% 1.41/1.60 tff(111,assumption,(~c2_1(a545)), introduced(assumption)).
% 1.41/1.60 tff(112,assumption,(~c1_1(a545)), introduced(assumption)).
% 1.41/1.60 tff(113,plain,
% 1.41/1.60 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U)) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U)))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(114,plain,
% 1.41/1.60 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U)) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[113])).
% 1.41/1.60 tff(115,plain,
% 1.41/1.60 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U)) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(116,plain,
% 1.41/1.60 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | hskp28) <=> (hskp28 | (~ndr1_0))), ((((~ndr1_0) | hskp28) | c1_1(U)) <=> ((hskp28 | (~ndr1_0)) | c1_1(U)))), rewrite(((hskp28 | (~ndr1_0)) | c1_1(U)) <=> (hskp28 | (~ndr1_0) | c1_1(U))), ((((~ndr1_0) | hskp28) | c1_1(U)) <=> (hskp28 | (~ndr1_0) | c1_1(U)))), (((((~ndr1_0) | hskp28) | c1_1(U)) | c0_1(U)) <=> ((hskp28 | (~ndr1_0) | c1_1(U)) | c0_1(U)))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U)) | c0_1(U)) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c1_1(U))), (((((~ndr1_0) | hskp28) | c1_1(U)) | c0_1(U)) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c1_1(U)))), ((((((~ndr1_0) | hskp28) | c1_1(U)) | c0_1(U)) | c2_1(U)) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c1_1(U)) | c2_1(U)))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c1_1(U)) | c2_1(U)) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))), ((((((~ndr1_0) | hskp28) | c1_1(U)) | c0_1(U)) | c2_1(U)) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(117,plain,
% 1.41/1.60 (![U: $i] : (((((~ndr1_0) | hskp28) | c1_1(U)) | c0_1(U)) | c2_1(U)) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[116])).
% 1.41/1.60 tff(118,axiom,(![U: $i] : (((((~ndr1_0) | hskp28) | c1_1(U)) | c0_1(U)) | c2_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause217')).
% 1.41/1.60 tff(119,plain,
% 1.41/1.60 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.41/1.60 tff(120,plain,
% 1.41/1.60 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[119, 115])).
% 1.41/1.60 tff(121,plain,(
% 1.41/1.60 ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))),
% 1.41/1.60 inference(skolemize,[status(sab)],[120])).
% 1.41/1.60 tff(122,plain,
% 1.41/1.60 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[121, 114])).
% 1.41/1.60 tff(123,assumption,(~ndr1_0), introduced(assumption)).
% 1.41/1.60 tff(124,plain,
% 1.41/1.60 ((ndr1_0 | (~hskp31)) <=> (ndr1_0 | (~hskp31))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(125,plain,
% 1.41/1.60 (((~hskp31) | ndr1_0) <=> (ndr1_0 | (~hskp31))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(126,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 1.41/1.60 tff(127,plain,
% 1.41/1.60 (ndr1_0 | (~hskp31)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.41/1.60 tff(128,plain,
% 1.41/1.60 (ndr1_0 | (~hskp31)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[127, 124])).
% 1.41/1.60 tff(129,plain,
% 1.41/1.60 (~hskp31),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[128, 123])).
% 1.41/1.60 tff(130,plain,
% 1.41/1.60 (((~hskp52) | ndr1_0) <=> ((~hskp52) | ndr1_0)),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(131,axiom,((~hskp52) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.41/1.60 tff(132,plain,
% 1.41/1.60 ((~hskp52) | ndr1_0),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.41/1.60 tff(133,plain,
% 1.41/1.60 ((~hskp52) | ndr1_0),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[132, 130])).
% 1.41/1.60 tff(134,plain,
% 1.41/1.60 ((~hskp52) | ndr1_0),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[133, 130])).
% 1.41/1.60 tff(135,plain,
% 1.41/1.60 ((~hskp52) | ndr1_0),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[134, 130])).
% 1.41/1.60 tff(136,plain,
% 1.41/1.60 ((~hskp52) | ndr1_0),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[135, 130])).
% 1.41/1.60 tff(137,plain,
% 1.41/1.60 (~hskp52),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[136, 123])).
% 1.41/1.60 tff(138,plain,
% 1.41/1.60 ((ndr1_0 | (~hskp40)) <=> (ndr1_0 | (~hskp40))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(139,plain,
% 1.41/1.60 (((~hskp40) | ndr1_0) <=> (ndr1_0 | (~hskp40))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(140,axiom,((~hskp40) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 1.41/1.60 tff(141,plain,
% 1.41/1.60 (ndr1_0 | (~hskp40)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.41/1.60 tff(142,plain,
% 1.41/1.60 (ndr1_0 | (~hskp40)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[141, 138])).
% 1.41/1.60 tff(143,plain,
% 1.41/1.60 (~hskp40),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[142, 123])).
% 1.41/1.60 tff(144,plain,
% 1.41/1.60 ((hskp52 | hskp40 | hskp31) <=> (hskp52 | hskp40 | hskp31)),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(145,plain,
% 1.41/1.60 (((hskp40 | hskp31) | hskp52) <=> (hskp52 | hskp40 | hskp31)),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(146,plain,
% 1.41/1.60 ((hskp40 | hskp31) <=> (hskp40 | hskp31)),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(147,plain,
% 1.41/1.60 (((hskp40 | hskp31) | hskp52) <=> ((hskp40 | hskp31) | hskp52)),
% 1.41/1.60 inference(monotonicity,[status(thm)],[146])).
% 1.41/1.60 tff(148,plain,
% 1.41/1.60 (((hskp40 | hskp31) | hskp52) <=> (hskp52 | hskp40 | hskp31)),
% 1.41/1.60 inference(transitivity,[status(thm)],[147, 145])).
% 1.41/1.60 tff(149,axiom,((hskp40 | hskp31) | hskp52), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.41/1.60 tff(150,plain,
% 1.41/1.60 (hskp52 | hskp40 | hskp31),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.41/1.60 tff(151,plain,
% 1.41/1.60 (hskp52 | hskp40 | hskp31),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[150, 144])).
% 1.41/1.60 tff(152,plain,
% 1.41/1.60 (hskp52 | hskp40 | hskp31),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[151, 144])).
% 1.41/1.60 tff(153,plain,
% 1.41/1.60 (hskp52 | hskp40 | hskp31),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[152, 144])).
% 1.41/1.60 tff(154,plain,
% 1.41/1.60 (hskp52 | hskp40 | hskp31),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[153, 144])).
% 1.41/1.60 tff(155,plain,
% 1.41/1.60 ($false),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[154, 143, 137, 129])).
% 1.41/1.60 tff(156,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.41/1.60 tff(157,plain,
% 1.41/1.60 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c1_1(a545) | c2_1(a545) | c0_1(a545) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a545) | c2_1(a545) | c0_1(a545) | (~ndr1_0))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(158,plain,
% 1.41/1.60 ((hskp28 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | c1_1(a545)) <=> (hskp28 | c1_1(a545) | c2_1(a545) | c0_1(a545) | (~ndr1_0))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(159,plain,
% 1.41/1.60 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | c1_1(a545))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c1_1(a545) | c2_1(a545) | c0_1(a545) | (~ndr1_0)))),
% 1.41/1.60 inference(monotonicity,[status(thm)],[158])).
% 1.41/1.60 tff(160,plain,
% 1.41/1.60 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | c1_1(a545))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a545) | c2_1(a545) | c0_1(a545) | (~ndr1_0))),
% 1.41/1.60 inference(transitivity,[status(thm)],[159, 157])).
% 1.41/1.60 tff(161,plain,
% 1.41/1.60 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | c1_1(a545))),
% 1.41/1.60 inference(quant_inst,[status(thm)],[])).
% 1.41/1.60 tff(162,plain,
% 1.41/1.60 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a545) | c2_1(a545) | c0_1(a545) | (~ndr1_0)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.41/1.60 tff(163,plain,
% 1.41/1.60 (hskp28 | c1_1(a545) | c2_1(a545)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[162, 156, 97, 122])).
% 1.41/1.60 tff(164,plain,
% 1.41/1.60 (hskp28),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[163, 112, 111])).
% 1.41/1.60 tff(165,plain,
% 1.41/1.60 (((~hskp28) | c2_1(a589)) <=> ((~hskp28) | c2_1(a589))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(166,axiom,((~hskp28) | c2_1(a589)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.41/1.60 tff(167,plain,
% 1.41/1.60 ((~hskp28) | c2_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.41/1.60 tff(168,plain,
% 1.41/1.60 ((~hskp28) | c2_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[167, 165])).
% 1.41/1.60 tff(169,plain,
% 1.41/1.60 ((~hskp28) | c2_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[168, 165])).
% 1.41/1.60 tff(170,plain,
% 1.41/1.60 ((~hskp28) | c2_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[169, 165])).
% 1.41/1.60 tff(171,plain,
% 1.41/1.60 ((~hskp28) | c2_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[170, 165])).
% 1.41/1.60 tff(172,plain,
% 1.41/1.60 (c2_1(a589)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[171, 164])).
% 1.41/1.60 tff(173,plain,
% 1.41/1.60 (((~hskp28) | (~c0_1(a589))) <=> ((~hskp28) | (~c0_1(a589)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(174,plain,
% 1.41/1.60 (((~c0_1(a589)) | (~hskp28)) <=> ((~hskp28) | (~c0_1(a589)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(175,axiom,((~c0_1(a589)) | (~hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.41/1.60 tff(176,plain,
% 1.41/1.60 ((~hskp28) | (~c0_1(a589))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.41/1.60 tff(177,plain,
% 1.41/1.60 ((~hskp28) | (~c0_1(a589))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[176, 173])).
% 1.41/1.60 tff(178,plain,
% 1.41/1.60 (~c0_1(a589)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[177, 164])).
% 1.41/1.60 tff(179,plain,
% 1.41/1.60 (((~hskp28) | c3_1(a589)) <=> ((~hskp28) | c3_1(a589))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(180,axiom,((~hskp28) | c3_1(a589)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.41/1.60 tff(181,plain,
% 1.41/1.60 ((~hskp28) | c3_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.41/1.60 tff(182,plain,
% 1.41/1.60 ((~hskp28) | c3_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[181, 179])).
% 1.41/1.60 tff(183,plain,
% 1.41/1.60 ((~hskp28) | c3_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[182, 179])).
% 1.41/1.60 tff(184,plain,
% 1.41/1.60 ((~hskp28) | c3_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[183, 179])).
% 1.41/1.60 tff(185,plain,
% 1.41/1.60 ((~hskp28) | c3_1(a589)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[184, 179])).
% 1.41/1.60 tff(186,plain,
% 1.41/1.60 (c3_1(a589)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[185, 164])).
% 1.41/1.60 tff(187,plain,
% 1.41/1.60 (((~hskp4) | c1_1(a545)) <=> ((~hskp4) | c1_1(a545))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(188,axiom,((~hskp4) | c1_1(a545)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.41/1.60 tff(189,plain,
% 1.41/1.60 ((~hskp4) | c1_1(a545)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.41/1.60 tff(190,plain,
% 1.41/1.60 ((~hskp4) | c1_1(a545)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[189, 187])).
% 1.41/1.60 tff(191,plain,
% 1.41/1.60 ((~hskp4) | c1_1(a545)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[190, 187])).
% 1.41/1.60 tff(192,plain,
% 1.41/1.60 ((~hskp4) | c1_1(a545)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[191, 187])).
% 1.41/1.60 tff(193,plain,
% 1.41/1.60 ((~hskp4) | c1_1(a545)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[192, 187])).
% 1.41/1.60 tff(194,plain,
% 1.41/1.60 (~hskp4),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[193, 112])).
% 1.41/1.60 tff(195,plain,
% 1.41/1.60 ((hskp27 | hskp6 | hskp4) <=> (hskp27 | hskp6 | hskp4)),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(196,plain,
% 1.41/1.60 (((hskp27 | hskp6) | hskp4) <=> (hskp27 | hskp6 | hskp4)),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(197,plain,
% 1.41/1.60 ((hskp6 | hskp27) <=> (hskp27 | hskp6)),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(198,plain,
% 1.41/1.60 (((hskp6 | hskp27) | hskp4) <=> ((hskp27 | hskp6) | hskp4)),
% 1.41/1.60 inference(monotonicity,[status(thm)],[197])).
% 1.41/1.60 tff(199,plain,
% 1.41/1.60 (((hskp6 | hskp27) | hskp4) <=> (hskp27 | hskp6 | hskp4)),
% 1.41/1.60 inference(transitivity,[status(thm)],[198, 196])).
% 1.41/1.60 tff(200,axiom,((hskp6 | hskp27) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.41/1.60 tff(201,plain,
% 1.41/1.60 (hskp27 | hskp6 | hskp4),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.41/1.60 tff(202,plain,
% 1.41/1.60 (hskp27 | hskp6 | hskp4),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[201, 195])).
% 1.41/1.60 tff(203,plain,
% 1.41/1.60 (hskp27 | hskp6 | hskp4),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[202, 195])).
% 1.41/1.60 tff(204,plain,
% 1.41/1.60 (hskp27 | hskp6 | hskp4),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[203, 195])).
% 1.41/1.60 tff(205,plain,
% 1.41/1.60 (hskp27 | hskp6 | hskp4),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[204, 195])).
% 1.41/1.60 tff(206,plain,
% 1.41/1.60 (hskp6),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[205, 194, 96])).
% 1.41/1.60 tff(207,plain,
% 1.41/1.60 (((~hskp6) | (~c0_1(a548))) <=> ((~hskp6) | (~c0_1(a548)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(208,plain,
% 1.41/1.60 (((~c0_1(a548)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a548)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(209,axiom,((~c0_1(a548)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 1.41/1.60 tff(210,plain,
% 1.41/1.60 ((~hskp6) | (~c0_1(a548))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.41/1.60 tff(211,plain,
% 1.41/1.60 ((~hskp6) | (~c0_1(a548))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[210, 207])).
% 1.41/1.60 tff(212,plain,
% 1.41/1.60 (~c0_1(a548)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[211, 206])).
% 1.41/1.60 tff(213,plain,
% 1.41/1.60 (((~hskp6) | (~c2_1(a548))) <=> ((~hskp6) | (~c2_1(a548)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(214,plain,
% 1.41/1.60 (((~c2_1(a548)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a548)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(215,axiom,((~c2_1(a548)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 1.41/1.60 tff(216,plain,
% 1.41/1.60 ((~hskp6) | (~c2_1(a548))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.41/1.60 tff(217,plain,
% 1.41/1.60 ((~hskp6) | (~c2_1(a548))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[216, 213])).
% 1.41/1.60 tff(218,plain,
% 1.41/1.60 (~c2_1(a548)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[217, 206])).
% 1.41/1.60 tff(219,plain,
% 1.41/1.60 (((~hskp6) | c3_1(a548)) <=> ((~hskp6) | c3_1(a548))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(220,axiom,((~hskp6) | c3_1(a548)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.41/1.60 tff(221,plain,
% 1.41/1.60 ((~hskp6) | c3_1(a548)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.41/1.60 tff(222,plain,
% 1.41/1.60 ((~hskp6) | c3_1(a548)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[221, 219])).
% 1.41/1.60 tff(223,plain,
% 1.41/1.60 ((~hskp6) | c3_1(a548)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[222, 219])).
% 1.41/1.60 tff(224,plain,
% 1.41/1.60 ((~hskp6) | c3_1(a548)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[223, 219])).
% 1.41/1.60 tff(225,plain,
% 1.41/1.60 ((~hskp6) | c3_1(a548)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[224, 219])).
% 1.41/1.60 tff(226,plain,
% 1.41/1.60 (c3_1(a548)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[225, 206])).
% 1.41/1.60 tff(227,assumption,(hskp41), introduced(assumption)).
% 1.41/1.60 tff(228,plain,
% 1.41/1.60 (((~hskp41) | (~c2_1(a555))) <=> ((~hskp41) | (~c2_1(a555)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(229,plain,
% 1.41/1.60 (((~c2_1(a555)) | (~hskp41)) <=> ((~hskp41) | (~c2_1(a555)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(230,axiom,((~c2_1(a555)) | (~hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.41/1.60 tff(231,plain,
% 1.41/1.60 ((~hskp41) | (~c2_1(a555))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.41/1.60 tff(232,plain,
% 1.41/1.60 ((~hskp41) | (~c2_1(a555))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[231, 228])).
% 1.41/1.60 tff(233,plain,
% 1.41/1.60 (~c2_1(a555)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[232, 227])).
% 1.41/1.60 tff(234,plain,
% 1.41/1.60 (((~hskp41) | c0_1(a555)) <=> ((~hskp41) | c0_1(a555))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(235,axiom,((~hskp41) | c0_1(a555)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.41/1.60 tff(236,plain,
% 1.41/1.60 ((~hskp41) | c0_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.41/1.60 tff(237,plain,
% 1.41/1.60 ((~hskp41) | c0_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[236, 234])).
% 1.41/1.60 tff(238,plain,
% 1.41/1.60 ((~hskp41) | c0_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[237, 234])).
% 1.41/1.60 tff(239,plain,
% 1.41/1.60 ((~hskp41) | c0_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[238, 234])).
% 1.41/1.60 tff(240,plain,
% 1.41/1.60 ((~hskp41) | c0_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[239, 234])).
% 1.41/1.60 tff(241,plain,
% 1.41/1.60 (c0_1(a555)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[240, 227])).
% 1.41/1.60 tff(242,plain,
% 1.41/1.60 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a555) | (~ndr1_0) | c1_1(a555) | (~c0_1(a555)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a555) | (~ndr1_0) | c1_1(a555) | (~c0_1(a555)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(243,plain,
% 1.41/1.60 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a555) | c1_1(a555) | (~c0_1(a555))) <=> (hskp50 | hskp19 | c2_1(a555) | (~ndr1_0) | c1_1(a555) | (~c0_1(a555)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(244,plain,
% 1.41/1.60 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a555) | c1_1(a555) | (~c0_1(a555)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a555) | (~ndr1_0) | c1_1(a555) | (~c0_1(a555))))),
% 1.41/1.60 inference(monotonicity,[status(thm)],[243])).
% 1.41/1.60 tff(245,plain,
% 1.41/1.60 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a555) | c1_1(a555) | (~c0_1(a555)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a555) | (~ndr1_0) | c1_1(a555) | (~c0_1(a555)))),
% 1.41/1.60 inference(transitivity,[status(thm)],[244, 242])).
% 1.41/1.60 tff(246,plain,
% 1.41/1.60 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a555) | c1_1(a555) | (~c0_1(a555)))),
% 1.41/1.60 inference(quant_inst,[status(thm)],[])).
% 1.41/1.60 tff(247,plain,
% 1.41/1.60 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a555) | (~ndr1_0) | c1_1(a555) | (~c0_1(a555))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.41/1.60 tff(248,plain,
% 1.41/1.60 (c1_1(a555)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[247, 156, 110, 98, 241, 233, 34])).
% 1.41/1.60 tff(249,assumption,(c3_1(a548)), introduced(assumption)).
% 1.41/1.60 tff(250,plain,
% 1.41/1.60 (((~hskp41) | c3_1(a555)) <=> ((~hskp41) | c3_1(a555))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(251,axiom,((~hskp41) | c3_1(a555)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.41/1.60 tff(252,plain,
% 1.41/1.60 ((~hskp41) | c3_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.41/1.60 tff(253,plain,
% 1.41/1.60 ((~hskp41) | c3_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[252, 250])).
% 1.41/1.60 tff(254,plain,
% 1.41/1.60 ((~hskp41) | c3_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[253, 250])).
% 1.41/1.60 tff(255,plain,
% 1.41/1.60 ((~hskp41) | c3_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[254, 250])).
% 1.41/1.60 tff(256,plain,
% 1.41/1.60 ((~hskp41) | c3_1(a555)),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[255, 250])).
% 1.41/1.60 tff(257,plain,
% 1.41/1.60 (c3_1(a555)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[256, 227])).
% 1.41/1.60 tff(258,plain,
% 1.41/1.60 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(259,plain,
% 1.41/1.60 ((hskp46 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548))) <=> (hskp46 | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(260,plain,
% 1.41/1.60 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a555)) | (~c1_1(a555))))),
% 1.41/1.60 inference(monotonicity,[status(thm)],[259])).
% 1.41/1.60 tff(261,plain,
% 1.41/1.60 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.41/1.60 inference(transitivity,[status(thm)],[260, 258])).
% 1.41/1.60 tff(262,plain,
% 1.41/1.60 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))),
% 1.41/1.60 inference(quant_inst,[status(thm)],[])).
% 1.41/1.60 tff(263,plain,
% 1.41/1.60 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a555)) | (~c1_1(a555))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.41/1.60 tff(264,plain,
% 1.41/1.60 (hskp46),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[263, 156, 257, 249, 233, 24, 56, 12, 248])).
% 1.41/1.60 tff(265,plain,
% 1.41/1.60 (~c0_1(a562)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[64, 264])).
% 1.41/1.60 tff(266,plain,
% 1.41/1.60 (((~hskp46) | (~c3_1(a562))) <=> ((~hskp46) | (~c3_1(a562)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(267,plain,
% 1.41/1.60 (((~c3_1(a562)) | (~hskp46)) <=> ((~hskp46) | (~c3_1(a562)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(268,axiom,((~c3_1(a562)) | (~hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.41/1.60 tff(269,plain,
% 1.41/1.60 ((~hskp46) | (~c3_1(a562))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.41/1.60 tff(270,plain,
% 1.41/1.60 ((~hskp46) | (~c3_1(a562))),
% 1.41/1.60 inference(modus_ponens,[status(thm)],[269, 266])).
% 1.41/1.60 tff(271,plain,
% 1.41/1.60 (~c3_1(a562)),
% 1.41/1.60 inference(unit_resolution,[status(thm)],[270, 264])).
% 1.41/1.60 tff(272,plain,
% 1.41/1.60 (^[V: $i, U: $i] : refl((hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.41/1.60 inference(bind,[status(th)],[])).
% 1.41/1.60 tff(273,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(quant_intro,[status(thm)],[272])).
% 1.41/1.60 tff(274,plain,
% 1.41/1.60 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.60 inference(rewrite,[status(thm)],[])).
% 1.41/1.60 tff(275,plain,
% 1.41/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) | c0_1(V)) | hskp39) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp39))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp39) <=> (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) | c0_1(V)) | hskp39) <=> (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.41/1.61 inference(bind,[status(th)],[])).
% 1.41/1.61 tff(276,plain,
% 1.41/1.61 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) | c0_1(V)) | hskp39) <=> ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.61 inference(quant_intro,[status(thm)],[275])).
% 1.41/1.61 tff(277,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(V)) | c0_1(V)) | hskp39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause241')).
% 1.41/1.61 tff(278,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.41/1.61 tff(279,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[278, 274])).
% 1.41/1.61 tff(280,plain,(
% 1.41/1.61 ![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.61 inference(skolemize,[status(sab)],[279])).
% 1.41/1.61 tff(281,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[280, 273])).
% 1.41/1.61 tff(282,plain,
% 1.41/1.61 (((~hskp46) | c1_1(a562)) <=> ((~hskp46) | c1_1(a562))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(283,axiom,((~hskp46) | c1_1(a562)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.41/1.61 tff(284,plain,
% 1.41/1.61 ((~hskp46) | c1_1(a562)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.41/1.61 tff(285,plain,
% 1.41/1.61 ((~hskp46) | c1_1(a562)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[284, 282])).
% 1.41/1.61 tff(286,plain,
% 1.41/1.61 ((~hskp46) | c1_1(a562)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[285, 282])).
% 1.41/1.61 tff(287,plain,
% 1.41/1.61 ((~hskp46) | c1_1(a562)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[286, 282])).
% 1.41/1.61 tff(288,plain,
% 1.41/1.61 ((~hskp46) | c1_1(a562)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[287, 282])).
% 1.41/1.61 tff(289,plain,
% 1.41/1.61 (c1_1(a562)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[288, 264])).
% 1.41/1.61 tff(290,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a555) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a555) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)) | (~c1_1(a562)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(291,plain,
% 1.41/1.61 ((hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a555) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)) | (~c1_1(a562)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(292,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a555) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)) | (~c1_1(a562))))),
% 1.41/1.61 inference(monotonicity,[status(thm)],[291])).
% 1.41/1.61 tff(293,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a555) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)) | (~c1_1(a562)))),
% 1.41/1.61 inference(transitivity,[status(thm)],[292, 290])).
% 1.41/1.61 tff(294,plain,
% 1.41/1.61 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.41/1.61 inference(quant_inst,[status(thm)],[])).
% 1.41/1.61 tff(295,plain,
% 1.41/1.61 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a555) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)) | (~c1_1(a562))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.41/1.61 tff(296,plain,
% 1.41/1.61 (hskp39),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[295, 156, 289, 257, 271, 265, 233, 281, 248])).
% 1.41/1.61 tff(297,plain,
% 1.41/1.61 (((~hskp39) | c1_1(a549)) <=> ((~hskp39) | c1_1(a549))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(298,axiom,((~hskp39) | c1_1(a549)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.41/1.61 tff(299,plain,
% 1.41/1.61 ((~hskp39) | c1_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.41/1.61 tff(300,plain,
% 1.41/1.61 ((~hskp39) | c1_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[299, 297])).
% 1.41/1.61 tff(301,plain,
% 1.41/1.61 ((~hskp39) | c1_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[300, 297])).
% 1.41/1.61 tff(302,plain,
% 1.41/1.61 ((~hskp39) | c1_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[301, 297])).
% 1.41/1.61 tff(303,plain,
% 1.41/1.61 ((~hskp39) | c1_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[302, 297])).
% 1.41/1.61 tff(304,plain,
% 1.41/1.61 (c1_1(a549)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[303, 296])).
% 1.41/1.61 tff(305,plain,
% 1.41/1.61 (((~hskp39) | c2_1(a549)) <=> ((~hskp39) | c2_1(a549))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(306,axiom,((~hskp39) | c2_1(a549)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.41/1.61 tff(307,plain,
% 1.41/1.61 ((~hskp39) | c2_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.41/1.61 tff(308,plain,
% 1.41/1.61 ((~hskp39) | c2_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[307, 305])).
% 1.41/1.61 tff(309,plain,
% 1.41/1.61 ((~hskp39) | c2_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[308, 305])).
% 1.41/1.61 tff(310,plain,
% 1.41/1.61 ((~hskp39) | c2_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[309, 305])).
% 1.41/1.61 tff(311,plain,
% 1.41/1.61 ((~hskp39) | c2_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[310, 305])).
% 1.41/1.61 tff(312,plain,
% 1.41/1.61 (c2_1(a549)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[311, 296])).
% 1.41/1.61 tff(313,plain,
% 1.41/1.61 (((~hskp39) | c3_1(a549)) <=> ((~hskp39) | c3_1(a549))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(314,axiom,((~hskp39) | c3_1(a549)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.41/1.61 tff(315,plain,
% 1.41/1.61 ((~hskp39) | c3_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.41/1.61 tff(316,plain,
% 1.41/1.61 ((~hskp39) | c3_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[315, 313])).
% 1.41/1.61 tff(317,plain,
% 1.41/1.61 ((~hskp39) | c3_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[316, 313])).
% 1.41/1.61 tff(318,plain,
% 1.41/1.61 ((~hskp39) | c3_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[317, 313])).
% 1.41/1.61 tff(319,plain,
% 1.41/1.61 ((~hskp39) | c3_1(a549)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[318, 313])).
% 1.41/1.61 tff(320,plain,
% 1.41/1.61 (c3_1(a549)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[319, 296])).
% 1.41/1.61 tff(321,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a562)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(322,plain,
% 1.41/1.61 ((hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a562)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(323,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a562))))),
% 1.41/1.61 inference(monotonicity,[status(thm)],[322])).
% 1.41/1.61 tff(324,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a562)))),
% 1.41/1.61 inference(transitivity,[status(thm)],[323, 321])).
% 1.41/1.61 tff(325,plain,
% 1.41/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.41/1.61 inference(quant_inst,[status(thm)],[])).
% 1.41/1.61 tff(326,plain,
% 1.41/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a562))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.41/1.61 tff(327,plain,
% 1.41/1.61 ($false),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[326, 156, 23, 289, 320, 312, 304, 271, 265, 22])).
% 1.41/1.61 tff(328,plain,((~hskp41) | hskp4 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.41/1.61 tff(329,plain,
% 1.41/1.61 (~hskp41),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[328, 194, 226, 218, 212, 110, 98])).
% 1.41/1.61 tff(330,assumption,(~hskp9), introduced(assumption)).
% 1.41/1.61 tff(331,assumption,(~hskp41), introduced(assumption)).
% 1.41/1.61 tff(332,assumption,(~hskp17), introduced(assumption)).
% 1.41/1.61 tff(333,plain,
% 1.41/1.61 (^[U: $i] : refl((hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.41/1.61 inference(bind,[status(th)],[])).
% 1.41/1.61 tff(334,plain,
% 1.41/1.61 (![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.61 inference(quant_intro,[status(thm)],[333])).
% 1.41/1.61 tff(335,plain,
% 1.41/1.61 (![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(336,plain,
% 1.41/1.61 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp41) <=> ((hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp41))), rewrite(((hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp41) <=> (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp41) <=> (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.41/1.61 inference(bind,[status(th)],[])).
% 1.41/1.61 tff(337,plain,
% 1.41/1.61 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp41) <=> ![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.61 inference(quant_intro,[status(thm)],[336])).
% 1.41/1.61 tff(338,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause224')).
% 1.41/1.61 tff(339,plain,
% 1.41/1.61 (![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.41/1.61 tff(340,plain,
% 1.41/1.61 (![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[339, 335])).
% 1.41/1.61 tff(341,plain,(
% 1.41/1.61 ![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.61 inference(skolemize,[status(sab)],[340])).
% 1.41/1.61 tff(342,plain,
% 1.41/1.61 (![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[341, 334])).
% 1.41/1.61 tff(343,assumption,(hskp16), introduced(assumption)).
% 1.41/1.61 tff(344,plain,
% 1.41/1.61 (((~hskp16) | (~c0_1(a570))) <=> ((~hskp16) | (~c0_1(a570)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(345,plain,
% 1.41/1.61 (((~c0_1(a570)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a570)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(346,axiom,((~c0_1(a570)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.41/1.61 tff(347,plain,
% 1.41/1.61 ((~hskp16) | (~c0_1(a570))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.41/1.61 tff(348,plain,
% 1.41/1.61 ((~hskp16) | (~c0_1(a570))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[347, 344])).
% 1.41/1.61 tff(349,plain,
% 1.41/1.61 (~c0_1(a570)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[348, 343])).
% 1.41/1.61 tff(350,plain,
% 1.41/1.61 (((~hskp16) | c1_1(a570)) <=> ((~hskp16) | c1_1(a570))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(351,axiom,((~hskp16) | c1_1(a570)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.41/1.61 tff(352,plain,
% 1.41/1.61 ((~hskp16) | c1_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.41/1.61 tff(353,plain,
% 1.41/1.61 ((~hskp16) | c1_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[352, 350])).
% 1.41/1.61 tff(354,plain,
% 1.41/1.61 ((~hskp16) | c1_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[353, 350])).
% 1.41/1.61 tff(355,plain,
% 1.41/1.61 ((~hskp16) | c1_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[354, 350])).
% 1.41/1.61 tff(356,plain,
% 1.41/1.61 ((~hskp16) | c1_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[355, 350])).
% 1.41/1.61 tff(357,plain,
% 1.41/1.61 (c1_1(a570)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[356, 343])).
% 1.41/1.61 tff(358,plain,
% 1.41/1.61 (((~hskp16) | c3_1(a570)) <=> ((~hskp16) | c3_1(a570))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(359,axiom,((~hskp16) | c3_1(a570)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.41/1.61 tff(360,plain,
% 1.41/1.61 ((~hskp16) | c3_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.41/1.61 tff(361,plain,
% 1.41/1.61 ((~hskp16) | c3_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[360, 358])).
% 1.41/1.61 tff(362,plain,
% 1.41/1.61 ((~hskp16) | c3_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[361, 358])).
% 1.41/1.61 tff(363,plain,
% 1.41/1.61 ((~hskp16) | c3_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[362, 358])).
% 1.41/1.61 tff(364,plain,
% 1.41/1.61 ((~hskp16) | c3_1(a570)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[363, 358])).
% 1.41/1.61 tff(365,plain,
% 1.41/1.61 (c3_1(a570)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[364, 343])).
% 1.41/1.61 tff(366,plain,
% 1.41/1.61 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a570) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a570) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(367,plain,
% 1.41/1.61 ((hskp41 | hskp9 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570))) <=> (hskp41 | hskp9 | c0_1(a570) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(368,plain,
% 1.41/1.61 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a570) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570))))),
% 1.41/1.61 inference(monotonicity,[status(thm)],[367])).
% 1.41/1.61 tff(369,plain,
% 1.41/1.61 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a570) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.41/1.61 inference(transitivity,[status(thm)],[368, 366])).
% 1.41/1.61 tff(370,plain,
% 1.41/1.61 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.41/1.61 inference(quant_inst,[status(thm)],[])).
% 1.41/1.61 tff(371,plain,
% 1.41/1.61 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a570) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.41/1.61 tff(372,plain,
% 1.41/1.61 ($false),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[371, 156, 331, 330, 365, 357, 349, 342])).
% 1.41/1.61 tff(373,plain,((~hskp16) | hskp41 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.41/1.61 tff(374,plain,
% 1.41/1.61 (~hskp16),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[373, 331, 330])).
% 1.41/1.61 tff(375,plain,
% 1.41/1.61 ((hskp18 | hskp17 | hskp16) <=> (hskp18 | hskp17 | hskp16)),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(376,plain,
% 1.41/1.61 (((hskp16 | hskp17) | hskp18) <=> (hskp18 | hskp17 | hskp16)),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(377,axiom,((hskp16 | hskp17) | hskp18), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.41/1.61 tff(378,plain,
% 1.41/1.61 (hskp18 | hskp17 | hskp16),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.41/1.61 tff(379,plain,
% 1.41/1.61 (hskp18 | hskp17 | hskp16),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[378, 375])).
% 1.41/1.61 tff(380,plain,
% 1.41/1.61 (hskp18 | hskp17 | hskp16),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[379, 375])).
% 1.41/1.61 tff(381,plain,
% 1.41/1.61 (hskp18 | hskp17 | hskp16),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[380, 375])).
% 1.41/1.61 tff(382,plain,
% 1.41/1.61 (hskp18 | hskp17 | hskp16),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[381, 375])).
% 1.41/1.61 tff(383,plain,
% 1.41/1.61 (hskp18),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[382, 374, 332])).
% 1.41/1.61 tff(384,assumption,(hskp18), introduced(assumption)).
% 1.41/1.61 tff(385,plain,
% 1.41/1.61 (((~hskp18) | (~c1_1(a572))) <=> ((~hskp18) | (~c1_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(386,plain,
% 1.41/1.61 (((~c1_1(a572)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(387,axiom,((~c1_1(a572)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.41/1.61 tff(388,plain,
% 1.41/1.61 ((~hskp18) | (~c1_1(a572))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.41/1.61 tff(389,plain,
% 1.41/1.61 ((~hskp18) | (~c1_1(a572))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[388, 385])).
% 1.41/1.61 tff(390,plain,
% 1.41/1.61 (~c1_1(a572)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[389, 384])).
% 1.41/1.61 tff(391,plain,
% 1.41/1.61 (((~hskp18) | c0_1(a572)) <=> ((~hskp18) | c0_1(a572))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(392,axiom,((~hskp18) | c0_1(a572)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.41/1.61 tff(393,plain,
% 1.41/1.61 ((~hskp18) | c0_1(a572)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.41/1.61 tff(394,plain,
% 1.41/1.61 ((~hskp18) | c0_1(a572)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[393, 391])).
% 1.41/1.61 tff(395,plain,
% 1.41/1.61 ((~hskp18) | c0_1(a572)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[394, 391])).
% 1.41/1.61 tff(396,plain,
% 1.41/1.61 ((~hskp18) | c0_1(a572)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[395, 391])).
% 1.41/1.61 tff(397,plain,
% 1.41/1.61 ((~hskp18) | c0_1(a572)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[396, 391])).
% 1.41/1.61 tff(398,plain,
% 1.41/1.61 (c0_1(a572)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[397, 384])).
% 1.41/1.61 tff(399,plain,
% 1.41/1.61 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(400,plain,
% 1.41/1.61 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572))) <=> (hskp50 | hskp19 | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(401,plain,
% 1.41/1.61 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572))))),
% 1.41/1.61 inference(monotonicity,[status(thm)],[400])).
% 1.41/1.61 tff(402,plain,
% 1.41/1.61 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)))),
% 1.41/1.61 inference(transitivity,[status(thm)],[401, 399])).
% 1.41/1.61 tff(403,plain,
% 1.41/1.61 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572)))),
% 1.41/1.61 inference(quant_inst,[status(thm)],[])).
% 1.41/1.61 tff(404,plain,
% 1.41/1.61 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.41/1.61 tff(405,plain,
% 1.41/1.61 (c2_1(a572)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[404, 156, 110, 98, 398, 390, 34])).
% 1.41/1.61 tff(406,plain,
% 1.41/1.61 (^[V: $i, U: $i] : refl((hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.41/1.61 inference(bind,[status(th)],[])).
% 1.41/1.61 tff(407,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.41/1.61 inference(quant_intro,[status(thm)],[406])).
% 1.41/1.61 tff(408,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(409,plain,
% 1.41/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp37) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp37))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp37) <=> (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp37) <=> (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.41/1.61 inference(bind,[status(th)],[])).
% 1.41/1.61 tff(410,plain,
% 1.41/1.61 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp37) <=> ![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.41/1.61 inference(quant_intro,[status(thm)],[409])).
% 1.41/1.61 tff(411,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause239')).
% 1.41/1.61 tff(412,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[411, 410])).
% 1.41/1.61 tff(413,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[412, 408])).
% 1.41/1.61 tff(414,plain,(
% 1.41/1.61 ![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.41/1.61 inference(skolemize,[status(sab)],[413])).
% 1.41/1.61 tff(415,plain,
% 1.41/1.61 (![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[414, 407])).
% 1.41/1.61 tff(416,plain,
% 1.41/1.61 (((~hskp18) | (~c3_1(a572))) <=> ((~hskp18) | (~c3_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(417,plain,
% 1.41/1.61 (((~c3_1(a572)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(418,axiom,((~c3_1(a572)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.41/1.61 tff(419,plain,
% 1.41/1.61 ((~hskp18) | (~c3_1(a572))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.41/1.61 tff(420,plain,
% 1.41/1.61 ((~hskp18) | (~c3_1(a572))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[419, 416])).
% 1.41/1.61 tff(421,plain,
% 1.41/1.61 (~c3_1(a572)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[420, 384])).
% 1.41/1.61 tff(422,assumption,(~hskp37), introduced(assumption)).
% 1.41/1.61 tff(423,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(424,plain,
% 1.41/1.61 ((hskp37 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c1_1(a572) | c3_1(a572) | (~c0_1(a572))) <=> (hskp37 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(425,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c1_1(a572) | c3_1(a572) | (~c0_1(a572)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572))))),
% 1.41/1.61 inference(monotonicity,[status(thm)],[424])).
% 1.41/1.61 tff(426,plain,
% 1.41/1.61 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c1_1(a572) | c3_1(a572) | (~c0_1(a572)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))),
% 1.41/1.61 inference(transitivity,[status(thm)],[425, 423])).
% 1.41/1.61 tff(427,plain,
% 1.41/1.61 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c1_1(a572) | c3_1(a572) | (~c0_1(a572)))),
% 1.41/1.61 inference(quant_inst,[status(thm)],[])).
% 1.41/1.61 tff(428,plain,
% 1.41/1.61 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.41/1.61 tff(429,plain,
% 1.41/1.61 ($false),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[428, 156, 422, 398, 421, 390, 415, 405])).
% 1.41/1.61 tff(430,plain,((~hskp18) | hskp37 | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.41/1.61 tff(431,plain,
% 1.41/1.61 (hskp37),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[430, 383, 110, 98])).
% 1.41/1.61 tff(432,plain,
% 1.41/1.61 (((~hskp37) | (~c2_1(a544))) <=> ((~hskp37) | (~c2_1(a544)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(433,plain,
% 1.41/1.61 (((~c2_1(a544)) | (~hskp37)) <=> ((~hskp37) | (~c2_1(a544)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(434,axiom,((~c2_1(a544)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.41/1.61 tff(435,plain,
% 1.41/1.61 ((~hskp37) | (~c2_1(a544))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.41/1.61 tff(436,plain,
% 1.41/1.61 ((~hskp37) | (~c2_1(a544))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[435, 432])).
% 1.41/1.61 tff(437,plain,
% 1.41/1.61 (~c2_1(a544)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[436, 431])).
% 1.41/1.61 tff(438,plain,
% 1.41/1.61 (((~hskp37) | c1_1(a544)) <=> ((~hskp37) | c1_1(a544))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(439,axiom,((~hskp37) | c1_1(a544)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.41/1.61 tff(440,plain,
% 1.41/1.61 ((~hskp37) | c1_1(a544)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.41/1.61 tff(441,plain,
% 1.41/1.61 ((~hskp37) | c1_1(a544)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[440, 438])).
% 1.41/1.61 tff(442,plain,
% 1.41/1.61 ((~hskp37) | c1_1(a544)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[441, 438])).
% 1.41/1.61 tff(443,plain,
% 1.41/1.61 ((~hskp37) | c1_1(a544)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[442, 438])).
% 1.41/1.61 tff(444,plain,
% 1.41/1.61 ((~hskp37) | c1_1(a544)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[443, 438])).
% 1.41/1.61 tff(445,plain,
% 1.41/1.61 (c1_1(a544)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[444, 431])).
% 1.41/1.61 tff(446,plain,
% 1.41/1.61 (((~hskp37) | (~c3_1(a544))) <=> ((~hskp37) | (~c3_1(a544)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(447,plain,
% 1.41/1.61 (((~c3_1(a544)) | (~hskp37)) <=> ((~hskp37) | (~c3_1(a544)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(448,axiom,((~c3_1(a544)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.41/1.61 tff(449,plain,
% 1.41/1.61 ((~hskp37) | (~c3_1(a544))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.41/1.61 tff(450,plain,
% 1.41/1.61 ((~hskp37) | (~c3_1(a544))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[449, 446])).
% 1.41/1.61 tff(451,plain,
% 1.41/1.61 (~c3_1(a544)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[450, 431])).
% 1.41/1.61 tff(452,assumption,(hskp7), introduced(assumption)).
% 1.41/1.61 tff(453,plain,
% 1.41/1.61 (((~hskp7) | (~c1_1(a550))) <=> ((~hskp7) | (~c1_1(a550)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(454,plain,
% 1.41/1.61 (((~c1_1(a550)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a550)))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(455,axiom,((~c1_1(a550)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 1.41/1.61 tff(456,plain,
% 1.41/1.61 ((~hskp7) | (~c1_1(a550))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[455, 454])).
% 1.41/1.61 tff(457,plain,
% 1.41/1.61 ((~hskp7) | (~c1_1(a550))),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[456, 453])).
% 1.41/1.61 tff(458,plain,
% 1.41/1.61 (~c1_1(a550)),
% 1.41/1.61 inference(unit_resolution,[status(thm)],[457, 452])).
% 1.41/1.61 tff(459,plain,
% 1.41/1.61 (((~hskp7) | c0_1(a550)) <=> ((~hskp7) | c0_1(a550))),
% 1.41/1.61 inference(rewrite,[status(thm)],[])).
% 1.41/1.61 tff(460,axiom,((~hskp7) | c0_1(a550)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.41/1.61 tff(461,plain,
% 1.41/1.61 ((~hskp7) | c0_1(a550)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[460, 459])).
% 1.41/1.61 tff(462,plain,
% 1.41/1.61 ((~hskp7) | c0_1(a550)),
% 1.41/1.61 inference(modus_ponens,[status(thm)],[461, 459])).
% 1.41/1.61 tff(463,plain,
% 1.41/1.62 ((~hskp7) | c0_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[462, 459])).
% 1.41/1.62 tff(464,plain,
% 1.41/1.62 ((~hskp7) | c0_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[463, 459])).
% 1.41/1.62 tff(465,plain,
% 1.41/1.62 ((~hskp7) | c0_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[464, 459])).
% 1.41/1.62 tff(466,plain,
% 1.41/1.62 (c0_1(a550)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[465, 452])).
% 1.41/1.62 tff(467,plain,
% 1.41/1.62 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a550) | (~ndr1_0) | c2_1(a550) | (~c0_1(a550)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a550) | (~ndr1_0) | c2_1(a550) | (~c0_1(a550)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(468,plain,
% 1.41/1.62 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a550) | c1_1(a550) | (~c0_1(a550))) <=> (hskp50 | hskp19 | c1_1(a550) | (~ndr1_0) | c2_1(a550) | (~c0_1(a550)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(469,plain,
% 1.41/1.62 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a550) | c1_1(a550) | (~c0_1(a550)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a550) | (~ndr1_0) | c2_1(a550) | (~c0_1(a550))))),
% 1.41/1.62 inference(monotonicity,[status(thm)],[468])).
% 1.41/1.62 tff(470,plain,
% 1.41/1.62 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a550) | c1_1(a550) | (~c0_1(a550)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a550) | (~ndr1_0) | c2_1(a550) | (~c0_1(a550)))),
% 1.41/1.62 inference(transitivity,[status(thm)],[469, 467])).
% 1.41/1.62 tff(471,plain,
% 1.41/1.62 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a550) | c1_1(a550) | (~c0_1(a550)))),
% 1.41/1.62 inference(quant_inst,[status(thm)],[])).
% 1.41/1.62 tff(472,plain,
% 1.41/1.62 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a550) | (~ndr1_0) | c2_1(a550) | (~c0_1(a550))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.41/1.62 tff(473,plain,
% 1.41/1.62 (c2_1(a550)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[472, 156, 110, 98, 466, 458, 34])).
% 1.41/1.62 tff(474,plain,
% 1.41/1.62 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.41/1.62 inference(bind,[status(th)],[])).
% 1.41/1.62 tff(475,plain,
% 1.41/1.62 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.41/1.62 inference(quant_intro,[status(thm)],[474])).
% 1.41/1.62 tff(476,plain,
% 1.41/1.62 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(477,plain,
% 1.41/1.62 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.41/1.62 inference(bind,[status(th)],[])).
% 1.41/1.62 tff(478,plain,
% 1.41/1.62 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.41/1.62 inference(quant_intro,[status(thm)],[477])).
% 1.41/1.62 tff(479,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause245')).
% 1.41/1.62 tff(480,plain,
% 1.41/1.62 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.41/1.62 tff(481,plain,
% 1.41/1.62 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[480, 476])).
% 1.41/1.62 tff(482,plain,(
% 1.41/1.62 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.41/1.62 inference(skolemize,[status(sab)],[481])).
% 1.41/1.62 tff(483,plain,
% 1.41/1.62 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[482, 475])).
% 1.41/1.62 tff(484,assumption,(~c3_1(a544)), introduced(assumption)).
% 1.41/1.62 tff(485,assumption,(~c2_1(a544)), introduced(assumption)).
% 1.41/1.62 tff(486,plain,
% 1.41/1.62 (((~hskp7) | c3_1(a550)) <=> ((~hskp7) | c3_1(a550))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(487,axiom,((~hskp7) | c3_1(a550)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.41/1.62 tff(488,plain,
% 1.41/1.62 ((~hskp7) | c3_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[487, 486])).
% 1.41/1.62 tff(489,plain,
% 1.41/1.62 ((~hskp7) | c3_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[488, 486])).
% 1.41/1.62 tff(490,plain,
% 1.41/1.62 ((~hskp7) | c3_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[489, 486])).
% 1.41/1.62 tff(491,plain,
% 1.41/1.62 ((~hskp7) | c3_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[490, 486])).
% 1.41/1.62 tff(492,plain,
% 1.41/1.62 ((~hskp7) | c3_1(a550)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[491, 486])).
% 1.41/1.62 tff(493,plain,
% 1.41/1.62 (c3_1(a550)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[492, 452])).
% 1.41/1.62 tff(494,assumption,(c1_1(a544)), introduced(assumption)).
% 1.41/1.62 tff(495,plain,
% 1.41/1.62 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | (~c2_1(a550)) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | (~c2_1(a550)) | (~c1_1(a544)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(496,plain,
% 1.41/1.62 ((hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a550) | (~c3_1(a550)) | (~c2_1(a550))) <=> (hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | (~c2_1(a550)) | (~c1_1(a544)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(497,plain,
% 1.41/1.62 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a550) | (~c3_1(a550)) | (~c2_1(a550)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | (~c2_1(a550)) | (~c1_1(a544))))),
% 1.41/1.62 inference(monotonicity,[status(thm)],[496])).
% 1.41/1.62 tff(498,plain,
% 1.41/1.62 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a550) | (~c3_1(a550)) | (~c2_1(a550)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | (~c2_1(a550)) | (~c1_1(a544)))),
% 1.41/1.62 inference(transitivity,[status(thm)],[497, 495])).
% 1.41/1.62 tff(499,plain,
% 1.41/1.62 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a550) | (~c3_1(a550)) | (~c2_1(a550)))),
% 1.41/1.62 inference(quant_inst,[status(thm)],[])).
% 1.41/1.62 tff(500,plain,
% 1.41/1.62 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | (~c2_1(a550)) | (~c1_1(a544))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.41/1.62 tff(501,plain,
% 1.41/1.62 ($false),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[500, 156, 109, 494, 493, 485, 484, 458, 483, 473])).
% 1.41/1.62 tff(502,plain,((~hskp7) | hskp15 | (~c1_1(a544)) | c2_1(a544) | c3_1(a544) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.41/1.62 tff(503,plain,
% 1.41/1.62 (~hskp7),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[502, 445, 109, 98, 451, 110, 437])).
% 1.41/1.62 tff(504,plain,
% 1.41/1.62 (^[U: $i] : refl((hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.41/1.62 inference(bind,[status(th)],[])).
% 1.41/1.62 tff(505,plain,
% 1.41/1.62 (![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.41/1.62 inference(quant_intro,[status(thm)],[504])).
% 1.41/1.62 tff(506,plain,
% 1.41/1.62 (![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(507,plain,
% 1.41/1.62 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp40) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp40))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp40) <=> (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp40) <=> (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.41/1.62 inference(bind,[status(th)],[])).
% 1.41/1.62 tff(508,plain,
% 1.41/1.62 (![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp40) <=> ![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.41/1.62 inference(quant_intro,[status(thm)],[507])).
% 1.41/1.62 tff(509,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause223')).
% 1.41/1.62 tff(510,plain,
% 1.41/1.62 (![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.41/1.62 tff(511,plain,
% 1.41/1.62 (![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[510, 506])).
% 1.41/1.62 tff(512,plain,(
% 1.41/1.62 ![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.41/1.62 inference(skolemize,[status(sab)],[511])).
% 1.41/1.62 tff(513,plain,
% 1.41/1.62 (![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[512, 505])).
% 1.41/1.62 tff(514,assumption,(~hskp7), introduced(assumption)).
% 1.41/1.62 tff(515,assumption,(~hskp40), introduced(assumption)).
% 1.41/1.62 tff(516,plain,
% 1.41/1.62 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(517,plain,
% 1.41/1.62 ((hskp40 | hskp7 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572))) <=> (hskp40 | hskp7 | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(518,plain,
% 1.41/1.62 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572))))),
% 1.41/1.62 inference(monotonicity,[status(thm)],[517])).
% 1.41/1.62 tff(519,plain,
% 1.41/1.62 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)))),
% 1.41/1.62 inference(transitivity,[status(thm)],[518, 516])).
% 1.41/1.62 tff(520,plain,
% 1.41/1.62 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)))),
% 1.41/1.62 inference(quant_inst,[status(thm)],[])).
% 1.41/1.62 tff(521,plain,
% 1.41/1.62 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.41/1.62 tff(522,plain,
% 1.41/1.62 (~c2_1(a572)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[521, 156, 515, 514, 398, 390, 513])).
% 1.41/1.62 tff(523,plain,
% 1.41/1.62 ($false),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[404, 156, 110, 98, 398, 390, 34, 522])).
% 1.41/1.62 tff(524,plain,((~hskp18) | hskp50 | hskp19 | hskp40 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.41/1.62 tff(525,plain,
% 1.41/1.62 (hskp40),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[524, 503, 110, 98, 383])).
% 1.41/1.62 tff(526,plain,
% 1.41/1.62 (((~hskp40) | c2_1(a551)) <=> ((~hskp40) | c2_1(a551))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(527,axiom,((~hskp40) | c2_1(a551)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.41/1.62 tff(528,plain,
% 1.41/1.62 ((~hskp40) | c2_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[527, 526])).
% 1.41/1.62 tff(529,plain,
% 1.41/1.62 ((~hskp40) | c2_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[528, 526])).
% 1.41/1.62 tff(530,plain,
% 1.41/1.62 ((~hskp40) | c2_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[529, 526])).
% 1.41/1.62 tff(531,plain,
% 1.41/1.62 ((~hskp40) | c2_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[530, 526])).
% 1.41/1.62 tff(532,plain,
% 1.41/1.62 ((~hskp40) | c2_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[531, 526])).
% 1.41/1.62 tff(533,plain,
% 1.41/1.62 (c2_1(a551)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[532, 525])).
% 1.41/1.62 tff(534,plain,
% 1.41/1.62 (((~hskp40) | c3_1(a551)) <=> ((~hskp40) | c3_1(a551))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(535,axiom,((~hskp40) | c3_1(a551)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.41/1.62 tff(536,plain,
% 1.41/1.62 ((~hskp40) | c3_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[535, 534])).
% 1.41/1.62 tff(537,plain,
% 1.41/1.62 ((~hskp40) | c3_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[536, 534])).
% 1.41/1.62 tff(538,plain,
% 1.41/1.62 ((~hskp40) | c3_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[537, 534])).
% 1.41/1.62 tff(539,plain,
% 1.41/1.62 ((~hskp40) | c3_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[538, 534])).
% 1.41/1.62 tff(540,plain,
% 1.41/1.62 ((~hskp40) | c3_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[539, 534])).
% 1.41/1.62 tff(541,plain,
% 1.41/1.62 (c3_1(a551)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[540, 525])).
% 1.41/1.62 tff(542,assumption,(~c1_1(a551)), introduced(assumption)).
% 1.41/1.62 tff(543,assumption,(c2_1(a551)), introduced(assumption)).
% 1.41/1.62 tff(544,assumption,(c3_1(a551)), introduced(assumption)).
% 1.41/1.62 tff(545,plain,
% 1.41/1.62 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | c1_1(a551))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | c1_1(a551))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(546,plain,
% 1.41/1.62 ((hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a551) | (~c3_1(a551)) | (~c2_1(a551))) <=> (hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | c1_1(a551))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(547,plain,
% 1.41/1.62 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a551) | (~c3_1(a551)) | (~c2_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | c1_1(a551)))),
% 1.41/1.62 inference(monotonicity,[status(thm)],[546])).
% 1.41/1.62 tff(548,plain,
% 1.41/1.62 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a551) | (~c3_1(a551)) | (~c2_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | c1_1(a551))),
% 1.41/1.62 inference(transitivity,[status(thm)],[547, 545])).
% 1.41/1.62 tff(549,plain,
% 1.41/1.62 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a551) | (~c3_1(a551)) | (~c2_1(a551)))),
% 1.41/1.62 inference(quant_inst,[status(thm)],[])).
% 1.41/1.62 tff(550,plain,
% 1.41/1.62 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | c1_1(a551)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[549, 548])).
% 1.41/1.62 tff(551,plain,
% 1.41/1.62 ($false),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[550, 156, 109, 544, 543, 494, 485, 484, 483, 542])).
% 1.41/1.62 tff(552,plain,(c1_1(a551) | hskp15 | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a544)) | c2_1(a544) | c3_1(a544)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.62 tff(553,plain,
% 1.41/1.62 (c1_1(a551)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[552, 541, 451, 533, 445, 437, 109])).
% 1.41/1.62 tff(554,plain,
% 1.41/1.62 (((~hskp40) | (~c0_1(a551))) <=> ((~hskp40) | (~c0_1(a551)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(555,plain,
% 1.41/1.62 (((~c0_1(a551)) | (~hskp40)) <=> ((~hskp40) | (~c0_1(a551)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(556,axiom,((~c0_1(a551)) | (~hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.41/1.62 tff(557,plain,
% 1.41/1.62 ((~hskp40) | (~c0_1(a551))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.41/1.62 tff(558,plain,
% 1.41/1.62 ((~hskp40) | (~c0_1(a551))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[557, 554])).
% 1.41/1.62 tff(559,plain,
% 1.41/1.62 (~c0_1(a551)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[558, 525])).
% 1.41/1.62 tff(560,plain,
% 1.41/1.62 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a551) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a551) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(561,plain,
% 1.41/1.62 ((hskp41 | hskp9 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551))) <=> (hskp41 | hskp9 | c0_1(a551) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(562,plain,
% 1.41/1.62 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a551) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.41/1.62 inference(monotonicity,[status(thm)],[561])).
% 1.41/1.62 tff(563,plain,
% 1.41/1.62 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a551) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.41/1.62 inference(transitivity,[status(thm)],[562, 560])).
% 1.41/1.62 tff(564,plain,
% 1.41/1.62 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.41/1.62 inference(quant_inst,[status(thm)],[])).
% 1.41/1.62 tff(565,plain,
% 1.41/1.62 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a551) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[564, 563])).
% 1.41/1.62 tff(566,plain,
% 1.41/1.62 ($false),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[565, 156, 331, 330, 541, 559, 342, 553])).
% 1.41/1.62 tff(567,plain,(hskp41 | hskp9 | hskp15 | hskp50 | hskp19 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.41/1.62 tff(568,plain,
% 1.41/1.62 (hskp17),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[567, 331, 110, 330, 98, 109])).
% 1.41/1.62 tff(569,plain,
% 1.41/1.62 (((~hskp17) | (~c2_1(a571))) <=> ((~hskp17) | (~c2_1(a571)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(570,plain,
% 1.41/1.62 (((~c2_1(a571)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a571)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(571,axiom,((~c2_1(a571)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.41/1.62 tff(572,plain,
% 1.41/1.62 ((~hskp17) | (~c2_1(a571))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.41/1.62 tff(573,plain,
% 1.41/1.62 ((~hskp17) | (~c2_1(a571))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[572, 569])).
% 1.41/1.62 tff(574,plain,
% 1.41/1.62 (~c2_1(a571)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[573, 568])).
% 1.41/1.62 tff(575,plain,
% 1.41/1.62 (((~hskp17) | c0_1(a571)) <=> ((~hskp17) | c0_1(a571))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(576,axiom,((~hskp17) | c0_1(a571)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.41/1.62 tff(577,plain,
% 1.41/1.62 ((~hskp17) | c0_1(a571)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[576, 575])).
% 1.41/1.62 tff(578,plain,
% 1.41/1.62 ((~hskp17) | c0_1(a571)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[577, 575])).
% 1.41/1.62 tff(579,plain,
% 1.41/1.62 ((~hskp17) | c0_1(a571)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[578, 575])).
% 1.41/1.62 tff(580,plain,
% 1.41/1.62 ((~hskp17) | c0_1(a571)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[579, 575])).
% 1.41/1.62 tff(581,plain,
% 1.41/1.62 ((~hskp17) | c0_1(a571)),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[580, 575])).
% 1.41/1.62 tff(582,plain,
% 1.41/1.62 (c0_1(a571)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[581, 568])).
% 1.41/1.62 tff(583,plain,
% 1.41/1.62 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a571) | (~ndr1_0) | c1_1(a571) | (~c0_1(a571)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a571) | (~ndr1_0) | c1_1(a571) | (~c0_1(a571)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(584,plain,
% 1.41/1.62 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a571) | c1_1(a571) | (~c0_1(a571))) <=> (hskp50 | hskp19 | c2_1(a571) | (~ndr1_0) | c1_1(a571) | (~c0_1(a571)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(585,plain,
% 1.41/1.62 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a571) | c1_1(a571) | (~c0_1(a571)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a571) | (~ndr1_0) | c1_1(a571) | (~c0_1(a571))))),
% 1.41/1.62 inference(monotonicity,[status(thm)],[584])).
% 1.41/1.62 tff(586,plain,
% 1.41/1.62 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a571) | c1_1(a571) | (~c0_1(a571)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a571) | (~ndr1_0) | c1_1(a571) | (~c0_1(a571)))),
% 1.41/1.62 inference(transitivity,[status(thm)],[585, 583])).
% 1.41/1.62 tff(587,plain,
% 1.41/1.62 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a571) | c1_1(a571) | (~c0_1(a571)))),
% 1.41/1.62 inference(quant_inst,[status(thm)],[])).
% 1.41/1.62 tff(588,plain,
% 1.41/1.62 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a571) | (~ndr1_0) | c1_1(a571) | (~c0_1(a571))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.41/1.62 tff(589,plain,
% 1.41/1.62 (c1_1(a571)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[588, 156, 110, 98, 582, 574, 34])).
% 1.41/1.62 tff(590,assumption,(~c0_1(a589)), introduced(assumption)).
% 1.41/1.62 tff(591,assumption,(c3_1(a589)), introduced(assumption)).
% 1.41/1.62 tff(592,plain,
% 1.41/1.62 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(593,plain,
% 1.41/1.62 ((hskp41 | hskp9 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589))) <=> (hskp41 | hskp9 | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.41/1.62 inference(rewrite,[status(thm)],[])).
% 1.41/1.62 tff(594,plain,
% 1.41/1.62 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.41/1.62 inference(monotonicity,[status(thm)],[593])).
% 1.41/1.62 tff(595,plain,
% 1.41/1.62 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.41/1.62 inference(transitivity,[status(thm)],[594, 592])).
% 1.41/1.62 tff(596,plain,
% 1.41/1.62 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.41/1.62 inference(quant_inst,[status(thm)],[])).
% 1.41/1.62 tff(597,plain,
% 1.41/1.62 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.41/1.62 inference(modus_ponens,[status(thm)],[596, 595])).
% 1.41/1.62 tff(598,plain,
% 1.41/1.62 (hskp41 | hskp9 | (~c1_1(a589))),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[597, 156, 591, 590, 342])).
% 1.41/1.62 tff(599,plain,
% 1.41/1.62 (~c1_1(a589)),
% 1.41/1.62 inference(unit_resolution,[status(thm)],[598, 331, 330])).
% 1.41/1.62 tff(600,plain,
% 1.41/1.62 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))))),
% 1.41/1.62 inference(bind,[status(th)],[])).
% 1.41/1.62 tff(601,plain,
% 1.41/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.41/1.62 inference(quant_intro,[status(thm)],[600])).
% 1.41/1.62 tff(602,plain,
% 1.41/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(603,plain,
% 1.41/1.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))))),
% 1.41/1.63 inference(bind,[status(th)],[])).
% 1.41/1.63 tff(604,plain,
% 1.41/1.63 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.41/1.63 inference(quant_intro,[status(thm)],[603])).
% 1.41/1.63 tff(605,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause257')).
% 1.41/1.63 tff(606,plain,
% 1.41/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.41/1.63 tff(607,plain,
% 1.41/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[606, 602])).
% 1.41/1.63 tff(608,plain,(
% 1.41/1.63 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.41/1.63 inference(skolemize,[status(sab)],[607])).
% 1.41/1.63 tff(609,plain,
% 1.41/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[608, 601])).
% 1.41/1.63 tff(610,plain,
% 1.41/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(611,plain,
% 1.41/1.63 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(612,plain,
% 1.41/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.41/1.63 inference(monotonicity,[status(thm)],[611])).
% 1.41/1.63 tff(613,plain,
% 1.41/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.41/1.63 inference(transitivity,[status(thm)],[612, 610])).
% 1.41/1.63 tff(614,plain,
% 1.41/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.41/1.63 inference(quant_inst,[status(thm)],[])).
% 1.41/1.63 tff(615,plain,
% 1.41/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589)),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.41/1.63 tff(616,plain,
% 1.41/1.63 (~c2_1(a586)),
% 1.41/1.63 inference(unit_resolution,[status(thm)],[615, 156, 591, 582, 590, 87, 86, 574, 609, 599, 589])).
% 1.41/1.63 tff(617,plain,
% 1.41/1.63 (((~hskp17) | c3_1(a571)) <=> ((~hskp17) | c3_1(a571))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(618,axiom,((~hskp17) | c3_1(a571)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.41/1.63 tff(619,plain,
% 1.41/1.63 ((~hskp17) | c3_1(a571)),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[618, 617])).
% 1.41/1.63 tff(620,plain,
% 1.41/1.63 ((~hskp17) | c3_1(a571)),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[619, 617])).
% 1.41/1.63 tff(621,plain,
% 1.41/1.63 ((~hskp17) | c3_1(a571)),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[620, 617])).
% 1.41/1.63 tff(622,plain,
% 1.41/1.63 ((~hskp17) | c3_1(a571)),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[621, 617])).
% 1.41/1.63 tff(623,plain,
% 1.41/1.63 ((~hskp17) | c3_1(a571)),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[622, 617])).
% 1.41/1.63 tff(624,plain,
% 1.41/1.63 (c3_1(a571)),
% 1.41/1.63 inference(unit_resolution,[status(thm)],[623, 568])).
% 1.41/1.63 tff(625,assumption,(c2_1(a589)), introduced(assumption)).
% 1.41/1.63 tff(626,plain,
% 1.41/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(627,plain,
% 1.41/1.63 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(628,plain,
% 1.41/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.41/1.63 inference(monotonicity,[status(thm)],[627])).
% 1.41/1.63 tff(629,plain,
% 1.41/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.41/1.63 inference(transitivity,[status(thm)],[628, 626])).
% 1.41/1.63 tff(630,plain,
% 1.41/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.41/1.63 inference(quant_inst,[status(thm)],[])).
% 1.41/1.63 tff(631,plain,
% 1.41/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[630, 629])).
% 1.41/1.63 tff(632,plain,
% 1.41/1.63 ($false),
% 1.41/1.63 inference(unit_resolution,[status(thm)],[631, 156, 625, 591, 88, 624, 86, 574, 45, 599, 616, 589])).
% 1.41/1.63 tff(633,plain,(hskp41 | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a586) | c3_1(a586) | c0_1(a589) | c0_1(a586) | hskp50 | hskp19 | hskp9 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.41/1.63 tff(634,plain,
% 1.41/1.63 (hskp9),
% 1.41/1.63 inference(unit_resolution,[status(thm)],[633, 329, 186, 88, 86, 178, 87, 110, 98, 172, 109])).
% 1.41/1.63 tff(635,plain,
% 1.41/1.63 (((~hskp9) | (~c1_1(a554))) <=> ((~hskp9) | (~c1_1(a554)))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(636,plain,
% 1.41/1.63 (((~c1_1(a554)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a554)))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(637,axiom,((~c1_1(a554)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.41/1.63 tff(638,plain,
% 1.41/1.63 ((~hskp9) | (~c1_1(a554))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[637, 636])).
% 1.41/1.63 tff(639,plain,
% 1.41/1.63 ((~hskp9) | (~c1_1(a554))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[638, 635])).
% 1.41/1.63 tff(640,plain,
% 1.41/1.63 (~c1_1(a554)),
% 1.41/1.63 inference(unit_resolution,[status(thm)],[639, 634])).
% 1.41/1.63 tff(641,plain,
% 1.41/1.63 (((~hskp9) | (~c2_1(a554))) <=> ((~hskp9) | (~c2_1(a554)))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(642,plain,
% 1.41/1.63 (((~c2_1(a554)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a554)))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(643,axiom,((~c2_1(a554)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.41/1.63 tff(644,plain,
% 1.41/1.63 ((~hskp9) | (~c2_1(a554))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.41/1.63 tff(645,plain,
% 1.41/1.63 ((~hskp9) | (~c2_1(a554))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[644, 641])).
% 1.41/1.63 tff(646,plain,
% 1.41/1.63 (~c2_1(a554)),
% 1.41/1.63 inference(unit_resolution,[status(thm)],[645, 634])).
% 1.41/1.63 tff(647,plain,
% 1.41/1.63 (((~hskp9) | (~c0_1(a554))) <=> ((~hskp9) | (~c0_1(a554)))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(648,plain,
% 1.41/1.63 (((~c0_1(a554)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a554)))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(649,axiom,((~c0_1(a554)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.41/1.63 tff(650,plain,
% 1.41/1.63 ((~hskp9) | (~c0_1(a554))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[649, 648])).
% 1.41/1.63 tff(651,plain,
% 1.41/1.63 ((~hskp9) | (~c0_1(a554))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[650, 647])).
% 1.41/1.63 tff(652,plain,
% 1.41/1.63 (~c0_1(a554)),
% 1.41/1.63 inference(unit_resolution,[status(thm)],[651, 634])).
% 1.41/1.63 tff(653,assumption,(~c2_1(a586)), introduced(assumption)).
% 1.41/1.63 tff(654,plain,
% 1.41/1.63 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.41/1.63 inference(bind,[status(th)],[])).
% 1.41/1.63 tff(655,plain,
% 1.41/1.63 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.63 inference(quant_intro,[status(thm)],[654])).
% 1.41/1.63 tff(656,plain,
% 1.41/1.63 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.63 inference(rewrite,[status(thm)],[])).
% 1.41/1.63 tff(657,plain,
% 1.41/1.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c2_1(V)) | hskp38) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp38))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c2_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.41/1.63 inference(bind,[status(th)],[])).
% 1.41/1.63 tff(658,plain,
% 1.41/1.63 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c2_1(V)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.63 inference(quant_intro,[status(thm)],[657])).
% 1.41/1.63 tff(659,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c2_1(V)) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause228')).
% 1.41/1.63 tff(660,plain,
% 1.41/1.63 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[659, 658])).
% 1.41/1.63 tff(661,plain,
% 1.41/1.63 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[660, 656])).
% 1.41/1.63 tff(662,plain,(
% 1.41/1.63 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.63 inference(skolemize,[status(sab)],[661])).
% 1.41/1.63 tff(663,plain,
% 1.41/1.63 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.41/1.63 inference(modus_ponens,[status(thm)],[662, 655])).
% 1.41/1.63 tff(664,plain,
% 1.41/1.63 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a586))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(665,plain,
% 1.48/1.63 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a586))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(666,plain,
% 1.48/1.63 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a586)))),
% 1.48/1.63 inference(monotonicity,[status(thm)],[665])).
% 1.48/1.63 tff(667,plain,
% 1.48/1.63 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a586))),
% 1.48/1.63 inference(transitivity,[status(thm)],[666, 664])).
% 1.48/1.63 tff(668,plain,
% 1.48/1.63 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.48/1.63 inference(quant_inst,[status(thm)],[])).
% 1.48/1.63 tff(669,plain,
% 1.48/1.63 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a586)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[668, 667])).
% 1.48/1.63 tff(670,plain,
% 1.48/1.63 (hskp38),
% 1.48/1.63 inference(unit_resolution,[status(thm)],[669, 156, 88, 226, 86, 218, 212, 663, 653])).
% 1.48/1.63 tff(671,plain,
% 1.48/1.63 (((~hskp38) | c0_1(a547)) <=> ((~hskp38) | c0_1(a547))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(672,axiom,((~hskp38) | c0_1(a547)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.48/1.63 tff(673,plain,
% 1.48/1.63 ((~hskp38) | c0_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[672, 671])).
% 1.48/1.63 tff(674,plain,
% 1.48/1.63 ((~hskp38) | c0_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[673, 671])).
% 1.48/1.63 tff(675,plain,
% 1.48/1.63 ((~hskp38) | c0_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[674, 671])).
% 1.48/1.63 tff(676,plain,
% 1.48/1.63 ((~hskp38) | c0_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[675, 671])).
% 1.48/1.63 tff(677,plain,
% 1.48/1.63 ((~hskp38) | c0_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[676, 671])).
% 1.48/1.63 tff(678,plain,
% 1.48/1.63 (c0_1(a547)),
% 1.48/1.63 inference(unit_resolution,[status(thm)],[677, 670])).
% 1.48/1.63 tff(679,plain,
% 1.48/1.63 (((~hskp38) | c1_1(a547)) <=> ((~hskp38) | c1_1(a547))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(680,axiom,((~hskp38) | c1_1(a547)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.48/1.63 tff(681,plain,
% 1.48/1.63 ((~hskp38) | c1_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[680, 679])).
% 1.48/1.63 tff(682,plain,
% 1.48/1.63 ((~hskp38) | c1_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[681, 679])).
% 1.48/1.63 tff(683,plain,
% 1.48/1.63 ((~hskp38) | c1_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[682, 679])).
% 1.48/1.63 tff(684,plain,
% 1.48/1.63 ((~hskp38) | c1_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[683, 679])).
% 1.48/1.63 tff(685,plain,
% 1.48/1.63 ((~hskp38) | c1_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[684, 679])).
% 1.48/1.63 tff(686,plain,
% 1.48/1.63 (c1_1(a547)),
% 1.48/1.63 inference(unit_resolution,[status(thm)],[685, 670])).
% 1.48/1.63 tff(687,plain,
% 1.48/1.63 (((~hskp38) | c2_1(a547)) <=> ((~hskp38) | c2_1(a547))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(688,axiom,((~hskp38) | c2_1(a547)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.48/1.63 tff(689,plain,
% 1.48/1.63 ((~hskp38) | c2_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[688, 687])).
% 1.48/1.63 tff(690,plain,
% 1.48/1.63 ((~hskp38) | c2_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[689, 687])).
% 1.48/1.63 tff(691,plain,
% 1.48/1.63 ((~hskp38) | c2_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[690, 687])).
% 1.48/1.63 tff(692,plain,
% 1.48/1.63 ((~hskp38) | c2_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[691, 687])).
% 1.48/1.63 tff(693,plain,
% 1.48/1.63 ((~hskp38) | c2_1(a547)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[692, 687])).
% 1.48/1.63 tff(694,plain,
% 1.48/1.63 (c2_1(a547)),
% 1.48/1.63 inference(unit_resolution,[status(thm)],[693, 670])).
% 1.48/1.63 tff(695,assumption,(~c1_1(a554)), introduced(assumption)).
% 1.48/1.63 tff(696,assumption,(~c2_1(a554)), introduced(assumption)).
% 1.48/1.63 tff(697,assumption,(~c0_1(a554)), introduced(assumption)).
% 1.48/1.63 tff(698,plain,
% 1.48/1.63 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))))),
% 1.48/1.63 inference(bind,[status(th)],[])).
% 1.48/1.63 tff(699,plain,
% 1.48/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.48/1.63 inference(quant_intro,[status(thm)],[698])).
% 1.48/1.63 tff(700,plain,
% 1.48/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(701,plain,
% 1.48/1.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) | c1_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) | c1_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))))),
% 1.48/1.63 inference(bind,[status(th)],[])).
% 1.48/1.63 tff(702,plain,
% 1.48/1.63 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) | c1_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.48/1.63 inference(quant_intro,[status(thm)],[701])).
% 1.48/1.63 tff(703,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | c2_1(V)) | c1_1(V)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause260')).
% 1.48/1.63 tff(704,plain,
% 1.48/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[703, 702])).
% 1.48/1.63 tff(705,plain,
% 1.48/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[704, 700])).
% 1.48/1.63 tff(706,plain,(
% 1.48/1.63 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.48/1.63 inference(skolemize,[status(sab)],[705])).
% 1.48/1.63 tff(707,plain,
% 1.48/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[706, 699])).
% 1.48/1.63 tff(708,assumption,(hskp0), introduced(assumption)).
% 1.48/1.63 tff(709,plain,
% 1.48/1.63 (((~hskp0) | (~c2_1(a535))) <=> ((~hskp0) | (~c2_1(a535)))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(710,plain,
% 1.48/1.63 (((~c2_1(a535)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a535)))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(711,axiom,((~c2_1(a535)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause216')).
% 1.48/1.63 tff(712,plain,
% 1.48/1.63 ((~hskp0) | (~c2_1(a535))),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[711, 710])).
% 1.48/1.63 tff(713,plain,
% 1.48/1.63 ((~hskp0) | (~c2_1(a535))),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[712, 709])).
% 1.48/1.63 tff(714,plain,
% 1.48/1.63 (~c2_1(a535)),
% 1.48/1.63 inference(unit_resolution,[status(thm)],[713, 708])).
% 1.48/1.63 tff(715,plain,
% 1.48/1.63 (((~hskp0) | c0_1(a535)) <=> ((~hskp0) | c0_1(a535))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(716,axiom,((~hskp0) | c0_1(a535)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.48/1.63 tff(717,plain,
% 1.48/1.63 ((~hskp0) | c0_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[716, 715])).
% 1.48/1.63 tff(718,plain,
% 1.48/1.63 ((~hskp0) | c0_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[717, 715])).
% 1.48/1.63 tff(719,plain,
% 1.48/1.63 ((~hskp0) | c0_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[718, 715])).
% 1.48/1.63 tff(720,plain,
% 1.48/1.63 ((~hskp0) | c0_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[719, 715])).
% 1.48/1.63 tff(721,plain,
% 1.48/1.63 ((~hskp0) | c0_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[720, 715])).
% 1.48/1.63 tff(722,plain,
% 1.48/1.63 (c0_1(a535)),
% 1.48/1.63 inference(unit_resolution,[status(thm)],[721, 708])).
% 1.48/1.63 tff(723,plain,
% 1.48/1.63 (((~hskp0) | c1_1(a535)) <=> ((~hskp0) | c1_1(a535))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(724,axiom,((~hskp0) | c1_1(a535)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.48/1.63 tff(725,plain,
% 1.48/1.63 ((~hskp0) | c1_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.48/1.63 tff(726,plain,
% 1.48/1.63 ((~hskp0) | c1_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[725, 723])).
% 1.48/1.63 tff(727,plain,
% 1.48/1.63 ((~hskp0) | c1_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[726, 723])).
% 1.48/1.63 tff(728,plain,
% 1.48/1.63 ((~hskp0) | c1_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[727, 723])).
% 1.48/1.63 tff(729,plain,
% 1.48/1.63 ((~hskp0) | c1_1(a535)),
% 1.48/1.63 inference(modus_ponens,[status(thm)],[728, 723])).
% 1.48/1.63 tff(730,plain,
% 1.48/1.63 (c1_1(a535)),
% 1.48/1.63 inference(unit_resolution,[status(thm)],[729, 708])).
% 1.48/1.63 tff(731,assumption,(c0_1(a547)), introduced(assumption)).
% 1.48/1.63 tff(732,assumption,(c1_1(a547)), introduced(assumption)).
% 1.48/1.63 tff(733,assumption,(c2_1(a547)), introduced(assumption)).
% 1.48/1.63 tff(734,plain,
% 1.48/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c2_1(a545) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a545) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(735,plain,
% 1.48/1.63 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | (~c3_1(a545)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c1_1(a545) | c2_1(a545) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.63 inference(rewrite,[status(thm)],[])).
% 1.48/1.63 tff(736,plain,
% 1.48/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | (~c3_1(a545)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c2_1(a545) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.48/1.63 inference(monotonicity,[status(thm)],[735])).
% 1.48/1.63 tff(737,plain,
% 1.48/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | (~c3_1(a545)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a545) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.64 inference(transitivity,[status(thm)],[736, 734])).
% 1.48/1.64 tff(738,plain,
% 1.48/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | (~c3_1(a545)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.48/1.64 inference(quant_inst,[status(thm)],[])).
% 1.48/1.64 tff(739,plain,
% 1.48/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a545) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.48/1.64 tff(740,plain,
% 1.48/1.64 (~c3_1(a545)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[739, 156, 733, 732, 731, 112, 730, 722, 111, 714, 707])).
% 1.48/1.64 tff(741,plain,
% 1.48/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a554) | c1_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a554)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a554) | c1_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a554)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(742,plain,
% 1.48/1.64 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a554) | c1_1(a554) | (~c3_1(a554)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c2_1(a554) | c1_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a554)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(743,plain,
% 1.48/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a554) | c1_1(a554) | (~c3_1(a554)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a554) | c1_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a554)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.48/1.64 inference(monotonicity,[status(thm)],[742])).
% 1.48/1.64 tff(744,plain,
% 1.48/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a554) | c1_1(a554) | (~c3_1(a554)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a554) | c1_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a554)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.64 inference(transitivity,[status(thm)],[743, 741])).
% 1.48/1.64 tff(745,plain,
% 1.48/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a554) | c1_1(a554) | (~c3_1(a554)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.48/1.64 inference(quant_inst,[status(thm)],[])).
% 1.48/1.64 tff(746,plain,
% 1.48/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a554) | c1_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a554)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.48/1.64 tff(747,plain,
% 1.48/1.64 (~c3_1(a554)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[746, 156, 733, 732, 731, 730, 722, 696, 695, 714, 707])).
% 1.48/1.64 tff(748,plain,
% 1.48/1.64 (^[V: $i, U: $i] : refl((hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) <=> (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)))),
% 1.48/1.64 inference(bind,[status(th)],[])).
% 1.48/1.64 tff(749,plain,
% 1.48/1.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.48/1.64 inference(quant_intro,[status(thm)],[748])).
% 1.48/1.64 tff(750,plain,
% 1.48/1.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(751,plain,
% 1.48/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp45) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) | hskp45))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V)) | hskp45) <=> (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp45) <=> (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))))),
% 1.48/1.64 inference(bind,[status(th)],[])).
% 1.48/1.64 tff(752,plain,
% 1.48/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp45) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.48/1.64 inference(quant_intro,[status(thm)],[751])).
% 1.48/1.64 tff(753,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause232')).
% 1.48/1.64 tff(754,plain,
% 1.48/1.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[753, 752])).
% 1.48/1.64 tff(755,plain,
% 1.48/1.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[754, 750])).
% 1.48/1.64 tff(756,plain,(
% 1.48/1.64 ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.48/1.64 inference(skolemize,[status(sab)],[755])).
% 1.48/1.64 tff(757,plain,
% 1.48/1.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[756, 749])).
% 1.48/1.64 tff(758,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a554) | c2_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a554))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a554) | c2_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a554))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(759,plain,
% 1.48/1.64 ((hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a554) | c3_1(a554) | c0_1(a554)) <=> (hskp45 | c0_1(a554) | c2_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a554))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(760,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a554) | c2_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a554)))),
% 1.48/1.64 inference(monotonicity,[status(thm)],[759])).
% 1.48/1.64 tff(761,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a554) | c2_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a554))),
% 1.48/1.64 inference(transitivity,[status(thm)],[760, 758])).
% 1.48/1.64 tff(762,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a554) | c3_1(a554) | c0_1(a554))),
% 1.48/1.64 inference(quant_inst,[status(thm)],[])).
% 1.48/1.64 tff(763,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a554) | c2_1(a554) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a554)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[762, 761])).
% 1.48/1.64 tff(764,plain,
% 1.48/1.64 (hskp45),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[763, 156, 730, 722, 697, 696, 714, 757, 747])).
% 1.48/1.64 tff(765,assumption,(~c3_1(a545)), introduced(assumption)).
% 1.48/1.64 tff(766,assumption,(hskp45), introduced(assumption)).
% 1.48/1.64 tff(767,plain,
% 1.48/1.64 (((~hskp45) | (~c3_1(a561))) <=> ((~hskp45) | (~c3_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(768,plain,
% 1.48/1.64 (((~c3_1(a561)) | (~hskp45)) <=> ((~hskp45) | (~c3_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(769,axiom,((~c3_1(a561)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.48/1.64 tff(770,plain,
% 1.48/1.64 ((~hskp45) | (~c3_1(a561))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.48/1.64 tff(771,plain,
% 1.48/1.64 ((~hskp45) | (~c3_1(a561))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[770, 767])).
% 1.48/1.64 tff(772,plain,
% 1.48/1.64 (~c3_1(a561)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[771, 766])).
% 1.48/1.64 tff(773,plain,
% 1.48/1.64 (((~hskp45) | c0_1(a561)) <=> ((~hskp45) | c0_1(a561))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(774,axiom,((~hskp45) | c0_1(a561)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.48/1.64 tff(775,plain,
% 1.48/1.64 ((~hskp45) | c0_1(a561)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[774, 773])).
% 1.48/1.64 tff(776,plain,
% 1.48/1.64 ((~hskp45) | c0_1(a561)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[775, 773])).
% 1.48/1.64 tff(777,plain,
% 1.48/1.64 ((~hskp45) | c0_1(a561)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[776, 773])).
% 1.48/1.64 tff(778,plain,
% 1.48/1.64 ((~hskp45) | c0_1(a561)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[777, 773])).
% 1.48/1.64 tff(779,plain,
% 1.48/1.64 ((~hskp45) | c0_1(a561)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[778, 773])).
% 1.48/1.64 tff(780,plain,
% 1.48/1.64 (c0_1(a561)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[779, 766])).
% 1.48/1.64 tff(781,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a561)) | (~c0_1(a561)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(782,plain,
% 1.48/1.64 ((hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | c3_1(a561) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(783,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a561)) | (~c0_1(a561))))),
% 1.48/1.64 inference(monotonicity,[status(thm)],[782])).
% 1.48/1.64 tff(784,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.48/1.64 inference(transitivity,[status(thm)],[783, 781])).
% 1.48/1.64 tff(785,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.48/1.64 inference(quant_inst,[status(thm)],[])).
% 1.48/1.64 tff(786,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a561)) | (~c0_1(a561))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.48/1.64 tff(787,plain,
% 1.48/1.64 (~c1_1(a561)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[786, 156, 35, 780, 772, 111, 97, 85, 765])).
% 1.48/1.64 tff(788,plain,
% 1.48/1.64 (((~hskp45) | (~c2_1(a561))) <=> ((~hskp45) | (~c2_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(789,plain,
% 1.48/1.64 (((~c2_1(a561)) | (~hskp45)) <=> ((~hskp45) | (~c2_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(790,axiom,((~c2_1(a561)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.48/1.64 tff(791,plain,
% 1.48/1.64 ((~hskp45) | (~c2_1(a561))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.48/1.64 tff(792,plain,
% 1.48/1.64 ((~hskp45) | (~c2_1(a561))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[791, 788])).
% 1.48/1.64 tff(793,plain,
% 1.48/1.64 (~c2_1(a561)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[792, 766])).
% 1.48/1.64 tff(794,assumption,(hskp50), introduced(assumption)).
% 1.48/1.64 tff(795,plain,
% 1.48/1.64 (((~hskp50) | (~c3_1(a574))) <=> ((~hskp50) | (~c3_1(a574)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(796,plain,
% 1.48/1.64 (((~c3_1(a574)) | (~hskp50)) <=> ((~hskp50) | (~c3_1(a574)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(797,axiom,((~c3_1(a574)) | (~hskp50)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.48/1.64 tff(798,plain,
% 1.48/1.64 ((~hskp50) | (~c3_1(a574))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[797, 796])).
% 1.48/1.64 tff(799,plain,
% 1.48/1.64 ((~hskp50) | (~c3_1(a574))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[798, 795])).
% 1.48/1.64 tff(800,plain,
% 1.48/1.64 (~c3_1(a574)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[799, 794])).
% 1.48/1.64 tff(801,plain,
% 1.48/1.64 (((~hskp50) | c1_1(a574)) <=> ((~hskp50) | c1_1(a574))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(802,axiom,((~hskp50) | c1_1(a574)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.48/1.64 tff(803,plain,
% 1.48/1.64 ((~hskp50) | c1_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[802, 801])).
% 1.48/1.64 tff(804,plain,
% 1.48/1.64 ((~hskp50) | c1_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[803, 801])).
% 1.48/1.64 tff(805,plain,
% 1.48/1.64 ((~hskp50) | c1_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[804, 801])).
% 1.48/1.64 tff(806,plain,
% 1.48/1.64 ((~hskp50) | c1_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[805, 801])).
% 1.48/1.64 tff(807,plain,
% 1.48/1.64 ((~hskp50) | c1_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[806, 801])).
% 1.48/1.64 tff(808,plain,
% 1.48/1.64 (c1_1(a574)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[807, 794])).
% 1.48/1.64 tff(809,plain,
% 1.48/1.64 (((~hskp50) | c0_1(a574)) <=> ((~hskp50) | c0_1(a574))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(810,axiom,((~hskp50) | c0_1(a574)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.48/1.64 tff(811,plain,
% 1.48/1.64 ((~hskp50) | c0_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.48/1.64 tff(812,plain,
% 1.48/1.64 ((~hskp50) | c0_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[811, 809])).
% 1.48/1.64 tff(813,plain,
% 1.48/1.64 ((~hskp50) | c0_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[812, 809])).
% 1.48/1.64 tff(814,plain,
% 1.48/1.64 ((~hskp50) | c0_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[813, 809])).
% 1.48/1.64 tff(815,plain,
% 1.48/1.64 ((~hskp50) | c0_1(a574)),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[814, 809])).
% 1.48/1.64 tff(816,plain,
% 1.48/1.64 (c0_1(a574)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[815, 794])).
% 1.48/1.64 tff(817,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(818,plain,
% 1.48/1.64 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | c3_1(a574) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(819,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a574)) | (~c1_1(a574))))),
% 1.48/1.64 inference(monotonicity,[status(thm)],[818])).
% 1.48/1.64 tff(820,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.48/1.64 inference(transitivity,[status(thm)],[819, 817])).
% 1.48/1.64 tff(821,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.48/1.64 inference(quant_inst,[status(thm)],[])).
% 1.48/1.64 tff(822,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a574)) | (~c1_1(a574))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.48/1.64 tff(823,plain,
% 1.48/1.64 ($false),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[822, 156, 35, 816, 808, 800, 111, 97, 85, 765])).
% 1.48/1.64 tff(824,plain,((~hskp50) | hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.64 tff(825,plain,
% 1.48/1.64 (~hskp50),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[824, 111, 35, 97, 765])).
% 1.48/1.64 tff(826,plain,
% 1.48/1.64 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a561) | (~ndr1_0) | c1_1(a561) | (~c0_1(a561)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a561) | (~ndr1_0) | c1_1(a561) | (~c0_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(827,plain,
% 1.48/1.64 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a561) | c1_1(a561) | (~c0_1(a561))) <=> (hskp50 | hskp19 | c2_1(a561) | (~ndr1_0) | c1_1(a561) | (~c0_1(a561)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(828,plain,
% 1.48/1.64 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a561) | c1_1(a561) | (~c0_1(a561)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a561) | (~ndr1_0) | c1_1(a561) | (~c0_1(a561))))),
% 1.48/1.64 inference(monotonicity,[status(thm)],[827])).
% 1.48/1.64 tff(829,plain,
% 1.48/1.64 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a561) | c1_1(a561) | (~c0_1(a561)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a561) | (~ndr1_0) | c1_1(a561) | (~c0_1(a561)))),
% 1.48/1.64 inference(transitivity,[status(thm)],[828, 826])).
% 1.48/1.64 tff(830,plain,
% 1.48/1.64 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a561) | c1_1(a561) | (~c0_1(a561)))),
% 1.48/1.64 inference(quant_inst,[status(thm)],[])).
% 1.48/1.64 tff(831,plain,
% 1.48/1.64 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a561) | (~ndr1_0) | c1_1(a561) | (~c0_1(a561))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[830, 829])).
% 1.48/1.64 tff(832,plain,
% 1.48/1.64 ($false),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[831, 156, 825, 98, 780, 793, 34, 787])).
% 1.48/1.64 tff(833,plain,((~hskp45) | hskp19 | hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.64 tff(834,plain,
% 1.48/1.64 ($false),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[833, 764, 740, 35, 111, 97, 98])).
% 1.48/1.64 tff(835,plain,((~hskp0) | hskp33 | c2_1(a545) | c0_1(a545) | hskp19 | c0_1(a554) | c2_1(a554) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c1_1(a545) | c1_1(a554)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.64 tff(836,plain,
% 1.48/1.64 (~hskp0),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[835, 694, 111, 97, 98, 697, 696, 35, 686, 678, 112, 695])).
% 1.48/1.64 tff(837,assumption,(~hskp0), introduced(assumption)).
% 1.48/1.64 tff(838,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(839,plain,
% 1.48/1.64 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(840,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.48/1.64 inference(monotonicity,[status(thm)],[839])).
% 1.48/1.64 tff(841,plain,
% 1.48/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.64 inference(transitivity,[status(thm)],[840, 838])).
% 1.48/1.64 tff(842,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.48/1.64 inference(quant_inst,[status(thm)],[])).
% 1.48/1.64 tff(843,plain,
% 1.48/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.48/1.64 inference(modus_ponens,[status(thm)],[842, 841])).
% 1.48/1.64 tff(844,plain,
% 1.48/1.64 ($false),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[843, 156, 837, 733, 732, 731, 88, 86, 108, 653])).
% 1.48/1.64 tff(845,plain,(c2_1(a586) | hskp0 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.64 tff(846,plain,
% 1.48/1.64 ($false),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[845, 836, 694, 653, 686, 678, 88, 86])).
% 1.48/1.64 tff(847,plain,(c2_1(a586) | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | hskp19 | c0_1(a554) | c2_1(a554) | hskp33 | c1_1(a545) | c1_1(a554)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.64 tff(848,plain,
% 1.48/1.64 (c2_1(a586)),
% 1.48/1.64 inference(unit_resolution,[status(thm)],[847, 652, 86, 111, 97, 98, 88, 646, 35, 112, 640])).
% 1.48/1.64 tff(849,plain,
% 1.48/1.64 (^[V: $i, U: $i] : refl((hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.48/1.64 inference(bind,[status(th)],[])).
% 1.48/1.64 tff(850,plain,
% 1.48/1.64 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.48/1.64 inference(quant_intro,[status(thm)],[849])).
% 1.48/1.64 tff(851,plain,
% 1.48/1.64 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.48/1.64 inference(rewrite,[status(thm)],[])).
% 1.48/1.64 tff(852,plain,
% 1.48/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) | c0_1(V)) | hskp46) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp46))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp46) <=> (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) | c0_1(V)) | hskp46) <=> (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.48/1.65 inference(bind,[status(th)],[])).
% 1.48/1.65 tff(853,plain,
% 1.48/1.65 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) | c0_1(V)) | hskp46) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.48/1.65 inference(quant_intro,[status(thm)],[852])).
% 1.48/1.65 tff(854,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(V)) | c0_1(V)) | hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause251')).
% 1.48/1.65 tff(855,plain,
% 1.48/1.65 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[854, 853])).
% 1.48/1.65 tff(856,plain,
% 1.48/1.65 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[855, 851])).
% 1.48/1.65 tff(857,plain,(
% 1.48/1.65 ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.48/1.65 inference(skolemize,[status(sab)],[856])).
% 1.48/1.65 tff(858,plain,
% 1.48/1.65 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[857, 850])).
% 1.48/1.65 tff(859,assumption,(~hskp39), introduced(assumption)).
% 1.48/1.65 tff(860,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a554) | c1_1(a554) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a554))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a554) | c1_1(a554) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a554))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(861,plain,
% 1.48/1.65 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a554) | c1_1(a554) | c3_1(a554)) <=> (hskp38 | c2_1(a554) | c1_1(a554) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a554))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(862,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a554) | c1_1(a554) | c3_1(a554))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a554) | c1_1(a554) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a554)))),
% 1.48/1.65 inference(monotonicity,[status(thm)],[861])).
% 1.48/1.65 tff(863,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a554) | c1_1(a554) | c3_1(a554))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a554) | c1_1(a554) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a554))),
% 1.48/1.65 inference(transitivity,[status(thm)],[862, 860])).
% 1.48/1.65 tff(864,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a554) | c1_1(a554) | c3_1(a554))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(865,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a554) | c1_1(a554) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a554)),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.48/1.65 tff(866,plain,
% 1.48/1.65 (hskp38 | c3_1(a554)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[865, 156, 226, 646, 640, 218, 212, 663])).
% 1.48/1.65 tff(867,plain,
% 1.48/1.65 (c3_1(a554)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[866, 58])).
% 1.48/1.65 tff(868,assumption,(c3_1(a554)), introduced(assumption)).
% 1.48/1.65 tff(869,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a586) | c3_1(a586) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c3_1(a554)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c3_1(a554)) | c2_1(a586))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(870,plain,
% 1.48/1.65 ((hskp38 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp38 | c1_1(a586) | c3_1(a586) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c3_1(a554)) | c2_1(a586))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(871,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a586) | c3_1(a586) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c3_1(a554)) | c2_1(a586)))),
% 1.48/1.65 inference(monotonicity,[status(thm)],[870])).
% 1.48/1.65 tff(872,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c3_1(a554)) | c2_1(a586))),
% 1.48/1.65 inference(transitivity,[status(thm)],[871, 869])).
% 1.48/1.65 tff(873,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(874,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c3_1(a554)) | c2_1(a586)),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.48/1.65 tff(875,plain,
% 1.48/1.65 ($false),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[874, 156, 58, 88, 86, 697, 696, 663, 653, 868])).
% 1.48/1.65 tff(876,plain,(c2_1(a586) | hskp38 | c1_1(a586) | c3_1(a586) | c0_1(a554) | c2_1(a554) | (~c3_1(a554))), inference(lemma,lemma(discharge,[]))).
% 1.48/1.65 tff(877,plain,
% 1.48/1.65 (c2_1(a586)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[876, 58, 88, 86, 652, 646, 867])).
% 1.48/1.65 tff(878,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a545) | c2_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a545) | c2_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(879,plain,
% 1.48/1.65 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a545) | c1_1(a545) | c3_1(a545)) <=> (hskp38 | c1_1(a545) | c2_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(880,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a545) | c1_1(a545) | c3_1(a545))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a545) | c2_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548))))),
% 1.48/1.65 inference(monotonicity,[status(thm)],[879])).
% 1.48/1.65 tff(881,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a545) | c1_1(a545) | c3_1(a545))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a545) | c2_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)))),
% 1.48/1.65 inference(transitivity,[status(thm)],[880, 878])).
% 1.48/1.65 tff(882,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a545) | c1_1(a545) | c3_1(a545))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(883,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a545) | c2_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.48/1.65 tff(884,plain,
% 1.48/1.65 (hskp38 | c3_1(a545)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[883, 156, 226, 112, 218, 212, 111, 663])).
% 1.48/1.65 tff(885,plain,
% 1.48/1.65 (c3_1(a545)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[884, 58])).
% 1.48/1.65 tff(886,plain,
% 1.48/1.65 (hskp37),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[430, 384, 110, 98])).
% 1.48/1.65 tff(887,plain,
% 1.48/1.65 (~c2_1(a544)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[436, 886])).
% 1.48/1.65 tff(888,plain,
% 1.48/1.65 (c1_1(a544)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[444, 886])).
% 1.48/1.65 tff(889,plain,
% 1.48/1.65 (~c3_1(a544)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[450, 886])).
% 1.48/1.65 tff(890,plain,
% 1.48/1.65 (~hskp7),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[502, 888, 109, 98, 889, 110, 887])).
% 1.48/1.65 tff(891,plain,
% 1.48/1.65 (hskp40),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[524, 890, 110, 98, 384])).
% 1.48/1.65 tff(892,plain,
% 1.48/1.65 (c2_1(a551)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[532, 891])).
% 1.48/1.65 tff(893,plain,
% 1.48/1.65 (c3_1(a551)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[540, 891])).
% 1.48/1.65 tff(894,plain,
% 1.48/1.65 (c1_1(a551)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[552, 893, 889, 892, 888, 887, 109])).
% 1.48/1.65 tff(895,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(896,plain,
% 1.48/1.65 ((hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544))) <=> (hskp4 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(897,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.48/1.65 inference(monotonicity,[status(thm)],[896])).
% 1.48/1.65 tff(898,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.48/1.65 inference(transitivity,[status(thm)],[897, 895])).
% 1.48/1.65 tff(899,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(900,plain,
% 1.48/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[899, 898])).
% 1.48/1.65 tff(901,plain,
% 1.48/1.65 (c0_1(a544)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[900, 156, 194, 893, 892, 888, 889, 22, 894])).
% 1.48/1.65 tff(902,assumption,(c2_1(a586)), introduced(assumption)).
% 1.48/1.65 tff(903,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(904,plain,
% 1.48/1.65 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c1_1(a545) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(905,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.48/1.65 inference(monotonicity,[status(thm)],[904])).
% 1.48/1.65 tff(906,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.48/1.65 inference(transitivity,[status(thm)],[905, 903])).
% 1.48/1.65 tff(907,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(908,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[907, 906])).
% 1.48/1.65 tff(909,plain,
% 1.48/1.65 ($false),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[908, 156, 888, 112, 887, 87, 86, 97, 609, 902, 2, 901])).
% 1.48/1.65 tff(910,plain,((~hskp18) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~c2_1(a586)) | (~c3_1(a545)) | hskp15 | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.48/1.65 tff(911,plain,
% 1.48/1.65 (~hskp18),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[910, 877, 87, 86, 97, 112, 885, 109, 110, 98])).
% 1.48/1.65 tff(912,plain,
% 1.48/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W))))),
% 1.48/1.65 inference(bind,[status(th)],[])).
% 1.48/1.65 tff(913,plain,
% 1.48/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))),
% 1.48/1.65 inference(quant_intro,[status(thm)],[912])).
% 1.48/1.65 tff(914,plain,
% 1.48/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(915,plain,
% 1.48/1.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))))),
% 1.48/1.65 inference(bind,[status(th)],[])).
% 1.48/1.65 tff(916,plain,
% 1.48/1.65 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))),
% 1.48/1.65 inference(quant_intro,[status(thm)],[915])).
% 1.48/1.65 tff(917,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause259')).
% 1.48/1.65 tff(918,plain,
% 1.48/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[917, 916])).
% 1.48/1.65 tff(919,plain,
% 1.48/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[918, 914])).
% 1.48/1.65 tff(920,plain,(
% 1.48/1.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))),
% 1.48/1.65 inference(skolemize,[status(sab)],[919])).
% 1.48/1.65 tff(921,plain,
% 1.48/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[920, 913])).
% 1.48/1.65 tff(922,assumption,(hskp17), introduced(assumption)).
% 1.48/1.65 tff(923,plain,
% 1.48/1.65 (~c2_1(a571)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[573, 922])).
% 1.48/1.65 tff(924,plain,
% 1.48/1.65 (c3_1(a571)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[623, 922])).
% 1.48/1.65 tff(925,plain,
% 1.48/1.65 (c0_1(a571)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[581, 922])).
% 1.48/1.65 tff(926,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(927,plain,
% 1.48/1.65 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571))) <=> (c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(928,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a586))))),
% 1.48/1.65 inference(monotonicity,[status(thm)],[927])).
% 1.48/1.65 tff(929,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.48/1.65 inference(transitivity,[status(thm)],[928, 926])).
% 1.48/1.65 tff(930,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(931,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a586))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.48/1.65 tff(932,plain,
% 1.48/1.65 (c1_1(a571)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[931, 156, 88, 925, 924, 86, 923, 921, 902])).
% 1.48/1.65 tff(933,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(934,plain,
% 1.48/1.65 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(935,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))))),
% 1.48/1.65 inference(monotonicity,[status(thm)],[934])).
% 1.48/1.65 tff(936,plain,
% 1.48/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.48/1.65 inference(transitivity,[status(thm)],[935, 933])).
% 1.48/1.65 tff(937,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(938,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.48/1.65 tff(939,plain,
% 1.48/1.65 ($false),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[938, 156, 925, 112, 87, 86, 923, 97, 609, 902, 2, 932])).
% 1.48/1.65 tff(940,plain,((~hskp17) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~c2_1(a586)) | (~c3_1(a545)) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.65 tff(941,plain,
% 1.48/1.65 (~hskp17),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[940, 877, 87, 86, 97, 112, 885, 88])).
% 1.48/1.65 tff(942,plain,
% 1.48/1.65 (hskp16),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[382, 941, 911])).
% 1.48/1.65 tff(943,plain,
% 1.48/1.65 (~c0_1(a570)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[348, 942])).
% 1.48/1.65 tff(944,plain,
% 1.48/1.65 (c1_1(a570)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[356, 942])).
% 1.48/1.65 tff(945,plain,
% 1.48/1.65 (c3_1(a570)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[364, 942])).
% 1.48/1.65 tff(946,assumption,(~hskp46), introduced(assumption)).
% 1.48/1.65 tff(947,assumption,(c1_1(a570)), introduced(assumption)).
% 1.48/1.65 tff(948,assumption,(c3_1(a570)), introduced(assumption)).
% 1.48/1.65 tff(949,plain,
% 1.48/1.65 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a586)))),
% 1.48/1.65 inference(rewrite,[status(thm)],[])).
% 1.48/1.65 tff(950,plain,
% 1.48/1.65 ((hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586))) <=> (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a586)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(951,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a586))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[950])).
% 1.48/1.66 tff(952,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a586)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[951, 949])).
% 1.48/1.66 tff(953,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(954,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a586))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[953, 952])).
% 1.48/1.66 tff(955,plain,
% 1.48/1.66 (hskp46 | (~c2_1(a570))),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[954, 156, 948, 947, 87, 86, 858, 902])).
% 1.48/1.66 tff(956,plain,
% 1.48/1.66 (~c2_1(a570)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[955, 946])).
% 1.48/1.66 tff(957,assumption,(~c0_1(a570)), introduced(assumption)).
% 1.48/1.66 tff(958,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(959,plain,
% 1.48/1.66 ((hskp46 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570))) <=> (hskp46 | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(960,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[959])).
% 1.48/1.66 tff(961,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[960, 958])).
% 1.48/1.66 tff(962,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(963,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[962, 961])).
% 1.48/1.66 tff(964,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[963, 156, 946, 948, 947, 957, 12, 956])).
% 1.48/1.66 tff(965,plain,(hskp46 | (~c3_1(a570)) | (~c1_1(a570)) | c0_1(a570) | c0_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(966,plain,
% 1.48/1.66 (hskp46),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[965, 945, 944, 943, 87, 86, 877])).
% 1.48/1.66 tff(967,plain,
% 1.48/1.66 (~c3_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[270, 966])).
% 1.48/1.66 tff(968,plain,
% 1.48/1.66 (~c0_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[64, 966])).
% 1.48/1.66 tff(969,plain,
% 1.48/1.66 (c1_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[288, 966])).
% 1.48/1.66 tff(970,assumption,(~c2_1(a570)), introduced(assumption)).
% 1.48/1.66 tff(971,assumption,(~c0_1(a562)), introduced(assumption)).
% 1.48/1.66 tff(972,assumption,(~c3_1(a562)), introduced(assumption)).
% 1.48/1.66 tff(973,assumption,(c1_1(a562)), introduced(assumption)).
% 1.48/1.66 tff(974,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(975,plain,
% 1.48/1.66 ((hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp39 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(976,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[975])).
% 1.48/1.66 tff(977,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[976, 974])).
% 1.48/1.66 tff(978,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(979,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.48/1.66 tff(980,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[979, 156, 859, 973, 948, 947, 972, 971, 281, 970])).
% 1.48/1.66 tff(981,plain,(c2_1(a570) | hskp39 | (~c1_1(a562)) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(982,plain,
% 1.48/1.66 (c2_1(a570)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[981, 969, 945, 968, 944, 967, 859])).
% 1.48/1.66 tff(983,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(984,plain,
% 1.48/1.66 ((hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(985,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[984])).
% 1.48/1.66 tff(986,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[985, 983])).
% 1.48/1.66 tff(987,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(988,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a562))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.48/1.66 tff(989,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[988, 156, 194, 969, 945, 944, 967, 968, 22, 982])).
% 1.48/1.66 tff(990,plain,(hskp38 | hskp39 | c0_1(a586) | c3_1(a586) | c0_1(a545) | c1_1(a545) | c1_1(a586) | hskp15 | hskp50 | hskp19 | c2_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(991,plain,
% 1.48/1.66 (hskp38),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[990, 859, 87, 86, 97, 112, 88, 109, 110, 98, 111])).
% 1.48/1.66 tff(992,plain,
% 1.48/1.66 (c0_1(a547)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[677, 991])).
% 1.48/1.66 tff(993,plain,
% 1.48/1.66 (c1_1(a547)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[685, 991])).
% 1.48/1.66 tff(994,plain,
% 1.48/1.66 (c2_1(a547)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[693, 991])).
% 1.48/1.66 tff(995,plain,
% 1.48/1.66 (~hskp0),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[835, 994, 111, 97, 98, 652, 646, 35, 993, 992, 112, 640])).
% 1.48/1.66 tff(996,plain,
% 1.48/1.66 (c2_1(a586)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[845, 995, 994, 993, 992, 88, 86])).
% 1.48/1.66 tff(997,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a545) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a545) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(998,plain,
% 1.48/1.66 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | c3_1(a545)) <=> (hskp0 | c1_1(a545) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(999,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | c3_1(a545))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a545) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[998])).
% 1.48/1.66 tff(1000,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | c3_1(a545))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a545) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[999, 997])).
% 1.48/1.66 tff(1001,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a545) | c1_1(a545) | c3_1(a545))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(1002,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a545) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.48/1.66 tff(1003,plain,
% 1.48/1.66 (hskp0 | c3_1(a545)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1002, 156, 994, 993, 992, 112, 111, 108])).
% 1.48/1.66 tff(1004,plain,
% 1.48/1.66 (c3_1(a545)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1003, 995])).
% 1.48/1.66 tff(1005,plain,
% 1.48/1.66 (~hskp18),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[910, 996, 87, 86, 97, 112, 1004, 109, 110, 98])).
% 1.48/1.66 tff(1006,plain,
% 1.48/1.66 (~hskp17),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[940, 996, 87, 86, 97, 112, 1004, 88])).
% 1.48/1.66 tff(1007,plain,
% 1.48/1.66 (hskp16),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[382, 1006, 1005])).
% 1.48/1.66 tff(1008,plain,
% 1.48/1.66 (~c0_1(a570)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[348, 1007])).
% 1.48/1.66 tff(1009,plain,
% 1.48/1.66 (c1_1(a570)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[356, 1007])).
% 1.48/1.66 tff(1010,plain,
% 1.48/1.66 (c3_1(a570)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[364, 1007])).
% 1.48/1.66 tff(1011,plain,
% 1.48/1.66 (hskp46),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[965, 1010, 1009, 1008, 87, 86, 996])).
% 1.48/1.66 tff(1012,plain,
% 1.48/1.66 (~c3_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[270, 1011])).
% 1.48/1.66 tff(1013,plain,
% 1.48/1.66 (~c0_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[64, 1011])).
% 1.48/1.66 tff(1014,plain,
% 1.48/1.66 (c1_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[288, 1011])).
% 1.48/1.66 tff(1015,plain,
% 1.48/1.66 (c2_1(a570)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[981, 1014, 1010, 1013, 1009, 1012, 859])).
% 1.48/1.66 tff(1016,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[988, 156, 194, 1014, 1010, 1009, 1012, 1013, 22, 1015])).
% 1.48/1.66 tff(1017,plain,(hskp39 | c0_1(a586) | c3_1(a586) | c0_1(a545) | c1_1(a545) | c1_1(a586) | hskp15 | hskp50 | hskp19 | c2_1(a545) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(1018,plain,
% 1.48/1.66 (hskp39),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1017, 112, 86, 97, 87, 88, 109, 110, 98, 111, 35])).
% 1.48/1.66 tff(1019,plain,
% 1.48/1.66 (c1_1(a549)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[303, 1018])).
% 1.48/1.66 tff(1020,plain,
% 1.48/1.66 (c2_1(a549)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[311, 1018])).
% 1.48/1.66 tff(1021,plain,
% 1.48/1.66 (c3_1(a549)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[319, 1018])).
% 1.48/1.66 tff(1022,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a586)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1023,plain,
% 1.48/1.66 ((hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586))) <=> (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a586)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1024,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a586))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[1023])).
% 1.48/1.66 tff(1025,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a586)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[1024, 1022])).
% 1.48/1.66 tff(1026,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(1027,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a586))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 1.48/1.66 tff(1028,plain,
% 1.48/1.66 (hskp46 | (~c2_1(a586))),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1027, 156, 1021, 1020, 1019, 87, 86, 858])).
% 1.48/1.66 tff(1029,plain,
% 1.48/1.66 (hskp46),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1028, 848])).
% 1.48/1.66 tff(1030,plain,
% 1.48/1.66 (~c0_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[64, 1029])).
% 1.48/1.66 tff(1031,plain,
% 1.48/1.66 (~c3_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[270, 1029])).
% 1.48/1.66 tff(1032,plain,
% 1.48/1.66 (c1_1(a562)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[288, 1029])).
% 1.48/1.66 tff(1033,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[326, 156, 194, 1032, 1021, 1020, 1019, 1031, 1030, 22])).
% 1.48/1.66 tff(1034,plain,(c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | hskp19 | c1_1(a586) | hskp33 | hskp15 | hskp50), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(1035,plain,
% 1.48/1.66 (c1_1(a545)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1034, 111, 86, 87, 97, 98, 88, 35, 109, 110])).
% 1.48/1.66 tff(1036,plain,
% 1.48/1.66 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.48/1.66 inference(bind,[status(th)],[])).
% 1.48/1.66 tff(1037,plain,
% 1.48/1.66 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.66 inference(quant_intro,[status(thm)],[1036])).
% 1.48/1.66 tff(1038,plain,
% 1.48/1.66 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1039,plain,
% 1.48/1.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.48/1.66 inference(bind,[status(th)],[])).
% 1.48/1.66 tff(1040,plain,
% 1.48/1.66 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.66 inference(quant_intro,[status(thm)],[1039])).
% 1.48/1.66 tff(1041,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause229')).
% 1.48/1.66 tff(1042,plain,
% 1.48/1.66 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 1.48/1.66 tff(1043,plain,
% 1.48/1.66 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1042, 1038])).
% 1.48/1.66 tff(1044,plain,(
% 1.48/1.66 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.66 inference(skolemize,[status(sab)],[1043])).
% 1.48/1.66 tff(1045,plain,
% 1.48/1.66 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1044, 1037])).
% 1.48/1.66 tff(1046,assumption,(c1_1(a545)), introduced(assumption)).
% 1.48/1.66 tff(1047,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp14 | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | c2_1(a586))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1048,plain,
% 1.48/1.66 ((hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp14 | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | c2_1(a586))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1049,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | c2_1(a586)))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[1048])).
% 1.48/1.66 tff(1050,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp14 | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | c2_1(a586))),
% 1.48/1.66 inference(transitivity,[status(thm)],[1049, 1047])).
% 1.48/1.66 tff(1051,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(1052,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp14 | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | c2_1(a586)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.48/1.66 tff(1053,plain,
% 1.48/1.66 (hskp14),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1052, 156, 88, 1046, 86, 111, 97, 1045, 653])).
% 1.48/1.66 tff(1054,plain,
% 1.48/1.66 (((~hskp14) | (~c1_1(a567))) <=> ((~hskp14) | (~c1_1(a567)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1055,plain,
% 1.48/1.66 (((~c1_1(a567)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a567)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1056,axiom,((~c1_1(a567)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.48/1.66 tff(1057,plain,
% 1.48/1.66 ((~hskp14) | (~c1_1(a567))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 1.48/1.66 tff(1058,plain,
% 1.48/1.66 ((~hskp14) | (~c1_1(a567))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1057, 1054])).
% 1.48/1.66 tff(1059,plain,
% 1.48/1.66 (~c1_1(a567)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1058, 1053])).
% 1.48/1.66 tff(1060,plain,
% 1.48/1.66 (((~hskp14) | c0_1(a567)) <=> ((~hskp14) | c0_1(a567))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1061,axiom,((~hskp14) | c0_1(a567)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.48/1.66 tff(1062,plain,
% 1.48/1.66 ((~hskp14) | c0_1(a567)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.48/1.66 tff(1063,plain,
% 1.48/1.66 ((~hskp14) | c0_1(a567)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1062, 1060])).
% 1.48/1.66 tff(1064,plain,
% 1.48/1.66 ((~hskp14) | c0_1(a567)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1063, 1060])).
% 1.48/1.66 tff(1065,plain,
% 1.48/1.66 ((~hskp14) | c0_1(a567)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1064, 1060])).
% 1.48/1.66 tff(1066,plain,
% 1.48/1.66 ((~hskp14) | c0_1(a567)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1065, 1060])).
% 1.48/1.66 tff(1067,plain,
% 1.48/1.66 (c0_1(a567)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1066, 1053])).
% 1.48/1.66 tff(1068,plain,
% 1.48/1.66 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | c2_1(a567))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | c2_1(a567))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1069,plain,
% 1.48/1.66 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a567) | c1_1(a567) | (~c0_1(a567))) <=> (hskp50 | hskp19 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | c2_1(a567))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1070,plain,
% 1.48/1.66 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a567) | c1_1(a567) | (~c0_1(a567)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | c2_1(a567)))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[1069])).
% 1.48/1.66 tff(1071,plain,
% 1.48/1.66 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a567) | c1_1(a567) | (~c0_1(a567)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | c2_1(a567))),
% 1.48/1.66 inference(transitivity,[status(thm)],[1070, 1068])).
% 1.48/1.66 tff(1072,plain,
% 1.48/1.66 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a567) | c1_1(a567) | (~c0_1(a567)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(1073,plain,
% 1.48/1.66 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | c2_1(a567)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.48/1.66 tff(1074,plain,
% 1.48/1.66 (c2_1(a567)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1073, 156, 110, 98, 1067, 1059, 34])).
% 1.48/1.66 tff(1075,plain,
% 1.48/1.66 (((~hskp14) | (~c3_1(a567))) <=> ((~hskp14) | (~c3_1(a567)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1076,plain,
% 1.48/1.66 (((~c3_1(a567)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a567)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1077,axiom,((~c3_1(a567)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.48/1.66 tff(1078,plain,
% 1.48/1.66 ((~hskp14) | (~c3_1(a567))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 1.48/1.66 tff(1079,plain,
% 1.48/1.66 ((~hskp14) | (~c3_1(a567))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[1078, 1075])).
% 1.48/1.66 tff(1080,plain,
% 1.48/1.66 (~c3_1(a567)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1079, 1053])).
% 1.48/1.66 tff(1081,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c1_1(a567) | c3_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a567) | c3_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1082,plain,
% 1.48/1.66 ((hskp37 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567)) | c1_1(a567) | c3_1(a567) | (~c0_1(a567))) <=> (hskp37 | c1_1(a567) | c3_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(1083,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567)) | c1_1(a567) | c3_1(a567) | (~c0_1(a567)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c1_1(a567) | c3_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567))))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[1082])).
% 1.48/1.67 tff(1084,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567)) | c1_1(a567) | c3_1(a567) | (~c0_1(a567)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a567) | c3_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))),
% 1.48/1.67 inference(transitivity,[status(thm)],[1083, 1081])).
% 1.48/1.67 tff(1085,plain,
% 1.48/1.67 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567)) | c1_1(a567) | c3_1(a567) | (~c0_1(a567)))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(1086,plain,
% 1.48/1.67 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a567) | c3_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 1.48/1.67 tff(1087,plain,
% 1.48/1.67 (hskp37),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1086, 156, 1067, 1059, 1080, 415, 1074])).
% 1.48/1.67 tff(1088,plain,
% 1.48/1.67 (~c2_1(a544)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[436, 1087])).
% 1.48/1.67 tff(1089,plain,
% 1.48/1.67 (c1_1(a544)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[444, 1087])).
% 1.48/1.67 tff(1090,plain,
% 1.48/1.67 (~c3_1(a544)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[450, 1087])).
% 1.48/1.67 tff(1091,plain,
% 1.48/1.67 (~hskp7),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[502, 1089, 109, 98, 1090, 110, 1088])).
% 1.48/1.67 tff(1092,plain,
% 1.48/1.67 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(1093,plain,
% 1.48/1.67 ((hskp40 | hskp7 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567))) <=> (hskp40 | hskp7 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(1094,plain,
% 1.48/1.67 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567))))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[1093])).
% 1.48/1.67 tff(1095,plain,
% 1.48/1.67 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567)))),
% 1.48/1.67 inference(transitivity,[status(thm)],[1094, 1092])).
% 1.48/1.67 tff(1096,plain,
% 1.48/1.67 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a567) | (~c2_1(a567)) | (~c0_1(a567)))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(1097,plain,
% 1.48/1.67 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c2_1(a567))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.48/1.67 tff(1098,plain,
% 1.48/1.67 (hskp40 | hskp7 | (~c2_1(a567))),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1097, 156, 1067, 1059, 513])).
% 1.48/1.67 tff(1099,plain,
% 1.48/1.67 (hskp40),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1098, 1091, 1074])).
% 1.48/1.67 tff(1100,plain,
% 1.48/1.67 (c2_1(a551)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[532, 1099])).
% 1.48/1.67 tff(1101,plain,
% 1.48/1.67 (c3_1(a551)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[540, 1099])).
% 1.48/1.67 tff(1102,plain,
% 1.48/1.67 (c1_1(a551)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[552, 1101, 1090, 1100, 1089, 1088, 109])).
% 1.48/1.67 tff(1103,plain,
% 1.48/1.67 (^[V: $i, U: $i] : refl((hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(1104,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[1103])).
% 1.48/1.67 tff(1105,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(1106,plain,
% 1.48/1.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp34) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp34))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp34) <=> (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp34) <=> (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(1107,plain,
% 1.48/1.67 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp34) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[1106])).
% 1.48/1.67 tff(1108,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause237')).
% 1.48/1.67 tff(1109,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.48/1.67 tff(1110,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[1109, 1105])).
% 1.48/1.67 tff(1111,plain,(
% 1.48/1.67 ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.67 inference(skolemize,[status(sab)],[1110])).
% 1.48/1.67 tff(1112,plain,
% 1.48/1.67 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[1111, 1104])).
% 1.48/1.67 tff(1113,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1114,plain,
% 1.52/1.67 ((hskp34 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1115,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.52/1.67 inference(monotonicity,[status(thm)],[1114])).
% 1.52/1.67 tff(1116,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.67 inference(transitivity,[status(thm)],[1115, 1113])).
% 1.52/1.67 tff(1117,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.52/1.67 inference(quant_inst,[status(thm)],[])).
% 1.52/1.67 tff(1118,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 1.52/1.67 tff(1119,plain,
% 1.52/1.67 (hskp34),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1118, 156, 1101, 1100, 88, 86, 1112, 653, 1102])).
% 1.52/1.67 tff(1120,plain,
% 1.52/1.67 (((~hskp34) | (~c1_1(a537))) <=> ((~hskp34) | (~c1_1(a537)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1121,plain,
% 1.52/1.67 (((~c1_1(a537)) | (~hskp34)) <=> ((~hskp34) | (~c1_1(a537)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1122,axiom,((~c1_1(a537)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.52/1.67 tff(1123,plain,
% 1.52/1.67 ((~hskp34) | (~c1_1(a537))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.52/1.67 tff(1124,plain,
% 1.52/1.67 ((~hskp34) | (~c1_1(a537))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1123, 1120])).
% 1.52/1.67 tff(1125,plain,
% 1.52/1.67 (~c1_1(a537)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1124, 1119])).
% 1.52/1.67 tff(1126,plain,
% 1.52/1.67 (((~hskp34) | c3_1(a537)) <=> ((~hskp34) | c3_1(a537))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1127,axiom,((~hskp34) | c3_1(a537)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.52/1.67 tff(1128,plain,
% 1.52/1.67 ((~hskp34) | c3_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.52/1.67 tff(1129,plain,
% 1.52/1.67 ((~hskp34) | c3_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1128, 1126])).
% 1.52/1.67 tff(1130,plain,
% 1.52/1.67 ((~hskp34) | c3_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1129, 1126])).
% 1.52/1.67 tff(1131,plain,
% 1.52/1.67 ((~hskp34) | c3_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1130, 1126])).
% 1.52/1.67 tff(1132,plain,
% 1.52/1.67 ((~hskp34) | c3_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1131, 1126])).
% 1.52/1.67 tff(1133,plain,
% 1.52/1.67 (c3_1(a537)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1132, 1119])).
% 1.52/1.67 tff(1134,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a544)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1135,plain,
% 1.52/1.67 ((hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a544)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1136,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a544))))),
% 1.52/1.67 inference(monotonicity,[status(thm)],[1135])).
% 1.52/1.67 tff(1137,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a544)))),
% 1.52/1.67 inference(transitivity,[status(thm)],[1136, 1134])).
% 1.52/1.67 tff(1138,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.67 inference(quant_inst,[status(thm)],[])).
% 1.52/1.67 tff(1139,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a544))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.52/1.67 tff(1140,plain,
% 1.52/1.67 (~c2_1(a537)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1139, 156, 109, 1089, 1133, 1088, 1090, 1125, 483])).
% 1.52/1.67 tff(1141,plain,
% 1.52/1.67 (((~hskp34) | c0_1(a537)) <=> ((~hskp34) | c0_1(a537))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1142,axiom,((~hskp34) | c0_1(a537)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.52/1.67 tff(1143,plain,
% 1.52/1.67 ((~hskp34) | c0_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.52/1.67 tff(1144,plain,
% 1.52/1.67 ((~hskp34) | c0_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1143, 1141])).
% 1.52/1.67 tff(1145,plain,
% 1.52/1.67 ((~hskp34) | c0_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1144, 1141])).
% 1.52/1.67 tff(1146,plain,
% 1.52/1.67 ((~hskp34) | c0_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1145, 1141])).
% 1.52/1.67 tff(1147,plain,
% 1.52/1.67 ((~hskp34) | c0_1(a537)),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1146, 1141])).
% 1.52/1.67 tff(1148,plain,
% 1.52/1.67 (c0_1(a537)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1147, 1119])).
% 1.52/1.67 tff(1149,plain,
% 1.52/1.67 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1150,plain,
% 1.52/1.67 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537))) <=> (hskp50 | hskp19 | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1151,plain,
% 1.52/1.67 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537))))),
% 1.52/1.67 inference(monotonicity,[status(thm)],[1150])).
% 1.52/1.67 tff(1152,plain,
% 1.52/1.67 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))),
% 1.52/1.67 inference(transitivity,[status(thm)],[1151, 1149])).
% 1.52/1.67 tff(1153,plain,
% 1.52/1.67 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)))),
% 1.52/1.67 inference(quant_inst,[status(thm)],[])).
% 1.52/1.67 tff(1154,plain,
% 1.52/1.67 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 1.52/1.67 tff(1155,plain,
% 1.52/1.67 ($false),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1154, 156, 110, 98, 1148, 1125, 34, 1140])).
% 1.52/1.67 tff(1156,plain,(c2_1(a586) | hskp50 | hskp19 | hskp15 | c1_1(a586) | c3_1(a586) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.67 tff(1157,plain,
% 1.52/1.67 (c2_1(a586)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1156, 1035, 98, 109, 88, 86, 110, 111, 97])).
% 1.52/1.67 tff(1158,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1159,plain,
% 1.52/1.67 ((hskp46 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545))) <=> (hskp46 | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1160,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545))))),
% 1.52/1.67 inference(monotonicity,[status(thm)],[1159])).
% 1.52/1.67 tff(1161,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.67 inference(transitivity,[status(thm)],[1160, 1158])).
% 1.52/1.67 tff(1162,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)))),
% 1.52/1.67 inference(quant_inst,[status(thm)],[])).
% 1.52/1.67 tff(1163,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 1.52/1.67 tff(1164,plain,
% 1.52/1.67 (hskp46 | (~c3_1(a545))),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1163, 156, 1046, 111, 97, 12])).
% 1.52/1.67 tff(1165,plain,
% 1.52/1.67 (hskp46),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1164, 2])).
% 1.52/1.67 tff(1166,plain,
% 1.52/1.67 (~c0_1(a562)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[64, 1165])).
% 1.52/1.67 tff(1167,plain,
% 1.52/1.67 (~c3_1(a562)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[270, 1165])).
% 1.52/1.67 tff(1168,plain,
% 1.52/1.67 (c1_1(a562)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[288, 1165])).
% 1.52/1.67 tff(1169,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a562)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1170,plain,
% 1.52/1.67 ((hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a562)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1171,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a562))))),
% 1.52/1.67 inference(monotonicity,[status(thm)],[1170])).
% 1.52/1.67 tff(1172,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a562)))),
% 1.52/1.67 inference(transitivity,[status(thm)],[1171, 1169])).
% 1.52/1.67 tff(1173,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.52/1.67 inference(quant_inst,[status(thm)],[])).
% 1.52/1.67 tff(1174,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a562))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 1.52/1.67 tff(1175,plain,
% 1.52/1.67 (hskp39),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1174, 156, 1168, 1046, 1167, 1166, 111, 281, 2])).
% 1.52/1.67 tff(1176,plain,
% 1.52/1.67 (c1_1(a549)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[303, 1175])).
% 1.52/1.67 tff(1177,plain,
% 1.52/1.67 (c2_1(a549)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[311, 1175])).
% 1.52/1.67 tff(1178,plain,
% 1.52/1.67 (c3_1(a549)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[319, 1175])).
% 1.52/1.67 tff(1179,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1180,plain,
% 1.52/1.67 ((hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545))) <=> (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1181,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549))))),
% 1.52/1.67 inference(monotonicity,[status(thm)],[1180])).
% 1.52/1.67 tff(1182,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.52/1.67 inference(transitivity,[status(thm)],[1181, 1179])).
% 1.52/1.67 tff(1183,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.67 inference(quant_inst,[status(thm)],[])).
% 1.52/1.67 tff(1184,plain,
% 1.52/1.67 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.52/1.67 tff(1185,plain,
% 1.52/1.67 (hskp25),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1184, 156, 1178, 1177, 1176, 1046, 111, 55, 2])).
% 1.52/1.67 tff(1186,plain,
% 1.52/1.67 (((~hskp25) | (~c1_1(a582))) <=> ((~hskp25) | (~c1_1(a582)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1187,plain,
% 1.52/1.67 (((~c1_1(a582)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a582)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1188,axiom,((~c1_1(a582)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.52/1.67 tff(1189,plain,
% 1.52/1.67 ((~hskp25) | (~c1_1(a582))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 1.52/1.67 tff(1190,plain,
% 1.52/1.67 ((~hskp25) | (~c1_1(a582))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1189, 1186])).
% 1.52/1.67 tff(1191,plain,
% 1.52/1.67 (~c1_1(a582)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1190, 1185])).
% 1.52/1.67 tff(1192,plain,
% 1.52/1.67 (((~hskp25) | (~c2_1(a582))) <=> ((~hskp25) | (~c2_1(a582)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1193,plain,
% 1.52/1.67 (((~c2_1(a582)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a582)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1194,axiom,((~c2_1(a582)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.52/1.67 tff(1195,plain,
% 1.52/1.67 ((~hskp25) | (~c2_1(a582))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 1.52/1.67 tff(1196,plain,
% 1.52/1.67 ((~hskp25) | (~c2_1(a582))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1195, 1192])).
% 1.52/1.67 tff(1197,plain,
% 1.52/1.67 (~c2_1(a582)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1196, 1185])).
% 1.52/1.67 tff(1198,plain,
% 1.52/1.67 (((~hskp25) | (~c3_1(a582))) <=> ((~hskp25) | (~c3_1(a582)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1199,plain,
% 1.52/1.67 (((~c3_1(a582)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a582)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1200,axiom,((~c3_1(a582)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.52/1.67 tff(1201,plain,
% 1.52/1.67 ((~hskp25) | (~c3_1(a582))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.52/1.67 tff(1202,plain,
% 1.52/1.67 ((~hskp25) | (~c3_1(a582))),
% 1.52/1.67 inference(modus_ponens,[status(thm)],[1201, 1198])).
% 1.52/1.67 tff(1203,plain,
% 1.52/1.67 (~c3_1(a582)),
% 1.52/1.67 inference(unit_resolution,[status(thm)],[1202, 1185])).
% 1.52/1.67 tff(1204,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1205,plain,
% 1.52/1.67 ((hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))),
% 1.52/1.67 inference(rewrite,[status(thm)],[])).
% 1.52/1.67 tff(1206,plain,
% 1.52/1.67 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545))))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1205])).
% 1.52/1.68 tff(1207,plain,
% 1.52/1.68 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1206, 1204])).
% 1.52/1.68 tff(1208,plain,
% 1.52/1.68 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1209,plain,
% 1.52/1.68 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 1.52/1.68 tff(1210,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1209, 156, 58, 1203, 1197, 1191, 111, 97, 663, 2])).
% 1.52/1.68 tff(1211,plain,((~c3_1(a545)) | hskp38 | c2_1(a545) | c0_1(a545) | (~c1_1(a545))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(1212,plain,
% 1.52/1.68 (~c3_1(a545)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1211, 58, 111, 97, 1035])).
% 1.52/1.68 tff(1213,assumption,(~hskp28), introduced(assumption)).
% 1.52/1.68 tff(1214,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c1_1(a586) | c0_1(a586) | (~ndr1_0) | c2_1(a586))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a586) | c0_1(a586) | (~ndr1_0) | c2_1(a586))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1215,plain,
% 1.52/1.68 ((hskp28 | (~ndr1_0) | c2_1(a586) | c0_1(a586) | c1_1(a586)) <=> (hskp28 | c1_1(a586) | c0_1(a586) | (~ndr1_0) | c2_1(a586))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1216,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a586) | c0_1(a586) | c1_1(a586))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c1_1(a586) | c0_1(a586) | (~ndr1_0) | c2_1(a586)))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1215])).
% 1.52/1.68 tff(1217,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a586) | c0_1(a586) | c1_1(a586))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a586) | c0_1(a586) | (~ndr1_0) | c2_1(a586))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1216, 1214])).
% 1.52/1.68 tff(1218,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a586) | c0_1(a586) | c1_1(a586))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1219,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a586) | c0_1(a586) | (~ndr1_0) | c2_1(a586)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.52/1.68 tff(1220,plain,
% 1.52/1.68 (hskp28 | c0_1(a586) | c2_1(a586)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1219, 156, 88, 122])).
% 1.52/1.68 tff(1221,plain,
% 1.52/1.68 (c2_1(a586)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1220, 1213, 87])).
% 1.52/1.68 tff(1222,assumption,(hskp1), introduced(assumption)).
% 1.52/1.68 tff(1223,plain,
% 1.52/1.68 (((~hskp1) | (~c0_1(a539))) <=> ((~hskp1) | (~c0_1(a539)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1224,plain,
% 1.52/1.68 (((~c0_1(a539)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a539)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1225,axiom,((~c0_1(a539)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause215')).
% 1.52/1.68 tff(1226,plain,
% 1.52/1.68 ((~hskp1) | (~c0_1(a539))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 1.52/1.68 tff(1227,plain,
% 1.52/1.68 ((~hskp1) | (~c0_1(a539))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1226, 1223])).
% 1.52/1.68 tff(1228,plain,
% 1.52/1.68 (~c0_1(a539)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1227, 1222])).
% 1.52/1.68 tff(1229,plain,
% 1.52/1.68 (((~hskp1) | (~c1_1(a539))) <=> ((~hskp1) | (~c1_1(a539)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1230,plain,
% 1.52/1.68 (((~c1_1(a539)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a539)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1231,axiom,((~c1_1(a539)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause214')).
% 1.52/1.68 tff(1232,plain,
% 1.52/1.68 ((~hskp1) | (~c1_1(a539))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 1.52/1.68 tff(1233,plain,
% 1.52/1.68 ((~hskp1) | (~c1_1(a539))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1232, 1229])).
% 1.52/1.68 tff(1234,plain,
% 1.52/1.68 (~c1_1(a539)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1233, 1222])).
% 1.52/1.68 tff(1235,plain,
% 1.52/1.68 (((~hskp1) | (~c2_1(a539))) <=> ((~hskp1) | (~c2_1(a539)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1236,plain,
% 1.52/1.68 (((~c2_1(a539)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a539)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1237,axiom,((~c2_1(a539)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause213')).
% 1.52/1.68 tff(1238,plain,
% 1.52/1.68 ((~hskp1) | (~c2_1(a539))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.52/1.68 tff(1239,plain,
% 1.52/1.68 ((~hskp1) | (~c2_1(a539))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1238, 1235])).
% 1.52/1.68 tff(1240,plain,
% 1.52/1.68 (~c2_1(a539)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1239, 1222])).
% 1.52/1.68 tff(1241,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1242,plain,
% 1.52/1.68 ((hskp28 | (~ndr1_0) | c2_1(a539) | c0_1(a539) | c1_1(a539)) <=> (hskp28 | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1243,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a539) | c0_1(a539) | c1_1(a539))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0)))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1242])).
% 1.52/1.68 tff(1244,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a539) | c0_1(a539) | c1_1(a539))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1243, 1241])).
% 1.52/1.68 tff(1245,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a539) | c0_1(a539) | c1_1(a539))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1246,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 1.52/1.68 tff(1247,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1246, 156, 1213, 1240, 1234, 1228, 122])).
% 1.52/1.68 tff(1248,plain,((~hskp1) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(1249,plain,
% 1.52/1.68 (~hskp1),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1248, 1213])).
% 1.52/1.68 tff(1250,assumption,(hskp15), introduced(assumption)).
% 1.52/1.68 tff(1251,plain,
% 1.52/1.68 (((~hskp15) | (~c2_1(a569))) <=> ((~hskp15) | (~c2_1(a569)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1252,plain,
% 1.52/1.68 (((~c2_1(a569)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a569)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1253,axiom,((~c2_1(a569)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.52/1.68 tff(1254,plain,
% 1.52/1.68 ((~hskp15) | (~c2_1(a569))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 1.52/1.68 tff(1255,plain,
% 1.52/1.68 ((~hskp15) | (~c2_1(a569))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1254, 1251])).
% 1.52/1.68 tff(1256,plain,
% 1.52/1.68 (~c2_1(a569)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1255, 1250])).
% 1.52/1.68 tff(1257,plain,
% 1.52/1.68 (((~hskp15) | (~c1_1(a569))) <=> ((~hskp15) | (~c1_1(a569)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1258,plain,
% 1.52/1.68 (((~c1_1(a569)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a569)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1259,axiom,((~c1_1(a569)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.52/1.68 tff(1260,plain,
% 1.52/1.68 ((~hskp15) | (~c1_1(a569))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.52/1.68 tff(1261,plain,
% 1.52/1.68 ((~hskp15) | (~c1_1(a569))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1260, 1257])).
% 1.52/1.68 tff(1262,plain,
% 1.52/1.68 (~c1_1(a569)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1261, 1250])).
% 1.52/1.68 tff(1263,plain,
% 1.52/1.68 (((~hskp15) | (~c0_1(a569))) <=> ((~hskp15) | (~c0_1(a569)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1264,plain,
% 1.52/1.68 (((~c0_1(a569)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a569)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1265,axiom,((~c0_1(a569)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.52/1.68 tff(1266,plain,
% 1.52/1.68 ((~hskp15) | (~c0_1(a569))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 1.52/1.68 tff(1267,plain,
% 1.52/1.68 ((~hskp15) | (~c0_1(a569))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1266, 1263])).
% 1.52/1.68 tff(1268,plain,
% 1.52/1.68 (~c0_1(a569)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1267, 1250])).
% 1.52/1.68 tff(1269,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1270,plain,
% 1.52/1.68 ((hskp28 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | c1_1(a569)) <=> (hskp28 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1271,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | c1_1(a569))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0)))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1270])).
% 1.52/1.68 tff(1272,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | c1_1(a569))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1271, 1269])).
% 1.52/1.68 tff(1273,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | c1_1(a569))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1274,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 1.52/1.68 tff(1275,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1274, 156, 1213, 1268, 1262, 1256, 122])).
% 1.52/1.68 tff(1276,plain,((~hskp15) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(1277,plain,
% 1.52/1.68 (~hskp15),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1276, 1213])).
% 1.52/1.68 tff(1278,assumption,(hskp25), introduced(assumption)).
% 1.52/1.68 tff(1279,plain,
% 1.52/1.68 (~c2_1(a582)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1196, 1278])).
% 1.52/1.68 tff(1280,plain,
% 1.52/1.68 (~c1_1(a582)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1190, 1278])).
% 1.52/1.68 tff(1281,assumption,(~c1_1(a582)), introduced(assumption)).
% 1.52/1.68 tff(1282,assumption,(~c2_1(a582)), introduced(assumption)).
% 1.52/1.68 tff(1283,plain,
% 1.52/1.68 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1284,plain,
% 1.52/1.68 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582))) <=> (hskp50 | hskp19 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1285,plain,
% 1.52/1.68 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582))))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1284])).
% 1.52/1.68 tff(1286,plain,
% 1.52/1.68 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1285, 1283])).
% 1.52/1.68 tff(1287,plain,
% 1.52/1.68 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582)))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1288,plain,
% 1.52/1.68 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.52/1.68 tff(1289,plain,
% 1.52/1.68 (c1_1(a582) | (~c0_1(a582))),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1288, 156, 110, 98, 1282, 34])).
% 1.52/1.68 tff(1290,plain,
% 1.52/1.68 (~c0_1(a582)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1289, 1281])).
% 1.52/1.68 tff(1291,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1292,plain,
% 1.52/1.68 ((hskp28 | (~ndr1_0) | c2_1(a582) | c0_1(a582) | c1_1(a582)) <=> (hskp28 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1293,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a582) | c0_1(a582) | c1_1(a582))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582)))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1292])).
% 1.52/1.68 tff(1294,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a582) | c0_1(a582) | c1_1(a582))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1293, 1291])).
% 1.52/1.68 tff(1295,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a582) | c0_1(a582) | c1_1(a582))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1296,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.52/1.68 tff(1297,plain,
% 1.52/1.68 (c1_1(a582) | c0_1(a582)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1296, 156, 1213, 1282, 122])).
% 1.52/1.68 tff(1298,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1297, 1290, 1281])).
% 1.52/1.68 tff(1299,plain,(c1_1(a582) | hskp28 | c2_1(a582) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(1300,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1299, 1280, 1279, 1213, 110, 98])).
% 1.52/1.68 tff(1301,plain,((~hskp25) | hskp28 | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(1302,plain,
% 1.52/1.68 (~hskp25),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1301, 1213, 98, 110])).
% 1.52/1.68 tff(1303,assumption,(hskp9), introduced(assumption)).
% 1.52/1.68 tff(1304,plain,
% 1.52/1.68 (~c1_1(a554)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[639, 1303])).
% 1.52/1.68 tff(1305,plain,
% 1.52/1.68 (~c2_1(a554)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[645, 1303])).
% 1.52/1.68 tff(1306,plain,
% 1.52/1.68 (~c0_1(a554)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[651, 1303])).
% 1.52/1.68 tff(1307,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1308,plain,
% 1.52/1.68 ((hskp28 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | c1_1(a554)) <=> (hskp28 | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1309,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | c1_1(a554))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0)))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1308])).
% 1.52/1.68 tff(1310,plain,
% 1.52/1.68 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | c1_1(a554))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1309, 1307])).
% 1.52/1.68 tff(1311,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a554) | c0_1(a554) | c1_1(a554))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1312,plain,
% 1.52/1.68 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0)),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.52/1.68 tff(1313,plain,
% 1.52/1.68 ($false),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1312, 156, 1213, 1306, 1305, 1304, 122])).
% 1.52/1.68 tff(1314,plain,((~hskp9) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.52/1.68 tff(1315,plain,
% 1.52/1.68 (~hskp9),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1314, 1213])).
% 1.52/1.68 tff(1316,assumption,(~hskp1), introduced(assumption)).
% 1.52/1.68 tff(1317,plain,
% 1.52/1.68 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.52/1.68 inference(bind,[status(th)],[])).
% 1.52/1.68 tff(1318,plain,
% 1.52/1.68 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.52/1.68 inference(quant_intro,[status(thm)],[1317])).
% 1.52/1.68 tff(1319,plain,
% 1.52/1.68 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1320,plain,
% 1.52/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) <=> (((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))))), rewrite((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp1) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.52/1.68 inference(bind,[status(th)],[])).
% 1.52/1.68 tff(1321,plain,
% 1.52/1.68 (![U: $i] : ((((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.52/1.68 inference(quant_intro,[status(thm)],[1320])).
% 1.52/1.68 tff(1322,axiom,(![U: $i] : ((((((~c3_1(U)) | (~c1_1(U))) | (~c0_1(U))) | (~ndr1_0)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause227')).
% 1.52/1.68 tff(1323,plain,
% 1.52/1.68 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 1.52/1.68 tff(1324,plain,
% 1.52/1.68 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1323, 1319])).
% 1.52/1.68 tff(1325,plain,(
% 1.52/1.68 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.52/1.68 inference(skolemize,[status(sab)],[1324])).
% 1.52/1.68 tff(1326,plain,
% 1.52/1.68 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1325, 1318])).
% 1.52/1.68 tff(1327,plain,
% 1.52/1.68 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c0_1(a571)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1328,plain,
% 1.52/1.68 ((hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c0_1(a571)) | (~c1_1(a571))) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1329,plain,
% 1.52/1.68 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c0_1(a571))))),
% 1.52/1.68 inference(monotonicity,[status(thm)],[1328])).
% 1.52/1.68 tff(1330,plain,
% 1.52/1.68 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.52/1.68 inference(transitivity,[status(thm)],[1329, 1327])).
% 1.52/1.68 tff(1331,plain,
% 1.52/1.68 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.52/1.68 inference(quant_inst,[status(thm)],[])).
% 1.52/1.68 tff(1332,plain,
% 1.52/1.68 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c0_1(a571))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 1.52/1.68 tff(1333,plain,
% 1.52/1.68 (hskp2),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1332, 156, 1316, 925, 924, 1326, 932])).
% 1.52/1.68 tff(1334,plain,
% 1.52/1.68 (((~hskp2) | (~c3_1(a540))) <=> ((~hskp2) | (~c3_1(a540)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1335,plain,
% 1.52/1.68 (((~c3_1(a540)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a540)))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1336,axiom,((~c3_1(a540)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause212')).
% 1.52/1.68 tff(1337,plain,
% 1.52/1.68 ((~hskp2) | (~c3_1(a540))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 1.52/1.68 tff(1338,plain,
% 1.52/1.68 ((~hskp2) | (~c3_1(a540))),
% 1.52/1.68 inference(modus_ponens,[status(thm)],[1337, 1334])).
% 1.52/1.68 tff(1339,plain,
% 1.52/1.68 (~c3_1(a540)),
% 1.52/1.68 inference(unit_resolution,[status(thm)],[1338, 1333])).
% 1.52/1.68 tff(1340,plain,
% 1.52/1.68 (((~hskp2) | c1_1(a540)) <=> ((~hskp2) | c1_1(a540))),
% 1.52/1.68 inference(rewrite,[status(thm)],[])).
% 1.52/1.68 tff(1341,axiom,((~hskp2) | c1_1(a540)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.52/1.69 tff(1342,plain,
% 1.52/1.69 ((~hskp2) | c1_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 1.52/1.69 tff(1343,plain,
% 1.52/1.69 ((~hskp2) | c1_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1342, 1340])).
% 1.52/1.69 tff(1344,plain,
% 1.52/1.69 ((~hskp2) | c1_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 1.52/1.69 tff(1345,plain,
% 1.52/1.69 ((~hskp2) | c1_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1344, 1340])).
% 1.52/1.69 tff(1346,plain,
% 1.52/1.69 ((~hskp2) | c1_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1345, 1340])).
% 1.52/1.69 tff(1347,plain,
% 1.52/1.69 (c1_1(a540)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1346, 1333])).
% 1.52/1.69 tff(1348,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a571) | c3_1(a540) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a571) | c3_1(a540) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1349,plain,
% 1.52/1.69 ((hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a540) | c0_1(a540) | (~c1_1(a540))) <=> (hskp39 | c2_1(a571) | c3_1(a540) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1350,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a540) | c0_1(a540) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a571) | c3_1(a540) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a571)) | (~c1_1(a571))))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1349])).
% 1.52/1.69 tff(1351,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a540) | c0_1(a540) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a571) | c3_1(a540) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1350, 1348])).
% 1.52/1.69 tff(1352,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a540) | c0_1(a540) | (~c1_1(a540)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1353,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a571) | c3_1(a540) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a571)) | (~c1_1(a571))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.52/1.69 tff(1354,plain,
% 1.52/1.69 (c0_1(a540)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1353, 156, 859, 924, 1347, 923, 1339, 281, 932])).
% 1.52/1.69 tff(1355,plain,
% 1.52/1.69 (^[V: $i, U: $i] : refl((hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 1.52/1.69 inference(bind,[status(th)],[])).
% 1.52/1.69 tff(1356,plain,
% 1.52/1.69 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.52/1.69 inference(quant_intro,[status(thm)],[1355])).
% 1.52/1.69 tff(1357,plain,
% 1.52/1.69 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1358,plain,
% 1.52/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | hskp42) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp42))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp42) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | hskp42) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.52/1.69 inference(bind,[status(th)],[])).
% 1.52/1.69 tff(1359,plain,
% 1.52/1.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | hskp42) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.52/1.69 inference(quant_intro,[status(thm)],[1358])).
% 1.52/1.69 tff(1360,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause254')).
% 1.52/1.69 tff(1361,plain,
% 1.52/1.69 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.52/1.69 tff(1362,plain,
% 1.52/1.69 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1361, 1357])).
% 1.52/1.69 tff(1363,plain,(
% 1.52/1.69 ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.52/1.69 inference(skolemize,[status(sab)],[1362])).
% 1.52/1.69 tff(1364,plain,
% 1.52/1.69 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1363, 1356])).
% 1.52/1.69 tff(1365,plain,
% 1.52/1.69 (((~hskp2) | c2_1(a540)) <=> ((~hskp2) | c2_1(a540))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1366,axiom,((~hskp2) | c2_1(a540)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.52/1.69 tff(1367,plain,
% 1.52/1.69 ((~hskp2) | c2_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 1.52/1.69 tff(1368,plain,
% 1.52/1.69 ((~hskp2) | c2_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1367, 1365])).
% 1.52/1.69 tff(1369,plain,
% 1.52/1.69 ((~hskp2) | c2_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1368, 1365])).
% 1.52/1.69 tff(1370,plain,
% 1.52/1.69 ((~hskp2) | c2_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1369, 1365])).
% 1.52/1.69 tff(1371,plain,
% 1.52/1.69 ((~hskp2) | c2_1(a540)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1370, 1365])).
% 1.52/1.69 tff(1372,plain,
% 1.52/1.69 (c2_1(a540)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1371, 1333])).
% 1.52/1.69 tff(1373,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a571) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a571) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1374,plain,
% 1.52/1.69 ((hskp42 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c0_1(a540))) <=> (hskp42 | c2_1(a571) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1375,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c0_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a571) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c3_1(a571)) | (~c1_1(a571))))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1374])).
% 1.52/1.69 tff(1376,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c0_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a571) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1375, 1373])).
% 1.52/1.69 tff(1377,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c0_1(a540)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1378,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a571) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c3_1(a571)) | (~c1_1(a571))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 1.52/1.69 tff(1379,plain,
% 1.52/1.69 (hskp42 | (~c0_1(a540))),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1378, 156, 924, 1372, 1347, 923, 1364, 932])).
% 1.52/1.69 tff(1380,plain,
% 1.52/1.69 (hskp42),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1379, 1354])).
% 1.52/1.69 tff(1381,plain,
% 1.52/1.69 (((~hskp42) | (~c2_1(a556))) <=> ((~hskp42) | (~c2_1(a556)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1382,plain,
% 1.52/1.69 (((~c2_1(a556)) | (~hskp42)) <=> ((~hskp42) | (~c2_1(a556)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1383,axiom,((~c2_1(a556)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.52/1.69 tff(1384,plain,
% 1.52/1.69 ((~hskp42) | (~c2_1(a556))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.52/1.69 tff(1385,plain,
% 1.52/1.69 ((~hskp42) | (~c2_1(a556))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1384, 1381])).
% 1.52/1.69 tff(1386,plain,
% 1.52/1.69 (~c2_1(a556)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1385, 1380])).
% 1.52/1.69 tff(1387,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a545))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1388,plain,
% 1.52/1.69 ((hskp33 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a545))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1389,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a545)))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1388])).
% 1.52/1.69 tff(1390,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a545))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1389, 1387])).
% 1.52/1.69 tff(1391,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1392,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a545) | c0_1(a545) | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a545)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 1.52/1.69 tff(1393,plain,
% 1.52/1.69 (c3_1(a545)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1392, 156, 35, 1347, 111, 97, 1339, 85, 1354])).
% 1.52/1.69 tff(1394,plain,
% 1.52/1.69 (hskp46),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1164, 1393])).
% 1.52/1.69 tff(1395,plain,
% 1.52/1.69 (~c0_1(a562)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[64, 1394])).
% 1.52/1.69 tff(1396,plain,
% 1.52/1.69 (~c3_1(a562)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[270, 1394])).
% 1.52/1.69 tff(1397,plain,
% 1.52/1.69 (((~hskp42) | c3_1(a556)) <=> ((~hskp42) | c3_1(a556))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1398,axiom,((~hskp42) | c3_1(a556)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.52/1.69 tff(1399,plain,
% 1.52/1.69 ((~hskp42) | c3_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 1.52/1.69 tff(1400,plain,
% 1.52/1.69 ((~hskp42) | c3_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1399, 1397])).
% 1.52/1.69 tff(1401,plain,
% 1.52/1.69 ((~hskp42) | c3_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1400, 1397])).
% 1.52/1.69 tff(1402,plain,
% 1.52/1.69 ((~hskp42) | c3_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1401, 1397])).
% 1.52/1.69 tff(1403,plain,
% 1.52/1.69 ((~hskp42) | c3_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1402, 1397])).
% 1.52/1.69 tff(1404,plain,
% 1.52/1.69 (c3_1(a556)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1403, 1380])).
% 1.52/1.69 tff(1405,plain,
% 1.52/1.69 (((~hskp42) | c1_1(a556)) <=> ((~hskp42) | c1_1(a556))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1406,axiom,((~hskp42) | c1_1(a556)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.52/1.69 tff(1407,plain,
% 1.52/1.69 ((~hskp42) | c1_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 1.52/1.69 tff(1408,plain,
% 1.52/1.69 ((~hskp42) | c1_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1407, 1405])).
% 1.52/1.69 tff(1409,plain,
% 1.52/1.69 ((~hskp42) | c1_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1408, 1405])).
% 1.52/1.69 tff(1410,plain,
% 1.52/1.69 ((~hskp42) | c1_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1409, 1405])).
% 1.52/1.69 tff(1411,plain,
% 1.52/1.69 ((~hskp42) | c1_1(a556)),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1410, 1405])).
% 1.52/1.69 tff(1412,plain,
% 1.52/1.69 (c1_1(a556)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1411, 1380])).
% 1.52/1.69 tff(1413,plain,
% 1.52/1.69 (c1_1(a562)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[288, 1394])).
% 1.52/1.69 tff(1414,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | (~c1_1(a562)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1415,plain,
% 1.52/1.69 ((hskp39 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | (~c1_1(a562)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1416,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | (~c1_1(a562))))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1415])).
% 1.52/1.69 tff(1417,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | (~c1_1(a562)))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1416, 1414])).
% 1.52/1.69 tff(1418,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1419,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | (~c1_1(a562))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.52/1.69 tff(1420,plain,
% 1.52/1.69 ($false),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1419, 156, 859, 1413, 1412, 1404, 1396, 1395, 1386, 281])).
% 1.52/1.69 tff(1421,plain,((~hskp17) | hskp39 | (~c1_1(a545)) | c2_1(a545) | c0_1(a545) | hskp33 | hskp1 | c1_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.69 tff(1422,plain,
% 1.52/1.69 (~hskp17),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1421, 859, 1046, 111, 97, 35, 1316, 88, 86, 902])).
% 1.52/1.69 tff(1423,assumption,(~hskp25), introduced(assumption)).
% 1.52/1.69 tff(1424,plain,
% 1.52/1.69 (~hskp7),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[502, 888, 109, 887, 889, 110, 98])).
% 1.52/1.69 tff(1425,plain,
% 1.52/1.69 (hskp40),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[524, 1424, 110, 98, 384])).
% 1.52/1.69 tff(1426,plain,
% 1.52/1.69 (c2_1(a551)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[532, 1425])).
% 1.52/1.69 tff(1427,plain,
% 1.52/1.69 (c3_1(a551)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[540, 1425])).
% 1.52/1.69 tff(1428,plain,
% 1.52/1.69 (c1_1(a551)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[552, 1427, 109, 1426, 888, 887, 889])).
% 1.52/1.69 tff(1429,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1430,plain,
% 1.52/1.69 ((hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545))) <=> (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1431,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1430])).
% 1.52/1.69 tff(1432,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1431, 1429])).
% 1.52/1.69 tff(1433,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1434,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.52/1.69 tff(1435,plain,
% 1.52/1.69 ((~c3_1(a545)) | (~c1_1(a551))),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1434, 156, 1423, 1427, 1426, 1046, 111, 55])).
% 1.52/1.69 tff(1436,plain,
% 1.52/1.69 (~c3_1(a545)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1435, 1428])).
% 1.52/1.69 tff(1437,plain,
% 1.52/1.69 (~c0_1(a551)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[558, 1425])).
% 1.52/1.69 tff(1438,plain,
% 1.52/1.69 (hskp41 | (~c1_1(a551))),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[565, 156, 330, 1427, 1437, 342])).
% 1.52/1.69 tff(1439,plain,
% 1.52/1.69 (hskp41),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1438, 1428])).
% 1.52/1.69 tff(1440,plain,
% 1.52/1.69 (~c2_1(a555)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[232, 1439])).
% 1.52/1.69 tff(1441,plain,
% 1.52/1.69 (c3_1(a555)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[256, 1439])).
% 1.52/1.69 tff(1442,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a555) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a555) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1443,plain,
% 1.52/1.69 ((hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp39 | c2_1(a555) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1444,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a555) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a555)) | (~c1_1(a555))))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1443])).
% 1.52/1.69 tff(1445,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a555) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1444, 1442])).
% 1.52/1.69 tff(1446,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1447,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a555) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a555)) | (~c1_1(a555))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 1.52/1.69 tff(1448,plain,
% 1.52/1.69 (~c1_1(a555)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1447, 156, 859, 1441, 1046, 1440, 97, 281, 1436])).
% 1.52/1.69 tff(1449,plain,
% 1.52/1.69 (c0_1(a555)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[240, 1439])).
% 1.52/1.69 tff(1450,plain,
% 1.52/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a555) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a555) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1451,plain,
% 1.52/1.69 (((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555))) <=> (c1_1(a586) | c2_1(a555) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1452,plain,
% 1.52/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a555) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1451])).
% 1.52/1.69 tff(1453,plain,
% 1.52/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a555) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1452, 1450])).
% 1.52/1.69 tff(1454,plain,
% 1.52/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1455,plain,
% 1.52/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a555) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 1.52/1.69 tff(1456,plain,
% 1.52/1.69 ($false),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1455, 156, 1441, 1449, 88, 1440, 86, 921, 902, 1448])).
% 1.52/1.69 tff(1457,plain,((~hskp18) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | hskp39 | (~c1_1(a545)) | c0_1(a545) | hskp9 | hskp25 | c2_1(a545) | hskp15 | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.52/1.69 tff(1458,plain,
% 1.52/1.69 (~hskp18),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1457, 859, 86, 902, 88, 1046, 97, 330, 1423, 111, 109, 110, 98])).
% 1.52/1.69 tff(1459,plain,
% 1.52/1.69 (hskp16),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[382, 1458, 1422])).
% 1.52/1.69 tff(1460,plain,
% 1.52/1.69 (c1_1(a570)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[356, 1459])).
% 1.52/1.69 tff(1461,plain,
% 1.52/1.69 (c3_1(a570)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[364, 1459])).
% 1.52/1.69 tff(1462,plain,
% 1.52/1.69 (~c3_1(a545)),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1164, 946])).
% 1.52/1.69 tff(1463,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1464,plain,
% 1.52/1.69 ((hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp39 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.69 inference(rewrite,[status(thm)],[])).
% 1.52/1.69 tff(1465,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570))))),
% 1.52/1.69 inference(monotonicity,[status(thm)],[1464])).
% 1.52/1.69 tff(1466,plain,
% 1.52/1.69 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.69 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.52/1.69 tff(1467,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 1.52/1.69 inference(quant_inst,[status(thm)],[])).
% 1.52/1.69 tff(1468,plain,
% 1.52/1.69 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570))),
% 1.52/1.69 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.52/1.69 tff(1469,plain,
% 1.52/1.69 ($false),
% 1.52/1.69 inference(unit_resolution,[status(thm)],[1468, 156, 859, 948, 947, 1046, 97, 281, 1462, 956])).
% 1.52/1.69 tff(1470,plain,(hskp46 | hskp39 | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a545)) | c0_1(a545) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c2_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(1471,plain,
% 1.52/1.70 (hskp46),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1470, 1461, 859, 1460, 1046, 97, 87, 86, 902, 111])).
% 1.52/1.70 tff(1472,plain,
% 1.52/1.70 (~c3_1(a562)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[270, 1471])).
% 1.52/1.70 tff(1473,plain,
% 1.52/1.70 (~c0_1(a562)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[64, 1471])).
% 1.52/1.70 tff(1474,plain,
% 1.52/1.70 (c1_1(a562)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[288, 1471])).
% 1.52/1.70 tff(1475,plain,
% 1.52/1.70 (c2_1(a570)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[981, 1474, 1461, 1473, 1460, 1472, 859])).
% 1.52/1.70 tff(1476,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1477,plain,
% 1.52/1.70 ((hskp25 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545))) <=> (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1478,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1477])).
% 1.52/1.70 tff(1479,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.52/1.70 tff(1480,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(1481,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.52/1.70 tff(1482,plain,
% 1.52/1.70 (~c3_1(a545)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1481, 156, 1423, 1461, 1460, 1046, 111, 55, 1475])).
% 1.52/1.70 tff(1483,plain,
% 1.52/1.70 (~c0_1(a570)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[348, 1459])).
% 1.52/1.70 tff(1484,plain,
% 1.52/1.70 (hskp41),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[371, 156, 330, 1461, 1460, 1483, 342])).
% 1.52/1.70 tff(1485,plain,
% 1.52/1.70 (~c2_1(a555)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[232, 1484])).
% 1.52/1.70 tff(1486,plain,
% 1.52/1.70 (c3_1(a555)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[256, 1484])).
% 1.52/1.70 tff(1487,plain,
% 1.52/1.70 (~c1_1(a555)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1447, 156, 859, 1486, 1046, 1485, 97, 281, 1482])).
% 1.52/1.70 tff(1488,plain,
% 1.52/1.70 (c0_1(a555)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[240, 1484])).
% 1.52/1.70 tff(1489,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1455, 156, 1486, 1488, 88, 1485, 86, 921, 902, 1487])).
% 1.52/1.70 tff(1490,plain,(hskp39 | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a545)) | c0_1(a545) | hskp9 | hskp25 | c2_1(a545) | c0_1(a586) | hskp15 | hskp50 | hskp19 | hskp33 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(1491,plain,
% 1.52/1.70 (hskp39),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1490, 1221, 86, 88, 1046, 97, 1315, 1302, 111, 87, 1277, 110, 98, 35, 1249])).
% 1.52/1.70 tff(1492,plain,
% 1.52/1.70 (c1_1(a549)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[303, 1491])).
% 1.52/1.70 tff(1493,plain,
% 1.52/1.70 (c2_1(a549)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[311, 1491])).
% 1.52/1.70 tff(1494,plain,
% 1.52/1.70 (c3_1(a549)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[319, 1491])).
% 1.52/1.70 tff(1495,plain,
% 1.52/1.70 (c1_1(a555)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1455, 156, 257, 241, 88, 233, 86, 921, 902])).
% 1.52/1.70 tff(1496,assumption,(c1_1(a549)), introduced(assumption)).
% 1.52/1.70 tff(1497,assumption,(c2_1(a549)), introduced(assumption)).
% 1.52/1.70 tff(1498,assumption,(c3_1(a549)), introduced(assumption)).
% 1.52/1.70 tff(1499,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1500,plain,
% 1.52/1.70 ((hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555))) <=> (hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1501,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a555)) | (~c1_1(a555))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1500])).
% 1.52/1.70 tff(1502,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[1501, 1499])).
% 1.52/1.70 tff(1503,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(1504,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a555)) | (~c1_1(a555))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 1.52/1.70 tff(1505,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1504, 156, 1423, 257, 1498, 1497, 1496, 233, 55, 1495])).
% 1.52/1.70 tff(1506,plain,((~hskp41) | hskp25 | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(1507,plain,
% 1.52/1.70 (~hskp41),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1506, 1302, 1494, 1493, 1492, 88, 86, 1221])).
% 1.52/1.70 tff(1508,plain,
% 1.52/1.70 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c1_1(a549)) | (~c3_1(a549)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1509,plain,
% 1.52/1.70 ((hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c3_1(a549)) | (~c1_1(a549))) <=> (hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1510,plain,
% 1.52/1.70 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c3_1(a549)) | (~c1_1(a549)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c1_1(a549)) | (~c3_1(a549))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1509])).
% 1.52/1.70 tff(1511,plain,
% 1.52/1.70 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c3_1(a549)) | (~c1_1(a549)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[1510, 1508])).
% 1.52/1.70 tff(1512,plain,
% 1.52/1.70 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c3_1(a549)) | (~c1_1(a549)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(1513,plain,
% 1.52/1.70 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | (~ndr1_0) | c0_1(a549) | (~c1_1(a549)) | (~c3_1(a549))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.52/1.70 tff(1514,plain,
% 1.52/1.70 (hskp41 | c0_1(a549)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1513, 156, 1315, 1494, 1492, 342])).
% 1.52/1.70 tff(1515,plain,
% 1.52/1.70 (c0_1(a549)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1514, 1507])).
% 1.52/1.70 tff(1516,plain,
% 1.52/1.70 (~c3_1(a545)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1184, 156, 1302, 1494, 1493, 1492, 1046, 111, 55])).
% 1.52/1.70 tff(1517,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1518,plain,
% 1.52/1.70 ((hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1519,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1518])).
% 1.52/1.70 tff(1520,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[1519, 1517])).
% 1.52/1.70 tff(1521,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(1522,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.52/1.70 tff(1523,plain,
% 1.52/1.70 (hskp34 | (~c0_1(a549))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1522, 156, 1493, 1492, 1046, 97, 75, 1516])).
% 1.52/1.70 tff(1524,plain,
% 1.52/1.70 (hskp34),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1523, 1515])).
% 1.52/1.70 tff(1525,plain,
% 1.52/1.70 (~c1_1(a537)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1124, 1524])).
% 1.52/1.70 tff(1526,plain,
% 1.52/1.70 (c0_1(a537)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1147, 1524])).
% 1.52/1.70 tff(1527,plain,
% 1.52/1.70 (c2_1(a537)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1154, 156, 110, 98, 1526, 1525, 34])).
% 1.52/1.70 tff(1528,plain,
% 1.52/1.70 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.52/1.70 inference(bind,[status(th)],[])).
% 1.52/1.70 tff(1529,plain,
% 1.52/1.70 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.52/1.70 inference(quant_intro,[status(thm)],[1528])).
% 1.52/1.70 tff(1530,plain,
% 1.52/1.70 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1531,plain,
% 1.52/1.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp38) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp38))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp38) <=> (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.52/1.70 inference(bind,[status(th)],[])).
% 1.52/1.70 tff(1532,plain,
% 1.52/1.70 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.52/1.70 inference(quant_intro,[status(thm)],[1531])).
% 1.52/1.70 tff(1533,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause253')).
% 1.52/1.70 tff(1534,plain,
% 1.52/1.70 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.52/1.70 tff(1535,plain,
% 1.52/1.70 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1534, 1530])).
% 1.52/1.70 tff(1536,plain,(
% 1.52/1.70 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.52/1.70 inference(skolemize,[status(sab)],[1535])).
% 1.52/1.70 tff(1537,plain,
% 1.52/1.70 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1536, 1529])).
% 1.52/1.70 tff(1538,plain,
% 1.52/1.70 (c3_1(a537)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1132, 1524])).
% 1.52/1.70 tff(1539,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1540,plain,
% 1.52/1.70 ((hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1541,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1540])).
% 1.52/1.70 tff(1542,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[1541, 1539])).
% 1.52/1.70 tff(1543,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(1544,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.52/1.70 tff(1545,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1544, 156, 58, 1494, 1493, 1492, 1538, 1525, 1537, 1527])).
% 1.52/1.70 tff(1546,plain,(hskp28 | hskp38 | hskp50 | hskp19 | (~c1_1(a545)) | c0_1(a545) | c1_1(a586) | c3_1(a586) | c2_1(a545) | c0_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(1547,plain,
% 1.52/1.70 (hskp28),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1546, 58, 88, 87, 110, 97, 1035, 86, 111, 98, 35])).
% 1.52/1.70 tff(1548,plain,
% 1.52/1.70 (c3_1(a589)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[185, 1547])).
% 1.52/1.70 tff(1549,plain,
% 1.52/1.70 (c2_1(a589)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[171, 1547])).
% 1.52/1.70 tff(1550,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1551,plain,
% 1.52/1.70 ((hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp4 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1552,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1551])).
% 1.52/1.70 tff(1553,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[1552, 1550])).
% 1.52/1.70 tff(1554,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(1555,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.52/1.70 tff(1556,plain,
% 1.52/1.70 (~c1_1(a589)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1555, 156, 23, 1549, 1548, 1035, 97, 22, 1212])).
% 1.52/1.70 tff(1557,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1558,plain,
% 1.52/1.70 ((hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp15 | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1559,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1558])).
% 1.52/1.70 tff(1560,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.70 inference(transitivity,[status(thm)],[1559, 1557])).
% 1.52/1.70 tff(1561,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(1562,plain,
% 1.52/1.70 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 1.52/1.70 tff(1563,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1562, 156, 109, 1549, 1548, 1035, 111, 483, 1556, 1212])).
% 1.52/1.70 tff(1564,plain,(hskp38 | hskp15 | c2_1(a545) | hskp4 | c0_1(a545) | c1_1(a586) | c0_1(a586) | hskp50 | c3_1(a586) | hskp19 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(1565,plain,
% 1.52/1.70 (hskp38),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1564, 23, 111, 109, 97, 88, 87, 110, 86, 98, 35])).
% 1.52/1.70 tff(1566,plain,
% 1.52/1.70 (c0_1(a547)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[677, 1565])).
% 1.52/1.70 tff(1567,plain,
% 1.52/1.70 (c1_1(a547)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[685, 1565])).
% 1.52/1.70 tff(1568,plain,
% 1.52/1.70 (c2_1(a547)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[693, 1565])).
% 1.52/1.70 tff(1569,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1570,plain,
% 1.52/1.70 ((hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547))) <=> (hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(1571,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1570])).
% 1.52/1.70 tff(1572,plain,
% 1.52/1.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1571, 1569])).
% 1.52/1.71 tff(1573,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1574,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 1.52/1.71 tff(1575,plain,
% 1.52/1.71 (hskp42 | (~c3_1(a545))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1574, 156, 733, 732, 731, 1046, 111, 1364])).
% 1.52/1.71 tff(1576,plain,
% 1.52/1.71 (hskp42),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1575, 2])).
% 1.52/1.71 tff(1577,plain,
% 1.52/1.71 (~c2_1(a556)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1385, 1576])).
% 1.52/1.71 tff(1578,plain,
% 1.52/1.71 (hskp46 | (~c3_1(a545)) | (~c1_1(a545))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1163, 156, 111, 97, 12])).
% 1.52/1.71 tff(1579,plain,
% 1.52/1.71 (hskp46),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1578, 2, 1046])).
% 1.52/1.71 tff(1580,plain,
% 1.52/1.71 (~c0_1(a562)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[64, 1579])).
% 1.52/1.71 tff(1581,plain,
% 1.52/1.71 (~c3_1(a562)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[270, 1579])).
% 1.52/1.71 tff(1582,plain,
% 1.52/1.71 (c3_1(a556)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1403, 1576])).
% 1.52/1.71 tff(1583,plain,
% 1.52/1.71 (c1_1(a556)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1411, 1576])).
% 1.52/1.71 tff(1584,plain,
% 1.52/1.71 (c1_1(a562)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[288, 1579])).
% 1.52/1.71 tff(1585,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1419, 156, 859, 1584, 1583, 1582, 1581, 1580, 1577, 281])).
% 1.52/1.71 tff(1586,plain,((~c3_1(a545)) | hskp39 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(1587,plain,
% 1.52/1.71 (~c3_1(a545)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1586, 1568, 859, 1567, 1566, 1035, 111, 97])).
% 1.52/1.71 tff(1588,plain,
% 1.52/1.71 (hskp6),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[205, 23, 96])).
% 1.52/1.71 tff(1589,plain,
% 1.52/1.71 (~c2_1(a548)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[217, 1588])).
% 1.52/1.71 tff(1590,plain,
% 1.52/1.71 (c3_1(a548)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[225, 1588])).
% 1.52/1.71 tff(1591,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a548) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a548) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1592,plain,
% 1.52/1.71 ((hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp39 | c2_1(a548) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1593,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a548) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a548)) | (~c1_1(a548))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[1592])).
% 1.52/1.71 tff(1594,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a548) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.52/1.71 tff(1595,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1596,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a548) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.52/1.71 tff(1597,plain,
% 1.52/1.71 (~c1_1(a548)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1596, 156, 859, 1590, 1035, 1589, 97, 281, 1587])).
% 1.52/1.71 tff(1598,plain,
% 1.52/1.71 (~c0_1(a548)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[211, 1588])).
% 1.52/1.71 tff(1599,plain,
% 1.52/1.71 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1600,plain,
% 1.52/1.71 ((hskp28 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | c1_1(a548)) <=> (hskp28 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1601,plain,
% 1.52/1.71 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | c1_1(a548))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[1600])).
% 1.52/1.71 tff(1602,plain,
% 1.52/1.71 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | c1_1(a548))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1601, 1599])).
% 1.52/1.71 tff(1603,plain,
% 1.52/1.71 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | c1_1(a548))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1604,plain,
% 1.52/1.71 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.52/1.71 tff(1605,plain,
% 1.52/1.71 (hskp28 | c1_1(a548)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1604, 156, 1589, 1598, 122])).
% 1.52/1.71 tff(1606,plain,
% 1.52/1.71 (hskp28),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1605, 1597])).
% 1.52/1.71 tff(1607,plain,
% 1.52/1.71 (c2_1(a589)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[171, 1606])).
% 1.52/1.71 tff(1608,plain,
% 1.52/1.71 (c3_1(a589)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[185, 1606])).
% 1.52/1.71 tff(1609,plain,
% 1.52/1.71 (~c1_1(a589)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1555, 156, 23, 625, 591, 1046, 97, 22, 765])).
% 1.52/1.71 tff(1610,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1562, 156, 109, 625, 591, 1046, 111, 483, 1609, 765])).
% 1.52/1.71 tff(1611,plain,(c3_1(a545) | hskp15 | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a545)) | c2_1(a545) | hskp4 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(1612,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1611, 1608, 1607, 109, 1587, 1035, 111, 23, 97])).
% 1.52/1.71 tff(1613,plain,(hskp4 | hskp15 | c2_1(a545) | c0_1(a545) | hskp39 | c1_1(a586) | c0_1(a586) | hskp50 | c3_1(a586) | hskp19 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(1614,plain,
% 1.52/1.71 (hskp4),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1613, 859, 111, 97, 109, 88, 87, 110, 86, 98, 35])).
% 1.52/1.71 tff(1615,assumption,(hskp26), introduced(assumption)).
% 1.52/1.71 tff(1616,plain,
% 1.52/1.71 (((~hskp26) | (~c3_1(a584))) <=> ((~hskp26) | (~c3_1(a584)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1617,plain,
% 1.52/1.71 (((~c3_1(a584)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a584)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1618,axiom,((~c3_1(a584)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.52/1.71 tff(1619,plain,
% 1.52/1.71 ((~hskp26) | (~c3_1(a584))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 1.52/1.71 tff(1620,plain,
% 1.52/1.71 ((~hskp26) | (~c3_1(a584))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1619, 1616])).
% 1.52/1.71 tff(1621,plain,
% 1.52/1.71 (~c3_1(a584)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1620, 1615])).
% 1.52/1.71 tff(1622,assumption,(hskp4), introduced(assumption)).
% 1.52/1.71 tff(1623,plain,
% 1.52/1.71 (((~hskp26) | c0_1(a584)) <=> ((~hskp26) | c0_1(a584))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1624,axiom,((~hskp26) | c0_1(a584)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.52/1.71 tff(1625,plain,
% 1.52/1.71 ((~hskp26) | c0_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.52/1.71 tff(1626,plain,
% 1.52/1.71 ((~hskp26) | c0_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1625, 1623])).
% 1.52/1.71 tff(1627,plain,
% 1.52/1.71 ((~hskp26) | c0_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1626, 1623])).
% 1.52/1.71 tff(1628,plain,
% 1.52/1.71 ((~hskp26) | c0_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1627, 1623])).
% 1.52/1.71 tff(1629,plain,
% 1.52/1.71 ((~hskp26) | c0_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1628, 1623])).
% 1.52/1.71 tff(1630,plain,
% 1.52/1.71 (c0_1(a584)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1629, 1615])).
% 1.52/1.71 tff(1631,plain,
% 1.52/1.71 (((~hskp26) | c1_1(a584)) <=> ((~hskp26) | c1_1(a584))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1632,axiom,((~hskp26) | c1_1(a584)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.52/1.71 tff(1633,plain,
% 1.52/1.71 ((~hskp26) | c1_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 1.52/1.71 tff(1634,plain,
% 1.52/1.71 ((~hskp26) | c1_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1633, 1631])).
% 1.52/1.71 tff(1635,plain,
% 1.52/1.71 ((~hskp26) | c1_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1634, 1631])).
% 1.52/1.71 tff(1636,plain,
% 1.52/1.71 ((~hskp26) | c1_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1635, 1631])).
% 1.52/1.71 tff(1637,plain,
% 1.52/1.71 ((~hskp26) | c1_1(a584)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1636, 1631])).
% 1.52/1.71 tff(1638,plain,
% 1.52/1.71 (c1_1(a584)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1637, 1615])).
% 1.52/1.71 tff(1639,plain,
% 1.52/1.71 (((~hskp4) | (~c2_1(a545))) <=> ((~hskp4) | (~c2_1(a545)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1640,plain,
% 1.52/1.71 (((~c2_1(a545)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a545)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1641,axiom,((~c2_1(a545)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause207')).
% 1.52/1.71 tff(1642,plain,
% 1.52/1.71 ((~hskp4) | (~c2_1(a545))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 1.52/1.71 tff(1643,plain,
% 1.52/1.71 ((~hskp4) | (~c2_1(a545))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1642, 1639])).
% 1.52/1.71 tff(1644,plain,
% 1.52/1.71 (~c2_1(a545)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1643, 1622])).
% 1.52/1.71 tff(1645,plain,
% 1.52/1.71 (c1_1(a545)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[193, 1622])).
% 1.52/1.71 tff(1646,plain,
% 1.52/1.71 (~c3_1(a545)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1211, 1645, 1644, 97, 58])).
% 1.52/1.71 tff(1647,assumption,(~c3_1(a584)), introduced(assumption)).
% 1.52/1.71 tff(1648,assumption,(c1_1(a584)), introduced(assumption)).
% 1.52/1.71 tff(1649,assumption,(c0_1(a584)), introduced(assumption)).
% 1.52/1.71 tff(1650,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a545))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1651,plain,
% 1.52/1.71 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | c3_1(a584) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a545))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1652,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a545)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[1651])).
% 1.52/1.71 tff(1653,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a545))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1652, 1650])).
% 1.52/1.71 tff(1654,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1655,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a545)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 1.52/1.71 tff(1656,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1655, 156, 35, 1649, 1648, 1647, 1644, 97, 85, 1646])).
% 1.52/1.71 tff(1657,plain,((~hskp4) | hskp33 | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584) | c0_1(a545) | hskp38), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(1658,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1657, 1638, 1630, 97, 1622, 1621, 35, 58])).
% 1.52/1.71 tff(1659,plain,((~hskp26) | c0_1(a545) | (~hskp4) | hskp33 | hskp38), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(1660,plain,
% 1.52/1.71 (~hskp26),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1659, 58, 1614, 35, 97])).
% 1.52/1.71 tff(1661,assumption,(~hskp26), introduced(assumption)).
% 1.52/1.71 tff(1662,plain,
% 1.52/1.71 (((~hskp4) | (~c0_1(a545))) <=> ((~hskp4) | (~c0_1(a545)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1663,plain,
% 1.52/1.71 (((~c0_1(a545)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a545)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1664,axiom,((~c0_1(a545)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause208')).
% 1.52/1.71 tff(1665,plain,
% 1.52/1.71 ((~hskp4) | (~c0_1(a545))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.52/1.71 tff(1666,plain,
% 1.52/1.71 ((~hskp4) | (~c0_1(a545))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1665, 1662])).
% 1.52/1.71 tff(1667,plain,
% 1.52/1.71 (~c0_1(a545)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1666, 1622])).
% 1.52/1.71 tff(1668,plain,
% 1.52/1.71 (~c3_1(a545)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1211, 1644, 58, 1667, 1645])).
% 1.52/1.71 tff(1669,assumption,(~hskp6), introduced(assumption)).
% 1.52/1.71 tff(1670,assumption,(hskp19), introduced(assumption)).
% 1.52/1.71 tff(1671,plain,
% 1.52/1.71 (((~hskp19) | (~c1_1(a573))) <=> ((~hskp19) | (~c1_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1672,plain,
% 1.52/1.71 (((~c1_1(a573)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1673,axiom,((~c1_1(a573)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.52/1.71 tff(1674,plain,
% 1.52/1.71 ((~hskp19) | (~c1_1(a573))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 1.52/1.71 tff(1675,plain,
% 1.52/1.71 ((~hskp19) | (~c1_1(a573))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1674, 1671])).
% 1.52/1.71 tff(1676,plain,
% 1.52/1.71 (~c1_1(a573)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1675, 1670])).
% 1.52/1.71 tff(1677,plain,
% 1.52/1.71 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.52/1.71 inference(bind,[status(th)],[])).
% 1.52/1.71 tff(1678,plain,
% 1.52/1.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.71 inference(quant_intro,[status(thm)],[1677])).
% 1.52/1.71 tff(1679,plain,
% 1.52/1.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1680,plain,
% 1.52/1.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp26))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.52/1.71 inference(bind,[status(th)],[])).
% 1.52/1.71 tff(1681,plain,
% 1.52/1.71 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.71 inference(quant_intro,[status(thm)],[1680])).
% 1.52/1.71 tff(1682,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 1.52/1.71 tff(1683,plain,
% 1.52/1.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.52/1.71 tff(1684,plain,
% 1.52/1.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1683, 1679])).
% 1.52/1.71 tff(1685,plain,(
% 1.52/1.71 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.71 inference(skolemize,[status(sab)],[1684])).
% 1.52/1.71 tff(1686,plain,
% 1.52/1.71 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1685, 1678])).
% 1.52/1.71 tff(1687,plain,
% 1.52/1.71 (((~hskp19) | (~c0_1(a573))) <=> ((~hskp19) | (~c0_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1688,plain,
% 1.52/1.71 (((~c0_1(a573)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1689,axiom,((~c0_1(a573)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.52/1.71 tff(1690,plain,
% 1.52/1.71 ((~hskp19) | (~c0_1(a573))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 1.52/1.71 tff(1691,plain,
% 1.52/1.71 ((~hskp19) | (~c0_1(a573))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1690, 1687])).
% 1.52/1.71 tff(1692,plain,
% 1.52/1.71 (~c0_1(a573)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1691, 1670])).
% 1.52/1.71 tff(1693,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1694,plain,
% 1.52/1.71 ((hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573))) <=> (hskp26 | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1695,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a573))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[1694])).
% 1.52/1.71 tff(1696,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a573)))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1695, 1693])).
% 1.52/1.71 tff(1697,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1698,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a573))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1697, 1696])).
% 1.52/1.71 tff(1699,plain,
% 1.52/1.71 (~c3_1(a573)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1698, 156, 1661, 1645, 1692, 1676, 1667, 1686, 765])).
% 1.52/1.71 tff(1700,plain,
% 1.52/1.71 (((~hskp19) | (~c2_1(a573))) <=> ((~hskp19) | (~c2_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1701,plain,
% 1.52/1.71 (((~c2_1(a573)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a573)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1702,axiom,((~c2_1(a573)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.52/1.71 tff(1703,plain,
% 1.52/1.71 ((~hskp19) | (~c2_1(a573))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.52/1.71 tff(1704,plain,
% 1.52/1.71 ((~hskp19) | (~c2_1(a573))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1703, 1700])).
% 1.52/1.71 tff(1705,plain,
% 1.52/1.71 (~c2_1(a573)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1704, 1670])).
% 1.52/1.71 tff(1706,plain,
% 1.52/1.71 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1707,plain,
% 1.52/1.71 ((hskp28 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | c1_1(a573)) <=> (hskp28 | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1708,plain,
% 1.52/1.71 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | c1_1(a573))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[1707])).
% 1.52/1.71 tff(1709,plain,
% 1.52/1.71 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | c1_1(a573))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1708, 1706])).
% 1.52/1.71 tff(1710,plain,
% 1.52/1.71 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | c1_1(a573))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1711,plain,
% 1.52/1.71 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 1.52/1.71 tff(1712,plain,
% 1.52/1.71 (hskp28),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1711, 156, 1705, 1692, 1676, 122])).
% 1.52/1.71 tff(1713,plain,
% 1.52/1.71 (c2_1(a589)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[171, 1712])).
% 1.52/1.71 tff(1714,plain,
% 1.52/1.71 (c3_1(a589)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[185, 1712])).
% 1.52/1.71 tff(1715,plain,
% 1.52/1.71 (~c0_1(a589)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[177, 1712])).
% 1.52/1.71 tff(1716,assumption,(~c1_1(a589)), introduced(assumption)).
% 1.52/1.71 tff(1717,assumption,(~c3_1(a573)), introduced(assumption)).
% 1.52/1.71 tff(1718,assumption,(~c1_1(a573)), introduced(assumption)).
% 1.52/1.71 tff(1719,assumption,(~c2_1(a573)), introduced(assumption)).
% 1.52/1.71 tff(1720,plain,
% 1.52/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a573) | c1_1(a573) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a573) | c1_1(a573) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1721,plain,
% 1.52/1.71 (((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573)) <=> (c2_1(a573) | c1_1(a573) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1722,plain,
% 1.52/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a573) | c1_1(a573) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[1721])).
% 1.52/1.71 tff(1723,plain,
% 1.52/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a573) | c1_1(a573) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1722, 1720])).
% 1.52/1.71 tff(1724,plain,
% 1.52/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1725,plain,
% 1.52/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a573) | c1_1(a573) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.52/1.71 tff(1726,plain,
% 1.52/1.71 (~c3_1(a545)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1725, 156, 625, 591, 1645, 1719, 1718, 1644, 45, 1717, 1716])).
% 1.52/1.71 tff(1727,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a589) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a589) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1728,plain,
% 1.52/1.71 ((hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589))) <=> (hskp26 | c0_1(a589) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(1729,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a589) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[1728])).
% 1.52/1.71 tff(1730,plain,
% 1.52/1.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a589) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1729, 1727])).
% 1.52/1.71 tff(1731,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(1732,plain,
% 1.52/1.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a589) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a589)) | c1_1(a589)),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 1.52/1.72 tff(1733,plain,
% 1.52/1.72 ($false),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1732, 156, 1661, 591, 1645, 590, 1667, 1686, 1716, 1726])).
% 1.52/1.72 tff(1734,plain,((~hskp4) | hskp26 | (~c3_1(a589)) | c0_1(a589) | c1_1(a589) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.72 tff(1735,plain,
% 1.52/1.72 (c1_1(a589)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1734, 1715, 1622, 1705, 1714, 1713, 1699, 1676, 1661])).
% 1.52/1.72 tff(1736,plain,
% 1.52/1.72 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.52/1.72 inference(bind,[status(th)],[])).
% 1.52/1.72 tff(1737,plain,
% 1.52/1.72 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.52/1.72 inference(quant_intro,[status(thm)],[1736])).
% 1.52/1.72 tff(1738,plain,
% 1.52/1.72 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1739,plain,
% 1.52/1.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.52/1.72 inference(bind,[status(th)],[])).
% 1.52/1.72 tff(1740,plain,
% 1.52/1.72 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.52/1.72 inference(quant_intro,[status(thm)],[1739])).
% 1.52/1.72 tff(1741,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause231')).
% 1.52/1.72 tff(1742,plain,
% 1.52/1.72 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 1.52/1.72 tff(1743,plain,
% 1.52/1.72 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1742, 1738])).
% 1.52/1.72 tff(1744,plain,(
% 1.52/1.72 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.52/1.72 inference(skolemize,[status(sab)],[1743])).
% 1.52/1.72 tff(1745,plain,
% 1.52/1.72 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1744, 1737])).
% 1.52/1.72 tff(1746,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1747,plain,
% 1.52/1.72 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c0_1(a573)) <=> (hskp6 | c0_1(a589) | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1748,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[1747])).
% 1.52/1.72 tff(1749,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(transitivity,[status(thm)],[1748, 1746])).
% 1.52/1.72 tff(1750,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c0_1(a573))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(1751,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a573) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 1.52/1.72 tff(1752,plain,
% 1.52/1.72 ($false),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1751, 156, 1669, 1714, 1715, 1705, 1692, 1676, 1745, 1735])).
% 1.52/1.72 tff(1753,plain,((~hskp19) | hskp6 | (~hskp4) | hskp26 | c3_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.72 tff(1754,plain,
% 1.52/1.72 (~hskp19),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1753, 1622, 1669, 1661, 1668])).
% 1.52/1.72 tff(1755,plain,
% 1.52/1.72 (~c3_1(a545)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1211, 111, 58, 97, 1046])).
% 1.52/1.72 tff(1756,plain,
% 1.52/1.72 (~hskp50),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[824, 111, 35, 97, 1755])).
% 1.52/1.72 tff(1757,plain,
% 1.52/1.72 (hskp28),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1546, 98, 110, 58, 1046, 97, 88, 86, 111, 87, 35])).
% 1.52/1.72 tff(1758,plain,
% 1.52/1.72 (~c0_1(a589)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[177, 1757])).
% 1.52/1.72 tff(1759,plain,
% 1.52/1.72 (c3_1(a589)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[185, 1757])).
% 1.52/1.72 tff(1760,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c1_1(a586) | c0_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c1_1(a586) | c0_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1761,plain,
% 1.52/1.72 ((hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c0_1(a586)) <=> (hskp6 | c1_1(a586) | c0_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1762,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c1_1(a586) | c0_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586)))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[1761])).
% 1.52/1.72 tff(1763,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c1_1(a586) | c0_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586))),
% 1.52/1.72 inference(transitivity,[status(thm)],[1762, 1760])).
% 1.52/1.72 tff(1764,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | c1_1(a586) | c0_1(a586))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(1765,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c1_1(a586) | c0_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586)),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 1.52/1.72 tff(1766,plain,
% 1.52/1.72 (~c3_1(a545)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1765, 156, 1669, 88, 1046, 87, 97, 1745, 653])).
% 1.52/1.72 tff(1767,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c1_1(a586) | c0_1(a589) | c0_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c1_1(a586) | c0_1(a589) | c0_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1768,plain,
% 1.52/1.72 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c0_1(a586)) <=> (hskp6 | c1_1(a586) | c0_1(a589) | c0_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1769,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c1_1(a586) | c0_1(a589) | c0_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[1768])).
% 1.52/1.72 tff(1770,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c1_1(a586) | c0_1(a589) | c0_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(transitivity,[status(thm)],[1769, 1767])).
% 1.52/1.72 tff(1771,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c0_1(a586))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(1772,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c1_1(a586) | c0_1(a589) | c0_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 1.52/1.72 tff(1773,plain,
% 1.52/1.72 (~c1_1(a589)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1772, 156, 1669, 591, 88, 590, 87, 1745, 653])).
% 1.52/1.72 tff(1774,plain,
% 1.52/1.72 ($false),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1732, 156, 1661, 591, 1046, 590, 97, 1686, 1773, 1766])).
% 1.52/1.72 tff(1775,plain,(c2_1(a586) | hskp26 | (~c3_1(a589)) | (~c1_1(a545)) | c0_1(a589) | c0_1(a545) | hskp6 | c1_1(a586) | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.72 tff(1776,plain,
% 1.52/1.72 (c2_1(a586)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1775, 1759, 1661, 1046, 1758, 97, 1669, 88, 87])).
% 1.52/1.72 tff(1777,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a569) | c1_1(a569) | c2_1(a569) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a569) | c1_1(a569) | c2_1(a569) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1778,plain,
% 1.52/1.72 ((hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a569) | c1_1(a569) | c0_1(a569)) <=> (hskp6 | c0_1(a569) | c1_1(a569) | c2_1(a569) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1779,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a569) | c1_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a569) | c1_1(a569) | c2_1(a569) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[1778])).
% 1.52/1.72 tff(1780,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a569) | c1_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a569) | c1_1(a569) | c2_1(a569) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.52/1.72 inference(transitivity,[status(thm)],[1779, 1777])).
% 1.52/1.72 tff(1781,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a569) | c1_1(a569) | c0_1(a569))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(1782,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a569) | c1_1(a569) | c2_1(a569) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 1.52/1.72 tff(1783,plain,
% 1.52/1.72 (~c3_1(a545)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1782, 156, 1669, 1046, 1268, 1262, 1256, 97, 1745])).
% 1.52/1.72 tff(1784,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1785,plain,
% 1.52/1.72 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a569) | c1_1(a569) | c0_1(a569)) <=> (hskp6 | c0_1(a589) | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1786,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a569) | c1_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[1785])).
% 1.52/1.72 tff(1787,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a569) | c1_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.72 inference(transitivity,[status(thm)],[1786, 1784])).
% 1.52/1.72 tff(1788,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a569) | c1_1(a569) | c0_1(a569))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(1789,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.52/1.72 tff(1790,plain,
% 1.52/1.72 (~c1_1(a589)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1789, 156, 1669, 591, 590, 1268, 1262, 1256, 1745])).
% 1.52/1.72 tff(1791,plain,
% 1.52/1.72 ($false),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1732, 156, 1661, 591, 1046, 590, 97, 1686, 1790, 1783])).
% 1.52/1.72 tff(1792,plain,((~hskp15) | hskp26 | (~c3_1(a589)) | (~c1_1(a545)) | c0_1(a589) | c0_1(a545) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.52/1.72 tff(1793,plain,
% 1.52/1.72 (~hskp15),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1792, 1759, 1661, 1046, 1758, 97, 1669])).
% 1.52/1.72 tff(1794,plain,
% 1.52/1.72 (c2_1(a589)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[171, 1757])).
% 1.52/1.72 tff(1795,assumption,(~hskp18), introduced(assumption)).
% 1.52/1.72 tff(1796,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a570) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a570) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1797,plain,
% 1.52/1.72 ((hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a554) | c1_1(a554) | c0_1(a554)) <=> (hskp6 | c0_1(a570) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1798,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a554) | c1_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a570) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[1797])).
% 1.52/1.72 tff(1799,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a554) | c1_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a570) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.72 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.52/1.72 tff(1800,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a554) | c1_1(a554) | c0_1(a554))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(1801,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a570) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.52/1.72 tff(1802,plain,
% 1.52/1.72 ($false),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1801, 156, 1669, 948, 947, 957, 1306, 1305, 1304, 1745])).
% 1.52/1.72 tff(1803,plain,((~hskp9) | hskp6 | (~c3_1(a570)) | (~c1_1(a570)) | c0_1(a570)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.72 tff(1804,plain,
% 1.52/1.72 (~hskp9),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1803, 365, 1669, 357, 349])).
% 1.52/1.72 tff(1805,plain,
% 1.52/1.72 (hskp1),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1490, 1804, 86, 88, 1046, 97, 902, 1423, 111, 87, 109, 110, 98, 35, 859])).
% 1.52/1.72 tff(1806,plain,
% 1.52/1.72 (~c0_1(a539)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1227, 1805])).
% 1.52/1.72 tff(1807,plain,
% 1.52/1.72 (~c1_1(a539)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1233, 1805])).
% 1.52/1.72 tff(1808,plain,
% 1.52/1.72 (~c2_1(a539)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[1239, 1805])).
% 1.52/1.72 tff(1809,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a570) | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a570) | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1810,plain,
% 1.52/1.72 ((hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a539) | c1_1(a539) | c0_1(a539)) <=> (hskp6 | c0_1(a570) | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(1811,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a539) | c1_1(a539) | c0_1(a539))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a570) | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[1810])).
% 1.52/1.72 tff(1812,plain,
% 1.52/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a539) | c1_1(a539) | c0_1(a539))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a570) | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.52/1.72 inference(transitivity,[status(thm)],[1811, 1809])).
% 1.52/1.72 tff(1813,plain,
% 1.52/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a539) | c1_1(a539) | c0_1(a539))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1814,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a570) | c2_1(a539) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a570)) | (~c1_1(a570))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 1.52/1.73 tff(1815,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1814, 156, 1669, 365, 357, 349, 1808, 1807, 1806, 1745])).
% 1.52/1.73 tff(1816,plain,((~hskp16) | hskp6 | c3_1(a586) | c1_1(a586) | (~c1_1(a545)) | c0_1(a545) | (~c2_1(a586)) | hskp25 | c2_1(a545) | c0_1(a586) | hskp15 | hskp50 | hskp19 | hskp33 | hskp39), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1817,plain,
% 1.52/1.73 (~hskp16),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1816, 859, 86, 88, 1046, 97, 902, 1423, 111, 87, 109, 110, 98, 35, 1669])).
% 1.52/1.73 tff(1818,plain,
% 1.52/1.73 (hskp17),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[382, 1817, 1795])).
% 1.52/1.73 tff(1819,plain,
% 1.52/1.73 (~c2_1(a571)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[573, 1818])).
% 1.52/1.73 tff(1820,plain,
% 1.52/1.73 (c3_1(a571)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[623, 1818])).
% 1.52/1.73 tff(1821,plain,
% 1.52/1.73 (c0_1(a571)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[581, 1818])).
% 1.52/1.73 tff(1822,plain,
% 1.52/1.73 (c1_1(a571)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[931, 156, 88, 1821, 1820, 86, 1819, 921, 902])).
% 1.52/1.73 tff(1823,plain,
% 1.52/1.73 (hskp1),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1421, 1818, 1046, 111, 97, 35, 859, 88, 86, 902])).
% 1.52/1.73 tff(1824,plain,
% 1.52/1.73 (~c0_1(a539)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1227, 1823])).
% 1.52/1.73 tff(1825,plain,
% 1.52/1.73 (~c1_1(a539)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1233, 1823])).
% 1.52/1.73 tff(1826,plain,
% 1.52/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1827,plain,
% 1.52/1.73 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a539) | c0_1(a539) | (~c3_1(a539)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c0_1(a586) | c3_1(a586) | c2_1(a571) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1828,plain,
% 1.52/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a539) | c0_1(a539) | (~c3_1(a539)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1827])).
% 1.52/1.73 tff(1829,plain,
% 1.52/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a539) | c0_1(a539) | (~c3_1(a539)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1828, 1826])).
% 1.52/1.73 tff(1830,plain,
% 1.52/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a539) | c0_1(a539) | (~c3_1(a539)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1831,plain,
% 1.52/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c1_1(a539) | c0_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.52/1.73 tff(1832,plain,
% 1.52/1.73 (~c3_1(a539)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1831, 156, 1821, 87, 86, 1819, 1825, 1824, 609, 902, 1822])).
% 1.52/1.73 tff(1833,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1834,plain,
% 1.52/1.73 ((hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571))) <=> (hskp25 | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1835,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1834])).
% 1.52/1.73 tff(1836,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1835, 1833])).
% 1.52/1.73 tff(1837,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1838,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 1.52/1.73 tff(1839,plain,
% 1.52/1.73 (~c1_1(a589)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1838, 156, 1423, 625, 591, 1820, 1819, 55, 1822])).
% 1.52/1.73 tff(1840,plain,
% 1.52/1.73 (~c2_1(a539)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1239, 1823])).
% 1.52/1.73 tff(1841,plain,
% 1.52/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a571) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a571) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1842,plain,
% 1.52/1.73 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a539) | c1_1(a539) | c3_1(a539)) <=> (c2_1(a571) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1843,plain,
% 1.52/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a539) | c1_1(a539) | c3_1(a539))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a571) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1842])).
% 1.52/1.73 tff(1844,plain,
% 1.52/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a539) | c1_1(a539) | c3_1(a539))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a571) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1843, 1841])).
% 1.52/1.73 tff(1845,plain,
% 1.52/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a539) | c1_1(a539) | c3_1(a539))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1846,plain,
% 1.52/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a571) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.52/1.73 tff(1847,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1846, 156, 625, 591, 1820, 1819, 1840, 1825, 45, 1839, 1822, 1832])).
% 1.52/1.73 tff(1848,plain,(hskp39 | (~c2_1(a589)) | (~c3_1(a589)) | hskp25 | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a586) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545) | hskp33 | hskp18 | hskp15 | hskp50 | hskp19 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1849,plain,
% 1.52/1.73 (hskp18),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1848, 859, 591, 109, 87, 86, 902, 88, 1046, 111, 97, 35, 1423, 625, 110, 98, 1669])).
% 1.52/1.73 tff(1850,plain,
% 1.52/1.73 (hskp37),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[430, 1849, 110, 98])).
% 1.52/1.73 tff(1851,plain,
% 1.52/1.73 (~c2_1(a544)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[436, 1850])).
% 1.52/1.73 tff(1852,plain,
% 1.52/1.73 (c1_1(a544)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[444, 1850])).
% 1.52/1.73 tff(1853,plain,
% 1.52/1.73 (~c3_1(a544)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[450, 1850])).
% 1.52/1.73 tff(1854,plain,
% 1.52/1.73 (~hskp7),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[502, 1851, 109, 1852, 1853, 110, 98])).
% 1.52/1.73 tff(1855,plain,
% 1.52/1.73 (hskp40),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[524, 1854, 110, 98, 1849])).
% 1.52/1.73 tff(1856,plain,
% 1.52/1.73 (c2_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[532, 1855])).
% 1.52/1.73 tff(1857,plain,
% 1.52/1.73 (c3_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[540, 1855])).
% 1.52/1.73 tff(1858,plain,
% 1.52/1.73 (c1_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[552, 1857, 1853, 1856, 1852, 1851, 109])).
% 1.52/1.73 tff(1859,plain,
% 1.52/1.73 (hskp9),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1457, 1849, 86, 902, 88, 1046, 97, 859, 1423, 111, 109, 110, 98])).
% 1.52/1.73 tff(1860,plain,
% 1.52/1.73 (~c1_1(a554)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[639, 1859])).
% 1.52/1.73 tff(1861,plain,
% 1.52/1.73 (~c2_1(a554)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[645, 1859])).
% 1.52/1.73 tff(1862,plain,
% 1.52/1.73 (~c0_1(a554)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[651, 1859])).
% 1.52/1.73 tff(1863,plain,
% 1.52/1.73 (~c0_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[558, 1855])).
% 1.52/1.73 tff(1864,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a551) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a551) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1865,plain,
% 1.52/1.73 ((hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a554) | c1_1(a554) | c0_1(a554)) <=> (hskp6 | c0_1(a551) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1866,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a554) | c1_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a551) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1865])).
% 1.52/1.73 tff(1867,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a554) | c1_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a551) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1866, 1864])).
% 1.52/1.73 tff(1868,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a554) | c1_1(a554) | c0_1(a554))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1869,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a551) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1868, 1867])).
% 1.52/1.73 tff(1870,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1869, 156, 1669, 1857, 1863, 1862, 1861, 1860, 1745, 1858])).
% 1.52/1.73 tff(1871,plain,(hskp39 | hskp6 | hskp15 | hskp50 | hskp19 | c3_1(a586) | (~c2_1(a586)) | c1_1(a586) | (~c1_1(a545)) | c0_1(a545) | hskp25 | c2_1(a545) | (~c3_1(a589)) | c0_1(a586) | hskp33 | (~c2_1(a589))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1872,plain,
% 1.52/1.73 (hskp39),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1871, 1423, 109, 110, 98, 86, 902, 88, 1046, 97, 1669, 111, 1759, 87, 35, 1794])).
% 1.52/1.73 tff(1873,assumption,(hskp39), introduced(assumption)).
% 1.52/1.73 tff(1874,plain,
% 1.52/1.73 (c1_1(a549)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[303, 1873])).
% 1.52/1.73 tff(1875,plain,
% 1.52/1.73 (c2_1(a549)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[311, 1873])).
% 1.52/1.73 tff(1876,plain,
% 1.52/1.73 (c3_1(a549)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[319, 1873])).
% 1.52/1.73 tff(1877,plain,
% 1.52/1.73 (~hskp41),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1506, 1876, 1423, 1875, 1874, 88, 86, 902])).
% 1.52/1.73 tff(1878,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a571) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a571) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1879,plain,
% 1.52/1.73 ((hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571))) <=> (hskp25 | c2_1(a571) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1880,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a571) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a571)) | (~c1_1(a571))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1879])).
% 1.52/1.73 tff(1881,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a571) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1880, 1878])).
% 1.52/1.73 tff(1882,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1883,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a571) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a571)) | (~c1_1(a571))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 1.52/1.73 tff(1884,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1883, 156, 1423, 1498, 1497, 1496, 924, 923, 55, 932])).
% 1.52/1.73 tff(1885,plain,((~hskp17) | hskp25 | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1886,plain,
% 1.52/1.73 (~hskp17),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1885, 1876, 1423, 1875, 1874, 88, 86, 902])).
% 1.52/1.73 tff(1887,plain,
% 1.52/1.73 (hskp16),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[382, 1886, 1795])).
% 1.52/1.73 tff(1888,plain,
% 1.52/1.73 (~c0_1(a570)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[348, 1887])).
% 1.52/1.73 tff(1889,plain,
% 1.52/1.73 (c1_1(a570)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[356, 1887])).
% 1.52/1.73 tff(1890,plain,
% 1.52/1.73 (c3_1(a570)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[364, 1887])).
% 1.52/1.73 tff(1891,plain,
% 1.52/1.73 (~hskp9),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1803, 1890, 1669, 1889, 1888])).
% 1.52/1.73 tff(1892,plain,
% 1.52/1.73 (~c1_1(a589)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[598, 1891, 1877])).
% 1.52/1.73 tff(1893,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1894,plain,
% 1.52/1.73 ((hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp38 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1895,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1894])).
% 1.52/1.73 tff(1896,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1895, 1893])).
% 1.52/1.73 tff(1897,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1898,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 1.52/1.73 tff(1899,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1898, 156, 58, 1876, 1875, 1874, 625, 591, 1537, 1892])).
% 1.52/1.73 tff(1900,plain,((~hskp39) | hskp38 | (~c2_1(a589)) | (~c3_1(a589)) | c0_1(a589) | hskp6 | hskp18 | hskp25 | c1_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1901,plain,
% 1.52/1.73 (hskp18),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1900, 1872, 1794, 1759, 1758, 1669, 58, 1423, 88, 86, 902])).
% 1.52/1.73 tff(1902,plain,
% 1.52/1.73 (hskp37),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[430, 1901, 110, 98])).
% 1.52/1.73 tff(1903,plain,
% 1.52/1.73 (~c2_1(a544)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[436, 1902])).
% 1.52/1.73 tff(1904,plain,
% 1.52/1.73 (c1_1(a544)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[444, 1902])).
% 1.52/1.73 tff(1905,plain,
% 1.52/1.73 (~c3_1(a544)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[450, 1902])).
% 1.52/1.73 tff(1906,plain,
% 1.52/1.73 (~hskp7),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[502, 1903, 109, 1904, 1905, 110, 98])).
% 1.52/1.73 tff(1907,plain,
% 1.52/1.73 (hskp40),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[524, 1906, 110, 98, 1901])).
% 1.52/1.73 tff(1908,plain,
% 1.52/1.73 (c2_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[532, 1907])).
% 1.52/1.73 tff(1909,plain,
% 1.52/1.73 (c3_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[540, 1907])).
% 1.52/1.73 tff(1910,plain,
% 1.52/1.73 (c1_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[552, 1909, 1905, 1908, 1904, 1903, 109])).
% 1.52/1.73 tff(1911,plain,
% 1.52/1.73 (~c0_1(a551)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[558, 1907])).
% 1.52/1.73 tff(1912,plain,
% 1.52/1.73 (c1_1(a549)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[303, 1872])).
% 1.52/1.73 tff(1913,plain,
% 1.52/1.73 (c2_1(a549)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[311, 1872])).
% 1.52/1.73 tff(1914,plain,
% 1.52/1.73 (c3_1(a549)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[319, 1872])).
% 1.52/1.73 tff(1915,plain,
% 1.52/1.73 (~hskp41),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1506, 1914, 1423, 1913, 1912, 88, 86, 902])).
% 1.52/1.73 tff(1916,plain,
% 1.52/1.73 (hskp9),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[565, 156, 1915, 1909, 1911, 342, 1910])).
% 1.52/1.73 tff(1917,plain,
% 1.52/1.73 (~c1_1(a554)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[639, 1916])).
% 1.52/1.73 tff(1918,plain,
% 1.52/1.73 (~c2_1(a554)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[645, 1916])).
% 1.52/1.73 tff(1919,plain,
% 1.52/1.73 (~c0_1(a554)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[651, 1916])).
% 1.52/1.73 tff(1920,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1869, 156, 1669, 1909, 1911, 1919, 1918, 1917, 1745, 1910])).
% 1.52/1.73 tff(1921,plain,(hskp25 | hskp6 | hskp15 | hskp50 | hskp19 | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | hskp38 | (~c1_1(a545)) | c0_1(a545) | c2_1(a545) | c0_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1922,plain,
% 1.52/1.73 (hskp25),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1921, 1793, 1669, 110, 98, 88, 86, 1776, 58, 1046, 97, 111, 87, 35])).
% 1.52/1.73 tff(1923,plain,
% 1.52/1.73 (~c1_1(a582)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1190, 1922])).
% 1.52/1.73 tff(1924,plain,
% 1.52/1.73 (~c2_1(a582)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1196, 1922])).
% 1.52/1.73 tff(1925,plain,
% 1.52/1.73 (~c3_1(a582)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1202, 1922])).
% 1.52/1.73 tff(1926,plain,
% 1.52/1.73 (~c3_1(a545)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1209, 156, 58, 1925, 1924, 1923, 111, 97, 663])).
% 1.52/1.73 tff(1927,plain,
% 1.52/1.73 (~c0_1(a582)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1288, 156, 110, 98, 1924, 1923, 34])).
% 1.52/1.73 tff(1928,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1929,plain,
% 1.52/1.73 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a582) | c1_1(a582) | c0_1(a582)) <=> (hskp6 | c0_1(a589) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1930,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1929])).
% 1.52/1.73 tff(1931,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1930, 1928])).
% 1.52/1.73 tff(1932,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a582) | c1_1(a582) | c0_1(a582))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1933,plain,
% 1.52/1.73 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.52/1.73 tff(1934,plain,
% 1.52/1.73 (c0_1(a582) | (~c1_1(a589))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1933, 156, 1669, 1759, 1758, 1924, 1923, 1745])).
% 1.52/1.73 tff(1935,plain,
% 1.52/1.73 (~c1_1(a589)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1934, 1927])).
% 1.52/1.73 tff(1936,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1562, 156, 1793, 1794, 1759, 1046, 111, 483, 1935, 1926])).
% 1.52/1.73 tff(1937,plain,(hskp19 | (~c1_1(a545)) | c2_1(a545) | hskp6 | hskp50 | hskp38 | c0_1(a545) | c1_1(a586) | c3_1(a586) | c0_1(a586) | hskp33 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1938,plain,
% 1.52/1.73 (c0_1(a586)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1937, 98, 111, 1669, 1046, 58, 97, 1756, 86, 88, 35, 1661])).
% 1.52/1.73 tff(1939,plain,
% 1.52/1.73 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | c2_1(a586))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | c2_1(a586))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1940,plain,
% 1.52/1.73 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a586) | c1_1(a586) | (~c0_1(a586))) <=> (hskp50 | hskp19 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | c2_1(a586))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1941,plain,
% 1.52/1.73 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a586) | c1_1(a586) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | c2_1(a586)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1940])).
% 1.52/1.73 tff(1942,plain,
% 1.52/1.73 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a586) | c1_1(a586) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | c2_1(a586))),
% 1.52/1.73 inference(transitivity,[status(thm)],[1941, 1939])).
% 1.52/1.73 tff(1943,plain,
% 1.52/1.73 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a586) | c1_1(a586) | (~c0_1(a586)))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(1944,plain,
% 1.52/1.73 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | c2_1(a586)),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 1.52/1.73 tff(1945,plain,
% 1.52/1.73 (hskp19 | (~c0_1(a586)) | c2_1(a586)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1944, 156, 1756, 88, 34])).
% 1.52/1.73 tff(1946,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1945, 1938, 98, 653])).
% 1.52/1.73 tff(1947,plain,(hskp19 | c2_1(a586) | c1_1(a586) | c2_1(a545) | hskp6 | (~c1_1(a545)) | hskp38 | c0_1(a545) | c3_1(a586) | hskp33 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(1948,plain,
% 1.52/1.73 (hskp19),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1947, 653, 88, 1644, 1669, 1645, 58, 1667, 86, 35, 1661])).
% 1.52/1.73 tff(1949,plain,
% 1.52/1.73 (~c1_1(a573)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1675, 1948])).
% 1.52/1.73 tff(1950,plain,
% 1.52/1.73 (~c0_1(a573)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1691, 1948])).
% 1.52/1.73 tff(1951,plain,
% 1.52/1.73 (~c2_1(a573)),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1704, 1948])).
% 1.52/1.73 tff(1952,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a586))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1953,plain,
% 1.52/1.73 ((hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a586))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(1954,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a586)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[1953])).
% 1.52/1.73 tff(1955,plain,
% 1.52/1.73 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a586))),
% 1.52/1.74 inference(transitivity,[status(thm)],[1954, 1952])).
% 1.52/1.74 tff(1956,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(1957,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a586) | c3_1(a586) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a586)),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 1.52/1.74 tff(1958,plain,
% 1.52/1.74 (~c3_1(a573)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1957, 156, 58, 88, 86, 1951, 1950, 663, 653])).
% 1.52/1.74 tff(1959,plain,
% 1.52/1.74 (hskp28),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1711, 156, 1951, 1950, 1949, 122])).
% 1.52/1.74 tff(1960,plain,
% 1.52/1.74 (c2_1(a589)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[171, 1959])).
% 1.52/1.74 tff(1961,plain,
% 1.52/1.74 (c3_1(a589)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[185, 1959])).
% 1.52/1.74 tff(1962,plain,
% 1.52/1.74 (~c0_1(a589)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[177, 1959])).
% 1.52/1.74 tff(1963,plain,
% 1.52/1.74 (c1_1(a589)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1734, 1962, 1622, 1951, 1961, 1960, 1958, 1949, 1661])).
% 1.52/1.74 tff(1964,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1751, 156, 1669, 1961, 1962, 1951, 1950, 1949, 1745, 1963])).
% 1.52/1.74 tff(1965,plain,(c2_1(a586) | hskp6 | (~hskp4) | hskp26 | hskp38 | c1_1(a586) | c3_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(1966,plain,
% 1.52/1.74 (c2_1(a586)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1965, 88, 1622, 1661, 58, 1669, 86, 35])).
% 1.52/1.74 tff(1967,plain,
% 1.52/1.74 (hskp28),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1276, 1250])).
% 1.52/1.74 tff(1968,plain,
% 1.52/1.74 (c3_1(a589)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[185, 1967])).
% 1.52/1.74 tff(1969,plain,
% 1.52/1.74 (~c0_1(a589)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[177, 1967])).
% 1.52/1.74 tff(1970,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1792, 1969, 1968, 1661, 1046, 1250, 97, 1669])).
% 1.52/1.74 tff(1971,plain,((~hskp15) | hskp26 | (~c1_1(a545)) | c0_1(a545) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(1972,plain,
% 1.52/1.74 (~hskp15),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1971, 1661, 1046, 97, 1669])).
% 1.52/1.74 tff(1973,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c1_1(a586) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a586) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(1974,plain,
% 1.52/1.74 ((hskp37 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a586) | c3_1(a586) | (~c0_1(a586))) <=> (hskp37 | c1_1(a586) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(1975,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a586) | c3_1(a586) | (~c0_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c1_1(a586) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[1974])).
% 1.52/1.74 tff(1976,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a586) | c3_1(a586) | (~c0_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a586) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[1975, 1973])).
% 1.52/1.74 tff(1977,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a586) | c3_1(a586) | (~c0_1(a586)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(1978,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a586) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 1.52/1.74 tff(1979,plain,
% 1.52/1.74 (hskp37 | (~c0_1(a586)) | (~c2_1(a586))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1978, 156, 88, 86, 415])).
% 1.52/1.74 tff(1980,plain,
% 1.52/1.74 (hskp37),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1979, 1938, 902])).
% 1.52/1.74 tff(1981,plain,
% 1.52/1.74 (~c2_1(a544)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[436, 1980])).
% 1.52/1.74 tff(1982,plain,
% 1.52/1.74 (c1_1(a544)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[444, 1980])).
% 1.52/1.74 tff(1983,plain,
% 1.52/1.74 (~c3_1(a544)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[450, 1980])).
% 1.52/1.74 tff(1984,plain,
% 1.52/1.74 (~hskp7),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[502, 1981, 1972, 1982, 1983, 1756, 98])).
% 1.52/1.74 tff(1985,plain,
% 1.52/1.74 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(1986,plain,
% 1.52/1.74 ((hskp40 | hskp7 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586))) <=> (hskp40 | hskp7 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(1987,plain,
% 1.52/1.74 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[1986])).
% 1.52/1.74 tff(1988,plain,
% 1.52/1.74 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[1987, 1985])).
% 1.52/1.74 tff(1989,plain,
% 1.52/1.74 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(1990,plain,
% 1.52/1.74 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a586) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.52/1.74 tff(1991,plain,
% 1.52/1.74 (hskp40 | hskp7 | (~c0_1(a586)) | (~c2_1(a586))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1990, 156, 88, 513])).
% 1.52/1.74 tff(1992,plain,
% 1.52/1.74 (hskp40),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1991, 1984, 1938, 902])).
% 1.52/1.74 tff(1993,plain,
% 1.52/1.74 (c2_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[532, 1992])).
% 1.52/1.74 tff(1994,plain,
% 1.52/1.74 (c3_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[540, 1992])).
% 1.52/1.74 tff(1995,plain,
% 1.52/1.74 (c1_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[552, 1994, 1983, 1993, 1982, 1981, 1972])).
% 1.52/1.74 tff(1996,assumption,(c0_1(a586)), introduced(assumption)).
% 1.52/1.74 tff(1997,plain,
% 1.52/1.74 (hskp19 | (~c0_1(a586)) | c2_1(a586)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1944, 156, 110, 88, 34])).
% 1.52/1.74 tff(1998,plain,
% 1.52/1.74 (c2_1(a586)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1997, 1996, 98])).
% 1.52/1.74 tff(1999,plain,
% 1.52/1.74 (hskp37),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1979, 1998, 1996])).
% 1.52/1.74 tff(2000,plain,
% 1.52/1.74 (~c2_1(a544)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[436, 1999])).
% 1.52/1.74 tff(2001,plain,
% 1.52/1.74 (c1_1(a544)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[444, 1999])).
% 1.52/1.74 tff(2002,plain,
% 1.52/1.74 (~c3_1(a544)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[450, 1999])).
% 1.52/1.74 tff(2003,plain,
% 1.52/1.74 (~hskp7),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[502, 109, 2000, 2001, 2002, 110, 98])).
% 1.52/1.74 tff(2004,plain,
% 1.52/1.74 (hskp40),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1991, 2003, 1996, 1998])).
% 1.52/1.74 tff(2005,plain,
% 1.52/1.74 (c2_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[532, 2004])).
% 1.52/1.74 tff(2006,plain,
% 1.52/1.74 (c3_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[540, 2004])).
% 1.52/1.74 tff(2007,plain,
% 1.52/1.74 (c1_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[552, 2006, 2002, 2005, 2001, 2000, 109])).
% 1.52/1.74 tff(2008,assumption,(c1_1(a551)), introduced(assumption)).
% 1.52/1.74 tff(2009,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2010,plain,
% 1.52/1.74 ((hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555))) <=> (hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2011,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c3_1(a555)) | (~c1_1(a555))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[2010])).
% 1.52/1.74 tff(2012,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[2011, 2009])).
% 1.52/1.74 tff(2013,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(2014,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a555) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c3_1(a555)) | (~c1_1(a555))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 1.52/1.74 tff(2015,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2014, 156, 1423, 257, 544, 543, 233, 55, 2008, 1495])).
% 1.52/1.74 tff(2016,plain,((~hskp41) | hskp25 | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(2017,plain,
% 1.52/1.74 (~hskp41),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2016, 2006, 1423, 2005, 2007, 88, 86, 1998])).
% 1.52/1.74 tff(2018,plain,
% 1.52/1.74 (~c0_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[558, 2004])).
% 1.52/1.74 tff(2019,plain,
% 1.52/1.74 (hskp41 | hskp9),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[565, 156, 2006, 2018, 342, 2007])).
% 1.52/1.74 tff(2020,plain,
% 1.52/1.74 (hskp9),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2019, 2017])).
% 1.52/1.74 tff(2021,plain,
% 1.52/1.74 (~c1_1(a554)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[639, 2020])).
% 1.52/1.74 tff(2022,plain,
% 1.52/1.74 (~c2_1(a554)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[645, 2020])).
% 1.52/1.74 tff(2023,plain,
% 1.52/1.74 (~c0_1(a554)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[651, 2020])).
% 1.52/1.74 tff(2024,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1869, 156, 1669, 2006, 2018, 2023, 2022, 2021, 1745, 2007])).
% 1.52/1.74 tff(2025,plain,(hskp15 | hskp6 | hskp25 | c1_1(a586) | c3_1(a586) | (~c0_1(a586)) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(2026,plain,
% 1.52/1.74 (hskp25),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2025, 1938, 1972, 88, 86, 1669, 1756, 98])).
% 1.52/1.74 tff(2027,plain,
% 1.52/1.74 (~c1_1(a582)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1190, 2026])).
% 1.52/1.74 tff(2028,plain,
% 1.52/1.74 (~c2_1(a582)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1196, 2026])).
% 1.52/1.74 tff(2029,plain,
% 1.52/1.74 (~c0_1(a551)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[558, 1992])).
% 1.52/1.74 tff(2030,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a551) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a551) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2031,plain,
% 1.52/1.74 ((hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a582) | c1_1(a582) | c0_1(a582)) <=> (hskp6 | c0_1(a551) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2032,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a551) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[2031])).
% 1.52/1.74 tff(2033,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a551) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[2032, 2030])).
% 1.52/1.74 tff(2034,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c1_1(a551)) | c2_1(a582) | c1_1(a582) | c0_1(a582))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(2035,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a551) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 1.52/1.74 tff(2036,plain,
% 1.52/1.74 (c0_1(a582)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2035, 156, 1669, 1994, 2029, 2028, 2027, 1745, 1995])).
% 1.52/1.74 tff(2037,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1288, 156, 1756, 98, 2028, 2027, 34, 2036])).
% 1.52/1.74 tff(2038,plain,(hskp19 | hskp6 | (~c2_1(a586)) | c1_1(a586) | c3_1(a586) | c2_1(a545) | (~c1_1(a545)) | hskp38 | c0_1(a545) | hskp33 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(2039,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2038, 1966, 88, 1669, 1754, 86, 1644, 1645, 58, 1667, 35, 1661])).
% 1.52/1.74 tff(2040,plain,(c1_1(a586) | hskp6 | c3_1(a586) | hskp38 | hskp33 | hskp26 | (~hskp4)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(2041,plain,
% 1.52/1.74 (hskp6),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2040, 1660, 88, 58, 35, 86, 1614])).
% 1.52/1.74 tff(2042,plain,
% 1.52/1.74 (~c2_1(a548)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[217, 2041])).
% 1.52/1.74 tff(2043,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1562, 156, 109, 625, 591, 1046, 111, 483, 1716, 765])).
% 1.52/1.74 tff(2044,plain,(c1_1(a589) | hskp15 | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a545)) | c2_1(a545) | c3_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(2045,plain,
% 1.52/1.74 (c1_1(a589)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2044, 1549, 109, 1548, 1035, 111, 765])).
% 1.52/1.74 tff(2046,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2047,plain,
% 1.52/1.74 ((hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586))) <=> (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2048,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[2047])).
% 1.52/1.74 tff(2049,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[2048, 2046])).
% 1.52/1.74 tff(2050,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c2_1(a586)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(2051,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 1.52/1.74 tff(2052,plain,
% 1.52/1.74 (hskp46 | (~c1_1(a589))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2051, 156, 1549, 1548, 87, 86, 858, 1157])).
% 1.52/1.74 tff(2053,plain,
% 1.52/1.74 (hskp46),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2052, 2045])).
% 1.52/1.74 tff(2054,plain,
% 1.52/1.74 (~c0_1(a562)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[64, 2053])).
% 1.52/1.74 tff(2055,plain,
% 1.52/1.74 (~c3_1(a562)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[270, 2053])).
% 1.52/1.74 tff(2056,plain,
% 1.52/1.74 (c3_1(a548)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[225, 2041])).
% 1.52/1.74 tff(2057,plain,
% 1.52/1.74 (c1_1(a562)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[288, 2053])).
% 1.52/1.74 tff(2058,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a562)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2059,plain,
% 1.52/1.74 ((hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a562)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2060,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a562))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[2059])).
% 1.52/1.74 tff(2061,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a562)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[2060, 2058])).
% 1.52/1.74 tff(2062,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(2063,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a562))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 1.52/1.74 tff(2064,plain,
% 1.52/1.74 (~c1_1(a548)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2063, 156, 859, 2057, 2056, 2055, 2054, 2042, 281])).
% 1.52/1.74 tff(2065,plain,
% 1.52/1.74 (~c0_1(a548)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[211, 2041])).
% 1.52/1.74 tff(2066,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a562)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2067,plain,
% 1.52/1.74 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548))) <=> (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a562)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2068,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a562))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[2067])).
% 1.52/1.74 tff(2069,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a562)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[2068, 2066])).
% 1.52/1.74 tff(2070,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(2071,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a562))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[2070, 2069])).
% 1.52/1.74 tff(2072,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2071, 156, 1660, 2057, 2056, 2055, 2054, 2065, 1686, 2064])).
% 1.52/1.74 tff(2073,plain,(hskp38 | hskp39 | c1_1(a586) | hskp33 | c3_1(a586) | c0_1(a545) | c0_1(a586) | hskp15 | c2_1(a545) | c3_1(a545) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(2074,plain,
% 1.52/1.74 (hskp38),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2073, 765, 88, 35, 86, 97, 87, 109, 111, 859, 110, 98])).
% 1.52/1.74 tff(2075,plain,
% 1.52/1.74 (c0_1(a547)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[677, 2074])).
% 1.52/1.74 tff(2076,plain,
% 1.52/1.74 (c1_1(a547)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[685, 2074])).
% 1.52/1.74 tff(2077,plain,
% 1.52/1.74 (c2_1(a547)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[693, 2074])).
% 1.52/1.74 tff(2078,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2079,plain,
% 1.52/1.74 ((hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2080,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[2079])).
% 1.52/1.74 tff(2081,plain,
% 1.52/1.74 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.74 inference(transitivity,[status(thm)],[2080, 2078])).
% 1.52/1.74 tff(2082,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(2083,plain,
% 1.52/1.74 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 1.52/1.74 tff(2084,plain,
% 1.52/1.74 (hskp34),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[2083, 156, 2077, 2076, 2075, 1035, 97, 75, 765])).
% 1.52/1.74 tff(2085,plain,
% 1.52/1.74 (~c1_1(a537)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1124, 2084])).
% 1.52/1.74 tff(2086,plain,
% 1.52/1.74 (c0_1(a537)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1147, 2084])).
% 1.52/1.74 tff(2087,plain,
% 1.52/1.74 (c2_1(a537)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1154, 156, 110, 98, 2086, 2085, 34])).
% 1.52/1.74 tff(2088,plain,
% 1.52/1.74 (c3_1(a537)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1132, 2084])).
% 1.52/1.75 tff(2089,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2090,plain,
% 1.52/1.75 ((hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp15 | c1_1(a537) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2091,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[2090])).
% 1.52/1.75 tff(2092,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.75 inference(transitivity,[status(thm)],[2091, 2089])).
% 1.52/1.75 tff(2093,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(2094,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.52/1.75 tff(2095,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2094, 156, 109, 2088, 1035, 2085, 111, 483, 765, 2087])).
% 1.52/1.75 tff(2096,plain,(c3_1(a545) | hskp15 | c2_1(a545) | hskp50 | hskp19 | c0_1(a545) | c1_1(a586) | hskp33 | c3_1(a586) | c0_1(a586) | hskp39), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(2097,plain,
% 1.52/1.75 (c3_1(a545)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2096, 859, 111, 110, 98, 97, 88, 35, 86, 87, 109])).
% 1.52/1.75 tff(2098,plain,
% 1.52/1.75 (hskp38),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1211, 2097, 111, 97, 1035])).
% 1.52/1.75 tff(2099,plain,
% 1.52/1.75 (c0_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[677, 2098])).
% 1.52/1.75 tff(2100,plain,
% 1.52/1.75 (c2_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[693, 2098])).
% 1.52/1.75 tff(2101,plain,
% 1.52/1.75 (c1_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[685, 2098])).
% 1.52/1.75 tff(2102,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1586, 2101, 2100, 859, 2097, 2099, 1035, 111, 97])).
% 1.52/1.75 tff(2103,plain,(hskp39 | c2_1(a545) | c0_1(a545) | hskp50 | hskp19 | c1_1(a586) | hskp33 | c3_1(a586) | c0_1(a586) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(2104,plain,
% 1.52/1.75 (hskp39),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2103, 111, 97, 110, 98, 88, 35, 86, 87, 109])).
% 1.52/1.75 tff(2105,plain,
% 1.52/1.75 (c1_1(a549)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[303, 2104])).
% 1.52/1.75 tff(2106,plain,
% 1.52/1.75 (c2_1(a549)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[311, 2104])).
% 1.52/1.75 tff(2107,plain,
% 1.52/1.75 (c3_1(a549)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[319, 2104])).
% 1.52/1.75 tff(2108,plain,
% 1.52/1.75 (hskp46),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1027, 156, 2107, 2106, 2105, 87, 86, 858, 1157])).
% 1.52/1.75 tff(2109,plain,
% 1.52/1.75 (~c0_1(a562)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[64, 2108])).
% 1.52/1.75 tff(2110,plain,
% 1.52/1.75 (~c3_1(a562)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[270, 2108])).
% 1.52/1.75 tff(2111,plain,
% 1.52/1.75 (~hskp45),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[833, 765, 35, 111, 97, 98])).
% 1.52/1.75 tff(2112,plain,
% 1.52/1.75 (hskp25),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1506, 227, 902, 1497, 1496, 88, 86, 1498])).
% 1.52/1.75 tff(2113,plain,
% 1.52/1.75 (~c1_1(a582)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1190, 2112])).
% 1.52/1.75 tff(2114,plain,
% 1.52/1.75 (~c2_1(a582)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1196, 2112])).
% 1.52/1.75 tff(2115,plain,
% 1.52/1.75 (~c0_1(a582)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1288, 156, 110, 98, 2114, 2113, 34])).
% 1.52/1.75 tff(2116,plain,
% 1.52/1.75 (~c3_1(a582)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1202, 2112])).
% 1.52/1.75 tff(2117,assumption,(~hskp45), introduced(assumption)).
% 1.52/1.75 tff(2118,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a555) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a555)) | (~c0_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a555)) | (~c0_1(a555)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2119,plain,
% 1.52/1.75 ((hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a582) | c3_1(a582) | c0_1(a582)) <=> (hskp45 | c2_1(a555) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a555)) | (~c0_1(a555)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2120,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a582) | c3_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a555) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a555)) | (~c0_1(a555))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[2119])).
% 1.52/1.75 tff(2121,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a582) | c3_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a555)) | (~c0_1(a555)))),
% 1.52/1.75 inference(transitivity,[status(thm)],[2120, 2118])).
% 1.52/1.75 tff(2122,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a582) | c3_1(a582) | c0_1(a582))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(2123,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a555)) | (~c0_1(a555))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.52/1.75 tff(2124,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2123, 156, 2117, 241, 233, 2116, 2114, 757, 2115, 1495])).
% 1.52/1.75 tff(2125,plain,((~hskp41) | hskp45 | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | hskp50 | hskp19 | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(2126,plain,
% 1.52/1.75 (~hskp41),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2125, 2111, 88, 86, 1157, 110, 98, 2106, 2105, 2107])).
% 1.52/1.75 tff(2127,plain,
% 1.52/1.75 (c1_1(a562)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[288, 2108])).
% 1.52/1.75 tff(2128,plain,
% 1.52/1.75 (hskp4),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[326, 156, 2127, 2107, 2106, 2105, 2110, 2109, 22])).
% 1.52/1.75 tff(2129,plain,
% 1.52/1.75 (~hskp26),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1659, 58, 2128, 35, 97])).
% 1.52/1.75 tff(2130,plain,
% 1.52/1.75 (hskp6),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2040, 2129, 88, 58, 35, 86, 2128])).
% 1.52/1.75 tff(2131,plain,
% 1.52/1.75 (~c0_1(a548)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[211, 2130])).
% 1.52/1.75 tff(2132,plain,
% 1.52/1.75 (~c2_1(a548)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[217, 2130])).
% 1.52/1.75 tff(2133,plain,
% 1.52/1.75 (c3_1(a548)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[225, 2130])).
% 1.52/1.75 tff(2134,plain,
% 1.52/1.75 (~c0_1(a589)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[177, 1547])).
% 1.52/1.75 tff(2135,plain,
% 1.52/1.75 (hskp9),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[633, 1548, 331, 88, 86, 2134, 87, 110, 98, 1549, 109])).
% 1.52/1.75 tff(2136,plain,
% 1.52/1.75 (~c0_1(a554)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[651, 2135])).
% 1.52/1.75 tff(2137,plain,
% 1.52/1.75 (~c2_1(a554)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[645, 2135])).
% 1.52/1.75 tff(2138,plain,
% 1.52/1.75 (~c1_1(a554)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[639, 2135])).
% 1.52/1.75 tff(2139,plain,
% 1.52/1.75 (c1_1(a554) | c3_1(a554)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[865, 156, 58, 249, 696, 24, 56, 663])).
% 1.52/1.75 tff(2140,plain,
% 1.52/1.75 (c3_1(a554)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2139, 695])).
% 1.52/1.75 tff(2141,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a562)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2142,plain,
% 1.52/1.75 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554))) <=> (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a562)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2143,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a562))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[2142])).
% 1.52/1.75 tff(2144,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a562)))),
% 1.52/1.75 inference(transitivity,[status(thm)],[2143, 2141])).
% 1.52/1.75 tff(2145,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(2146,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a562))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[2145, 2144])).
% 1.52/1.75 tff(2147,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2146, 156, 1661, 973, 972, 971, 697, 695, 1686, 2140])).
% 1.52/1.75 tff(2148,plain,(c1_1(a554) | hskp26 | (~c1_1(a562)) | c3_1(a562) | c0_1(a562) | c0_1(a554) | hskp38 | (~c3_1(a548)) | c2_1(a554) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(2149,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2148, 2138, 2137, 2127, 2110, 2109, 2136, 58, 2133, 2129, 2132, 2131])).
% 1.52/1.75 tff(2150,plain,(hskp38 | hskp41 | c1_1(a586) | c3_1(a586) | c0_1(a586) | hskp50 | hskp19 | hskp15 | hskp33 | c0_1(a545) | c2_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(2151,plain,
% 1.52/1.75 (hskp38),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2150, 2126, 88, 86, 87, 110, 98, 109, 35, 97, 111])).
% 1.52/1.75 tff(2152,plain,
% 1.52/1.75 (c0_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[677, 2151])).
% 1.52/1.75 tff(2153,plain,
% 1.52/1.75 (c1_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[685, 2151])).
% 1.52/1.75 tff(2154,plain,
% 1.52/1.75 (c2_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[693, 2151])).
% 1.52/1.75 tff(2155,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c1_1(a562)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c1_1(a562)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2156,plain,
% 1.52/1.75 ((hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c1_1(a562)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(2157,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c1_1(a562)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[2156])).
% 1.52/1.75 tff(2158,plain,
% 1.52/1.75 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c1_1(a562)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.52/1.75 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.52/1.75 tff(2159,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(2160,plain,
% 1.52/1.75 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c1_1(a562)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.52/1.75 tff(2161,plain,
% 1.52/1.75 (hskp34),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2160, 156, 2127, 2154, 2153, 2152, 2110, 2109, 75])).
% 1.52/1.75 tff(2162,plain,
% 1.52/1.75 (~c1_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1124, 2161])).
% 1.52/1.75 tff(2163,plain,
% 1.52/1.75 (c0_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1147, 2161])).
% 1.52/1.75 tff(2164,plain,
% 1.52/1.75 (c2_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1154, 156, 110, 98, 2163, 2162, 34])).
% 1.52/1.75 tff(2165,plain,
% 1.52/1.75 (c3_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1132, 2161])).
% 1.52/1.75 tff(2166,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2094, 156, 109, 2165, 1035, 2162, 111, 483, 765, 2164])).
% 1.52/1.75 tff(2167,plain,(c3_1(a545) | hskp15 | c2_1(a545) | hskp50 | hskp19 | c1_1(a586) | c3_1(a586) | c0_1(a586) | hskp33 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(2168,plain,
% 1.52/1.75 (c3_1(a545)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2167, 111, 109, 110, 98, 88, 86, 87, 35, 97])).
% 1.52/1.75 tff(2169,plain,
% 1.52/1.75 (hskp38),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1211, 2168, 111, 97, 1035])).
% 1.52/1.75 tff(2170,plain,
% 1.52/1.75 (c0_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[677, 2169])).
% 1.52/1.75 tff(2171,plain,
% 1.52/1.75 (c1_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[685, 2169])).
% 1.52/1.75 tff(2172,plain,
% 1.52/1.75 (c2_1(a547)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[693, 2169])).
% 1.52/1.75 tff(2173,plain,
% 1.52/1.75 (hskp34),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2160, 156, 2127, 2172, 2171, 2170, 2110, 2109, 75])).
% 1.52/1.75 tff(2174,plain,
% 1.52/1.75 (~c1_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1124, 2173])).
% 1.52/1.75 tff(2175,plain,
% 1.52/1.75 (c0_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1147, 2173])).
% 1.52/1.75 tff(2176,plain,
% 1.52/1.75 (c2_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1154, 156, 110, 98, 2175, 2174, 34])).
% 1.52/1.75 tff(2177,plain,
% 1.52/1.75 (hskp25 | (~c3_1(a545))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1184, 156, 2107, 2106, 2105, 1035, 111, 55])).
% 1.52/1.75 tff(2178,plain,
% 1.52/1.75 (hskp25),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2177, 2168])).
% 1.52/1.75 tff(2179,plain,
% 1.52/1.75 (~c1_1(a582)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1190, 2178])).
% 1.52/1.75 tff(2180,plain,
% 1.52/1.75 (~c2_1(a582)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1196, 2178])).
% 1.52/1.75 tff(2181,plain,
% 1.52/1.75 (~c3_1(a582)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1202, 2178])).
% 1.52/1.75 tff(2182,plain,
% 1.52/1.75 (hskp42),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1574, 156, 2172, 2171, 2170, 1035, 111, 1364, 2168])).
% 1.52/1.75 tff(2183,plain,
% 1.52/1.75 (~c2_1(a556)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1385, 2182])).
% 1.52/1.75 tff(2184,plain,
% 1.52/1.75 (c3_1(a537)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1132, 2173])).
% 1.52/1.75 tff(2185,plain,
% 1.52/1.75 (c3_1(a556)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1403, 2182])).
% 1.52/1.75 tff(2186,plain,
% 1.52/1.75 (c1_1(a556)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1411, 2182])).
% 1.52/1.75 tff(2187,plain,
% 1.52/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.60/1.75 inference(rewrite,[status(thm)],[])).
% 1.60/1.75 tff(2188,plain,
% 1.60/1.75 (((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (c2_1(a556) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.60/1.75 inference(rewrite,[status(thm)],[])).
% 1.60/1.75 tff(2189,plain,
% 1.60/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 1.60/1.75 inference(monotonicity,[status(thm)],[2188])).
% 1.60/1.75 tff(2190,plain,
% 1.60/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.60/1.75 inference(transitivity,[status(thm)],[2189, 2187])).
% 1.60/1.75 tff(2191,plain,
% 1.60/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.60/1.75 inference(quant_inst,[status(thm)],[])).
% 1.60/1.75 tff(2192,plain,
% 1.60/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))),
% 1.60/1.75 inference(modus_ponens,[status(thm)],[2191, 2190])).
% 1.60/1.75 tff(2193,plain,
% 1.60/1.75 ($false),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[2192, 156, 2186, 2185, 2184, 2183, 2174, 2181, 2180, 2179, 45, 2176])).
% 1.60/1.75 tff(2194,plain,(c2_1(a545) | hskp50 | hskp19 | c0_1(a545) | hskp15 | c1_1(a586) | c3_1(a586) | c0_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.60/1.75 tff(2195,plain,
% 1.60/1.75 (c2_1(a545)),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[2194, 110, 98, 97, 109, 88, 86, 87, 35])).
% 1.60/1.75 tff(2196,plain,
% 1.60/1.75 (~hskp4),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[1643, 2195])).
% 1.60/1.75 tff(2197,plain,
% 1.60/1.75 (hskp6),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[205, 2196, 96])).
% 1.60/1.75 tff(2198,plain,
% 1.60/1.75 (~c0_1(a548)),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[211, 2197])).
% 1.60/1.75 tff(2199,plain,
% 1.60/1.75 (~c2_1(a548)),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[217, 2197])).
% 1.60/1.75 tff(2200,plain,
% 1.60/1.75 (c3_1(a548)),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[225, 2197])).
% 1.60/1.75 tff(2201,plain,
% 1.60/1.75 (~hskp41),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[328, 2200, 2196, 2199, 2198, 110, 98])).
% 1.60/1.75 tff(2202,plain,
% 1.60/1.75 (~hskp41),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[328, 1590, 23, 1589, 1598, 110, 98])).
% 1.60/1.75 tff(2203,plain,
% 1.60/1.75 ($false),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[669, 156, 58, 88, 249, 86, 24, 56, 663, 653])).
% 1.60/1.75 tff(2204,plain,(c2_1(a586) | hskp38 | c1_1(a586) | (~c3_1(a548)) | c3_1(a586) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.75 tff(2205,plain,
% 1.60/1.75 (c2_1(a586)),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[2204, 58, 88, 249, 86, 24, 56])).
% 1.60/1.75 tff(2206,plain,
% 1.60/1.75 (^[V: $i, U: $i] : refl((hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.60/1.75 inference(bind,[status(th)],[])).
% 1.60/1.75 tff(2207,plain,
% 1.60/1.75 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.60/1.75 inference(quant_intro,[status(thm)],[2206])).
% 1.60/1.75 tff(2208,plain,
% 1.60/1.75 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.60/1.75 inference(rewrite,[status(thm)],[])).
% 1.60/1.75 tff(2209,plain,
% 1.60/1.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | hskp46) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp46))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp46) <=> (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | hskp46) <=> (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.60/1.75 inference(bind,[status(th)],[])).
% 1.60/1.75 tff(2210,plain,
% 1.60/1.75 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | hskp46) <=> ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.60/1.75 inference(quant_intro,[status(thm)],[2209])).
% 1.60/1.75 tff(2211,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause248')).
% 1.60/1.75 tff(2212,plain,
% 1.60/1.75 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.60/1.75 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.60/1.75 tff(2213,plain,
% 1.60/1.75 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.60/1.75 inference(modus_ponens,[status(thm)],[2212, 2208])).
% 1.60/1.75 tff(2214,plain,(
% 1.60/1.75 ![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.60/1.75 inference(skolemize,[status(sab)],[2213])).
% 1.60/1.75 tff(2215,plain,
% 1.60/1.75 (![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.60/1.75 inference(modus_ponens,[status(thm)],[2214, 2207])).
% 1.60/1.75 tff(2216,plain,
% 1.60/1.75 (~c0_1(a551)),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[558, 891])).
% 1.60/1.75 tff(2217,plain,
% 1.60/1.75 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c0_1(a551) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c2_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a551) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c2_1(a551)) | (~c1_1(a551)))),
% 1.60/1.75 inference(rewrite,[status(thm)],[])).
% 1.60/1.75 tff(2218,plain,
% 1.60/1.75 ((hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a551) | (~c1_1(a551)) | (~c2_1(a551))) <=> (hskp46 | c0_1(a551) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c2_1(a551)) | (~c1_1(a551)))),
% 1.60/1.75 inference(rewrite,[status(thm)],[])).
% 1.60/1.75 tff(2219,plain,
% 1.60/1.75 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a551) | (~c1_1(a551)) | (~c2_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c0_1(a551) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c2_1(a551)) | (~c1_1(a551))))),
% 1.60/1.75 inference(monotonicity,[status(thm)],[2218])).
% 1.60/1.75 tff(2220,plain,
% 1.60/1.75 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a551) | (~c1_1(a551)) | (~c2_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a551) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c2_1(a551)) | (~c1_1(a551)))),
% 1.60/1.75 inference(transitivity,[status(thm)],[2219, 2217])).
% 1.60/1.75 tff(2221,plain,
% 1.60/1.75 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a551) | (~c1_1(a551)) | (~c2_1(a551)))),
% 1.60/1.75 inference(quant_inst,[status(thm)],[])).
% 1.60/1.75 tff(2222,plain,
% 1.60/1.75 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a551) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c2_1(a551)) | (~c1_1(a551))),
% 1.60/1.75 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.60/1.75 tff(2223,plain,
% 1.60/1.75 ($false),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[2222, 156, 946, 892, 398, 2216, 390, 2215, 405, 894])).
% 1.60/1.75 tff(2224,plain,((~hskp18) | hskp46 | hskp50 | hskp19 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.60/1.75 tff(2225,plain,
% 1.60/1.75 (~hskp18),
% 1.60/1.75 inference(unit_resolution,[status(thm)],[2224, 946, 110, 98, 109])).
% 1.60/1.75 tff(2226,plain,
% 1.60/1.75 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.60/1.75 inference(rewrite,[status(thm)],[])).
% 1.60/1.75 tff(2227,plain,
% 1.60/1.75 ((hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548))) <=> (hskp46 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.60/1.75 inference(rewrite,[status(thm)],[])).
% 1.60/1.75 tff(2228,plain,
% 1.60/1.75 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))))),
% 1.60/1.75 inference(monotonicity,[status(thm)],[2227])).
% 1.60/1.75 tff(2229,plain,
% 1.60/1.75 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.60/1.75 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.60/1.75 tff(2230,plain,
% 1.60/1.75 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))),
% 1.60/1.75 inference(quant_inst,[status(thm)],[])).
% 1.60/1.75 tff(2231,plain,
% 1.60/1.75 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.60/1.75 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.60/1.76 tff(2232,plain,
% 1.60/1.76 (hskp46 | (~c1_1(a548))),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2231, 156, 249, 24, 56, 12])).
% 1.60/1.76 tff(2233,plain,
% 1.60/1.76 (~c1_1(a548)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2232, 946])).
% 1.60/1.76 tff(2234,plain,
% 1.60/1.76 (hskp28 | c1_1(a548)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[1604, 156, 24, 56, 122])).
% 1.60/1.76 tff(2235,plain,
% 1.60/1.76 (hskp28),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2234, 2233])).
% 1.60/1.76 tff(2236,plain,
% 1.60/1.76 (c2_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[171, 2235])).
% 1.60/1.76 tff(2237,plain,
% 1.60/1.76 (~c0_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[177, 2235])).
% 1.60/1.76 tff(2238,plain,
% 1.60/1.76 (c3_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[185, 2235])).
% 1.60/1.76 tff(2239,plain,
% 1.60/1.76 (hskp9),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[633, 2238, 331, 88, 86, 2237, 87, 110, 98, 2236, 109])).
% 1.60/1.76 tff(2240,plain,
% 1.60/1.76 (~c1_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[639, 2239])).
% 1.60/1.76 tff(2241,plain,
% 1.60/1.76 (~c2_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[645, 2239])).
% 1.60/1.76 tff(2242,plain,
% 1.60/1.76 (c3_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[865, 156, 58, 249, 2241, 2240, 24, 56, 663])).
% 1.60/1.76 tff(2243,plain,
% 1.60/1.76 (~c0_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[651, 2239])).
% 1.60/1.76 tff(2244,plain,
% 1.60/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2245,plain,
% 1.60/1.76 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2246,plain,
% 1.60/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))))),
% 1.60/1.76 inference(monotonicity,[status(thm)],[2245])).
% 1.60/1.76 tff(2247,plain,
% 1.60/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.60/1.76 inference(transitivity,[status(thm)],[2246, 2244])).
% 1.60/1.76 tff(2248,plain,
% 1.60/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.60/1.76 inference(quant_inst,[status(thm)],[])).
% 1.60/1.76 tff(2249,plain,
% 1.60/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))),
% 1.60/1.76 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 1.60/1.76 tff(2250,plain,
% 1.60/1.76 ($false),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2249, 156, 925, 87, 86, 923, 697, 695, 609, 902, 868, 932])).
% 1.60/1.76 tff(2251,plain,((~hskp17) | c0_1(a586) | c3_1(a586) | c0_1(a554) | c1_1(a554) | (~c2_1(a586)) | (~c3_1(a554)) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.76 tff(2252,plain,
% 1.60/1.76 (~hskp17),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2251, 2243, 86, 87, 2240, 2205, 2242, 88])).
% 1.60/1.76 tff(2253,plain,
% 1.60/1.76 (hskp16),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[382, 2252, 2225])).
% 1.60/1.76 tff(2254,plain,
% 1.60/1.76 (~c0_1(a570)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[348, 2253])).
% 1.60/1.76 tff(2255,plain,
% 1.60/1.76 (c3_1(a570)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[364, 2253])).
% 1.60/1.76 tff(2256,plain,
% 1.60/1.76 (c1_1(a570)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[356, 2253])).
% 1.60/1.76 tff(2257,plain,
% 1.60/1.76 ($false),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[965, 2256, 2255, 946, 2254, 87, 86, 2205])).
% 1.60/1.76 tff(2258,plain,(hskp46 | c0_1(a586) | c3_1(a586) | c1_1(a586) | hskp50 | hskp19 | hskp15 | hskp38 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | hskp41), inference(lemma,lemma(discharge,[]))).
% 1.60/1.76 tff(2259,plain,
% 1.60/1.76 (hskp46),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2258, 58, 86, 88, 110, 98, 109, 87, 1590, 1589, 1598, 2202])).
% 1.60/1.76 tff(2260,plain,
% 1.60/1.76 (~c0_1(a562)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[64, 2259])).
% 1.60/1.76 tff(2261,plain,
% 1.60/1.76 (~c3_1(a562)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[270, 2259])).
% 1.60/1.76 tff(2262,plain,
% 1.60/1.76 (c1_1(a562)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[288, 2259])).
% 1.60/1.76 tff(2263,plain,
% 1.60/1.76 (hskp39 | (~c1_1(a548))),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2063, 156, 2262, 1590, 2261, 2260, 1589, 281])).
% 1.60/1.76 tff(2264,plain,
% 1.60/1.76 (~c1_1(a548)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2263, 859])).
% 1.60/1.76 tff(2265,plain,
% 1.60/1.76 (hskp28),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[1605, 2264])).
% 1.60/1.76 tff(2266,plain,
% 1.60/1.76 (c2_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[171, 2265])).
% 1.60/1.76 tff(2267,plain,
% 1.60/1.76 (~c0_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[177, 2265])).
% 1.60/1.76 tff(2268,plain,
% 1.60/1.76 (c3_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[185, 2265])).
% 1.60/1.76 tff(2269,plain,
% 1.60/1.76 (hskp9),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[633, 2268, 2202, 88, 86, 2267, 87, 110, 98, 2266, 109])).
% 1.60/1.76 tff(2270,plain,
% 1.60/1.76 (~c0_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[651, 2269])).
% 1.60/1.76 tff(2271,plain,
% 1.60/1.76 (c2_1(a586)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2204, 58, 88, 1590, 86, 1589, 1598])).
% 1.60/1.76 tff(2272,plain,
% 1.60/1.76 (~c1_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[639, 2269])).
% 1.60/1.76 tff(2273,plain,
% 1.60/1.76 (~c2_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[645, 2269])).
% 1.60/1.76 tff(2274,plain,
% 1.60/1.76 (hskp26),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2148, 2272, 2261, 2262, 2260, 2270, 58, 1590, 2273, 1589, 1598])).
% 1.60/1.76 tff(2275,plain,
% 1.60/1.76 (~c3_1(a584)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[1620, 2274])).
% 1.60/1.76 tff(2276,plain,
% 1.60/1.76 (c1_1(a584)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[1637, 2274])).
% 1.60/1.76 tff(2277,plain,
% 1.60/1.76 (c0_1(a584)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[1629, 2274])).
% 1.60/1.76 tff(2278,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a554))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a554))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2279,plain,
% 1.60/1.76 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a554) | c3_1(a554) | c0_1(a554)) <=> (hskp33 | c3_1(a584) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a554))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2280,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a554)))),
% 1.60/1.76 inference(monotonicity,[status(thm)],[2279])).
% 1.60/1.76 tff(2281,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a554))),
% 1.60/1.76 inference(transitivity,[status(thm)],[2280, 2278])).
% 1.60/1.76 tff(2282,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a554) | c3_1(a554) | c0_1(a554))),
% 1.60/1.76 inference(quant_inst,[status(thm)],[])).
% 1.60/1.76 tff(2283,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a554)),
% 1.60/1.76 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.60/1.76 tff(2284,plain,
% 1.60/1.76 (c3_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2283, 156, 35, 2277, 2276, 2275, 2270, 2273, 85])).
% 1.60/1.76 tff(2285,plain,
% 1.60/1.76 (~hskp17),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2251, 2284, 86, 87, 2272, 2271, 2270, 88])).
% 1.60/1.76 tff(2286,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c1_1(a562)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2287,plain,
% 1.60/1.76 ((hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c1_1(a562)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2288,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c1_1(a562))))),
% 1.60/1.76 inference(monotonicity,[status(thm)],[2287])).
% 1.60/1.76 tff(2289,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c1_1(a562)))),
% 1.60/1.76 inference(transitivity,[status(thm)],[2288, 2286])).
% 1.60/1.76 tff(2290,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.60/1.76 inference(quant_inst,[status(thm)],[])).
% 1.60/1.76 tff(2291,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c1_1(a562))),
% 1.60/1.76 inference(modus_ponens,[status(thm)],[2290, 2289])).
% 1.60/1.76 tff(2292,plain,
% 1.60/1.76 (~c1_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2291, 156, 23, 2262, 2266, 2268, 2261, 2260, 22])).
% 1.60/1.76 tff(2293,plain,
% 1.60/1.76 (c2_1(a570)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[981, 365, 973, 971, 357, 972, 859])).
% 1.60/1.76 tff(2294,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2295,plain,
% 1.60/1.76 ((hskp38 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp38 | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2296,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.60/1.76 inference(monotonicity,[status(thm)],[2295])).
% 1.60/1.76 tff(2297,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.60/1.76 inference(transitivity,[status(thm)],[2296, 2294])).
% 1.60/1.76 tff(2298,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.60/1.76 inference(quant_inst,[status(thm)],[])).
% 1.60/1.76 tff(2299,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 1.60/1.76 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.60/1.76 tff(2300,plain,
% 1.60/1.76 ($false),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2299, 156, 58, 625, 591, 365, 357, 1537, 1716, 2293])).
% 1.60/1.76 tff(2301,plain,((~hskp16) | hskp38 | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a562)) | c0_1(a562) | c3_1(a562) | hskp39), inference(lemma,lemma(discharge,[]))).
% 1.60/1.76 tff(2302,plain,
% 1.60/1.76 (~hskp16),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2301, 2266, 58, 2268, 2292, 2262, 2260, 2261, 859])).
% 1.60/1.76 tff(2303,plain,
% 1.60/1.76 (hskp18),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[382, 2302, 2285])).
% 1.60/1.76 tff(2304,plain,
% 1.60/1.76 (hskp37),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[430, 2303, 110, 98])).
% 1.60/1.76 tff(2305,plain,
% 1.60/1.76 (~c2_1(a544)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[436, 2304])).
% 1.60/1.76 tff(2306,plain,
% 1.60/1.76 (c1_1(a544)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[444, 2304])).
% 1.60/1.76 tff(2307,plain,
% 1.60/1.76 (~c3_1(a544)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[450, 2304])).
% 1.60/1.76 tff(2308,plain,
% 1.60/1.76 (~hskp7),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[502, 2306, 109, 98, 2307, 110, 2305])).
% 1.60/1.76 tff(2309,plain,
% 1.60/1.76 (hskp40),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[524, 2308, 110, 98, 2303])).
% 1.60/1.76 tff(2310,plain,
% 1.60/1.76 (c2_1(a551)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[532, 2309])).
% 1.60/1.76 tff(2311,plain,
% 1.60/1.76 (c3_1(a551)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[540, 2309])).
% 1.60/1.76 tff(2312,plain,
% 1.60/1.76 (c1_1(a551)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[552, 2311, 2307, 2310, 2306, 2305, 109])).
% 1.60/1.76 tff(2313,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2314,plain,
% 1.60/1.76 ((hskp38 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp38 | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2315,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.60/1.76 inference(monotonicity,[status(thm)],[2314])).
% 1.60/1.76 tff(2316,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.60/1.76 inference(transitivity,[status(thm)],[2315, 2313])).
% 1.60/1.76 tff(2317,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.60/1.76 inference(quant_inst,[status(thm)],[])).
% 1.60/1.76 tff(2318,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.60/1.76 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 1.60/1.76 tff(2319,plain,
% 1.60/1.76 ($false),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2318, 156, 58, 2311, 2310, 2266, 2268, 1537, 2292, 2312])).
% 1.60/1.76 tff(2320,plain,(hskp39 | hskp38 | hskp15 | hskp50 | hskp19 | c3_1(a586) | c0_1(a586) | c1_1(a586) | hskp4 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.60/1.76 tff(2321,plain,
% 1.60/1.76 (hskp39),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2320, 58, 109, 110, 98, 86, 87, 88, 23, 35])).
% 1.60/1.76 tff(2322,plain,
% 1.60/1.76 (c1_1(a549)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[303, 2321])).
% 1.60/1.76 tff(2323,plain,
% 1.60/1.76 (c2_1(a549)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[311, 2321])).
% 1.60/1.76 tff(2324,plain,
% 1.60/1.76 (c3_1(a549)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[319, 2321])).
% 1.60/1.76 tff(2325,plain,
% 1.60/1.76 ($false),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[326, 156, 23, 2262, 2324, 2323, 2322, 2261, 2260, 22])).
% 1.60/1.76 tff(2326,plain,(hskp38 | hskp4 | hskp15 | hskp50 | hskp19 | c3_1(a586) | c0_1(a586) | c1_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.60/1.76 tff(2327,plain,
% 1.60/1.76 (hskp38),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2326, 2196, 109, 110, 98, 86, 87, 88, 35])).
% 1.60/1.76 tff(2328,plain,
% 1.60/1.76 (c0_1(a547)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[677, 2327])).
% 1.60/1.76 tff(2329,plain,
% 1.60/1.76 (c1_1(a547)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[685, 2327])).
% 1.60/1.76 tff(2330,plain,
% 1.60/1.76 (c2_1(a547)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[693, 2327])).
% 1.60/1.76 tff(2331,plain,
% 1.60/1.76 (hskp0),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[845, 653, 733, 732, 731, 88, 86])).
% 1.60/1.76 tff(2332,plain,
% 1.60/1.76 (~c2_1(a535)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[713, 2331])).
% 1.60/1.76 tff(2333,plain,
% 1.60/1.76 (hskp28),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[1220, 653, 87])).
% 1.60/1.76 tff(2334,plain,
% 1.60/1.76 (c2_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[171, 2333])).
% 1.60/1.76 tff(2335,plain,
% 1.60/1.76 (~c0_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[177, 2333])).
% 1.60/1.76 tff(2336,plain,
% 1.60/1.76 (c3_1(a589)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[185, 2333])).
% 1.60/1.76 tff(2337,plain,
% 1.60/1.76 (hskp9),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[633, 2336, 331, 88, 86, 2335, 87, 110, 98, 2334, 109])).
% 1.60/1.76 tff(2338,plain,
% 1.60/1.76 (~c1_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[639, 2337])).
% 1.60/1.76 tff(2339,plain,
% 1.60/1.76 (~c2_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[645, 2337])).
% 1.60/1.76 tff(2340,plain,
% 1.60/1.76 (c0_1(a535)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[721, 2331])).
% 1.60/1.76 tff(2341,plain,
% 1.60/1.76 (c1_1(a535)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[729, 2331])).
% 1.60/1.76 tff(2342,plain,
% 1.60/1.76 (~c3_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[746, 156, 733, 732, 731, 2341, 2340, 2339, 2338, 2332, 707])).
% 1.60/1.76 tff(2343,plain,
% 1.60/1.76 (~c0_1(a554)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[651, 2337])).
% 1.60/1.76 tff(2344,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2345,plain,
% 1.60/1.76 ((hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a586) | c3_1(a586) | c0_1(a586)) <=> (hskp45 | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2346,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586)))),
% 1.60/1.76 inference(monotonicity,[status(thm)],[2345])).
% 1.60/1.76 tff(2347,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586))),
% 1.60/1.76 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.60/1.76 tff(2348,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a586) | c3_1(a586) | c0_1(a586))),
% 1.60/1.76 inference(quant_inst,[status(thm)],[])).
% 1.60/1.76 tff(2349,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586)),
% 1.60/1.76 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.60/1.76 tff(2350,plain,
% 1.60/1.76 (hskp45),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2349, 156, 2341, 2340, 87, 86, 2332, 757, 653])).
% 1.60/1.76 tff(2351,plain,
% 1.60/1.76 (~c3_1(a561)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[771, 2350])).
% 1.60/1.76 tff(2352,plain,
% 1.60/1.76 (c0_1(a561)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[779, 2350])).
% 1.60/1.76 tff(2353,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a561)) | (~c0_1(a561)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2354,plain,
% 1.60/1.76 ((hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a554) | c3_1(a554) | c0_1(a554)) <=> (hskp33 | c3_1(a561) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.60/1.76 inference(rewrite,[status(thm)],[])).
% 1.60/1.76 tff(2355,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a561)) | (~c0_1(a561))))),
% 1.60/1.76 inference(monotonicity,[status(thm)],[2354])).
% 1.60/1.76 tff(2356,plain,
% 1.60/1.76 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.60/1.76 inference(transitivity,[status(thm)],[2355, 2353])).
% 1.60/1.76 tff(2357,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a554) | c3_1(a554) | c0_1(a554))),
% 1.60/1.76 inference(quant_inst,[status(thm)],[])).
% 1.60/1.76 tff(2358,plain,
% 1.60/1.76 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a561)) | (~c0_1(a561))),
% 1.60/1.76 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 1.60/1.76 tff(2359,plain,
% 1.60/1.76 (~c1_1(a561)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2358, 156, 35, 2352, 2351, 2343, 2339, 85, 2342])).
% 1.60/1.76 tff(2360,plain,
% 1.60/1.76 (~c2_1(a561)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[792, 2350])).
% 1.60/1.76 tff(2361,plain,
% 1.60/1.76 ($false),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[831, 156, 110, 98, 2352, 2360, 34, 2359])).
% 1.60/1.76 tff(2362,plain,(c2_1(a586) | hskp50 | hskp19 | hskp33 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c0_1(a586) | c3_1(a586) | hskp41 | c1_1(a586) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.60/1.76 tff(2363,plain,
% 1.60/1.76 (c2_1(a586)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2362, 110, 98, 35, 2330, 2329, 2328, 87, 86, 2201, 88, 109])).
% 1.60/1.76 tff(2364,plain,
% 1.60/1.76 ($false),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[965, 357, 365, 946, 349, 87, 86, 902])).
% 1.60/1.76 tff(2365,plain,((~hskp16) | hskp46 | c0_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.60/1.76 tff(2366,plain,
% 1.60/1.76 (~hskp16),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[2365, 946, 87, 86, 902])).
% 1.60/1.76 tff(2367,plain,
% 1.60/1.76 (hskp17),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[382, 2366, 2225])).
% 1.60/1.76 tff(2368,plain,
% 1.60/1.76 (~c2_1(a571)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[573, 2367])).
% 1.60/1.76 tff(2369,plain,
% 1.60/1.76 (c3_1(a571)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[623, 2367])).
% 1.60/1.76 tff(2370,plain,
% 1.60/1.76 (c0_1(a571)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[581, 2367])).
% 1.60/1.76 tff(2371,plain,
% 1.60/1.76 (c1_1(a571)),
% 1.60/1.76 inference(unit_resolution,[status(thm)],[931, 156, 88, 2370, 2369, 86, 2368, 921, 902])).
% 1.60/1.76 tff(2372,plain,
% 1.60/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2373,plain,
% 1.60/1.77 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2374,plain,
% 1.60/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2373])).
% 1.60/1.77 tff(2375,plain,
% 1.60/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2374, 2372])).
% 1.60/1.77 tff(2376,plain,
% 1.60/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2377,plain,
% 1.60/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2376, 2375])).
% 1.60/1.77 tff(2378,plain,
% 1.60/1.77 ($false),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2377, 156, 733, 732, 731, 2370, 249, 2368, 24, 707, 2233, 2371])).
% 1.60/1.77 tff(2379,plain,(hskp46 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | (~c3_1(a548)) | c2_1(a548) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | c0_1(a586) | hskp50 | hskp19 | hskp15 | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.77 tff(2380,plain,
% 1.60/1.77 (hskp46),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2379, 2330, 2329, 2328, 2200, 2199, 88, 86, 2363, 87, 110, 98, 109, 2198])).
% 1.60/1.77 tff(2381,plain,
% 1.60/1.77 (~c0_1(a562)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[64, 2380])).
% 1.60/1.77 tff(2382,plain,
% 1.60/1.77 (~c3_1(a562)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[270, 2380])).
% 1.60/1.77 tff(2383,plain,
% 1.60/1.77 (c1_1(a548)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2234, 1213])).
% 1.60/1.77 tff(2384,plain,
% 1.60/1.77 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2385,plain,
% 1.60/1.77 ((hskp41 | hskp9 | (~ndr1_0) | c0_1(a548) | (~c3_1(a548)) | (~c1_1(a548))) <=> (hskp41 | hskp9 | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2386,plain,
% 1.60/1.77 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2385])).
% 1.60/1.77 tff(2387,plain,
% 1.60/1.77 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2386, 2384])).
% 1.60/1.77 tff(2388,plain,
% 1.60/1.77 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2389,plain,
% 1.60/1.77 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 1.60/1.77 tff(2390,plain,
% 1.60/1.77 (hskp9 | (~c1_1(a548))),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2389, 156, 331, 249, 56, 342])).
% 1.60/1.77 tff(2391,plain,
% 1.60/1.77 ($false),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2390, 2383, 1315])).
% 1.60/1.77 tff(2392,plain,(hskp28 | hskp41 | (~c3_1(a548)) | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.77 tff(2393,plain,
% 1.60/1.77 (hskp28),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2392, 2201, 2200, 2198, 2199])).
% 1.60/1.77 tff(2394,plain,
% 1.60/1.77 (c3_1(a589)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[185, 2393])).
% 1.60/1.77 tff(2395,plain,
% 1.60/1.77 (c2_1(a589)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[171, 2393])).
% 1.60/1.77 tff(2396,plain,
% 1.60/1.77 (c1_1(a562)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[288, 2380])).
% 1.60/1.77 tff(2397,plain,
% 1.60/1.77 (~c1_1(a589)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2291, 156, 2196, 2396, 2395, 2394, 2382, 2381, 22])).
% 1.60/1.77 tff(2398,plain,
% 1.60/1.77 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.60/1.77 inference(bind,[status(th)],[])).
% 1.60/1.77 tff(2399,plain,
% 1.60/1.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.60/1.77 inference(quant_intro,[status(thm)],[2398])).
% 1.60/1.77 tff(2400,plain,
% 1.60/1.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2401,plain,
% 1.60/1.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.60/1.77 inference(bind,[status(th)],[])).
% 1.60/1.77 tff(2402,plain,
% 1.60/1.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.60/1.77 inference(quant_intro,[status(thm)],[2401])).
% 1.60/1.77 tff(2403,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause242')).
% 1.60/1.77 tff(2404,plain,
% 1.60/1.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.60/1.77 tff(2405,plain,
% 1.60/1.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2404, 2400])).
% 1.60/1.77 tff(2406,plain,(
% 1.60/1.77 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.60/1.77 inference(skolemize,[status(sab)],[2405])).
% 1.60/1.77 tff(2407,plain,
% 1.60/1.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2406, 2399])).
% 1.60/1.77 tff(2408,plain,
% 1.60/1.77 (~c0_1(a589)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[177, 2393])).
% 1.60/1.77 tff(2409,plain,
% 1.60/1.77 (hskp34),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2160, 156, 2396, 2330, 2329, 2328, 2382, 2381, 75])).
% 1.60/1.77 tff(2410,plain,
% 1.60/1.77 (~c1_1(a537)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1124, 2409])).
% 1.60/1.77 tff(2411,plain,
% 1.60/1.77 (c3_1(a537)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1132, 2409])).
% 1.60/1.77 tff(2412,plain,
% 1.60/1.77 (c0_1(a537)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1147, 2409])).
% 1.60/1.77 tff(2413,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | c1_1(a589) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | c1_1(a589) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2414,plain,
% 1.60/1.77 ((hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589))) <=> (hskp8 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | c1_1(a589) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2415,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | c1_1(a589) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2414])).
% 1.60/1.77 tff(2416,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | c1_1(a589) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2415, 2413])).
% 1.60/1.77 tff(2417,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589)))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2418,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | c1_1(a589) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 1.60/1.77 tff(2419,plain,
% 1.60/1.77 (hskp8),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2418, 156, 2412, 2411, 2395, 2410, 2408, 2407, 2397])).
% 1.60/1.77 tff(2420,plain,
% 1.60/1.77 (((~hskp8) | (~c2_1(a552))) <=> ((~hskp8) | (~c2_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2421,plain,
% 1.60/1.77 (((~c2_1(a552)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2422,axiom,((~c2_1(a552)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 1.60/1.77 tff(2423,plain,
% 1.60/1.77 ((~hskp8) | (~c2_1(a552))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.60/1.77 tff(2424,plain,
% 1.60/1.77 ((~hskp8) | (~c2_1(a552))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2423, 2420])).
% 1.60/1.77 tff(2425,plain,
% 1.60/1.77 (~c2_1(a552)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2424, 2419])).
% 1.60/1.77 tff(2426,plain,
% 1.60/1.77 (((~hskp8) | (~c3_1(a552))) <=> ((~hskp8) | (~c3_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2427,plain,
% 1.60/1.77 (((~c3_1(a552)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2428,axiom,((~c3_1(a552)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.60/1.77 tff(2429,plain,
% 1.60/1.77 ((~hskp8) | (~c3_1(a552))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 1.60/1.77 tff(2430,plain,
% 1.60/1.77 ((~hskp8) | (~c3_1(a552))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2429, 2426])).
% 1.60/1.77 tff(2431,plain,
% 1.60/1.77 (~c3_1(a552)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2430, 2419])).
% 1.60/1.77 tff(2432,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a562)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2433,plain,
% 1.60/1.77 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589))) <=> (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a562)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2434,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a562))))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2433])).
% 1.60/1.77 tff(2435,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a562)))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2434, 2432])).
% 1.60/1.77 tff(2436,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2437,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a562))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.60/1.77 tff(2438,plain,
% 1.60/1.77 (hskp26),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2437, 156, 2396, 2394, 2382, 2381, 2408, 1686, 2397])).
% 1.60/1.77 tff(2439,plain,
% 1.60/1.77 (~c3_1(a584)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1620, 2438])).
% 1.60/1.77 tff(2440,plain,
% 1.60/1.77 (c1_1(a584)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1637, 2438])).
% 1.60/1.77 tff(2441,plain,
% 1.60/1.77 (c0_1(a584)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1629, 2438])).
% 1.60/1.77 tff(2442,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a552))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a552))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2443,plain,
% 1.60/1.77 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a552) | c3_1(a552) | c0_1(a552)) <=> (hskp33 | c3_1(a584) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a552))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2444,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a552) | c3_1(a552) | c0_1(a552))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a552)))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2443])).
% 1.60/1.77 tff(2445,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a552) | c3_1(a552) | c0_1(a552))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a552))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2444, 2442])).
% 1.60/1.77 tff(2446,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a552) | c3_1(a552) | c0_1(a552))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2447,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a552)),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 1.60/1.77 tff(2448,plain,
% 1.60/1.77 (c0_1(a552)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2447, 156, 35, 2441, 2440, 2439, 2431, 2425, 85])).
% 1.60/1.77 tff(2449,plain,
% 1.60/1.77 (((~hskp8) | (~c1_1(a552))) <=> ((~hskp8) | (~c1_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2450,plain,
% 1.60/1.77 (((~c1_1(a552)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2451,axiom,((~c1_1(a552)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.60/1.77 tff(2452,plain,
% 1.60/1.77 ((~hskp8) | (~c1_1(a552))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 1.60/1.77 tff(2453,plain,
% 1.60/1.77 ((~hskp8) | (~c1_1(a552))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2452, 2449])).
% 1.60/1.77 tff(2454,plain,
% 1.60/1.77 (~c1_1(a552)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2453, 2419])).
% 1.60/1.77 tff(2455,plain,
% 1.60/1.77 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2456,plain,
% 1.60/1.77 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552))) <=> (hskp50 | hskp19 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2457,plain,
% 1.60/1.77 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552))))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2456])).
% 1.60/1.77 tff(2458,plain,
% 1.60/1.77 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2457, 2455])).
% 1.60/1.77 tff(2459,plain,
% 1.60/1.77 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2460,plain,
% 1.60/1.77 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 1.60/1.77 tff(2461,plain,
% 1.60/1.77 ($false),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2460, 156, 110, 98, 2454, 2425, 34, 2448])).
% 1.60/1.77 tff(2462,plain,(hskp50 | hskp19 | hskp33 | c1_1(a586) | c3_1(a586) | c0_1(a586) | hskp15 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.77 tff(2463,plain,
% 1.60/1.77 (hskp50),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2462, 109, 35, 88, 86, 87, 98, 97])).
% 1.60/1.77 tff(2464,plain,
% 1.60/1.77 (~c3_1(a574)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[799, 2463])).
% 1.60/1.77 tff(2465,plain,
% 1.60/1.77 (c1_1(a574)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[807, 2463])).
% 1.60/1.77 tff(2466,plain,
% 1.60/1.77 (c0_1(a574)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[815, 2463])).
% 1.60/1.77 tff(2467,plain,
% 1.60/1.77 (hskp4),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[205, 1669, 96])).
% 1.60/1.77 tff(2468,plain,
% 1.60/1.77 (~hskp26),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1659, 2467, 58, 35, 97])).
% 1.60/1.77 tff(2469,plain,
% 1.60/1.77 ($false),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2040, 2468, 2467, 88, 58, 35, 86, 1669])).
% 1.60/1.77 tff(2470,plain,(hskp6 | c1_1(a586) | hskp38 | hskp33 | c3_1(a586) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.77 tff(2471,plain,
% 1.60/1.77 (hskp6),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2470, 58, 88, 35, 86, 97])).
% 1.60/1.77 tff(2472,plain,
% 1.60/1.77 (~c2_1(a548)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[217, 2471])).
% 1.60/1.77 tff(2473,plain,
% 1.60/1.77 (~c0_1(a548)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[211, 2471])).
% 1.60/1.77 tff(2474,assumption,(~c3_1(a574)), introduced(assumption)).
% 1.60/1.77 tff(2475,assumption,(c1_1(a574)), introduced(assumption)).
% 1.60/1.77 tff(2476,assumption,(c0_1(a574)), introduced(assumption)).
% 1.60/1.77 tff(2477,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2478,plain,
% 1.60/1.77 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a586) | c3_1(a586) | c0_1(a586)) <=> (hskp33 | c3_1(a574) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2479,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c0_1(a574)) | (~c1_1(a574))))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2478])).
% 1.60/1.77 tff(2480,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2479, 2477])).
% 1.60/1.77 tff(2481,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a586) | c3_1(a586) | c0_1(a586))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2482,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c0_1(a574)) | (~c1_1(a574))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.60/1.77 tff(2483,plain,
% 1.60/1.77 ($false),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2482, 156, 35, 2476, 2475, 2474, 87, 86, 85, 653])).
% 1.60/1.77 tff(2484,plain,(c2_1(a586) | hskp33 | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | c0_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.77 tff(2485,plain,
% 1.60/1.77 (c2_1(a586)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2484, 808, 86, 816, 800, 87, 35])).
% 1.60/1.77 tff(2486,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c3_1(a574) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a574) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2487,plain,
% 1.60/1.77 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a548) | c3_1(a548) | c0_1(a548)) <=> (hskp33 | c3_1(a548) | c3_1(a574) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.60/1.77 inference(rewrite,[status(thm)],[])).
% 1.60/1.77 tff(2488,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c3_1(a574) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574))))),
% 1.60/1.77 inference(monotonicity,[status(thm)],[2487])).
% 1.60/1.77 tff(2489,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a574) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.60/1.77 inference(transitivity,[status(thm)],[2488, 2486])).
% 1.60/1.77 tff(2490,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a548) | c3_1(a548) | c0_1(a548))),
% 1.60/1.77 inference(quant_inst,[status(thm)],[])).
% 1.60/1.77 tff(2491,plain,
% 1.60/1.77 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a574) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574))),
% 1.60/1.77 inference(modus_ponens,[status(thm)],[2490, 2489])).
% 1.60/1.77 tff(2492,plain,
% 1.60/1.77 (c3_1(a548)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2491, 156, 35, 816, 808, 800, 24, 56, 85])).
% 1.60/1.77 tff(2493,plain,
% 1.60/1.77 (c3_1(a545)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[824, 111, 794, 97, 35])).
% 1.60/1.77 tff(2494,plain,
% 1.60/1.77 (~c1_1(a545)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[1211, 2493, 58, 97, 111])).
% 1.60/1.77 tff(2495,plain,
% 1.60/1.77 (~hskp17),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[940, 2493, 87, 86, 97, 2494, 2485, 88])).
% 1.60/1.77 tff(2496,plain,
% 1.60/1.77 (hskp28),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[163, 2494, 111])).
% 1.60/1.77 tff(2497,plain,
% 1.60/1.77 (c2_1(a589)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[171, 2496])).
% 1.60/1.77 tff(2498,plain,
% 1.60/1.77 (c3_1(a589)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[185, 2496])).
% 1.60/1.77 tff(2499,plain,
% 1.60/1.77 (hskp46 | (~c1_1(a589))),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2051, 156, 625, 591, 87, 86, 858, 902])).
% 1.60/1.77 tff(2500,plain,
% 1.60/1.77 (~c1_1(a589)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[2499, 946])).
% 1.60/1.77 tff(2501,assumption,(hskp37), introduced(assumption)).
% 1.60/1.77 tff(2502,plain,
% 1.60/1.77 (~c3_1(a544)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[450, 2501])).
% 1.60/1.77 tff(2503,plain,
% 1.60/1.77 (~c2_1(a544)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[436, 2501])).
% 1.60/1.77 tff(2504,plain,
% 1.60/1.77 (c1_1(a544)),
% 1.60/1.77 inference(unit_resolution,[status(thm)],[444, 2501])).
% 1.60/1.77 tff(2505,plain,
% 1.60/1.77 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a544)))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(2506,plain,
% 1.60/1.78 ((hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a544)))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(2507,plain,
% 1.60/1.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a544))))),
% 1.60/1.78 inference(monotonicity,[status(thm)],[2506])).
% 1.60/1.78 tff(2508,plain,
% 1.60/1.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a544)))),
% 1.60/1.78 inference(transitivity,[status(thm)],[2507, 2505])).
% 1.60/1.78 tff(2509,plain,
% 1.60/1.78 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.60/1.78 inference(quant_inst,[status(thm)],[])).
% 1.60/1.78 tff(2510,plain,
% 1.60/1.78 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a544) | c3_1(a544) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a544))),
% 1.60/1.78 inference(modus_ponens,[status(thm)],[2509, 2508])).
% 1.60/1.78 tff(2511,plain,
% 1.60/1.78 ($false),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2510, 156, 109, 2504, 625, 591, 2503, 2502, 483, 1716])).
% 1.60/1.78 tff(2512,plain,((~hskp37) | hskp15 | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.78 tff(2513,plain,
% 1.60/1.78 (~hskp37),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2512, 2500, 625, 591, 109])).
% 1.60/1.78 tff(2514,plain,
% 1.60/1.78 (hskp18),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[382, 2366, 332])).
% 1.60/1.78 tff(2515,plain,
% 1.60/1.78 (~c1_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[389, 2514])).
% 1.60/1.78 tff(2516,plain,
% 1.60/1.78 (~c3_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[420, 2514])).
% 1.60/1.78 tff(2517,plain,
% 1.60/1.78 (c0_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[397, 2514])).
% 1.60/1.78 tff(2518,plain,
% 1.60/1.78 (hskp37 | (~c2_1(a572))),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[428, 156, 2517, 2516, 2515, 415])).
% 1.60/1.78 tff(2519,plain,
% 1.60/1.78 (~c2_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2518, 2513])).
% 1.60/1.78 tff(2520,plain,
% 1.60/1.78 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a572) | c1_1(a572) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a572))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a572) | c1_1(a572) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a572))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(2521,plain,
% 1.60/1.78 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a572) | c1_1(a572) | c3_1(a572)) <=> (hskp38 | c3_1(a572) | c1_1(a572) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a572))),
% 1.60/1.78 inference(rewrite,[status(thm)],[])).
% 1.60/1.78 tff(2522,plain,
% 1.60/1.78 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a572) | c1_1(a572) | c3_1(a572))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a572) | c1_1(a572) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a572)))),
% 1.60/1.78 inference(monotonicity,[status(thm)],[2521])).
% 1.60/1.78 tff(2523,plain,
% 1.60/1.78 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a572) | c1_1(a572) | c3_1(a572))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a572) | c1_1(a572) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a572))),
% 1.60/1.78 inference(transitivity,[status(thm)],[2522, 2520])).
% 1.60/1.78 tff(2524,plain,
% 1.60/1.78 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a572) | c1_1(a572) | c3_1(a572))),
% 1.60/1.78 inference(quant_inst,[status(thm)],[])).
% 1.60/1.78 tff(2525,plain,
% 1.60/1.78 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a572) | c1_1(a572) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a572)),
% 1.60/1.78 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.60/1.78 tff(2526,plain,
% 1.60/1.78 ($false),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2525, 156, 58, 249, 2516, 2515, 24, 56, 663, 2519])).
% 1.60/1.78 tff(2527,plain,(hskp46 | hskp38 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | (~c2_1(a589)) | (~c3_1(a589)) | hskp15 | hskp17 | c0_1(a586) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.60/1.78 tff(2528,plain,
% 1.60/1.78 (hskp46),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2527, 2497, 2492, 24, 56, 58, 2498, 109, 2495, 87, 86, 2485])).
% 1.60/1.78 tff(2529,plain,
% 1.60/1.78 (~c0_1(a562)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[64, 2528])).
% 1.60/1.78 tff(2530,plain,
% 1.60/1.78 (~c3_1(a562)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[270, 2528])).
% 1.60/1.78 tff(2531,plain,
% 1.60/1.78 (c1_1(a562)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[288, 2528])).
% 1.60/1.78 tff(2532,plain,
% 1.60/1.78 (~hskp4),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[193, 2494])).
% 1.60/1.78 tff(2533,plain,
% 1.60/1.78 (~c1_1(a589)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2291, 156, 2532, 2531, 2497, 2498, 2530, 2529, 22])).
% 1.60/1.78 tff(2534,plain,
% 1.60/1.78 ($false),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[1898, 156, 58, 1876, 1875, 1874, 625, 591, 1537, 1716])).
% 1.60/1.78 tff(2535,plain,((~hskp39) | hskp38 | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.78 tff(2536,plain,
% 1.60/1.78 (~hskp39),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2535, 2533, 58, 2498, 2497])).
% 1.60/1.78 tff(2537,plain,
% 1.60/1.78 (~hskp16),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2301, 2533, 58, 2498, 2497, 2531, 2529, 2530, 2536])).
% 1.60/1.78 tff(2538,plain,
% 1.60/1.78 (hskp18),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[382, 2537, 2495])).
% 1.60/1.78 tff(2539,plain,
% 1.60/1.78 (~c1_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[389, 2538])).
% 1.60/1.78 tff(2540,plain,
% 1.60/1.78 (~c3_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[420, 2538])).
% 1.60/1.78 tff(2541,plain,
% 1.60/1.78 (c0_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[397, 2538])).
% 1.60/1.78 tff(2542,plain,
% 1.60/1.78 (~hskp37),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2512, 2533, 2497, 2498, 109])).
% 1.60/1.78 tff(2543,plain,
% 1.60/1.78 (~c2_1(a572)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[428, 156, 2542, 2541, 2540, 2539, 415])).
% 1.60/1.78 tff(2544,plain,
% 1.60/1.78 ($false),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2525, 156, 58, 2492, 2540, 2539, 24, 56, 663, 2543])).
% 1.60/1.78 tff(2545,plain,(c2_1(a545) | hskp38 | c2_1(a548) | c0_1(a548) | hskp15 | c0_1(a586) | c3_1(a586) | c0_1(a545) | c1_1(a586) | (~hskp50) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.60/1.78 tff(2546,plain,
% 1.60/1.78 (c2_1(a545)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2545, 24, 58, 56, 109, 87, 86, 97, 88, 794, 35])).
% 1.60/1.78 tff(2547,plain,
% 1.60/1.78 (~hskp4),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[1643, 2546])).
% 1.60/1.78 tff(2548,assumption,(c1_1(a548)), introduced(assumption)).
% 1.60/1.78 tff(2549,plain,
% 1.60/1.78 (hskp46 | (~c3_1(a548)) | (~c1_1(a548))),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2231, 156, 24, 56, 12])).
% 1.60/1.78 tff(2550,plain,
% 1.60/1.78 (hskp46),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2549, 2548, 249])).
% 1.60/1.78 tff(2551,plain,
% 1.60/1.78 (~c0_1(a562)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[64, 2550])).
% 1.60/1.78 tff(2552,plain,
% 1.60/1.78 (~c3_1(a562)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[270, 2550])).
% 1.60/1.78 tff(2553,plain,
% 1.60/1.78 (c1_1(a562)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[288, 2550])).
% 1.60/1.78 tff(2554,plain,
% 1.60/1.78 (hskp39),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2063, 156, 2553, 249, 2552, 2551, 24, 281, 2548])).
% 1.60/1.78 tff(2555,plain,
% 1.60/1.78 (c1_1(a549)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[303, 2554])).
% 1.60/1.78 tff(2556,plain,
% 1.60/1.78 (c2_1(a549)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[311, 2554])).
% 1.60/1.78 tff(2557,plain,
% 1.60/1.78 (c3_1(a549)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[319, 2554])).
% 1.60/1.78 tff(2558,plain,
% 1.60/1.78 ($false),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[326, 156, 23, 2553, 2557, 2556, 2555, 2552, 2551, 22])).
% 1.60/1.78 tff(2559,plain,((~c1_1(a548)) | hskp4 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.78 tff(2560,plain,
% 1.60/1.78 (~c1_1(a548)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2559, 2547, 2492, 24, 56])).
% 1.60/1.78 tff(2561,plain,
% 1.60/1.78 (hskp28 | c2_1(a548) | c1_1(a548)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[1604, 156, 56, 122])).
% 1.60/1.78 tff(2562,plain,
% 1.60/1.78 (hskp28),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2561, 2560, 24])).
% 1.60/1.78 tff(2563,plain,
% 1.60/1.78 (c2_1(a589)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[171, 2562])).
% 1.60/1.78 tff(2564,plain,
% 1.60/1.78 (c3_1(a589)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[185, 2562])).
% 1.60/1.78 tff(2565,plain,
% 1.60/1.78 (~c0_1(a589)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[177, 2562])).
% 1.60/1.78 tff(2566,plain,
% 1.60/1.78 (hskp17),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[2527, 946, 249, 24, 56, 58, 591, 109, 625, 87, 86, 902])).
% 1.60/1.78 tff(2567,plain,
% 1.60/1.78 (~c2_1(a571)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[573, 2566])).
% 1.60/1.78 tff(2568,plain,
% 1.60/1.78 (c3_1(a571)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[623, 2566])).
% 1.60/1.78 tff(2569,plain,
% 1.60/1.78 (c0_1(a571)),
% 1.60/1.78 inference(unit_resolution,[status(thm)],[581, 2566])).
% 1.63/1.78 tff(2570,plain,
% 1.63/1.78 (c1_1(a571)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[931, 156, 88, 2569, 2568, 86, 2567, 921, 902])).
% 1.63/1.78 tff(2571,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[615, 156, 591, 2569, 590, 87, 86, 2567, 609, 2500, 902, 2570])).
% 1.63/1.78 tff(2572,plain,(hskp46 | (~c3_1(a589)) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a586) | (~c2_1(a589)) | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | hskp38 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(2573,plain,
% 1.63/1.78 (hskp46),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2572, 2564, 2565, 87, 86, 2485, 88, 2563, 2492, 24, 56, 58, 109])).
% 1.63/1.78 tff(2574,plain,
% 1.63/1.78 (~c0_1(a562)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[64, 2573])).
% 1.63/1.78 tff(2575,plain,
% 1.63/1.78 (~c3_1(a562)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[270, 2573])).
% 1.63/1.78 tff(2576,plain,
% 1.63/1.78 (c1_1(a562)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[288, 2573])).
% 1.63/1.78 tff(2577,plain,
% 1.63/1.78 (~c1_1(a589)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2291, 156, 2547, 2576, 2563, 2564, 2575, 2574, 22])).
% 1.63/1.78 tff(2578,plain,
% 1.63/1.78 (~hskp39),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2535, 2577, 58, 2564, 2563])).
% 1.63/1.78 tff(2579,plain,
% 1.63/1.78 (~hskp16),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2301, 2577, 58, 2564, 2563, 2576, 2574, 2575, 2578])).
% 1.63/1.78 tff(2580,plain,
% 1.63/1.78 (~hskp37),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2512, 2577, 2563, 2564, 109])).
% 1.63/1.78 tff(2581,plain,
% 1.63/1.78 (~c2_1(a572)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[428, 156, 422, 398, 421, 390, 415])).
% 1.63/1.78 tff(2582,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2525, 156, 58, 249, 421, 390, 24, 56, 663, 2581])).
% 1.63/1.78 tff(2583,plain,((~hskp18) | hskp38 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | hskp37), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(2584,plain,
% 1.63/1.78 (~hskp18),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2583, 2492, 58, 24, 56, 2580])).
% 1.63/1.78 tff(2585,plain,
% 1.63/1.78 (hskp17),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[382, 2584, 2579])).
% 1.63/1.78 tff(2586,plain,
% 1.63/1.78 (~c2_1(a571)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[573, 2585])).
% 1.63/1.78 tff(2587,plain,
% 1.63/1.78 (c3_1(a571)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[623, 2585])).
% 1.63/1.78 tff(2588,plain,
% 1.63/1.78 (c0_1(a571)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[581, 2585])).
% 1.63/1.78 tff(2589,plain,
% 1.63/1.78 (c1_1(a571)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[931, 156, 88, 2588, 2587, 86, 2586, 921, 2485])).
% 1.63/1.78 tff(2590,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[615, 156, 2564, 2588, 2565, 87, 86, 2586, 609, 2577, 2485, 2589])).
% 1.63/1.78 tff(2591,plain,(c2_1(a548) | c0_1(a586) | c3_1(a586) | c1_1(a586) | hskp38 | c0_1(a548) | hskp15 | c0_1(a545) | (~hskp50) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(2592,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2591, 2473, 2472, 86, 88, 58, 87, 109, 97, 794, 35])).
% 1.63/1.78 tff(2593,plain,(hskp38 | c3_1(a586) | c1_1(a586) | c0_1(a586) | hskp15 | c0_1(a545) | (~hskp50) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(2594,plain,
% 1.63/1.78 (hskp38),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2593, 109, 88, 87, 86, 97, 2463, 35])).
% 1.63/1.78 tff(2595,plain,
% 1.63/1.78 (c2_1(a547)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[693, 2594])).
% 1.63/1.78 tff(2596,plain,
% 1.63/1.78 (c0_1(a547)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[677, 2594])).
% 1.63/1.78 tff(2597,plain,
% 1.63/1.78 (c1_1(a547)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[685, 2594])).
% 1.63/1.78 tff(2598,plain,
% 1.63/1.78 (c2_1(a586)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2484, 2465, 86, 2466, 2464, 87, 35])).
% 1.63/1.78 tff(2599,plain,
% 1.63/1.78 (^[V: $i, U: $i] : refl((hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.63/1.78 inference(bind,[status(th)],[])).
% 1.63/1.78 tff(2600,plain,
% 1.63/1.78 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.63/1.78 inference(quant_intro,[status(thm)],[2599])).
% 1.63/1.78 tff(2601,plain,
% 1.63/1.78 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2602,plain,
% 1.63/1.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp51) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp51))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp51) <=> (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp51) <=> (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.63/1.78 inference(bind,[status(th)],[])).
% 1.63/1.78 tff(2603,plain,
% 1.63/1.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp51) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.63/1.78 inference(quant_intro,[status(thm)],[2602])).
% 1.63/1.78 tff(2604,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c3_1(V)) | c2_1(V)) | c1_1(V)) | hskp51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause234')).
% 1.63/1.78 tff(2605,plain,
% 1.63/1.78 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2604, 2603])).
% 1.63/1.78 tff(2606,plain,
% 1.63/1.78 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2605, 2601])).
% 1.63/1.78 tff(2607,plain,(
% 1.63/1.78 ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.63/1.78 inference(skolemize,[status(sab)],[2606])).
% 1.63/1.78 tff(2608,plain,
% 1.63/1.78 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2607, 2600])).
% 1.63/1.78 tff(2609,plain,
% 1.63/1.78 (c3_1(a545)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[824, 1644, 794, 97, 35])).
% 1.63/1.78 tff(2610,plain,
% 1.63/1.78 (hskp39),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1586, 2609, 733, 732, 731, 1645, 1644, 97])).
% 1.63/1.78 tff(2611,plain,
% 1.63/1.78 (c1_1(a549)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[303, 2610])).
% 1.63/1.78 tff(2612,plain,
% 1.63/1.78 (c2_1(a549)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[311, 2610])).
% 1.63/1.78 tff(2613,plain,
% 1.63/1.78 (c3_1(a549)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[319, 2610])).
% 1.63/1.78 tff(2614,plain,
% 1.63/1.78 (hskp25),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1184, 156, 2613, 2612, 2611, 1645, 1644, 55, 2609])).
% 1.63/1.78 tff(2615,plain,
% 1.63/1.78 (~c1_1(a582)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1190, 2614])).
% 1.63/1.78 tff(2616,plain,
% 1.63/1.78 (~c2_1(a582)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1196, 2614])).
% 1.63/1.78 tff(2617,plain,
% 1.63/1.78 (~c3_1(a582)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1202, 2614])).
% 1.63/1.78 tff(2618,plain,
% 1.63/1.78 (hskp46),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1163, 156, 1645, 1644, 97, 12, 2609])).
% 1.63/1.78 tff(2619,plain,
% 1.63/1.78 (~c0_1(a562)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[64, 2618])).
% 1.63/1.78 tff(2620,plain,
% 1.63/1.78 (~c3_1(a562)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[270, 2618])).
% 1.63/1.78 tff(2621,plain,
% 1.63/1.78 (c1_1(a562)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[288, 2618])).
% 1.63/1.78 tff(2622,plain,
% 1.63/1.78 (hskp34),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2160, 156, 2621, 733, 732, 731, 2620, 2619, 75])).
% 1.63/1.78 tff(2623,plain,
% 1.63/1.78 (~c1_1(a537)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1124, 2622])).
% 1.63/1.78 tff(2624,plain,
% 1.63/1.78 (c3_1(a537)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1132, 2622])).
% 1.63/1.78 tff(2625,plain,
% 1.63/1.78 (c0_1(a537)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1147, 2622])).
% 1.63/1.78 tff(2626,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2627,plain,
% 1.63/1.78 ((hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (hskp51 | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2628,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[2627])).
% 1.63/1.78 tff(2629,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[2628, 2626])).
% 1.63/1.78 tff(2630,plain,
% 1.63/1.78 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(2631,plain,
% 1.63/1.78 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 1.63/1.78 tff(2632,plain,
% 1.63/1.78 (hskp51),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2631, 156, 2625, 2624, 2623, 2617, 2616, 2615, 2608])).
% 1.63/1.78 tff(2633,plain,
% 1.63/1.78 (((~hskp51) | (~c2_1(a583))) <=> ((~hskp51) | (~c2_1(a583)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2634,plain,
% 1.63/1.78 (((~c2_1(a583)) | (~hskp51)) <=> ((~hskp51) | (~c2_1(a583)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2635,axiom,((~c2_1(a583)) | (~hskp51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.63/1.78 tff(2636,plain,
% 1.63/1.78 ((~hskp51) | (~c2_1(a583))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 1.63/1.78 tff(2637,plain,
% 1.63/1.78 ((~hskp51) | (~c2_1(a583))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2636, 2633])).
% 1.63/1.78 tff(2638,plain,
% 1.63/1.78 (~c2_1(a583)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2637, 2632])).
% 1.63/1.78 tff(2639,plain,
% 1.63/1.78 (((~hskp51) | c3_1(a583)) <=> ((~hskp51) | c3_1(a583))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2640,axiom,((~hskp51) | c3_1(a583)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.63/1.78 tff(2641,plain,
% 1.63/1.78 ((~hskp51) | c3_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.63/1.78 tff(2642,plain,
% 1.63/1.78 ((~hskp51) | c3_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2641, 2639])).
% 1.63/1.78 tff(2643,plain,
% 1.63/1.78 ((~hskp51) | c3_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2642, 2639])).
% 1.63/1.78 tff(2644,plain,
% 1.63/1.78 ((~hskp51) | c3_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2643, 2639])).
% 1.63/1.78 tff(2645,plain,
% 1.63/1.78 ((~hskp51) | c3_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2644, 2639])).
% 1.63/1.78 tff(2646,plain,
% 1.63/1.78 (c3_1(a583)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2645, 2632])).
% 1.63/1.78 tff(2647,plain,
% 1.63/1.78 (((~hskp51) | c0_1(a583)) <=> ((~hskp51) | c0_1(a583))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2648,axiom,((~hskp51) | c0_1(a583)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.63/1.78 tff(2649,plain,
% 1.63/1.78 ((~hskp51) | c0_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 1.63/1.78 tff(2650,plain,
% 1.63/1.78 ((~hskp51) | c0_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2649, 2647])).
% 1.63/1.78 tff(2651,plain,
% 1.63/1.78 ((~hskp51) | c0_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2650, 2647])).
% 1.63/1.78 tff(2652,plain,
% 1.63/1.78 ((~hskp51) | c0_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2651, 2647])).
% 1.63/1.78 tff(2653,plain,
% 1.63/1.78 ((~hskp51) | c0_1(a583)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2652, 2647])).
% 1.63/1.78 tff(2654,plain,
% 1.63/1.78 (c0_1(a583)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2653, 2632])).
% 1.63/1.78 tff(2655,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a583) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a583) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2656,plain,
% 1.63/1.78 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583))) <=> (c1_1(a586) | c2_1(a583) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2657,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a583) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[2656])).
% 1.63/1.78 tff(2658,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a583) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[2657, 2655])).
% 1.63/1.78 tff(2659,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(2660,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a583) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 1.63/1.78 tff(2661,plain,
% 1.63/1.78 (c1_1(a583)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2660, 156, 2654, 2646, 88, 2638, 86, 921, 902])).
% 1.63/1.78 tff(2662,plain,
% 1.63/1.78 (hskp42),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1574, 156, 733, 732, 731, 1645, 1644, 1364, 2609])).
% 1.63/1.78 tff(2663,plain,
% 1.63/1.78 (~c2_1(a556)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1385, 2662])).
% 1.63/1.78 tff(2664,plain,
% 1.63/1.78 (c3_1(a556)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1403, 2662])).
% 1.63/1.78 tff(2665,plain,
% 1.63/1.78 (c1_1(a556)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[1411, 2662])).
% 1.63/1.78 tff(2666,plain,
% 1.63/1.78 (~c2_1(a537)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2192, 156, 2665, 2664, 2624, 2663, 2623, 2617, 2616, 2615, 45])).
% 1.63/1.78 tff(2667,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a583)) | (~c0_1(a583)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a583)) | (~c0_1(a583)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2668,plain,
% 1.63/1.78 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583))) <=> (c2_1(a583) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a583)) | (~c0_1(a583)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(2669,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a583)) | (~c0_1(a583)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[2668])).
% 1.63/1.78 tff(2670,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a583)) | (~c0_1(a583)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[2669, 2667])).
% 1.63/1.78 tff(2671,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(2672,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a583)) | (~c0_1(a583)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 1.63/1.78 tff(2673,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2672, 156, 2654, 733, 732, 731, 2624, 2638, 2623, 707, 2666, 2661])).
% 1.63/1.78 tff(2674,plain,((~hskp4) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | c0_1(a545) | (~hskp50) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.63/1.78 tff(2675,plain,
% 1.63/1.78 (~hskp4),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2674, 2595, 2597, 2596, 88, 86, 2598, 97, 2463, 35])).
% 1.63/1.78 tff(2676,plain,
% 1.63/1.78 (hskp6),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[205, 2675, 96])).
% 1.63/1.78 tff(2677,plain,
% 1.63/1.78 (~c2_1(a548)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[217, 2676])).
% 1.63/1.78 tff(2678,plain,
% 1.63/1.78 (~c0_1(a548)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[211, 2676])).
% 1.63/1.78 tff(2679,plain,
% 1.63/1.78 (c3_1(a548)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2491, 156, 35, 2476, 2475, 2474, 24, 56, 85])).
% 1.63/1.78 tff(2680,plain,
% 1.63/1.78 (c2_1(a586)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2484, 2475, 86, 2476, 2474, 87, 35])).
% 1.63/1.78 tff(2681,plain,
% 1.63/1.78 (~c1_1(a548)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2549, 946, 249])).
% 1.63/1.78 tff(2682,plain,
% 1.63/1.78 (hskp28),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2561, 2681, 24])).
% 1.63/1.78 tff(2683,plain,
% 1.63/1.78 (c3_1(a589)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[185, 2682])).
% 1.63/1.78 tff(2684,plain,
% 1.63/1.78 (c2_1(a589)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[171, 2682])).
% 1.63/1.78 tff(2685,plain,
% 1.63/1.78 (~c1_1(a589)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2051, 156, 946, 2684, 2683, 87, 86, 858, 902])).
% 1.63/1.78 tff(2686,plain,
% 1.63/1.78 (~hskp37),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2512, 2685, 2684, 2683, 109])).
% 1.63/1.78 tff(2687,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2688,plain,
% 1.63/1.79 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2689,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2688])).
% 1.63/1.79 tff(2690,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2689, 2687])).
% 1.63/1.79 tff(2691,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2692,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2691, 2690])).
% 1.63/1.79 tff(2693,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2692, 156, 733, 732, 731, 249, 730, 722, 24, 714, 707, 57])).
% 1.63/1.79 tff(2694,plain,((~hskp0) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | (~c3_1(a548)) | c2_1(a548) | c1_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2695,plain,
% 1.63/1.79 (~hskp0),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2694, 2681, 732, 731, 249, 24, 733])).
% 1.63/1.79 tff(2696,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2697,plain,
% 1.63/1.79 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a572) | c1_1(a572) | c3_1(a572)) <=> (hskp0 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2698,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a572) | c1_1(a572) | c3_1(a572))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2697])).
% 1.63/1.79 tff(2699,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a572) | c1_1(a572) | c3_1(a572))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2698, 2696])).
% 1.63/1.79 tff(2700,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a572) | c1_1(a572) | c3_1(a572))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2701,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a572) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2700, 2699])).
% 1.63/1.79 tff(2702,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2701, 156, 837, 733, 732, 731, 421, 390, 108, 2581])).
% 1.63/1.79 tff(2703,plain,((~hskp18) | hskp0 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp37), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2704,plain,
% 1.63/1.79 (~hskp18),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2703, 2695, 733, 732, 731, 2686])).
% 1.63/1.79 tff(2705,plain,
% 1.63/1.79 (hskp17),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[382, 2704, 2366])).
% 1.63/1.79 tff(2706,plain,
% 1.63/1.79 (~c2_1(a571)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[573, 2705])).
% 1.63/1.79 tff(2707,plain,
% 1.63/1.79 (c3_1(a571)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[623, 2705])).
% 1.63/1.79 tff(2708,plain,
% 1.63/1.79 (c0_1(a571)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[581, 2705])).
% 1.63/1.79 tff(2709,plain,
% 1.63/1.79 (c1_1(a571)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[931, 156, 88, 2708, 2707, 86, 2706, 921, 902])).
% 1.63/1.79 tff(2710,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2377, 156, 733, 732, 731, 2708, 249, 2706, 24, 707, 2681, 2709])).
% 1.63/1.79 tff(2711,plain,(hskp46 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | (~c3_1(a548)) | c2_1(a548) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | hskp15 | c0_1(a586) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2712,plain,
% 1.63/1.79 (hskp46),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2711, 2679, 732, 731, 733, 24, 88, 86, 2680, 109, 87, 56])).
% 1.63/1.79 tff(2713,plain,
% 1.63/1.79 (~c0_1(a562)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[64, 2712])).
% 1.63/1.79 tff(2714,plain,
% 1.63/1.79 (~c3_1(a562)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[270, 2712])).
% 1.63/1.79 tff(2715,plain,
% 1.63/1.79 (c1_1(a562)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[288, 2712])).
% 1.63/1.79 tff(2716,plain,
% 1.63/1.79 (hskp34),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2160, 156, 2715, 733, 732, 731, 2714, 2713, 75])).
% 1.63/1.79 tff(2717,plain,
% 1.63/1.79 (~c1_1(a537)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1124, 2716])).
% 1.63/1.79 tff(2718,plain,
% 1.63/1.79 (c3_1(a537)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1132, 2716])).
% 1.63/1.79 tff(2719,plain,
% 1.63/1.79 (c0_1(a537)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1147, 2716])).
% 1.63/1.79 tff(2720,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a586) | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a586) | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2721,plain,
% 1.63/1.79 ((hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c0_1(a586) | (~c2_1(a586))) <=> (hskp8 | c1_1(a586) | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2722,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a586) | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2721])).
% 1.63/1.79 tff(2723,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c0_1(a586) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a586) | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2722, 2720])).
% 1.63/1.79 tff(2724,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c0_1(a586) | (~c2_1(a586)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2725,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a586) | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2724, 2723])).
% 1.63/1.79 tff(2726,plain,
% 1.63/1.79 (hskp8),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2725, 156, 2719, 2718, 88, 2717, 87, 2407, 2680])).
% 1.63/1.79 tff(2727,plain,
% 1.63/1.79 (~c2_1(a552)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2424, 2726])).
% 1.63/1.79 tff(2728,plain,
% 1.63/1.79 (~c1_1(a552)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2453, 2726])).
% 1.63/1.79 tff(2729,plain,
% 1.63/1.79 (~c3_1(a552)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2430, 2726])).
% 1.63/1.79 tff(2730,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2731,plain,
% 1.63/1.79 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2732,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2731])).
% 1.63/1.79 tff(2733,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2732, 2730])).
% 1.63/1.79 tff(2734,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2735,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 1.63/1.79 tff(2736,plain,
% 1.63/1.79 (hskp0),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2735, 156, 733, 732, 731, 2729, 2728, 2727, 108])).
% 1.63/1.79 tff(2737,plain,
% 1.63/1.79 (c1_1(a548)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2694, 2736, 732, 731, 2679, 24, 733])).
% 1.63/1.79 tff(2738,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2739,plain,
% 1.63/1.79 (((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2740,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2739])).
% 1.63/1.79 tff(2741,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2740, 2738])).
% 1.63/1.79 tff(2742,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2743,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 1.63/1.79 tff(2744,plain,
% 1.63/1.79 ((~c1_1(a548)) | (~c2_1(a537))),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2743, 156, 2718, 2679, 2717, 2729, 2728, 2727, 24, 45])).
% 1.63/1.79 tff(2745,plain,
% 1.63/1.79 (~c2_1(a537)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2744, 2737])).
% 1.63/1.79 tff(2746,plain,
% 1.63/1.79 (~c2_1(a535)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[713, 2736])).
% 1.63/1.79 tff(2747,plain,
% 1.63/1.79 (c0_1(a535)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[721, 2736])).
% 1.63/1.79 tff(2748,plain,
% 1.63/1.79 (c1_1(a535)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[729, 2736])).
% 1.63/1.79 tff(2749,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2750,plain,
% 1.63/1.79 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2751,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2750])).
% 1.63/1.79 tff(2752,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2751, 2749])).
% 1.63/1.79 tff(2753,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2754,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 1.63/1.79 tff(2755,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2754, 156, 733, 732, 731, 2718, 2748, 2747, 2717, 2746, 707, 2745])).
% 1.63/1.79 tff(2756,plain,(c2_1(a548) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c1_1(a586) | c0_1(a586) | c3_1(a586) | hskp15 | c0_1(a548) | hskp33 | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2757,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2756, 2678, 2677, 2597, 2596, 88, 87, 86, 109, 2595, 35, 2466, 2465, 2464])).
% 1.63/1.79 tff(2758,plain,(hskp15 | c1_1(a586) | c0_1(a586) | c3_1(a586) | hskp33 | c0_1(a545) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2759,plain,
% 1.63/1.79 (hskp15),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2758, 98, 87, 86, 35, 97, 88])).
% 1.63/1.79 tff(2760,plain,
% 1.63/1.79 (hskp28),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1276, 2759])).
% 1.63/1.79 tff(2761,plain,
% 1.63/1.79 (c2_1(a589)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[171, 2760])).
% 1.63/1.79 tff(2762,plain,
% 1.63/1.79 (~c1_1(a569)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1261, 2759])).
% 1.63/1.79 tff(2763,plain,
% 1.63/1.79 (~c2_1(a569)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1255, 2759])).
% 1.63/1.79 tff(2764,plain,
% 1.63/1.79 (~c0_1(a569)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1267, 2759])).
% 1.63/1.79 tff(2765,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2484, 808, 816, 86, 653, 800, 87, 35])).
% 1.63/1.79 tff(2766,plain,((~hskp50) | c3_1(a586) | c2_1(a586) | c0_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2767,plain,
% 1.63/1.79 (~hskp50),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2766, 653, 86, 87, 35])).
% 1.63/1.79 tff(2768,assumption,(hskp38), introduced(assumption)).
% 1.63/1.79 tff(2769,plain,
% 1.63/1.79 (c0_1(a547)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[677, 2768])).
% 1.63/1.79 tff(2770,plain,
% 1.63/1.79 (c1_1(a547)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[685, 2768])).
% 1.63/1.79 tff(2771,plain,
% 1.63/1.79 (c2_1(a547)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[693, 2768])).
% 1.63/1.79 tff(2772,plain,
% 1.63/1.79 (hskp0),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[845, 2771, 653, 2770, 2769, 88, 86])).
% 1.63/1.79 tff(2773,plain,
% 1.63/1.79 (~c2_1(a535)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[713, 2772])).
% 1.63/1.79 tff(2774,assumption,(~c2_1(a569)), introduced(assumption)).
% 1.63/1.79 tff(2775,assumption,(~c1_1(a569)), introduced(assumption)).
% 1.63/1.79 tff(2776,plain,
% 1.63/1.79 (c0_1(a535)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[721, 2772])).
% 1.63/1.79 tff(2777,plain,
% 1.63/1.79 (c1_1(a535)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[729, 2772])).
% 1.63/1.79 tff(2778,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2779,plain,
% 1.63/1.79 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2780,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2779])).
% 1.63/1.79 tff(2781,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2780, 2778])).
% 1.63/1.79 tff(2782,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2783,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2782, 2781])).
% 1.63/1.79 tff(2784,plain,
% 1.63/1.79 (~c3_1(a569)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2783, 156, 2771, 2770, 2769, 2777, 2776, 2775, 2774, 2773, 707])).
% 1.63/1.79 tff(2785,assumption,(~c0_1(a569)), introduced(assumption)).
% 1.63/1.79 tff(2786,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a569))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2787,plain,
% 1.63/1.79 ((hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a569) | c3_1(a569) | c0_1(a569)) <=> (hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a569))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2788,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a569)))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2787])).
% 1.63/1.79 tff(2789,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a569))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2788, 2786])).
% 1.63/1.79 tff(2790,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a569) | c3_1(a569) | c0_1(a569))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2791,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a569)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 1.63/1.79 tff(2792,plain,
% 1.63/1.79 (hskp45),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2791, 156, 2777, 2776, 2785, 2774, 2773, 757, 2784])).
% 1.63/1.79 tff(2793,plain,
% 1.63/1.79 (~c3_1(a561)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[771, 2792])).
% 1.63/1.79 tff(2794,plain,
% 1.63/1.79 (c0_1(a561)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[779, 2792])).
% 1.63/1.79 tff(2795,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c1_1(a561)) | (~c0_1(a561)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2796,plain,
% 1.63/1.79 ((hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a569) | c3_1(a569) | c0_1(a569)) <=> (hskp33 | c3_1(a561) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2797,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c1_1(a561)) | (~c0_1(a561))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[2796])).
% 1.63/1.79 tff(2798,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[2797, 2795])).
% 1.63/1.79 tff(2799,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a569) | c3_1(a569) | c0_1(a569))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(2800,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c1_1(a561)) | (~c0_1(a561))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 1.63/1.79 tff(2801,plain,
% 1.63/1.79 (~c1_1(a561)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2800, 156, 35, 2794, 2793, 2785, 2774, 85, 2784])).
% 1.63/1.79 tff(2802,plain,
% 1.63/1.79 (~c2_1(a561)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[792, 2792])).
% 1.63/1.79 tff(2803,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[831, 156, 110, 98, 2794, 2802, 34, 2801])).
% 1.63/1.79 tff(2804,plain,((~hskp38) | hskp50 | hskp19 | hskp33 | c0_1(a569) | c2_1(a569) | c1_1(a569) | c2_1(a586) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2805,plain,
% 1.63/1.79 (~hskp38),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2804, 2767, 98, 35, 2764, 2763, 2762, 653, 88, 86])).
% 1.63/1.79 tff(2806,plain,
% 1.63/1.79 (hskp6),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2470, 2805, 88, 35, 86, 97])).
% 1.63/1.79 tff(2807,plain,
% 1.63/1.79 (~c3_1(a548)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2204, 58, 88, 653, 86, 24, 56])).
% 1.63/1.79 tff(2808,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[225, 2471, 2807])).
% 1.63/1.79 tff(2809,plain,(hskp38 | c1_1(a586) | hskp33 | c3_1(a586) | c0_1(a545) | c2_1(a586) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2810,plain,
% 1.63/1.79 (c0_1(a548)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2809, 2805, 35, 86, 97, 653, 24, 88])).
% 1.63/1.79 tff(2811,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[211, 2810, 2806])).
% 1.63/1.79 tff(2812,plain,(c2_1(a586) | hskp33 | c3_1(a586) | c0_1(a545) | c2_1(a548) | c1_1(a586) | hskp19 | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(2813,plain,
% 1.63/1.79 (c2_1(a586)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2812, 24, 86, 97, 35, 88, 98, 87])).
% 1.63/1.79 tff(2814,plain,
% 1.63/1.79 (c3_1(a589)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[185, 2760])).
% 1.63/1.79 tff(2815,plain,
% 1.63/1.79 (c3_1(a548)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[225, 2471])).
% 1.63/1.79 tff(2816,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a569) | c2_1(a569) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a569) | c2_1(a569) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a569))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(2817,plain,
% 1.63/1.80 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (hskp38 | c1_1(a569) | c2_1(a569) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a569))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2818,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c1_1(a569) | c2_1(a569) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a569)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2817])).
% 1.63/1.80 tff(2819,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a569) | c2_1(a569) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a569))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2818, 2816])).
% 1.63/1.80 tff(2820,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2821,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c1_1(a569) | c2_1(a569) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a569)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2820, 2819])).
% 1.63/1.80 tff(2822,plain,
% 1.63/1.80 (hskp38 | c0_1(a548) | (~c3_1(a548)) | c3_1(a569)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2821, 156, 2775, 2774, 24, 663])).
% 1.63/1.80 tff(2823,plain,
% 1.63/1.80 (c3_1(a569)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2822, 2473, 58, 2815])).
% 1.63/1.80 tff(2824,assumption,(c3_1(a569)), introduced(assumption)).
% 1.63/1.80 tff(2825,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2826,plain,
% 1.63/1.80 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2827,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2826])).
% 1.63/1.80 tff(2828,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2827, 2825])).
% 1.63/1.80 tff(2829,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2830,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 1.63/1.80 tff(2831,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2830, 156, 925, 87, 86, 923, 2785, 2775, 609, 902, 2824, 932])).
% 1.63/1.80 tff(2832,plain,((~hskp17) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~c2_1(a586)) | (~c3_1(a569)) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(2833,plain,
% 1.63/1.80 (~hskp17),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2832, 2823, 86, 2785, 2775, 902, 87, 88])).
% 1.63/1.80 tff(2834,plain,
% 1.63/1.80 (hskp46 | c0_1(a548) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2231, 156, 24, 12])).
% 1.63/1.80 tff(2835,plain,
% 1.63/1.80 (~c1_1(a548)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2834, 946, 56, 249])).
% 1.63/1.80 tff(2836,plain,
% 1.63/1.80 (hskp37),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2583, 2514, 58, 24, 56, 249])).
% 1.63/1.80 tff(2837,plain,
% 1.63/1.80 (~c2_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[436, 2836])).
% 1.63/1.80 tff(2838,plain,
% 1.63/1.80 (c1_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[444, 2836])).
% 1.63/1.80 tff(2839,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2840,plain,
% 1.63/1.80 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2841,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2840])).
% 1.63/1.80 tff(2842,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2841, 2839])).
% 1.63/1.80 tff(2843,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2844,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 1.63/1.80 tff(2845,plain,
% 1.63/1.80 (~c0_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2844, 156, 2838, 249, 2837, 87, 86, 56, 609, 902, 2835])).
% 1.63/1.80 tff(2846,plain,
% 1.63/1.80 (~c3_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[450, 2836])).
% 1.63/1.80 tff(2847,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a544) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c0_1(a544) | (~c1_1(a544)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2848,plain,
% 1.63/1.80 ((hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569))) <=> (hskp26 | c3_1(a544) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c0_1(a544) | (~c1_1(a544)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2849,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a544) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c0_1(a544) | (~c1_1(a544))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2848])).
% 1.63/1.80 tff(2850,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c0_1(a544) | (~c1_1(a544)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2849, 2847])).
% 1.63/1.80 tff(2851,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2852,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c0_1(a544) | (~c1_1(a544))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 1.63/1.80 tff(2853,plain,
% 1.63/1.80 (hskp26),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2852, 156, 2838, 2846, 2785, 2775, 1686, 2824, 2845])).
% 1.63/1.80 tff(2854,plain,
% 1.63/1.80 (~c3_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1620, 2853])).
% 1.63/1.80 tff(2855,plain,
% 1.63/1.80 (c1_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1637, 2853])).
% 1.63/1.80 tff(2856,plain,
% 1.63/1.80 (c0_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1629, 2853])).
% 1.63/1.80 tff(2857,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a544) | c3_1(a544) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a544) | c3_1(a544) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a544))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2858,plain,
% 1.63/1.80 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a544) | c3_1(a544) | c0_1(a544)) <=> (hskp33 | c2_1(a544) | c3_1(a544) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a544))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2859,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a544) | c3_1(a544) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a544)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2858])).
% 1.63/1.80 tff(2860,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a544) | c3_1(a544) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a544))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2859, 2857])).
% 1.63/1.80 tff(2861,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a544) | c3_1(a544) | c0_1(a544))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2862,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a544) | c3_1(a544) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a544)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2861, 2860])).
% 1.63/1.80 tff(2863,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2862, 156, 35, 2856, 2855, 2837, 2846, 2854, 85, 2845])).
% 1.63/1.80 tff(2864,plain,(hskp46 | hskp33 | c0_1(a569) | c1_1(a569) | (~c3_1(a569)) | (~c3_1(a548)) | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~c2_1(a586)) | hskp38 | c2_1(a548) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(2865,plain,
% 1.63/1.80 (hskp46),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2864, 2823, 2785, 2775, 35, 2815, 87, 86, 2473, 902, 58, 24, 2833])).
% 1.63/1.80 tff(2866,plain,
% 1.63/1.80 (~c0_1(a562)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[64, 2865])).
% 1.63/1.80 tff(2867,plain,
% 1.63/1.80 (~c3_1(a562)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[270, 2865])).
% 1.63/1.80 tff(2868,plain,
% 1.63/1.80 (c1_1(a562)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[288, 2865])).
% 1.63/1.80 tff(2869,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a562)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2870,plain,
% 1.63/1.80 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569))) <=> (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a562)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2871,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a562))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2870])).
% 1.63/1.80 tff(2872,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a562)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2871, 2869])).
% 1.63/1.80 tff(2873,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2874,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c1_1(a562))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2873, 2872])).
% 1.63/1.80 tff(2875,plain,
% 1.63/1.80 (hskp26),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2874, 156, 2868, 2867, 2866, 2785, 2775, 1686, 2823])).
% 1.63/1.80 tff(2876,plain,
% 1.63/1.80 (~hskp4),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1659, 2875, 58, 35, 97])).
% 1.63/1.80 tff(2877,plain,
% 1.63/1.80 (~c1_1(a548)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2559, 2876, 2473, 24, 2815])).
% 1.63/1.80 tff(2878,plain,
% 1.63/1.80 (hskp4 | (~c1_1(a589))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2291, 156, 2868, 625, 591, 2867, 2866, 22])).
% 1.63/1.80 tff(2879,plain,
% 1.63/1.80 (~c1_1(a589)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2878, 2876])).
% 1.63/1.80 tff(2880,plain,
% 1.63/1.80 (~hskp39),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2535, 2879, 58, 591, 625])).
% 1.63/1.80 tff(2881,plain,
% 1.63/1.80 (~hskp16),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2301, 2880, 58, 591, 625, 2868, 2866, 2867, 2879])).
% 1.63/1.80 tff(2882,plain,
% 1.63/1.80 (hskp18),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[382, 2881, 2833])).
% 1.63/1.80 tff(2883,plain,
% 1.63/1.80 (hskp37),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2583, 2882, 58, 24, 2473, 2815])).
% 1.63/1.80 tff(2884,plain,
% 1.63/1.80 (~c2_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[436, 2883])).
% 1.63/1.80 tff(2885,plain,
% 1.63/1.80 (c1_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[444, 2883])).
% 1.63/1.80 tff(2886,plain,
% 1.63/1.80 (~c0_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2844, 156, 2885, 2815, 2884, 87, 86, 2473, 609, 902, 2877])).
% 1.63/1.80 tff(2887,plain,
% 1.63/1.80 (~c3_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1620, 2875])).
% 1.63/1.80 tff(2888,plain,
% 1.63/1.80 (~c3_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[450, 2883])).
% 1.63/1.80 tff(2889,plain,
% 1.63/1.80 (c1_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1637, 2875])).
% 1.63/1.80 tff(2890,plain,
% 1.63/1.80 (c0_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1629, 2875])).
% 1.63/1.80 tff(2891,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2862, 156, 35, 2890, 2889, 2884, 2888, 2887, 85, 2886])).
% 1.63/1.80 tff(2892,plain,(hskp38 | hskp33 | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c2_1(a548) | (~c3_1(a589)) | (~c2_1(a589)) | c0_1(a545) | c0_1(a569) | c1_1(a569) | c1_1(a586) | c2_1(a569)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(2893,plain,
% 1.63/1.80 (hskp38),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2892, 2813, 87, 86, 35, 24, 2814, 2761, 97, 2764, 2762, 88, 2763])).
% 1.63/1.80 tff(2894,plain,
% 1.63/1.80 (c2_1(a547)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[693, 2893])).
% 1.63/1.80 tff(2895,assumption,(~c3_1(a548)), introduced(assumption)).
% 1.63/1.80 tff(2896,plain,
% 1.63/1.80 (~hskp6),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[225, 2895])).
% 1.63/1.80 tff(2897,assumption,(~hskp27), introduced(assumption)).
% 1.63/1.80 tff(2898,plain,
% 1.63/1.80 (hskp4),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[205, 2896, 2897])).
% 1.63/1.80 tff(2899,plain,
% 1.63/1.80 (c1_1(a545)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[193, 2898])).
% 1.63/1.80 tff(2900,plain,
% 1.63/1.80 (hskp26),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1971, 2899, 1250, 97, 2896])).
% 1.63/1.80 tff(2901,plain,
% 1.63/1.80 (~c3_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1620, 2900])).
% 1.63/1.80 tff(2902,plain,
% 1.63/1.80 (c1_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1637, 2900])).
% 1.63/1.80 tff(2903,plain,
% 1.63/1.80 (c0_1(a584)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1629, 2900])).
% 1.63/1.80 tff(2904,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c3_1(a584) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a584) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2905,plain,
% 1.63/1.80 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a548) | c3_1(a548) | c0_1(a548)) <=> (hskp33 | c3_1(a548) | c3_1(a584) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2906,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c3_1(a584) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2905])).
% 1.63/1.80 tff(2907,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a584) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.63/1.80 tff(2908,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a548) | c3_1(a548) | c0_1(a548))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2909,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a584) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.63/1.80 tff(2910,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2909, 156, 35, 2903, 2902, 2895, 2901, 24, 56, 85])).
% 1.63/1.80 tff(2911,plain,(c3_1(a548) | hskp33 | c2_1(a548) | c0_1(a548) | (~hskp15) | c0_1(a545) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(2912,plain,
% 1.63/1.80 (c3_1(a548)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2911, 56, 24, 35, 2759, 97, 96])).
% 1.63/1.80 tff(2913,plain,
% 1.63/1.80 (c0_1(a547)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[677, 2893])).
% 1.63/1.80 tff(2914,plain,
% 1.63/1.80 (c1_1(a547)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[685, 2893])).
% 1.63/1.80 tff(2915,plain,
% 1.63/1.80 (~c0_1(a589)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[177, 2760])).
% 1.63/1.80 tff(2916,plain,
% 1.63/1.80 (hskp46 | (~c2_1(a586)) | (~c1_1(a589))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2051, 156, 625, 591, 87, 86, 858])).
% 1.63/1.80 tff(2917,plain,
% 1.63/1.80 (~c1_1(a589)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2916, 946, 902])).
% 1.63/1.80 tff(2918,plain,
% 1.63/1.80 (~hskp0),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2694, 2835, 732, 731, 249, 24, 733])).
% 1.63/1.80 tff(2919,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2920,plain,
% 1.63/1.80 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (hskp0 | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2921,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[2920])).
% 1.63/1.80 tff(2922,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[2921, 2919])).
% 1.63/1.80 tff(2923,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(2924,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 1.63/1.80 tff(2925,plain,
% 1.63/1.80 (hskp0 | c3_1(a569)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2924, 156, 733, 732, 731, 2775, 2774, 108])).
% 1.63/1.80 tff(2926,plain,
% 1.63/1.80 (c3_1(a569)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2925, 2918])).
% 1.63/1.80 tff(2927,plain,
% 1.63/1.80 (~hskp17),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2832, 2926, 86, 2785, 2775, 902, 87, 88])).
% 1.63/1.80 tff(2928,plain,
% 1.63/1.80 (hskp18),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[382, 2927, 2366])).
% 1.63/1.80 tff(2929,plain,
% 1.63/1.80 (hskp37),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[430, 2928, 110, 98])).
% 1.63/1.80 tff(2930,plain,
% 1.63/1.80 (~c2_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[436, 2929])).
% 1.63/1.80 tff(2931,plain,
% 1.63/1.80 (c1_1(a544)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[444, 2929])).
% 1.63/1.80 tff(2932,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2933,plain,
% 1.63/1.80 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(2934,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2933])).
% 1.63/1.81 tff(2935,plain,
% 1.63/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[2934, 2932])).
% 1.63/1.81 tff(2936,plain,
% 1.63/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(2937,plain,
% 1.63/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 1.63/1.81 tff(2938,plain,
% 1.63/1.81 (~c0_1(a544)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2937, 156, 2931, 591, 2930, 590, 87, 86, 609, 2917, 902])).
% 1.63/1.81 tff(2939,plain,
% 1.63/1.81 (~c3_1(a544)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[450, 2929])).
% 1.63/1.81 tff(2940,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(2941,plain,
% 1.63/1.81 ((hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544))) <=> (hskp34 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(2942,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2941])).
% 1.63/1.81 tff(2943,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[2942, 2940])).
% 1.63/1.81 tff(2944,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(2945,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[2944, 2943])).
% 1.63/1.81 tff(2946,plain,
% 1.63/1.81 (hskp34 | c0_1(a544)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2945, 156, 733, 732, 731, 2931, 2939, 75])).
% 1.63/1.81 tff(2947,plain,
% 1.63/1.81 (hskp34),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2946, 2938])).
% 1.63/1.81 tff(2948,plain,
% 1.63/1.81 (~c1_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1124, 2947])).
% 1.63/1.81 tff(2949,plain,
% 1.63/1.81 (c3_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1132, 2947])).
% 1.63/1.81 tff(2950,plain,
% 1.63/1.81 (c0_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1147, 2947])).
% 1.63/1.81 tff(2951,plain,
% 1.63/1.81 (hskp8),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2725, 156, 2950, 2949, 88, 2948, 87, 2407, 902])).
% 1.63/1.81 tff(2952,plain,
% 1.63/1.81 (~c2_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2424, 2951])).
% 1.63/1.81 tff(2953,plain,
% 1.63/1.81 (~c1_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2453, 2951])).
% 1.63/1.81 tff(2954,plain,
% 1.63/1.81 (~c3_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2430, 2951])).
% 1.63/1.81 tff(2955,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2735, 156, 2918, 733, 732, 731, 2954, 2953, 2952, 108])).
% 1.63/1.81 tff(2956,plain,(hskp46 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c1_1(a586) | c0_1(a586) | (~c2_1(a586)) | (~c3_1(a589)) | c0_1(a589) | c3_1(a586) | hskp50 | hskp19 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | (~c2_1(a589))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(2957,plain,
% 1.63/1.81 (hskp46),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2956, 110, 732, 731, 88, 87, 902, 591, 590, 86, 733, 98, 2785, 2775, 2774, 249, 24, 56, 625])).
% 1.63/1.81 tff(2958,plain,
% 1.63/1.81 (~c0_1(a562)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[64, 2957])).
% 1.63/1.81 tff(2959,plain,
% 1.63/1.81 (~c3_1(a562)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[270, 2957])).
% 1.63/1.81 tff(2960,plain,
% 1.63/1.81 (c1_1(a562)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[288, 2957])).
% 1.63/1.81 tff(2961,plain,
% 1.63/1.81 (hskp34),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2160, 156, 2960, 733, 732, 731, 2959, 2958, 75])).
% 1.63/1.81 tff(2962,plain,
% 1.63/1.81 (~c1_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1124, 2961])).
% 1.63/1.81 tff(2963,plain,
% 1.63/1.81 (c0_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1147, 2961])).
% 1.63/1.81 tff(2964,plain,
% 1.63/1.81 (c2_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1154, 156, 110, 98, 2963, 2962, 34])).
% 1.63/1.81 tff(2965,plain,
% 1.63/1.81 (c3_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1132, 2961])).
% 1.63/1.81 tff(2966,plain,
% 1.63/1.81 (hskp8),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2725, 156, 2963, 2965, 88, 2962, 87, 2407, 902])).
% 1.63/1.81 tff(2967,plain,
% 1.63/1.81 (~c2_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2424, 2966])).
% 1.63/1.81 tff(2968,plain,
% 1.63/1.81 (~c1_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2453, 2966])).
% 1.63/1.81 tff(2969,plain,
% 1.63/1.81 (~c3_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2430, 2966])).
% 1.63/1.81 tff(2970,plain,
% 1.63/1.81 (~c1_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2743, 156, 2965, 249, 2962, 2969, 2968, 2967, 24, 45, 2964])).
% 1.63/1.81 tff(2971,plain,
% 1.63/1.81 (hskp0),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2735, 156, 733, 732, 731, 2969, 2968, 2967, 108])).
% 1.63/1.81 tff(2972,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2694, 2971, 2970, 732, 731, 249, 24, 733])).
% 1.63/1.81 tff(2973,plain,(hskp50 | (~c1_1(a547)) | (~c0_1(a547)) | (~c3_1(a548)) | c2_1(a548) | (~c2_1(a547)) | c1_1(a586) | c0_1(a586) | (~c2_1(a586)) | hskp19 | (~c3_1(a589)) | c0_1(a589) | c3_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a569) | c0_1(a548) | (~c2_1(a589))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(2974,plain,
% 1.63/1.81 (hskp50),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2973, 2912, 2913, 2914, 24, 2894, 88, 87, 2813, 98, 2814, 2915, 86, 2764, 2762, 2763, 56, 2761])).
% 1.63/1.81 tff(2975,plain,
% 1.63/1.81 (~hskp4),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2674, 2974, 2813, 2913, 88, 86, 2894, 97, 2914, 35])).
% 1.63/1.81 tff(2976,plain,
% 1.63/1.81 (~c1_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2559, 2975, 56, 24, 2912])).
% 1.63/1.81 tff(2977,plain,
% 1.63/1.81 (~hskp0),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2694, 2976, 2914, 2913, 2912, 24, 2894])).
% 1.63/1.81 tff(2978,plain,
% 1.63/1.81 (hskp0 | c3_1(a569)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2924, 156, 2894, 2914, 2913, 2762, 2763, 108])).
% 1.63/1.81 tff(2979,plain,
% 1.63/1.81 (c3_1(a569)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2978, 2977])).
% 1.63/1.81 tff(2980,plain,
% 1.63/1.81 (~hskp17),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2832, 2979, 86, 2764, 2762, 2813, 87, 88])).
% 1.63/1.81 tff(2981,plain,
% 1.63/1.81 (~c3_1(a574)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[799, 2974])).
% 1.63/1.81 tff(2982,plain,
% 1.63/1.81 (c1_1(a574)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[807, 2974])).
% 1.63/1.81 tff(2983,plain,
% 1.63/1.81 (c0_1(a574)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[815, 2974])).
% 1.63/1.81 tff(2984,plain,
% 1.63/1.81 (hskp37),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2703, 2514, 733, 732, 731, 837])).
% 1.63/1.81 tff(2985,plain,
% 1.63/1.81 (~c2_1(a544)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[436, 2984])).
% 1.63/1.81 tff(2986,plain,
% 1.63/1.81 (c1_1(a544)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[444, 2984])).
% 1.63/1.81 tff(2987,plain,
% 1.63/1.81 (~c0_1(a544)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2937, 156, 2986, 591, 2985, 590, 87, 86, 609, 2917, 902])).
% 1.63/1.81 tff(2988,plain,
% 1.63/1.81 (~c3_1(a544)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[450, 2984])).
% 1.63/1.81 tff(2989,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(2990,plain,
% 1.63/1.81 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a544) | c3_1(a544) | c0_1(a544)) <=> (hskp33 | c3_1(a574) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(2991,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c0_1(a574)) | (~c1_1(a574))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2990])).
% 1.63/1.81 tff(2992,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[2991, 2989])).
% 1.63/1.81 tff(2993,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a544) | c3_1(a544) | c0_1(a544))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(2994,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c0_1(a574)) | (~c1_1(a574))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[2993, 2992])).
% 1.63/1.81 tff(2995,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2994, 156, 35, 2476, 2475, 2474, 2985, 2988, 85, 2987])).
% 1.63/1.81 tff(2996,plain,(hskp46 | hskp33 | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | (~c3_1(a589)) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp0 | hskp17 | (~c2_1(a589))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(2997,plain,
% 1.63/1.81 (hskp46),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2996, 2983, 35, 2982, 2981, 2814, 2915, 87, 86, 2813, 2894, 2914, 2913, 2977, 2980, 2761])).
% 1.63/1.81 tff(2998,plain,
% 1.63/1.81 (~c0_1(a562)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[64, 2997])).
% 1.63/1.81 tff(2999,plain,
% 1.63/1.81 (~c3_1(a562)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[270, 2997])).
% 1.63/1.81 tff(3000,plain,
% 1.63/1.81 (c1_1(a562)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[288, 2997])).
% 1.63/1.81 tff(3001,plain,
% 1.63/1.81 (~c1_1(a589)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2291, 156, 2975, 3000, 2761, 2814, 2999, 2998, 22])).
% 1.63/1.81 tff(3002,plain,
% 1.63/1.81 (hskp34),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2160, 156, 3000, 2894, 2914, 2913, 2999, 2998, 75])).
% 1.63/1.81 tff(3003,plain,
% 1.63/1.81 (~c1_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1124, 3002])).
% 1.63/1.81 tff(3004,plain,
% 1.63/1.81 (c3_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1132, 3002])).
% 1.63/1.81 tff(3005,plain,
% 1.63/1.81 (c0_1(a537)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1147, 3002])).
% 1.63/1.81 tff(3006,plain,
% 1.63/1.81 (hskp8),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2418, 156, 3005, 3004, 2761, 3003, 2915, 2407, 3001])).
% 1.63/1.81 tff(3007,plain,
% 1.63/1.81 (~c2_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2424, 3006])).
% 1.63/1.81 tff(3008,plain,
% 1.63/1.81 (~c1_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2453, 3006])).
% 1.63/1.81 tff(3009,plain,
% 1.63/1.81 (~c3_1(a552)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2430, 3006])).
% 1.63/1.81 tff(3010,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2735, 156, 2977, 2894, 2914, 2913, 3009, 3008, 3007, 108])).
% 1.63/1.81 tff(3011,plain,(c0_1(a548) | hskp33 | c0_1(a586) | c3_1(a586) | c1_1(a586) | c2_1(a548) | c0_1(a545) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3012,plain,
% 1.63/1.81 (c0_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3011, 24, 87, 86, 88, 35, 97, 98])).
% 1.63/1.81 tff(3013,plain,
% 1.63/1.81 (~hskp6),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[211, 3012])).
% 1.63/1.81 tff(3014,plain,
% 1.63/1.81 (hskp4),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[205, 3013, 96])).
% 1.63/1.81 tff(3015,plain,
% 1.63/1.81 (~hskp50),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2674, 3014, 2813, 2913, 88, 86, 2894, 97, 2914, 35])).
% 1.63/1.81 tff(3016,plain,
% 1.63/1.81 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3017,plain,
% 1.63/1.81 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548))) <=> (hskp50 | hskp19 | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3018,plain,
% 1.63/1.81 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3017])).
% 1.63/1.81 tff(3019,plain,
% 1.63/1.81 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3018, 3016])).
% 1.63/1.81 tff(3020,plain,
% 1.63/1.81 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3021,plain,
% 1.63/1.81 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 1.63/1.81 tff(3022,plain,
% 1.63/1.81 (hskp50 | (~c0_1(a548)) | c1_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3021, 156, 98, 24, 34])).
% 1.63/1.81 tff(3023,plain,
% 1.63/1.81 (c1_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3022, 3015, 3012])).
% 1.63/1.81 tff(3024,plain,
% 1.63/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a586)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3025,plain,
% 1.63/1.81 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))) <=> (c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a586)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3026,plain,
% 1.63/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a586))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3025])).
% 1.63/1.81 tff(3027,plain,
% 1.63/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a586)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3026, 3024])).
% 1.63/1.81 tff(3028,plain,
% 1.63/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3029,plain,
% 1.63/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a586))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3028, 3027])).
% 1.63/1.81 tff(3030,plain,
% 1.63/1.81 ((~c0_1(a548)) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a586))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3029, 156, 87, 86, 2764, 2762, 24, 609])).
% 1.63/1.81 tff(3031,plain,
% 1.63/1.81 (~c3_1(a569)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3030, 3023, 2813, 3012])).
% 1.63/1.81 tff(3032,plain,
% 1.63/1.81 (~c2_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1643, 3014])).
% 1.63/1.81 tff(3033,plain,
% 1.63/1.81 (c1_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[193, 3014])).
% 1.63/1.81 tff(3034,plain,
% 1.63/1.81 (hskp6 | (~c3_1(a545)) | (~c1_1(a545))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1782, 156, 2764, 2762, 2763, 97, 1745])).
% 1.63/1.81 tff(3035,plain,
% 1.63/1.81 (~c3_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3034, 3033, 3013])).
% 1.63/1.81 tff(3036,plain,
% 1.63/1.81 (~hskp45),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[833, 3035, 35, 3032, 97, 98])).
% 1.63/1.81 tff(3037,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3038,plain,
% 1.63/1.81 ((hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569)) <=> (hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3039,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3038])).
% 1.63/1.81 tff(3040,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3039, 3037])).
% 1.63/1.81 tff(3041,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3042,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c0_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3041, 3040])).
% 1.63/1.81 tff(3043,plain,
% 1.63/1.81 (hskp45 | (~c0_1(a548)) | (~c1_1(a548)) | c3_1(a569)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3042, 156, 2764, 2763, 24, 757])).
% 1.63/1.81 tff(3044,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3043, 3036, 3023, 3012, 3031])).
% 1.63/1.81 tff(3045,plain,(c2_1(a548) | c0_1(a586) | c3_1(a586) | hskp33 | c0_1(a545) | hskp19 | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3046,plain,
% 1.63/1.81 (c2_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3045, 98, 86, 35, 97, 87, 88])).
% 1.63/1.81 tff(3047,plain,
% 1.63/1.81 (~hskp6),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[217, 3046])).
% 1.63/1.81 tff(3048,plain,
% 1.63/1.81 (hskp4),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[205, 3047, 96])).
% 1.63/1.81 tff(3049,plain,
% 1.63/1.81 (c1_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[193, 3048])).
% 1.63/1.81 tff(3050,plain,
% 1.63/1.81 (~c3_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3034, 3049, 3047])).
% 1.63/1.81 tff(3051,plain,
% 1.63/1.81 (~c2_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1643, 3048])).
% 1.63/1.81 tff(3052,plain,
% 1.63/1.81 (hskp26),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1971, 3049, 2759, 97, 3047])).
% 1.63/1.81 tff(3053,plain,
% 1.63/1.81 (~c3_1(a584)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1620, 3052])).
% 1.63/1.81 tff(3054,plain,
% 1.63/1.81 (c1_1(a584)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1637, 3052])).
% 1.63/1.81 tff(3055,plain,
% 1.63/1.81 (c0_1(a584)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1629, 3052])).
% 1.63/1.81 tff(3056,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1655, 156, 35, 3055, 3054, 3053, 3051, 97, 85, 3050])).
% 1.63/1.81 tff(3057,plain,(hskp19 | hskp33 | c0_1(a545) | c3_1(a586) | c0_1(a586) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3058,plain,
% 1.63/1.81 (hskp19),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3057, 35, 97, 86, 87, 88])).
% 1.63/1.81 tff(3059,plain,
% 1.63/1.81 (~c0_1(a573)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1691, 3058])).
% 1.63/1.81 tff(3060,plain,
% 1.63/1.81 (~c2_1(a573)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1704, 3058])).
% 1.63/1.81 tff(3061,plain,
% 1.63/1.81 (hskp4),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[205, 1669, 2897])).
% 1.63/1.81 tff(3062,plain,
% 1.63/1.81 (c1_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[193, 3061])).
% 1.63/1.81 tff(3063,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c2_1(a573) | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a573) | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3064,plain,
% 1.63/1.81 ((hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a573) | c1_1(a573) | c0_1(a573)) <=> (hskp6 | c2_1(a573) | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3065,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a573) | c1_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c2_1(a573) | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3064])).
% 1.63/1.81 tff(3066,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a573) | c1_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a573) | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3065, 3063])).
% 1.63/1.81 tff(3067,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a573) | c1_1(a573) | c0_1(a573))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3068,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a573) | c0_1(a573) | c1_1(a573) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 1.63/1.81 tff(3069,plain,
% 1.63/1.81 (hskp6 | (~c3_1(a545)) | (~c1_1(a545))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3068, 156, 1705, 1692, 1676, 97, 1745])).
% 1.63/1.81 tff(3070,plain,
% 1.63/1.81 (~c3_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3069, 3062, 1669])).
% 1.63/1.81 tff(3071,plain,
% 1.63/1.81 (~c2_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1643, 3061])).
% 1.63/1.81 tff(3072,plain,
% 1.63/1.81 (hskp26),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1753, 3070, 1670, 1669, 3061])).
% 1.63/1.81 tff(3073,plain,
% 1.63/1.81 (~c3_1(a584)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1620, 3072])).
% 1.63/1.81 tff(3074,plain,
% 1.63/1.81 (c1_1(a584)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1637, 3072])).
% 1.63/1.81 tff(3075,plain,
% 1.63/1.81 (c0_1(a584)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1629, 3072])).
% 1.63/1.81 tff(3076,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1655, 156, 35, 3075, 3074, 3073, 3071, 97, 85, 3070])).
% 1.63/1.81 tff(3077,plain,(hskp6 | hskp33 | c0_1(a545) | (~hskp19) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3078,plain,
% 1.63/1.81 (hskp6),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3077, 35, 97, 3058, 96])).
% 1.63/1.81 tff(3079,plain,
% 1.63/1.81 (~c0_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[211, 3078])).
% 1.63/1.81 tff(3080,plain,
% 1.63/1.81 (~c2_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[217, 3078])).
% 1.63/1.81 tff(3081,plain,
% 1.63/1.81 (~c1_1(a573)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1675, 3058])).
% 1.63/1.81 tff(3082,plain,
% 1.63/1.81 (c3_1(a548)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[225, 3078])).
% 1.63/1.81 tff(3083,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a573) | c1_1(a573) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c1_1(a573) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a573))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3084,plain,
% 1.63/1.81 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a573) | c1_1(a573) | c3_1(a573)) <=> (hskp38 | c2_1(a573) | c1_1(a573) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a573))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3085,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a573) | c1_1(a573) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a573)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3084])).
% 1.63/1.81 tff(3086,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c1_1(a573) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a573))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3085, 3083])).
% 1.63/1.81 tff(3087,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a573) | c1_1(a573) | c3_1(a573))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3088,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c1_1(a573) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c3_1(a573)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 1.63/1.81 tff(3089,plain,
% 1.63/1.81 (hskp38 | c3_1(a573)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3088, 156, 3082, 3060, 3081, 3080, 3079, 663])).
% 1.63/1.81 tff(3090,plain,
% 1.63/1.81 (c3_1(a573)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3089, 58])).
% 1.63/1.81 tff(3091,plain,
% 1.63/1.81 (hskp28),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1711, 156, 3060, 3059, 3081, 122])).
% 1.63/1.81 tff(3092,plain,
% 1.63/1.81 (c3_1(a589)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[185, 3091])).
% 1.63/1.81 tff(3093,plain,
% 1.63/1.81 (c2_1(a589)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[171, 3091])).
% 1.63/1.81 tff(3094,plain,
% 1.63/1.81 (~c0_1(a589)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[177, 3091])).
% 1.63/1.81 tff(3095,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a586) | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a586) | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3096,plain,
% 1.63/1.81 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586) | c3_1(a586) | c0_1(a586)) <=> (hskp33 | c0_1(a586) | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3097,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a586) | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3096])).
% 1.63/1.81 tff(3098,plain,
% 1.63/1.81 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a586) | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3097, 3095])).
% 1.63/1.81 tff(3099,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586) | c3_1(a586) | c0_1(a586))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3100,plain,
% 1.63/1.81 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a586) | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a586)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3099, 3098])).
% 1.63/1.81 tff(3101,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3100, 156, 35, 1649, 1648, 87, 86, 1647, 85, 653])).
% 1.63/1.81 tff(3102,plain,(c2_1(a586) | hskp33 | (~c0_1(a584)) | (~c1_1(a584)) | c0_1(a586) | c3_1(a586) | c3_1(a584)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3103,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3102, 1621, 1630, 653, 1638, 87, 86, 35])).
% 1.63/1.81 tff(3104,plain,((~hskp26) | c2_1(a586) | c0_1(a586) | c3_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3105,plain,
% 1.63/1.81 (~hskp26),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3104, 653, 87, 86, 35])).
% 1.63/1.81 tff(3106,plain,
% 1.63/1.81 (~c1_1(a545)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1775, 1669, 87, 653, 1661, 97, 591, 88, 590])).
% 1.63/1.81 tff(3107,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[193, 3106, 2467])).
% 1.63/1.82 tff(3108,plain,(hskp6 | c0_1(a586) | c2_1(a586) | hskp26 | c0_1(a545) | (~c3_1(a589)) | c1_1(a586) | c0_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3109,plain,
% 1.63/1.82 (hskp6),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3108, 653, 87, 3105, 97, 3092, 88, 3094])).
% 1.63/1.82 tff(3110,plain,
% 1.63/1.82 (~c2_1(a548)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[217, 3109])).
% 1.63/1.82 tff(3111,plain,
% 1.63/1.82 (~c0_1(a548)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[211, 3109])).
% 1.63/1.82 tff(3112,plain,
% 1.63/1.82 (hskp38),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2809, 56, 35, 86, 97, 653, 24, 88])).
% 1.63/1.82 tff(3113,plain,
% 1.63/1.82 (c0_1(a547)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[677, 3112])).
% 1.63/1.82 tff(3114,plain,
% 1.63/1.82 (c1_1(a547)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[685, 3112])).
% 1.63/1.82 tff(3115,plain,
% 1.63/1.82 (c2_1(a547)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[693, 3112])).
% 1.63/1.82 tff(3116,plain,
% 1.63/1.82 (hskp0),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[845, 3115, 653, 3114, 3113, 88, 86])).
% 1.63/1.82 tff(3117,plain,
% 1.63/1.82 (~c2_1(a535)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[713, 3116])).
% 1.63/1.82 tff(3118,plain,
% 1.63/1.82 (c0_1(a535)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[721, 3116])).
% 1.63/1.82 tff(3119,plain,
% 1.63/1.82 (c1_1(a535)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[729, 3116])).
% 1.63/1.82 tff(3120,plain,
% 1.63/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a573)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a573)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3121,plain,
% 1.63/1.82 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a573)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3122,plain,
% 1.63/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a573)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3121])).
% 1.63/1.82 tff(3123,plain,
% 1.63/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a573)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3122, 3120])).
% 1.63/1.82 tff(3124,plain,
% 1.63/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3125,plain,
% 1.63/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a573)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3124, 3123])).
% 1.63/1.82 tff(3126,plain,
% 1.63/1.82 (~c3_1(a573)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3125, 156, 3115, 3114, 3113, 3119, 3118, 3060, 3081, 3117, 707])).
% 1.63/1.82 tff(3127,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a573) | c0_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a573) | c0_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a573))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3128,plain,
% 1.63/1.82 ((hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a573) | c3_1(a573) | c0_1(a573)) <=> (hskp45 | c2_1(a573) | c0_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a573))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3129,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a573) | c3_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a573) | c0_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a573)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3128])).
% 1.63/1.82 tff(3130,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a573) | c3_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a573) | c0_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a573))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3129, 3127])).
% 1.63/1.82 tff(3131,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a573) | c3_1(a573) | c0_1(a573))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3132,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a573) | c0_1(a573) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c3_1(a573)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3131, 3130])).
% 1.63/1.82 tff(3133,plain,
% 1.63/1.82 (hskp45),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3132, 156, 3119, 3118, 3060, 3059, 3117, 757, 3126])).
% 1.63/1.82 tff(3134,plain,
% 1.63/1.82 (~c3_1(a561)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[771, 3133])).
% 1.63/1.82 tff(3135,plain,
% 1.63/1.82 (c0_1(a561)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[779, 3133])).
% 1.63/1.82 tff(3136,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | c3_1(a573) | (~c1_1(a561)) | (~c0_1(a561)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | c3_1(a573) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3137,plain,
% 1.63/1.82 ((hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a573) | c3_1(a573) | c0_1(a573)) <=> (hskp33 | c3_1(a561) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | c3_1(a573) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3138,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a573) | c3_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a561) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | c3_1(a573) | (~c1_1(a561)) | (~c0_1(a561))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3137])).
% 1.63/1.82 tff(3139,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a573) | c3_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | c3_1(a573) | (~c1_1(a561)) | (~c0_1(a561)))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3138, 3136])).
% 1.63/1.82 tff(3140,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a561) | (~c0_1(a561)) | (~c1_1(a561)) | c2_1(a573) | c3_1(a573) | c0_1(a573))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3141,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a561) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | c3_1(a573) | (~c1_1(a561)) | (~c0_1(a561))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 1.63/1.82 tff(3142,plain,
% 1.63/1.82 (~c1_1(a561)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3141, 156, 35, 3135, 3134, 3060, 3059, 85, 3126])).
% 1.63/1.82 tff(3143,assumption,(~c0_1(a573)), introduced(assumption)).
% 1.63/1.82 tff(3144,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a573))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3145,plain,
% 1.63/1.82 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a573) | c3_1(a573) | c0_1(a573)) <=> (hskp33 | c3_1(a584) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a573))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3146,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a573) | c3_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a573)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3145])).
% 1.63/1.82 tff(3147,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a573) | c3_1(a573) | c0_1(a573))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a573))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3146, 3144])).
% 1.63/1.82 tff(3148,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a573) | c3_1(a573) | c0_1(a573))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3149,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a573)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3148, 3147])).
% 1.63/1.82 tff(3150,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3149, 156, 35, 1630, 1638, 1621, 1719, 3143, 85, 1717])).
% 1.63/1.82 tff(3151,plain,((~hskp26) | hskp33 | c2_1(a573) | c0_1(a573) | c3_1(a573)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3152,plain,
% 1.63/1.82 (~hskp26),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3151, 3126, 3060, 3059, 35])).
% 1.63/1.82 tff(3153,plain,
% 1.63/1.82 (hskp28),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1711, 156, 1719, 3143, 1718, 122])).
% 1.63/1.82 tff(3154,plain,
% 1.63/1.82 (c3_1(a589)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[185, 3153])).
% 1.63/1.82 tff(3155,plain,
% 1.63/1.82 (~c0_1(a589)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[177, 3153])).
% 1.63/1.82 tff(3156,plain,
% 1.63/1.82 (c2_1(a589)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[171, 3153])).
% 1.63/1.82 tff(3157,plain,
% 1.63/1.82 (hskp6 | (~c1_1(a589))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1751, 156, 3154, 3155, 1719, 3143, 1718, 1745])).
% 1.63/1.82 tff(3158,plain,
% 1.63/1.82 (~c1_1(a589)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3157, 1669])).
% 1.63/1.82 tff(3159,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3160,plain,
% 1.63/1.82 ((hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589))) <=> (hskp26 | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3161,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3160])).
% 1.63/1.82 tff(3162,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3161, 3159])).
% 1.63/1.82 tff(3163,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3164,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a589)) | c1_1(a589)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3163, 3162])).
% 1.63/1.82 tff(3165,plain,
% 1.63/1.82 (hskp26 | (~c1_1(a586))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3164, 156, 591, 590, 87, 86, 1686, 1716])).
% 1.63/1.82 tff(3166,plain,
% 1.63/1.82 (~c1_1(a586)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3165, 1661])).
% 1.63/1.82 tff(3167,plain,
% 1.63/1.82 (~hskp27),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[95, 3166])).
% 1.63/1.82 tff(3168,plain,
% 1.63/1.82 (hskp4),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[205, 3167, 1669])).
% 1.63/1.82 tff(3169,plain,
% 1.63/1.82 (~c2_1(a545)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1643, 3168])).
% 1.63/1.82 tff(3170,plain,
% 1.63/1.82 (c1_1(a545)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[193, 3168])).
% 1.63/1.82 tff(3171,plain,
% 1.63/1.82 (~c3_1(a545)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1725, 156, 625, 591, 3170, 1719, 1718, 3169, 45, 1716, 1717])).
% 1.63/1.82 tff(3172,plain,
% 1.63/1.82 (~c0_1(a545)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1666, 3168])).
% 1.63/1.82 tff(3173,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1732, 156, 1661, 591, 3170, 590, 3172, 1686, 1716, 3171])).
% 1.63/1.82 tff(3174,plain,(hskp26 | (~c3_1(a589)) | c0_1(a589) | c1_1(a589) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573) | hskp6 | c0_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3175,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3174, 3158, 1669, 86, 1719, 1718, 3156, 3155, 1717, 1661, 87, 3154])).
% 1.63/1.82 tff(3176,plain,(hskp6 | c3_1(a586) | c2_1(a573) | c1_1(a573) | c3_1(a573) | hskp26 | c0_1(a586) | c0_1(a573)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3177,plain,
% 1.63/1.82 (hskp6),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3176, 3126, 3060, 3081, 86, 3152, 87, 3059])).
% 1.63/1.82 tff(3178,plain,
% 1.63/1.82 (c3_1(a548)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[225, 3177])).
% 1.63/1.82 tff(3179,plain,
% 1.63/1.82 (c1_1(a548)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2694, 3178, 3114, 3113, 3116, 24, 3115])).
% 1.63/1.82 tff(3180,plain,
% 1.63/1.82 (hskp4),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2559, 3179, 56, 24, 3178])).
% 1.63/1.82 tff(3181,plain,
% 1.63/1.82 (c1_1(a589)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1734, 3180, 3060, 3094, 3092, 3093, 3126, 3081, 3152])).
% 1.63/1.82 tff(3182,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3183,plain,
% 1.63/1.82 ((hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3184,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3183])).
% 1.63/1.82 tff(3185,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3184, 3182])).
% 1.63/1.82 tff(3186,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3187,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.63/1.82 tff(3188,plain,
% 1.63/1.82 (hskp34 | (~c1_1(a589))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3187, 156, 3093, 3092, 88, 86, 1112, 653])).
% 1.63/1.82 tff(3189,plain,
% 1.63/1.82 (hskp34),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3188, 3181])).
% 1.63/1.82 tff(3190,plain,
% 1.63/1.82 (~c1_1(a537)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1124, 3189])).
% 1.63/1.82 tff(3191,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3192,plain,
% 1.63/1.82 ((hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547))) <=> (hskp42 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3193,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3192])).
% 1.63/1.82 tff(3194,plain,
% 1.63/1.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3193, 3191])).
% 1.63/1.82 tff(3195,plain,
% 1.63/1.82 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))),
% 1.68/1.82 inference(quant_inst,[status(thm)],[])).
% 1.68/1.82 tff(3196,plain,
% 1.68/1.82 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.68/1.82 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 1.68/1.82 tff(3197,plain,
% 1.68/1.82 (hskp42 | (~c3_1(a548)) | (~c1_1(a548))),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[3196, 156, 3115, 3114, 3113, 24, 1364])).
% 1.68/1.82 tff(3198,plain,
% 1.68/1.82 (hskp42),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[3197, 3178, 3179])).
% 1.68/1.82 tff(3199,plain,
% 1.68/1.82 (~c2_1(a556)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[1385, 3198])).
% 1.68/1.82 tff(3200,plain,
% 1.68/1.82 (~c2_1(a561)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[792, 3133])).
% 1.68/1.82 tff(3201,plain,
% 1.68/1.82 (c3_1(a537)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[1132, 3189])).
% 1.68/1.82 tff(3202,plain,
% 1.68/1.82 (c3_1(a556)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[1403, 3198])).
% 1.68/1.82 tff(3203,plain,
% 1.68/1.82 (c1_1(a556)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[1411, 3198])).
% 1.68/1.82 tff(3204,plain,
% 1.68/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a561) | c2_1(a561) | c2_1(a556) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a561))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a561) | c2_1(a561) | c2_1(a556) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a561))),
% 1.68/1.82 inference(rewrite,[status(thm)],[])).
% 1.68/1.82 tff(3205,plain,
% 1.68/1.82 (((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a561) | c1_1(a561) | c3_1(a561)) <=> (c3_1(a561) | c2_1(a561) | c2_1(a556) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a561))),
% 1.68/1.82 inference(rewrite,[status(thm)],[])).
% 1.68/1.82 tff(3206,plain,
% 1.68/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a561) | c1_1(a561) | c3_1(a561))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a561) | c2_1(a561) | c2_1(a556) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a561)))),
% 1.68/1.82 inference(monotonicity,[status(thm)],[3205])).
% 1.68/1.82 tff(3207,plain,
% 1.68/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a561) | c1_1(a561) | c3_1(a561))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a561) | c2_1(a561) | c2_1(a556) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a561))),
% 1.68/1.82 inference(transitivity,[status(thm)],[3206, 3204])).
% 1.68/1.82 tff(3208,plain,
% 1.68/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a561) | c1_1(a561) | c3_1(a561))),
% 1.68/1.82 inference(quant_inst,[status(thm)],[])).
% 1.68/1.82 tff(3209,plain,
% 1.68/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a561) | c2_1(a561) | c2_1(a556) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a561)),
% 1.68/1.82 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 1.68/1.82 tff(3210,plain,
% 1.68/1.82 (~c2_1(a537)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[3209, 156, 3203, 3202, 3201, 3134, 3200, 3199, 3190, 45, 3142])).
% 1.68/1.82 tff(3211,plain,
% 1.68/1.82 ($false),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[2754, 156, 3115, 3114, 3113, 3201, 3119, 3118, 3190, 3117, 707, 3210])).
% 1.68/1.82 tff(3212,plain,(c0_1(a548) | c1_1(a586) | c3_1(a586) | c2_1(a586) | c2_1(a548) | c0_1(a586) | hskp33 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.82 tff(3213,plain,
% 1.68/1.82 ($false),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[3212, 3111, 3110, 86, 653, 88, 87, 35, 97])).
% 1.68/1.82 tff(3214,plain,(c2_1(a586) | c3_1(a586) | c1_1(a586) | c0_1(a586) | hskp33 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.82 tff(3215,plain,
% 1.68/1.82 (c2_1(a586)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[3214, 35, 88, 87, 86, 97])).
% 1.68/1.82 tff(3216,plain,
% 1.68/1.82 ($false),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[2892, 1262, 1268, 87, 86, 35, 3215, 3092, 3093, 97, 3080, 58, 88, 1256])).
% 1.68/1.82 tff(3217,plain,((~hskp15) | c0_1(a586) | c3_1(a586) | hskp33 | c0_1(a545) | hskp38 | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.82 tff(3218,plain,
% 1.68/1.82 (~hskp15),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[3217, 58, 86, 35, 97, 87, 88])).
% 1.68/1.82 tff(3219,plain,
% 1.68/1.82 (hskp46),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[2572, 3218, 3094, 87, 86, 3215, 88, 3093, 58, 3080, 3079, 3092, 3082])).
% 1.68/1.82 tff(3220,plain,
% 1.68/1.82 (~c0_1(a562)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[64, 3219])).
% 1.68/1.82 tff(3221,plain,
% 1.68/1.82 (~c3_1(a562)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[270, 3219])).
% 1.68/1.82 tff(3222,plain,
% 1.68/1.82 (c1_1(a562)),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[288, 3219])).
% 1.68/1.82 tff(3223,plain,
% 1.68/1.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a562)))),
% 1.68/1.82 inference(rewrite,[status(thm)],[])).
% 1.68/1.82 tff(3224,plain,
% 1.68/1.82 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573))) <=> (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a562)))),
% 1.68/1.82 inference(rewrite,[status(thm)],[])).
% 1.68/1.82 tff(3225,plain,
% 1.68/1.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a562))))),
% 1.68/1.82 inference(monotonicity,[status(thm)],[3224])).
% 1.68/1.82 tff(3226,plain,
% 1.68/1.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a562)))),
% 1.68/1.82 inference(transitivity,[status(thm)],[3225, 3223])).
% 1.68/1.82 tff(3227,plain,
% 1.68/1.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))),
% 1.68/1.82 inference(quant_inst,[status(thm)],[])).
% 1.68/1.82 tff(3228,plain,
% 1.68/1.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a562))),
% 1.68/1.82 inference(modus_ponens,[status(thm)],[3227, 3226])).
% 1.68/1.82 tff(3229,plain,
% 1.68/1.82 ($false),
% 1.68/1.82 inference(unit_resolution,[status(thm)],[3228, 156, 1661, 3222, 3221, 3220, 3059, 3081, 1686, 3090])).
% 1.68/1.83 tff(3230,plain,(hskp38 | hskp26 | c0_1(a586) | c3_1(a586) | c1_1(a586) | hskp33 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3231,plain,
% 1.68/1.83 (hskp38),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3230, 1661, 87, 86, 88, 35, 97])).
% 1.68/1.83 tff(3232,plain,
% 1.68/1.83 (c2_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[693, 3231])).
% 1.68/1.83 tff(3233,plain,
% 1.68/1.83 (c0_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[677, 3231])).
% 1.68/1.83 tff(3234,plain,
% 1.68/1.83 (c1_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[685, 3231])).
% 1.68/1.83 tff(3235,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3236,plain,
% 1.68/1.83 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | c3_1(a573)) <=> (hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3237,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[3236])).
% 1.68/1.83 tff(3238,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.68/1.83 inference(transitivity,[status(thm)],[3237, 3235])).
% 1.68/1.83 tff(3239,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | c3_1(a573))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(3240,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 1.68/1.83 tff(3241,plain,
% 1.68/1.83 (hskp0 | c3_1(a573)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3240, 156, 733, 732, 731, 1719, 1718, 108])).
% 1.68/1.83 tff(3242,plain,
% 1.68/1.83 (c3_1(a573)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3241, 837])).
% 1.68/1.83 tff(3243,assumption,(c3_1(a573)), introduced(assumption)).
% 1.68/1.83 tff(3244,plain,
% 1.68/1.83 (~c3_1(a562)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[270, 59])).
% 1.68/1.83 tff(3245,plain,
% 1.68/1.83 (c1_1(a562)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[288, 59])).
% 1.68/1.83 tff(3246,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3228, 156, 1661, 3245, 3244, 65, 3143, 1718, 1686, 3243])).
% 1.68/1.83 tff(3247,plain,((~hskp46) | hskp26 | c0_1(a573) | c1_1(a573) | (~c3_1(a573))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3248,plain,
% 1.68/1.83 (~hskp46),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3247, 3242, 3143, 1718, 1661])).
% 1.68/1.83 tff(3249,plain,
% 1.68/1.83 (~hskp16),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2365, 3248, 87, 86, 902])).
% 1.68/1.83 tff(3250,plain,
% 1.68/1.83 (hskp15),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2711, 3248, 732, 731, 733, 24, 88, 86, 902, 249, 87, 56])).
% 1.68/1.83 tff(3251,plain,
% 1.68/1.83 (~c1_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1261, 3250])).
% 1.68/1.83 tff(3252,plain,
% 1.68/1.83 (~c0_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1267, 3250])).
% 1.68/1.83 tff(3253,plain,
% 1.68/1.83 (~c2_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1255, 3250])).
% 1.68/1.83 tff(3254,plain,
% 1.68/1.83 (c3_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2924, 156, 837, 733, 732, 731, 3251, 3253, 108])).
% 1.68/1.83 tff(3255,plain,
% 1.68/1.83 (~hskp17),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2832, 3254, 86, 3252, 3251, 902, 87, 88])).
% 1.68/1.83 tff(3256,plain,
% 1.68/1.83 (hskp18),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[382, 3255, 3249])).
% 1.68/1.83 tff(3257,plain,
% 1.68/1.83 (hskp37),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2703, 3256, 733, 732, 731, 837])).
% 1.68/1.83 tff(3258,plain,
% 1.68/1.83 (~c2_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[436, 3257])).
% 1.68/1.83 tff(3259,plain,
% 1.68/1.83 (c1_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[444, 3257])).
% 1.68/1.83 tff(3260,plain,
% 1.68/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3261,plain,
% 1.68/1.83 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3262,plain,
% 1.68/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[3261])).
% 1.68/1.83 tff(3263,plain,
% 1.68/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.68/1.83 inference(transitivity,[status(thm)],[3262, 3260])).
% 1.68/1.83 tff(3264,plain,
% 1.68/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(3265,plain,
% 1.68/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3264, 3263])).
% 1.68/1.83 tff(3266,plain,
% 1.68/1.83 (~c0_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3265, 156, 733, 732, 731, 3259, 3258, 1719, 1718, 707, 3242])).
% 1.68/1.83 tff(3267,plain,
% 1.68/1.83 (~c3_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[450, 3257])).
% 1.68/1.83 tff(3268,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a544) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c0_1(a544) | (~c1_1(a544)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3269,plain,
% 1.68/1.83 ((hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573))) <=> (hskp26 | c3_1(a544) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c0_1(a544) | (~c1_1(a544)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3270,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a544) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c0_1(a544) | (~c1_1(a544))))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[3269])).
% 1.68/1.83 tff(3271,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c0_1(a544) | (~c1_1(a544)))),
% 1.68/1.83 inference(transitivity,[status(thm)],[3270, 3268])).
% 1.68/1.83 tff(3272,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(3273,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c0_1(a544) | (~c1_1(a544))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 1.68/1.83 tff(3274,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3273, 156, 1661, 3259, 3267, 3143, 1718, 1686, 3242, 3266])).
% 1.68/1.83 tff(3275,plain,(hskp0 | hskp26 | c0_1(a573) | c1_1(a573) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c2_1(a573) | c3_1(a586) | (~c2_1(a586)) | c0_1(a586) | c1_1(a586) | c2_1(a548) | (~c3_1(a548)) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3276,plain,
% 1.68/1.83 (hskp0),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3275, 1661, 3059, 3081, 3232, 3234, 3233, 3060, 86, 3215, 87, 88, 3080, 3082, 3079])).
% 1.68/1.83 tff(3277,plain,
% 1.68/1.83 (c1_1(a548)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2694, 3276, 3234, 3233, 3082, 3080, 3232])).
% 1.68/1.83 tff(3278,plain,
% 1.68/1.83 (hskp4),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2559, 3277, 3079, 3080, 3082])).
% 1.68/1.83 tff(3279,plain,
% 1.68/1.83 (hskp46 | (~c1_1(a548))),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2231, 156, 3082, 3080, 3079, 12])).
% 1.68/1.83 tff(3280,plain,
% 1.68/1.83 (hskp46),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3279, 3277])).
% 1.68/1.83 tff(3281,plain,
% 1.68/1.83 (~c3_1(a573)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3247, 3280, 3059, 3081, 1661])).
% 1.68/1.83 tff(3282,plain,
% 1.68/1.83 (c1_1(a589)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1734, 3281, 3060, 3094, 3092, 3093, 1661, 3081, 3278])).
% 1.68/1.83 tff(3283,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3284,plain,
% 1.68/1.83 ((hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548))) <=> (hskp25 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3285,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[3284])).
% 1.68/1.83 tff(3286,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.68/1.83 inference(transitivity,[status(thm)],[3285, 3283])).
% 1.68/1.83 tff(3287,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(3288,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 1.68/1.83 tff(3289,plain,
% 1.68/1.83 (hskp25 | (~c1_1(a548)) | (~c1_1(a589))),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3288, 156, 3093, 3092, 3082, 3080, 55])).
% 1.68/1.83 tff(3290,plain,
% 1.68/1.83 (hskp25),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3289, 3282, 3277])).
% 1.68/1.83 tff(3291,plain,
% 1.68/1.83 (~c1_1(a582)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1190, 3290])).
% 1.68/1.83 tff(3292,plain,
% 1.68/1.83 (~c2_1(a582)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1196, 3290])).
% 1.68/1.83 tff(3293,plain,
% 1.68/1.83 (~c3_1(a582)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1202, 3290])).
% 1.68/1.83 tff(3294,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3295,plain,
% 1.68/1.83 ((hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573)) <=> (hskp34 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3296,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[3295])).
% 1.68/1.83 tff(3297,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.68/1.83 inference(transitivity,[status(thm)],[3296, 3294])).
% 1.68/1.83 tff(3298,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(3299,plain,
% 1.68/1.83 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3298, 3297])).
% 1.68/1.83 tff(3300,plain,
% 1.68/1.83 (hskp34 | c3_1(a573) | (~c1_1(a589))),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3299, 156, 3093, 3092, 3060, 3081, 1112])).
% 1.68/1.83 tff(3301,plain,
% 1.68/1.83 (hskp34),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3300, 3282, 3281])).
% 1.68/1.83 tff(3302,plain,
% 1.68/1.83 (~c1_1(a537)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1124, 3301])).
% 1.68/1.83 tff(3303,plain,
% 1.68/1.83 (hskp42 | (~c1_1(a548))),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3196, 156, 3232, 3234, 3233, 3082, 3080, 1364])).
% 1.68/1.83 tff(3304,plain,
% 1.68/1.83 (hskp42),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3303, 3277])).
% 1.68/1.83 tff(3305,plain,
% 1.68/1.83 (~c2_1(a556)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1385, 3304])).
% 1.68/1.83 tff(3306,plain,
% 1.68/1.83 (c3_1(a537)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1132, 3301])).
% 1.68/1.83 tff(3307,plain,
% 1.68/1.83 (c3_1(a556)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1403, 3304])).
% 1.68/1.83 tff(3308,plain,
% 1.68/1.83 (c1_1(a556)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1411, 3304])).
% 1.68/1.83 tff(3309,plain,
% 1.68/1.83 (~c2_1(a537)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2192, 156, 3308, 3307, 3306, 3305, 3302, 3293, 3292, 3291, 45])).
% 1.68/1.83 tff(3310,plain,
% 1.68/1.83 (~c2_1(a535)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[713, 3276])).
% 1.68/1.83 tff(3311,plain,
% 1.68/1.83 (c0_1(a535)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[721, 3276])).
% 1.68/1.83 tff(3312,plain,
% 1.68/1.83 (c1_1(a535)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[729, 3276])).
% 1.68/1.83 tff(3313,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2754, 156, 3232, 3234, 3233, 3306, 3312, 3311, 3302, 3310, 707, 3309])).
% 1.68/1.83 tff(3314,plain,(hskp26 | c3_1(a586) | c0_1(a586) | c1_1(a586) | hskp33 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3315,plain,
% 1.68/1.83 (hskp26),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3314, 35, 87, 88, 86, 97])).
% 1.68/1.83 tff(3316,plain,
% 1.68/1.83 (c3_1(a573)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3151, 3315, 3060, 3059, 35])).
% 1.68/1.83 tff(3317,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2572, 3218, 58, 3094, 87, 86, 3215, 88, 3093, 946, 3080, 3079, 3092, 3082])).
% 1.68/1.83 tff(3318,plain,(hskp38 | c0_1(a586) | c3_1(a586) | c1_1(a586) | hskp46 | hskp33 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3319,plain,
% 1.68/1.83 (hskp38),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3318, 946, 86, 88, 87, 35, 97])).
% 1.68/1.83 tff(3320,plain,
% 1.68/1.83 (c2_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[693, 3319])).
% 1.68/1.83 tff(3321,plain,
% 1.68/1.83 (c0_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[677, 3319])).
% 1.68/1.83 tff(3322,plain,
% 1.68/1.83 (~c1_1(a548)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3279, 946])).
% 1.68/1.83 tff(3323,plain,
% 1.68/1.83 (c1_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[685, 3319])).
% 1.68/1.83 tff(3324,plain,
% 1.68/1.83 (~hskp0),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2694, 3323, 3322, 3321, 3082, 3080, 3320])).
% 1.68/1.83 tff(3325,plain,
% 1.68/1.83 (~hskp16),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2365, 946, 87, 86, 3215])).
% 1.68/1.83 tff(3326,plain,
% 1.68/1.83 (hskp15),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2711, 3323, 946, 3321, 3320, 3080, 88, 86, 3215, 3082, 87, 3079])).
% 1.68/1.83 tff(3327,plain,
% 1.68/1.83 (~c1_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1261, 3326])).
% 1.68/1.83 tff(3328,plain,
% 1.68/1.83 (~c0_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1267, 3326])).
% 1.68/1.83 tff(3329,plain,
% 1.68/1.83 (~c2_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1255, 3326])).
% 1.68/1.83 tff(3330,plain,
% 1.68/1.83 (c3_1(a569)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2924, 156, 3324, 3320, 3323, 3321, 3327, 3329, 108])).
% 1.68/1.83 tff(3331,plain,
% 1.68/1.83 (~hskp17),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2832, 3330, 86, 3328, 3327, 3215, 87, 88])).
% 1.68/1.83 tff(3332,plain,
% 1.68/1.83 (hskp18),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[382, 3331, 3325])).
% 1.68/1.83 tff(3333,plain,
% 1.68/1.83 (hskp37),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2703, 3332, 3320, 3323, 3321, 3324])).
% 1.68/1.83 tff(3334,plain,
% 1.68/1.83 (~c2_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[436, 3333])).
% 1.68/1.83 tff(3335,plain,
% 1.68/1.83 (c1_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[444, 3333])).
% 1.68/1.83 tff(3336,plain,
% 1.68/1.83 (~c0_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3265, 156, 3320, 3323, 3321, 3335, 3334, 3060, 3081, 707, 3316])).
% 1.68/1.83 tff(3337,plain,
% 1.68/1.83 (~c3_1(a584)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1620, 3315])).
% 1.68/1.83 tff(3338,plain,
% 1.68/1.83 (~c3_1(a544)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[450, 3333])).
% 1.68/1.83 tff(3339,plain,
% 1.68/1.83 (c1_1(a584)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1637, 3315])).
% 1.68/1.83 tff(3340,plain,
% 1.68/1.83 (c0_1(a584)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1629, 3315])).
% 1.68/1.83 tff(3341,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2862, 156, 35, 3340, 3339, 3334, 3338, 3337, 85, 3336])).
% 1.68/1.83 tff(3342,plain,(hskp46 | hskp33 | c3_1(a586) | c0_1(a586) | c1_1(a586) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3343,plain,
% 1.68/1.83 (hskp46),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3342, 35, 86, 87, 88, 97])).
% 1.68/1.83 tff(3344,plain,
% 1.68/1.83 (~c0_1(a562)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[64, 3343])).
% 1.68/1.83 tff(3345,plain,
% 1.68/1.83 (~c3_1(a562)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[270, 3343])).
% 1.68/1.83 tff(3346,plain,
% 1.68/1.83 (~hskp4),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1659, 58, 3315, 35, 97])).
% 1.68/1.83 tff(3347,plain,
% 1.68/1.83 (c1_1(a562)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[288, 3343])).
% 1.68/1.83 tff(3348,plain,
% 1.68/1.83 (hskp4 | (~c1_1(a589))),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2291, 156, 3347, 3093, 3092, 3345, 3344, 22])).
% 1.68/1.83 tff(3349,plain,
% 1.68/1.83 (~c1_1(a589)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3348, 3346])).
% 1.68/1.83 tff(3350,plain,
% 1.68/1.83 (~hskp39),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2535, 3349, 58, 3092, 3093])).
% 1.68/1.83 tff(3351,plain,
% 1.68/1.83 (~hskp16),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2301, 3350, 58, 3092, 3093, 3347, 3344, 3345, 3349])).
% 1.68/1.83 tff(3352,plain,
% 1.68/1.83 (~hskp37),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2512, 3218, 3093, 3092, 3349])).
% 1.68/1.83 tff(3353,plain,
% 1.68/1.83 (~hskp18),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2583, 3352, 58, 3080, 3079, 3082])).
% 1.68/1.83 tff(3354,plain,
% 1.68/1.83 (hskp17),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[382, 3353, 3351])).
% 1.68/1.83 tff(3355,plain,
% 1.68/1.83 (~c2_1(a571)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[573, 3354])).
% 1.68/1.83 tff(3356,plain,
% 1.68/1.83 (c3_1(a571)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[623, 3354])).
% 1.68/1.83 tff(3357,plain,
% 1.68/1.83 (c0_1(a571)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[581, 3354])).
% 1.68/1.83 tff(3358,plain,
% 1.68/1.83 (c1_1(a571)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[931, 156, 88, 3357, 3356, 86, 3355, 921, 3215])).
% 1.68/1.83 tff(3359,plain,
% 1.68/1.83 (~c1_1(a548)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2559, 3346, 3079, 3080, 3082])).
% 1.68/1.83 tff(3360,plain,
% 1.68/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3361,plain,
% 1.68/1.83 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3362,plain,
% 1.68/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))))),
% 1.68/1.83 inference(monotonicity,[status(thm)],[3361])).
% 1.68/1.83 tff(3363,plain,
% 1.68/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586)))),
% 1.68/1.83 inference(transitivity,[status(thm)],[3362, 3360])).
% 1.68/1.83 tff(3364,plain,
% 1.68/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.68/1.83 inference(quant_inst,[status(thm)],[])).
% 1.68/1.83 tff(3365,plain,
% 1.68/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a586) | c3_1(a586) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a586))),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3364, 3363])).
% 1.68/1.83 tff(3366,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3365, 156, 3357, 3082, 87, 86, 3355, 3079, 609, 3215, 3359, 3358])).
% 1.68/1.83 tff(3367,plain,(hskp38 | c0_1(a586) | c3_1(a586) | c1_1(a586) | hskp33 | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3368,plain,
% 1.68/1.83 (hskp38),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3367, 35, 86, 88, 87, 97])).
% 1.68/1.83 tff(3369,plain,
% 1.68/1.83 (c0_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[677, 3368])).
% 1.68/1.83 tff(3370,plain,
% 1.68/1.83 (c1_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[685, 3368])).
% 1.68/1.83 tff(3371,plain,
% 1.68/1.83 (c2_1(a547)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[693, 3368])).
% 1.68/1.83 tff(3372,plain,
% 1.68/1.83 (hskp34),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2160, 156, 3347, 3371, 3370, 3369, 3345, 3344, 75])).
% 1.68/1.83 tff(3373,plain,
% 1.68/1.83 (~c1_1(a537)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1124, 3372])).
% 1.68/1.83 tff(3374,plain,
% 1.68/1.83 (c3_1(a537)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1132, 3372])).
% 1.68/1.83 tff(3375,plain,
% 1.68/1.83 (c0_1(a537)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[1147, 3372])).
% 1.68/1.83 tff(3376,plain,
% 1.68/1.83 (hskp8),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2725, 156, 3375, 3374, 88, 3373, 87, 2407, 3215])).
% 1.68/1.83 tff(3377,plain,
% 1.68/1.83 (~c2_1(a552)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2424, 3376])).
% 1.68/1.83 tff(3378,plain,
% 1.68/1.83 (~c1_1(a552)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2453, 3376])).
% 1.68/1.83 tff(3379,plain,
% 1.68/1.83 (~c3_1(a552)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2430, 3376])).
% 1.68/1.83 tff(3380,plain,
% 1.68/1.83 (hskp0),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[2735, 156, 3371, 3370, 3369, 3379, 3378, 3377, 108])).
% 1.68/1.83 tff(3381,plain,
% 1.68/1.83 (~c2_1(a535)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[713, 3380])).
% 1.68/1.83 tff(3382,plain,
% 1.68/1.83 (c0_1(a535)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[721, 3380])).
% 1.68/1.83 tff(3383,plain,
% 1.68/1.83 (c1_1(a535)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[729, 3380])).
% 1.68/1.83 tff(3384,plain,
% 1.68/1.83 ($false),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3125, 156, 3371, 3370, 3369, 3383, 3382, 3060, 3081, 3381, 707, 3316])).
% 1.68/1.83 tff(3385,plain,(hskp33 | c1_1(a586) | c0_1(a586) | c3_1(a586) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.83 tff(3386,plain,
% 1.68/1.83 (hskp33),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3385, 97, 87, 86, 88])).
% 1.68/1.83 tff(3387,plain,
% 1.68/1.83 (((~hskp33) | c0_1(a536)) <=> ((~hskp33) | c0_1(a536))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3388,axiom,((~hskp33) | c0_1(a536)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.68/1.83 tff(3389,plain,
% 1.68/1.83 ((~hskp33) | c0_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3388, 3387])).
% 1.68/1.83 tff(3390,plain,
% 1.68/1.83 ((~hskp33) | c0_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3389, 3387])).
% 1.68/1.83 tff(3391,plain,
% 1.68/1.83 ((~hskp33) | c0_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3390, 3387])).
% 1.68/1.83 tff(3392,plain,
% 1.68/1.83 ((~hskp33) | c0_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3391, 3387])).
% 1.68/1.83 tff(3393,plain,
% 1.68/1.83 ((~hskp33) | c0_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3392, 3387])).
% 1.68/1.83 tff(3394,plain,
% 1.68/1.83 (c0_1(a536)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3393, 3386])).
% 1.68/1.83 tff(3395,plain,
% 1.68/1.83 (((~hskp33) | c2_1(a536)) <=> ((~hskp33) | c2_1(a536))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3396,axiom,((~hskp33) | c2_1(a536)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.68/1.83 tff(3397,plain,
% 1.68/1.83 ((~hskp33) | c2_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3396, 3395])).
% 1.68/1.83 tff(3398,plain,
% 1.68/1.83 ((~hskp33) | c2_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3397, 3395])).
% 1.68/1.83 tff(3399,plain,
% 1.68/1.83 ((~hskp33) | c2_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3398, 3395])).
% 1.68/1.83 tff(3400,plain,
% 1.68/1.83 ((~hskp33) | c2_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3399, 3395])).
% 1.68/1.83 tff(3401,plain,
% 1.68/1.83 ((~hskp33) | c2_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3400, 3395])).
% 1.68/1.83 tff(3402,plain,
% 1.68/1.83 (c2_1(a536)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3401, 3386])).
% 1.68/1.83 tff(3403,plain,
% 1.68/1.83 (((~hskp33) | c1_1(a536)) <=> ((~hskp33) | c1_1(a536))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3404,axiom,((~hskp33) | c1_1(a536)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.68/1.83 tff(3405,plain,
% 1.68/1.83 ((~hskp33) | c1_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 1.68/1.83 tff(3406,plain,
% 1.68/1.83 ((~hskp33) | c1_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3405, 3403])).
% 1.68/1.83 tff(3407,plain,
% 1.68/1.83 ((~hskp33) | c1_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3406, 3403])).
% 1.68/1.83 tff(3408,plain,
% 1.68/1.83 ((~hskp33) | c1_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3407, 3403])).
% 1.68/1.83 tff(3409,plain,
% 1.68/1.83 ((~hskp33) | c1_1(a536)),
% 1.68/1.83 inference(modus_ponens,[status(thm)],[3408, 3403])).
% 1.68/1.83 tff(3410,plain,
% 1.68/1.83 (c1_1(a536)),
% 1.68/1.83 inference(unit_resolution,[status(thm)],[3409, 3386])).
% 1.68/1.83 tff(3411,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a586))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3412,plain,
% 1.68/1.83 ((hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a586))),
% 1.68/1.83 inference(rewrite,[status(thm)],[])).
% 1.68/1.83 tff(3413,plain,
% 1.68/1.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a586)))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[3412])).
% 1.68/1.84 tff(3414,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a586))),
% 1.68/1.84 inference(transitivity,[status(thm)],[3413, 3411])).
% 1.68/1.84 tff(3415,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(3416,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c1_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a586)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 1.68/1.84 tff(3417,plain,
% 1.68/1.84 (hskp0),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[3416, 156, 3410, 3402, 3394, 88, 86, 108, 653])).
% 1.68/1.84 tff(3418,plain,
% 1.68/1.84 (~c2_1(a535)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[713, 3417])).
% 1.68/1.84 tff(3419,plain,
% 1.68/1.84 (c0_1(a535)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[721, 3417])).
% 1.68/1.84 tff(3420,plain,
% 1.68/1.84 (c1_1(a535)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[729, 3417])).
% 1.68/1.84 tff(3421,plain,
% 1.68/1.84 (hskp6 | (~c1_1(a589))),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1772, 156, 2336, 88, 2335, 87, 1745, 653])).
% 1.68/1.84 tff(3422,plain,
% 1.68/1.84 (~c1_1(a589)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[3421, 1669])).
% 1.68/1.84 tff(3423,plain,
% 1.68/1.84 (c1_1(a545)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[193, 2467])).
% 1.68/1.84 tff(3424,plain,
% 1.68/1.84 (hskp6 | (~c3_1(a545)) | (~c1_1(a545))),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1765, 156, 88, 87, 97, 1745, 653])).
% 1.68/1.84 tff(3425,plain,
% 1.68/1.84 (~c3_1(a545)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[3424, 3423, 1669])).
% 1.68/1.84 tff(3426,assumption,(c0_1(a536)), introduced(assumption)).
% 1.68/1.84 tff(3427,assumption,(c2_1(a536)), introduced(assumption)).
% 1.68/1.84 tff(3428,assumption,(c1_1(a536)), introduced(assumption)).
% 1.68/1.84 tff(3429,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3430,plain,
% 1.68/1.84 ((hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3431,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[3430])).
% 1.68/1.84 tff(3432,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[3431, 3429])).
% 1.68/1.84 tff(3433,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(3434,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[3433, 3432])).
% 1.68/1.84 tff(3435,plain,
% 1.68/1.84 (hskp34),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[3434, 156, 3428, 3427, 3426, 3423, 97, 75, 3425])).
% 1.68/1.84 tff(3436,plain,
% 1.68/1.84 (~c1_1(a537)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1124, 3435])).
% 1.68/1.84 tff(3437,plain,
% 1.68/1.84 (c3_1(a537)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1132, 3435])).
% 1.68/1.84 tff(3438,plain,
% 1.68/1.84 (c0_1(a537)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1147, 3435])).
% 1.68/1.84 tff(3439,plain,
% 1.68/1.84 (hskp8),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2418, 156, 3438, 3437, 2334, 3436, 2335, 2407, 3422])).
% 1.68/1.84 tff(3440,plain,
% 1.68/1.84 (~c2_1(a552)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2424, 3439])).
% 1.68/1.84 tff(3441,plain,
% 1.68/1.84 (~c1_1(a552)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2453, 3439])).
% 1.68/1.84 tff(3442,plain,
% 1.68/1.84 (~c3_1(a552)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2430, 3439])).
% 1.68/1.84 tff(3443,assumption,(~c2_1(a535)), introduced(assumption)).
% 1.68/1.84 tff(3444,plain,
% 1.68/1.84 (~c2_1(a545)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1643, 2467])).
% 1.68/1.84 tff(3445,plain,
% 1.68/1.84 (hskp15),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2044, 3425, 3423, 3422, 2336, 3444, 2334])).
% 1.68/1.84 tff(3446,plain,
% 1.68/1.84 (~c2_1(a569)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1255, 3445])).
% 1.68/1.84 tff(3447,plain,
% 1.68/1.84 (~c1_1(a569)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[1261, 3445])).
% 1.68/1.84 tff(3448,assumption,(c0_1(a535)), introduced(assumption)).
% 1.68/1.84 tff(3449,assumption,(c1_1(a535)), introduced(assumption)).
% 1.68/1.84 tff(3450,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3451,plain,
% 1.68/1.84 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3452,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[3451])).
% 1.68/1.84 tff(3453,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[3452, 3450])).
% 1.68/1.84 tff(3454,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(3455,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.68/1.84 tff(3456,plain,
% 1.68/1.84 (~c3_1(a569)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[3455, 156, 3428, 3427, 3426, 3449, 3448, 3447, 3446, 3443, 707])).
% 1.68/1.84 tff(3457,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3458,plain,
% 1.68/1.84 ((hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (hskp51 | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3459,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[3458])).
% 1.68/1.84 tff(3460,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[3459, 3457])).
% 1.68/1.84 tff(3461,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(3462,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.68/1.84 tff(3463,plain,
% 1.68/1.84 (hskp51),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[3462, 156, 3438, 3437, 3436, 3447, 3446, 2608, 3456])).
% 1.68/1.84 tff(3464,plain,
% 1.68/1.84 (~c2_1(a583)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2637, 3463])).
% 1.68/1.84 tff(3465,plain,
% 1.68/1.84 (c3_1(a583)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2645, 3463])).
% 1.68/1.84 tff(3466,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3467,plain,
% 1.68/1.84 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (c2_1(a583) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3468,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[3467])).
% 1.68/1.84 tff(3469,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[3468, 3466])).
% 1.68/1.84 tff(3470,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(3471,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 1.68/1.84 tff(3472,plain,
% 1.68/1.84 (~c1_1(a583)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[3471, 156, 3465, 2334, 2336, 3464, 3442, 3441, 3440, 45, 3422])).
% 1.68/1.84 tff(3473,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a583)) | c1_1(a583))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a583)) | c1_1(a583))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(3474,plain,
% 1.68/1.84 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a583)) | c1_1(a583))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3475,plain,
% 1.69/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a583)) | c1_1(a583)))),
% 1.69/1.84 inference(monotonicity,[status(thm)],[3474])).
% 1.69/1.84 tff(3476,plain,
% 1.69/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a583)) | c1_1(a583))),
% 1.69/1.84 inference(transitivity,[status(thm)],[3475, 3473])).
% 1.69/1.84 tff(3477,plain,
% 1.69/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.69/1.84 inference(quant_inst,[status(thm)],[])).
% 1.69/1.84 tff(3478,plain,
% 1.69/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a583)) | c1_1(a583)),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3477, 3476])).
% 1.69/1.84 tff(3479,plain,
% 1.69/1.84 ($false),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3478, 156, 3465, 3428, 3427, 3426, 3449, 3448, 3464, 3443, 707, 3472])).
% 1.69/1.84 tff(3480,plain,(hskp6 | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a535) | c0_1(a545) | c1_1(a586) | c0_1(a586) | c2_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.84 tff(3481,plain,
% 1.69/1.84 (hskp6),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3480, 3420, 3402, 3394, 3410, 3419, 3418, 97, 88, 87, 653])).
% 1.69/1.84 tff(3482,plain,
% 1.69/1.84 (~c2_1(a548)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[217, 3481])).
% 1.69/1.84 tff(3483,plain,
% 1.69/1.84 (~c0_1(a548)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[211, 3481])).
% 1.69/1.84 tff(3484,plain,
% 1.69/1.84 (~hskp6),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[225, 2807])).
% 1.69/1.84 tff(3485,plain,
% 1.69/1.84 (~c1_1(a589)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3421, 3484])).
% 1.69/1.84 tff(3486,plain,
% 1.69/1.84 (~hskp39),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2535, 3485, 58, 2336, 2334])).
% 1.69/1.84 tff(3487,plain,
% 1.69/1.84 (^[U: $i] : refl((hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.69/1.84 inference(bind,[status(th)],[])).
% 1.69/1.84 tff(3488,plain,
% 1.69/1.84 (![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.69/1.84 inference(quant_intro,[status(thm)],[3487])).
% 1.69/1.84 tff(3489,plain,
% 1.69/1.84 (![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3490,plain,
% 1.69/1.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp39) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp39))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp39) <=> (hskp39 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp39) <=> (hskp39 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp39) | hskp24) <=> ((hskp39 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24))), rewrite(((hskp39 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24) <=> (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp39) | hskp24) <=> (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.69/1.84 inference(bind,[status(th)],[])).
% 1.69/1.84 tff(3491,plain,
% 1.69/1.84 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp39) | hskp24) <=> ![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.69/1.84 inference(quant_intro,[status(thm)],[3490])).
% 1.69/1.84 tff(3492,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp39) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause221')).
% 1.69/1.84 tff(3493,plain,
% 1.69/1.84 (![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3492, 3491])).
% 1.69/1.84 tff(3494,plain,
% 1.69/1.84 (![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3493, 3489])).
% 1.69/1.84 tff(3495,plain,(
% 1.69/1.84 ![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.69/1.84 inference(skolemize,[status(sab)],[3494])).
% 1.69/1.84 tff(3496,plain,
% 1.69/1.84 (![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3495, 3488])).
% 1.69/1.84 tff(3497,plain,
% 1.69/1.84 (hskp45),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2349, 156, 3420, 3419, 87, 86, 3418, 757, 653])).
% 1.69/1.84 tff(3498,plain,
% 1.69/1.84 (~c2_1(a561)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[792, 3497])).
% 1.69/1.84 tff(3499,plain,
% 1.69/1.84 (~c3_1(a561)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[771, 3497])).
% 1.69/1.84 tff(3500,plain,
% 1.69/1.84 (c0_1(a561)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[779, 3497])).
% 1.69/1.84 tff(3501,plain,
% 1.69/1.84 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a561) | c2_1(a561) | (~ndr1_0) | (~c0_1(a561)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a561) | c2_1(a561) | (~ndr1_0) | (~c0_1(a561)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3502,plain,
% 1.69/1.84 ((hskp39 | hskp24 | (~ndr1_0) | c2_1(a561) | c3_1(a561) | (~c0_1(a561))) <=> (hskp39 | hskp24 | c3_1(a561) | c2_1(a561) | (~ndr1_0) | (~c0_1(a561)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3503,plain,
% 1.69/1.84 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a561) | c3_1(a561) | (~c0_1(a561)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a561) | c2_1(a561) | (~ndr1_0) | (~c0_1(a561))))),
% 1.69/1.84 inference(monotonicity,[status(thm)],[3502])).
% 1.69/1.84 tff(3504,plain,
% 1.69/1.84 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a561) | c3_1(a561) | (~c0_1(a561)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a561) | c2_1(a561) | (~ndr1_0) | (~c0_1(a561)))),
% 1.69/1.84 inference(transitivity,[status(thm)],[3503, 3501])).
% 1.69/1.84 tff(3505,plain,
% 1.69/1.84 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a561) | c3_1(a561) | (~c0_1(a561)))),
% 1.69/1.84 inference(quant_inst,[status(thm)],[])).
% 1.69/1.84 tff(3506,plain,
% 1.69/1.84 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a561) | c2_1(a561) | (~ndr1_0) | (~c0_1(a561))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3505, 3504])).
% 1.69/1.84 tff(3507,plain,
% 1.69/1.84 (hskp39 | hskp24),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3506, 156, 3500, 3499, 3498, 3496])).
% 1.69/1.84 tff(3508,plain,
% 1.69/1.84 (hskp24),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3507, 3486])).
% 1.69/1.84 tff(3509,plain,
% 1.69/1.84 (((~hskp24) | (~c3_1(a581))) <=> ((~hskp24) | (~c3_1(a581)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3510,plain,
% 1.69/1.84 (((~c3_1(a581)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a581)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3511,axiom,((~c3_1(a581)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.69/1.84 tff(3512,plain,
% 1.69/1.84 ((~hskp24) | (~c3_1(a581))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3511, 3510])).
% 1.69/1.84 tff(3513,plain,
% 1.69/1.84 ((~hskp24) | (~c3_1(a581))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3512, 3509])).
% 1.69/1.84 tff(3514,plain,
% 1.69/1.84 (~c3_1(a581)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3513, 3508])).
% 1.69/1.84 tff(3515,plain,
% 1.69/1.84 (((~hskp24) | (~c1_1(a581))) <=> ((~hskp24) | (~c1_1(a581)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3516,plain,
% 1.69/1.84 (((~c1_1(a581)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a581)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3517,axiom,((~c1_1(a581)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.69/1.84 tff(3518,plain,
% 1.69/1.84 ((~hskp24) | (~c1_1(a581))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3517, 3516])).
% 1.69/1.84 tff(3519,plain,
% 1.69/1.84 ((~hskp24) | (~c1_1(a581))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3518, 3515])).
% 1.69/1.84 tff(3520,plain,
% 1.69/1.84 (~c1_1(a581)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3519, 3508])).
% 1.69/1.84 tff(3521,plain,
% 1.69/1.84 (hskp4),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[205, 3484, 96])).
% 1.69/1.84 tff(3522,plain,
% 1.69/1.84 (~c2_1(a545)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[1643, 3521])).
% 1.69/1.84 tff(3523,plain,
% 1.69/1.84 (c1_1(a545)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[193, 3521])).
% 1.69/1.84 tff(3524,plain,
% 1.69/1.84 (~c3_1(a545)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3424, 3523, 3484])).
% 1.69/1.84 tff(3525,plain,
% 1.69/1.84 (hskp15),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2044, 3524, 3523, 3485, 2336, 3522, 2334])).
% 1.69/1.84 tff(3526,plain,
% 1.69/1.84 (~c2_1(a569)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[1255, 3525])).
% 1.69/1.84 tff(3527,plain,
% 1.69/1.84 (~c1_1(a569)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[1261, 3525])).
% 1.69/1.84 tff(3528,plain,
% 1.69/1.84 (~c3_1(a569)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3455, 156, 3410, 3402, 3394, 3420, 3419, 3527, 3526, 3418, 707])).
% 1.69/1.84 tff(3529,plain,
% 1.69/1.84 (hskp34),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3434, 156, 3410, 3402, 3394, 3523, 97, 75, 3524])).
% 1.69/1.84 tff(3530,plain,
% 1.69/1.84 (~c1_1(a537)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[1124, 3529])).
% 1.69/1.84 tff(3531,plain,
% 1.69/1.84 (c3_1(a537)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[1132, 3529])).
% 1.69/1.84 tff(3532,plain,
% 1.69/1.84 (c0_1(a537)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[1147, 3529])).
% 1.69/1.84 tff(3533,plain,
% 1.69/1.84 (hskp51),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3462, 156, 3532, 3531, 3530, 3527, 3526, 2608, 3528])).
% 1.69/1.84 tff(3534,plain,
% 1.69/1.84 (~c2_1(a583)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2637, 3533])).
% 1.69/1.84 tff(3535,plain,
% 1.69/1.84 (((~hskp24) | c2_1(a581)) <=> ((~hskp24) | c2_1(a581))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3536,axiom,((~hskp24) | c2_1(a581)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.69/1.84 tff(3537,plain,
% 1.69/1.84 ((~hskp24) | c2_1(a581)),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3536, 3535])).
% 1.69/1.84 tff(3538,plain,
% 1.69/1.84 ((~hskp24) | c2_1(a581)),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3537, 3535])).
% 1.69/1.84 tff(3539,plain,
% 1.69/1.84 ((~hskp24) | c2_1(a581)),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3538, 3535])).
% 1.69/1.84 tff(3540,plain,
% 1.69/1.84 ((~hskp24) | c2_1(a581)),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3539, 3535])).
% 1.69/1.84 tff(3541,plain,
% 1.69/1.84 ((~hskp24) | c2_1(a581)),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3540, 3535])).
% 1.69/1.84 tff(3542,plain,
% 1.69/1.84 (c2_1(a581)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3541, 3508])).
% 1.69/1.84 tff(3543,plain,
% 1.69/1.84 (c3_1(a583)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2645, 3533])).
% 1.69/1.84 tff(3544,plain,
% 1.69/1.84 (c0_1(a583)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2653, 3533])).
% 1.69/1.84 tff(3545,plain,
% 1.69/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3546,plain,
% 1.69/1.84 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583))) <=> (c2_1(a583) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.69/1.84 inference(rewrite,[status(thm)],[])).
% 1.69/1.84 tff(3547,plain,
% 1.69/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))))),
% 1.69/1.84 inference(monotonicity,[status(thm)],[3546])).
% 1.69/1.84 tff(3548,plain,
% 1.69/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.69/1.84 inference(transitivity,[status(thm)],[3547, 3545])).
% 1.69/1.84 tff(3549,plain,
% 1.69/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))),
% 1.69/1.84 inference(quant_inst,[status(thm)],[])).
% 1.69/1.84 tff(3550,plain,
% 1.69/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))),
% 1.69/1.84 inference(modus_ponens,[status(thm)],[3549, 3548])).
% 1.69/1.84 tff(3551,plain,
% 1.69/1.84 (c1_1(a583)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3550, 156, 3544, 3543, 3542, 3534, 3520, 3514, 921])).
% 1.69/1.84 tff(3552,plain,
% 1.69/1.84 (hskp8),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2418, 156, 3532, 3531, 2334, 3530, 2335, 2407, 3485])).
% 1.69/1.84 tff(3553,plain,
% 1.69/1.84 (~c2_1(a552)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2424, 3552])).
% 1.69/1.84 tff(3554,plain,
% 1.69/1.84 (~c1_1(a552)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2453, 3552])).
% 1.69/1.84 tff(3555,plain,
% 1.69/1.84 (~c3_1(a552)),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[2430, 3552])).
% 1.69/1.84 tff(3556,plain,
% 1.69/1.84 ($false),
% 1.69/1.84 inference(unit_resolution,[status(thm)],[3471, 156, 3543, 2334, 2336, 3534, 3555, 3554, 3553, 45, 3485, 3551])).
% 1.69/1.85 tff(3557,plain,(hskp38 | c0_1(a545) | c1_1(a586) | c0_1(a586) | c2_1(a586) | c3_1(a586) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3558,plain,
% 1.69/1.85 (hskp38),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3557, 56, 88, 87, 653, 86, 24, 97])).
% 1.69/1.85 tff(3559,plain,
% 1.69/1.85 (c0_1(a547)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[677, 3558])).
% 1.69/1.85 tff(3560,plain,
% 1.69/1.85 (c1_1(a547)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[685, 3558])).
% 1.69/1.85 tff(3561,plain,
% 1.69/1.85 (c2_1(a547)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[693, 3558])).
% 1.69/1.85 tff(3562,plain,
% 1.69/1.85 (hskp34),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2083, 156, 733, 732, 731, 3423, 97, 75, 3425])).
% 1.69/1.85 tff(3563,plain,
% 1.69/1.85 (~c1_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1124, 3562])).
% 1.69/1.85 tff(3564,plain,
% 1.69/1.85 (c3_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1132, 3562])).
% 1.69/1.85 tff(3565,plain,
% 1.69/1.85 (c0_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1147, 3562])).
% 1.69/1.85 tff(3566,plain,
% 1.69/1.85 (hskp8),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2418, 156, 3565, 3564, 2334, 3563, 2335, 2407, 3422])).
% 1.69/1.85 tff(3567,plain,
% 1.69/1.85 (~c2_1(a552)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2424, 3566])).
% 1.69/1.85 tff(3568,plain,
% 1.69/1.85 (~c1_1(a552)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2453, 3566])).
% 1.69/1.85 tff(3569,plain,
% 1.69/1.85 (~c3_1(a552)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2430, 3566])).
% 1.69/1.85 tff(3570,plain,
% 1.69/1.85 (~c3_1(a569)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2783, 156, 733, 732, 731, 3449, 3448, 3447, 3446, 3443, 707])).
% 1.69/1.85 tff(3571,plain,
% 1.69/1.85 (hskp51),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3462, 156, 3565, 3564, 3563, 3447, 3446, 2608, 3570])).
% 1.69/1.85 tff(3572,plain,
% 1.69/1.85 (~c2_1(a583)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2637, 3571])).
% 1.69/1.85 tff(3573,plain,
% 1.69/1.85 (c3_1(a583)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2645, 3571])).
% 1.69/1.85 tff(3574,plain,
% 1.69/1.85 (~c1_1(a583)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3471, 156, 3573, 2334, 2336, 3572, 3569, 3568, 3567, 45, 3422])).
% 1.69/1.85 tff(3575,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a583)) | c1_1(a583) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a583)) | c1_1(a583) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3576,plain,
% 1.69/1.85 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a583)) | c1_1(a583) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3577,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a583)) | c1_1(a583) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3576])).
% 1.69/1.85 tff(3578,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a583)) | c1_1(a583) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3577, 3575])).
% 1.69/1.85 tff(3579,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3580,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a583)) | c1_1(a583) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 1.69/1.85 tff(3581,plain,
% 1.69/1.85 ($false),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3580, 156, 3573, 733, 732, 731, 3449, 3448, 3572, 3443, 707, 3574])).
% 1.69/1.85 tff(3582,plain,(hskp6 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a535) | c0_1(a545) | c1_1(a586) | c0_1(a586) | c2_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3583,plain,
% 1.69/1.85 (hskp6),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3582, 3561, 3560, 3559, 3420, 3419, 3418, 97, 88, 87, 653])).
% 1.69/1.85 tff(3584,plain,
% 1.69/1.85 (c3_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[225, 3583])).
% 1.69/1.85 tff(3585,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3586,plain,
% 1.69/1.85 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3587,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548)))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3586])).
% 1.69/1.85 tff(3588,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3587, 3585])).
% 1.69/1.85 tff(3589,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3590,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a548) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548)),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 1.69/1.85 tff(3591,plain,
% 1.69/1.85 ((~c3_1(a548)) | c1_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3590, 156, 3410, 3402, 3394, 3420, 3419, 24, 3418, 707])).
% 1.69/1.85 tff(3592,plain,
% 1.69/1.85 (c1_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3591, 3584])).
% 1.69/1.85 tff(3593,plain,
% 1.69/1.85 (hskp46),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2834, 3584, 56, 3592])).
% 1.69/1.85 tff(3594,plain,
% 1.69/1.85 (~c0_1(a562)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[64, 3593])).
% 1.69/1.85 tff(3595,plain,
% 1.69/1.85 (~c3_1(a562)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[270, 3593])).
% 1.69/1.85 tff(3596,plain,
% 1.69/1.85 (c1_1(a562)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[288, 3593])).
% 1.69/1.85 tff(3597,plain,
% 1.69/1.85 (hskp34),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2160, 156, 3596, 3561, 3560, 3559, 3595, 3594, 75])).
% 1.69/1.85 tff(3598,plain,
% 1.69/1.85 (~c1_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1124, 3597])).
% 1.69/1.85 tff(3599,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3600,plain,
% 1.69/1.85 ((hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536))) <=> (hskp42 | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3601,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | (~c1_1(a548))))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3600])).
% 1.69/1.85 tff(3602,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3601, 3599])).
% 1.69/1.85 tff(3603,plain,
% 1.69/1.85 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3604,plain,
% 1.69/1.85 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3603, 3602])).
% 1.69/1.85 tff(3605,plain,
% 1.69/1.85 (hskp42 | (~c3_1(a548)) | (~c1_1(a548))),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3604, 156, 3410, 3402, 3394, 24, 1364])).
% 1.69/1.85 tff(3606,plain,
% 1.69/1.85 (hskp42),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3605, 3584, 3592])).
% 1.69/1.85 tff(3607,plain,
% 1.69/1.85 (~c2_1(a556)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1385, 3606])).
% 1.69/1.85 tff(3608,plain,
% 1.69/1.85 (c3_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1132, 3597])).
% 1.69/1.85 tff(3609,plain,
% 1.69/1.85 (c3_1(a556)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1403, 3606])).
% 1.69/1.85 tff(3610,plain,
% 1.69/1.85 (c1_1(a556)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1411, 3606])).
% 1.69/1.85 tff(3611,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c2_1(a556) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a556) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3612,plain,
% 1.69/1.85 (((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (c1_1(a586) | c2_1(a556) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3613,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c2_1(a556) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3612])).
% 1.69/1.85 tff(3614,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a556) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3613, 3611])).
% 1.69/1.85 tff(3615,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3616,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a556) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3615, 3614])).
% 1.69/1.85 tff(3617,plain,
% 1.69/1.85 (~c2_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3616, 156, 3610, 3609, 3608, 88, 3607, 3598, 86, 45, 653])).
% 1.69/1.85 tff(3618,plain,
% 1.69/1.85 ($false),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2754, 156, 3561, 3560, 3559, 3608, 3420, 3419, 3598, 3418, 707, 3617])).
% 1.69/1.85 tff(3619,plain,(c0_1(a548) | c1_1(a586) | c3_1(a586) | c2_1(a586) | c2_1(a548) | c0_1(a545) | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3620,plain,
% 1.69/1.85 ($false),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3619, 3483, 3482, 86, 653, 88, 97, 87])).
% 1.69/1.85 tff(3621,plain,(c2_1(a586) | c3_1(a586) | c1_1(a586) | c0_1(a545) | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3622,plain,
% 1.69/1.85 (c2_1(a586)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3621, 97, 88, 86, 87])).
% 1.69/1.85 tff(3623,assumption,(hskp34), introduced(assumption)).
% 1.69/1.85 tff(3624,plain,
% 1.69/1.85 (~c1_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1124, 3623])).
% 1.69/1.85 tff(3625,plain,
% 1.69/1.85 (c3_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1132, 3623])).
% 1.69/1.85 tff(3626,plain,
% 1.69/1.85 (c0_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1147, 3623])).
% 1.69/1.85 tff(3627,plain,
% 1.69/1.85 (hskp8),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2725, 156, 3626, 3625, 88, 3624, 87, 2407, 902])).
% 1.69/1.85 tff(3628,plain,
% 1.69/1.85 (~c2_1(a552)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2424, 3627])).
% 1.69/1.85 tff(3629,plain,
% 1.69/1.85 (~c1_1(a552)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2453, 3627])).
% 1.69/1.85 tff(3630,plain,
% 1.69/1.85 (~c3_1(a552)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2430, 3627])).
% 1.69/1.85 tff(3631,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3632,plain,
% 1.69/1.85 ((hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (hskp51 | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3633,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3632])).
% 1.69/1.85 tff(3634,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3633, 3631])).
% 1.69/1.85 tff(3635,plain,
% 1.69/1.85 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3636,plain,
% 1.69/1.85 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3635, 3634])).
% 1.69/1.85 tff(3637,plain,
% 1.69/1.85 (hskp51),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3636, 156, 3626, 3625, 3624, 3630, 3629, 3628, 2608])).
% 1.69/1.85 tff(3638,plain,
% 1.69/1.85 (~c2_1(a583)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2637, 3637])).
% 1.69/1.85 tff(3639,plain,
% 1.69/1.85 (c3_1(a583)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2645, 3637])).
% 1.69/1.85 tff(3640,plain,
% 1.69/1.85 (c0_1(a583)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2653, 3637])).
% 1.69/1.85 tff(3641,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a583) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a583) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3642,plain,
% 1.69/1.85 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c1_1(a586) | c2_1(a583) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3643,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a583) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a583)) | (~c0_1(a583))))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3642])).
% 1.69/1.85 tff(3644,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a583) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3643, 3641])).
% 1.69/1.85 tff(3645,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3646,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a583) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a583)) | (~c0_1(a583))),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3645, 3644])).
% 1.69/1.85 tff(3647,plain,
% 1.69/1.85 ($false),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3646, 156, 3640, 3639, 3626, 3625, 88, 3638, 3624, 86, 921, 902])).
% 1.69/1.85 tff(3648,plain,((~hskp34) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3649,plain,
% 1.69/1.85 (~hskp34),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3648, 3622, 86, 88, 87])).
% 1.69/1.85 tff(3650,assumption,(~hskp34), introduced(assumption)).
% 1.69/1.85 tff(3651,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a562)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3652,plain,
% 1.69/1.85 ((hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a562)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3653,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a562))))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3652])).
% 1.69/1.85 tff(3654,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a562)))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3653, 3651])).
% 1.69/1.85 tff(3655,plain,
% 1.69/1.85 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3656,plain,
% 1.69/1.85 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a562))),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3655, 3654])).
% 1.69/1.85 tff(3657,plain,
% 1.69/1.85 ($false),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3656, 156, 3650, 3245, 3428, 3427, 3426, 3244, 65, 75])).
% 1.69/1.85 tff(3658,plain,((~hskp46) | hskp34 | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536))), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3659,plain,
% 1.69/1.85 (~hskp46),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3658, 3650, 3428, 3427, 3426])).
% 1.69/1.85 tff(3660,plain,
% 1.69/1.85 (~c3_1(a545)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1163, 156, 3659, 1645, 1644, 97, 12])).
% 1.69/1.85 tff(3661,plain,
% 1.69/1.85 ($false),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3434, 156, 3650, 3428, 3427, 3426, 1645, 97, 75, 3660])).
% 1.69/1.85 tff(3662,plain,((~hskp4) | hskp34 | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3663,plain,
% 1.69/1.85 (~hskp4),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3662, 3649, 3410, 3402, 3394, 97])).
% 1.69/1.85 tff(3664,plain,
% 1.69/1.85 (hskp6),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[205, 3663, 96])).
% 1.69/1.85 tff(3665,plain,
% 1.69/1.85 (~c2_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[217, 3664])).
% 1.69/1.85 tff(3666,plain,
% 1.69/1.85 (~c0_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[211, 3664])).
% 1.69/1.85 tff(3667,assumption,(hskp33), introduced(assumption)).
% 1.69/1.85 tff(3668,plain,
% 1.69/1.85 (hskp28 | c0_1(a548) | c1_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1604, 156, 24, 122])).
% 1.69/1.85 tff(3669,plain,
% 1.69/1.85 (c1_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3668, 1213, 56])).
% 1.69/1.85 tff(3670,plain,
% 1.69/1.85 (c0_1(a536)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3393, 3667])).
% 1.69/1.85 tff(3671,plain,
% 1.69/1.85 (c2_1(a536)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3401, 3667])).
% 1.69/1.85 tff(3672,plain,
% 1.69/1.85 (c1_1(a536)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3409, 3667])).
% 1.69/1.85 tff(3673,plain,
% 1.69/1.85 (hskp46),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2834, 249, 56, 3669])).
% 1.69/1.85 tff(3674,plain,
% 1.69/1.85 (~c0_1(a562)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[64, 3673])).
% 1.69/1.85 tff(3675,plain,
% 1.69/1.85 (~c3_1(a562)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[270, 3673])).
% 1.69/1.85 tff(3676,plain,
% 1.69/1.85 (c1_1(a562)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[288, 3673])).
% 1.69/1.85 tff(3677,plain,
% 1.69/1.85 (hskp34),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3656, 156, 3676, 3428, 3427, 3426, 3675, 3674, 75])).
% 1.69/1.85 tff(3678,plain,
% 1.69/1.85 (~c1_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1124, 3677])).
% 1.69/1.85 tff(3679,plain,
% 1.69/1.85 (hskp41),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[2392, 249, 1213, 56, 24])).
% 1.69/1.85 tff(3680,plain,
% 1.69/1.85 (~c2_1(a555)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[232, 3679])).
% 1.69/1.85 tff(3681,plain,
% 1.69/1.85 (c3_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1132, 3677])).
% 1.69/1.85 tff(3682,plain,
% 1.69/1.85 (c0_1(a537)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[1147, 3677])).
% 1.69/1.85 tff(3683,plain,
% 1.69/1.85 (c0_1(a555)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[240, 3679])).
% 1.69/1.85 tff(3684,plain,
% 1.69/1.85 (c3_1(a555)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[256, 3679])).
% 1.69/1.85 tff(3685,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a555) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a555)) | (~c0_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a555) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a555)) | (~c0_1(a555)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3686,plain,
% 1.69/1.85 (((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c1_1(a586) | c2_1(a555) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a555)) | (~c0_1(a555)))),
% 1.69/1.85 inference(rewrite,[status(thm)],[])).
% 1.69/1.85 tff(3687,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c2_1(a555) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a555)) | (~c0_1(a555))))),
% 1.69/1.85 inference(monotonicity,[status(thm)],[3686])).
% 1.69/1.85 tff(3688,plain,
% 1.69/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a555) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a555)) | (~c0_1(a555)))),
% 1.69/1.85 inference(transitivity,[status(thm)],[3687, 3685])).
% 1.69/1.85 tff(3689,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 1.69/1.85 inference(quant_inst,[status(thm)],[])).
% 1.69/1.85 tff(3690,plain,
% 1.69/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c2_1(a555) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)) | (~c3_1(a555)) | (~c0_1(a555))),
% 1.69/1.85 inference(modus_ponens,[status(thm)],[3689, 3688])).
% 1.69/1.85 tff(3691,plain,
% 1.69/1.85 ($false),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3690, 156, 3684, 3683, 3682, 3681, 88, 3680, 3678, 86, 921, 902])).
% 1.69/1.85 tff(3692,plain,((~c3_1(a548)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | hskp28 | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.85 tff(3693,plain,
% 1.69/1.85 (~c3_1(a548)),
% 1.69/1.85 inference(unit_resolution,[status(thm)],[3692, 1213, 86, 902, 3672, 3671, 3670, 88, 56, 24])).
% 1.69/1.85 tff(3694,plain,
% 1.69/1.85 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3695,plain,
% 1.69/1.86 ((hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548))) <=> (hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3696,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3695])).
% 1.69/1.86 tff(3697,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3696, 3694])).
% 1.69/1.86 tff(3698,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3699,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3698, 3697])).
% 1.69/1.86 tff(3700,plain,
% 1.69/1.86 (hskp34),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3699, 156, 3428, 3427, 3426, 2895, 56, 75, 2548])).
% 1.69/1.86 tff(3701,plain,
% 1.69/1.86 (~c1_1(a537)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1124, 3700])).
% 1.69/1.86 tff(3702,plain,
% 1.69/1.86 (c3_1(a537)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1132, 3700])).
% 1.69/1.86 tff(3703,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3704,plain,
% 1.69/1.86 ((hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp15 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3705,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3704])).
% 1.69/1.86 tff(3706,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3705, 3703])).
% 1.69/1.86 tff(3707,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3708,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3707, 3706])).
% 1.69/1.86 tff(3709,plain,
% 1.69/1.86 (~c2_1(a537)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3708, 156, 109, 3702, 2895, 3701, 24, 483, 2548])).
% 1.69/1.86 tff(3710,plain,
% 1.69/1.86 (c0_1(a537)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1147, 3700])).
% 1.69/1.86 tff(3711,plain,
% 1.69/1.86 (hskp8),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[2725, 156, 3710, 3702, 88, 3701, 87, 2407, 902])).
% 1.69/1.86 tff(3712,plain,
% 1.69/1.86 (~c1_1(a552)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[2453, 3711])).
% 1.69/1.86 tff(3713,plain,
% 1.69/1.86 (~c2_1(a552)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[2424, 3711])).
% 1.69/1.86 tff(3714,plain,
% 1.69/1.86 (~c3_1(a552)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[2430, 3711])).
% 1.69/1.86 tff(3715,assumption,(~c2_1(a552)), introduced(assumption)).
% 1.69/1.86 tff(3716,assumption,(~c1_1(a552)), introduced(assumption)).
% 1.69/1.86 tff(3717,assumption,(~c3_1(a552)), introduced(assumption)).
% 1.69/1.86 tff(3718,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3719,plain,
% 1.69/1.86 ((hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3720,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3719])).
% 1.69/1.86 tff(3721,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3720, 3718])).
% 1.69/1.86 tff(3722,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3723,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3722, 3721])).
% 1.69/1.86 tff(3724,plain,
% 1.69/1.86 ($false),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3723, 156, 837, 3672, 3671, 3670, 3717, 3716, 3715, 108])).
% 1.69/1.86 tff(3725,plain,((~hskp33) | hskp0 | c3_1(a552) | c1_1(a552) | c2_1(a552)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.86 tff(3726,plain,
% 1.69/1.86 (~hskp33),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3725, 3715, 3717, 3716, 837])).
% 1.69/1.86 tff(3727,plain,
% 1.69/1.86 (c3_1(a545)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[822, 156, 35, 2476, 2475, 2474, 1644, 1667, 85])).
% 1.69/1.86 tff(3728,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3729,plain,
% 1.69/1.86 ((hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3730,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3729])).
% 1.69/1.86 tff(3731,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3730, 3728])).
% 1.69/1.86 tff(3732,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3733,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 1.69/1.86 tff(3734,plain,
% 1.69/1.86 ($false),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3733, 156, 58, 3717, 3716, 3715, 1644, 1667, 663, 3727])).
% 1.69/1.86 tff(3735,plain,((~hskp4) | hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552) | hskp33 | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.86 tff(3736,plain,
% 1.69/1.86 ($false),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3735, 808, 816, 3717, 3716, 3715, 35, 58, 1622, 800])).
% 1.69/1.86 tff(3737,plain,((~hskp50) | c3_1(a552) | c1_1(a552) | c2_1(a552) | hskp33 | hskp38 | (~hskp4)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.86 tff(3738,plain,
% 1.69/1.86 (~hskp50),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3737, 1622, 3716, 3715, 35, 58, 3717])).
% 1.69/1.86 tff(3739,plain,
% 1.69/1.86 (hskp50 | hskp19 | c2_1(a552) | (~c0_1(a552))),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[2460, 156, 3716, 34])).
% 1.69/1.86 tff(3740,plain,
% 1.69/1.86 (~c0_1(a552)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3739, 3738, 3715, 98])).
% 1.69/1.86 tff(3741,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp14 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3742,plain,
% 1.69/1.86 ((hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (hskp14 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3743,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3742])).
% 1.69/1.86 tff(3744,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp14 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3743, 3741])).
% 1.69/1.86 tff(3745,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp14 | (~ndr1_0) | c2_1(a545) | c0_1(a545) | (~c1_1(a545)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3746,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp14 | c3_1(a552) | c1_1(a552) | c2_1(a552) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3745, 3744])).
% 1.69/1.86 tff(3747,plain,
% 1.69/1.86 (hskp14),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3746, 156, 1645, 3717, 3716, 3715, 1644, 1667, 1045])).
% 1.69/1.86 tff(3748,plain,
% 1.69/1.86 (~c1_1(a567)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1058, 3747])).
% 1.69/1.86 tff(3749,plain,
% 1.69/1.86 (c0_1(a567)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1066, 3747])).
% 1.69/1.86 tff(3750,plain,
% 1.69/1.86 (hskp50 | c2_1(a567)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1073, 156, 98, 3749, 3748, 34])).
% 1.69/1.86 tff(3751,plain,
% 1.69/1.86 (c2_1(a567)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3750, 3738])).
% 1.69/1.86 tff(3752,plain,
% 1.69/1.86 (~c3_1(a567)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1079, 3747])).
% 1.69/1.86 tff(3753,plain,
% 1.69/1.86 (hskp37 | (~c2_1(a567))),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[1086, 156, 3749, 3748, 3752, 415])).
% 1.69/1.86 tff(3754,plain,
% 1.69/1.86 (hskp37),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3753, 3751])).
% 1.69/1.86 tff(3755,plain,
% 1.69/1.86 (~c3_1(a544)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[450, 3754])).
% 1.69/1.86 tff(3756,plain,
% 1.69/1.86 (c1_1(a544)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[444, 3754])).
% 1.69/1.86 tff(3757,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3758,plain,
% 1.69/1.86 ((hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a552) | c3_1(a552) | c0_1(a552)) <=> (hskp33 | c3_1(a544) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3759,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a552) | c3_1(a552) | c0_1(a552))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3758])).
% 1.69/1.86 tff(3760,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a552) | c3_1(a552) | c0_1(a552))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3759, 3757])).
% 1.69/1.86 tff(3761,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a552) | c3_1(a552) | c0_1(a552))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3762,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 1.69/1.86 tff(3763,plain,
% 1.69/1.86 (~c0_1(a544)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3762, 156, 35, 3756, 3755, 3717, 3715, 85, 3740])).
% 1.69/1.86 tff(3764,plain,
% 1.69/1.86 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3765,plain,
% 1.69/1.86 ((hskp28 | (~ndr1_0) | c2_1(a552) | c0_1(a552) | c1_1(a552)) <=> (hskp28 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3766,plain,
% 1.69/1.86 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a552) | c0_1(a552) | c1_1(a552))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552)))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3765])).
% 1.69/1.86 tff(3767,plain,
% 1.69/1.86 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a552) | c0_1(a552) | c1_1(a552))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3766, 3764])).
% 1.69/1.86 tff(3768,plain,
% 1.69/1.86 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a552) | c0_1(a552) | c1_1(a552))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3769,plain,
% 1.69/1.86 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552)),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3768, 3767])).
% 1.69/1.86 tff(3770,plain,
% 1.69/1.86 (hskp28 | c2_1(a552) | c0_1(a552)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3769, 156, 3716, 122])).
% 1.69/1.86 tff(3771,plain,
% 1.69/1.86 (hskp28),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3770, 3740, 3715])).
% 1.69/1.86 tff(3772,plain,
% 1.69/1.86 (~c0_1(a589)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[177, 3771])).
% 1.69/1.86 tff(3773,plain,
% 1.69/1.86 (c3_1(a589)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[185, 3771])).
% 1.69/1.86 tff(3774,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3775,plain,
% 1.69/1.86 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a552) | c1_1(a552) | c0_1(a552)) <=> (hskp6 | c0_1(a589) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3776,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a552) | c1_1(a552) | c0_1(a552))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3775])).
% 1.69/1.86 tff(3777,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a552) | c1_1(a552) | c0_1(a552))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3776, 3774])).
% 1.69/1.86 tff(3778,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a552) | c1_1(a552) | c0_1(a552))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3779,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | c0_1(a552) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3778, 3777])).
% 1.69/1.86 tff(3780,plain,
% 1.69/1.86 (~c1_1(a589)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3779, 156, 1669, 3773, 3772, 3716, 3715, 1745, 3740])).
% 1.69/1.86 tff(3781,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a544) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | c0_1(a544) | (~c1_1(a544)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3782,plain,
% 1.69/1.86 ((hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589))) <=> (hskp26 | c3_1(a544) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | c0_1(a544) | (~c1_1(a544)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3783,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a544) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | c0_1(a544) | (~c1_1(a544))))),
% 1.69/1.86 inference(monotonicity,[status(thm)],[3782])).
% 1.69/1.86 tff(3784,plain,
% 1.69/1.86 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | c0_1(a544) | (~c1_1(a544)))),
% 1.69/1.86 inference(transitivity,[status(thm)],[3783, 3781])).
% 1.69/1.86 tff(3785,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a544) | c3_1(a544) | (~c1_1(a544)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)))),
% 1.69/1.86 inference(quant_inst,[status(thm)],[])).
% 1.69/1.86 tff(3786,plain,
% 1.69/1.86 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a544) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | c0_1(a544) | (~c1_1(a544))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3785, 3784])).
% 1.69/1.86 tff(3787,plain,
% 1.69/1.86 ($false),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3786, 156, 1661, 3756, 3773, 3755, 3772, 1686, 3780, 3763])).
% 1.69/1.86 tff(3788,plain,((~hskp4) | hskp26 | hskp6 | c1_1(a552) | c2_1(a552) | hskp33 | c3_1(a552) | hskp19 | hskp38), inference(lemma,lemma(discharge,[]))).
% 1.69/1.86 tff(3789,plain,
% 1.69/1.86 (~hskp4),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3788, 1661, 1669, 3716, 3715, 35, 3717, 98, 58])).
% 1.69/1.86 tff(3790,plain,
% 1.69/1.86 (hskp27),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[205, 3789, 1669])).
% 1.69/1.86 tff(3791,plain,
% 1.69/1.86 (hskp27),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[205, 23, 1669])).
% 1.69/1.86 tff(3792,plain,
% 1.69/1.86 (c1_1(a586)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[95, 3791])).
% 1.69/1.86 tff(3793,assumption,(c0_1(a552)), introduced(assumption)).
% 1.69/1.86 tff(3794,plain,
% 1.69/1.86 (hskp50),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3739, 3793, 3715, 98])).
% 1.69/1.86 tff(3795,plain,
% 1.69/1.86 (~c3_1(a574)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[799, 3794])).
% 1.69/1.86 tff(3796,plain,
% 1.69/1.86 (c1_1(a574)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[807, 3794])).
% 1.69/1.86 tff(3797,assumption,(c1_1(a586)), introduced(assumption)).
% 1.69/1.86 tff(3798,assumption,(hskp43), introduced(assumption)).
% 1.69/1.86 tff(3799,plain,
% 1.69/1.86 (((~hskp43) | (~c1_1(a557))) <=> ((~hskp43) | (~c1_1(a557)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3800,plain,
% 1.69/1.86 (((~c1_1(a557)) | (~hskp43)) <=> ((~hskp43) | (~c1_1(a557)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3801,axiom,((~c1_1(a557)) | (~hskp43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.69/1.86 tff(3802,plain,
% 1.69/1.86 ((~hskp43) | (~c1_1(a557))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 1.69/1.86 tff(3803,plain,
% 1.69/1.86 ((~hskp43) | (~c1_1(a557))),
% 1.69/1.86 inference(modus_ponens,[status(thm)],[3802, 3799])).
% 1.69/1.86 tff(3804,plain,
% 1.69/1.86 (~c1_1(a557)),
% 1.69/1.86 inference(unit_resolution,[status(thm)],[3803, 3798])).
% 1.69/1.86 tff(3805,plain,
% 1.69/1.86 (^[V: $i, U: $i] : refl((hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.69/1.86 inference(bind,[status(th)],[])).
% 1.69/1.86 tff(3806,plain,
% 1.69/1.86 (![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.69/1.86 inference(quant_intro,[status(thm)],[3805])).
% 1.69/1.86 tff(3807,plain,
% 1.69/1.86 (![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.69/1.86 inference(rewrite,[status(thm)],[])).
% 1.69/1.86 tff(3808,plain,
% 1.69/1.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp49) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp49))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp49) <=> (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp49) <=> (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.69/1.87 inference(bind,[status(th)],[])).
% 1.69/1.87 tff(3809,plain,
% 1.69/1.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp49) <=> ![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.69/1.87 inference(quant_intro,[status(thm)],[3808])).
% 1.69/1.87 tff(3810,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | hskp49)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause244')).
% 1.69/1.87 tff(3811,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 1.69/1.87 tff(3812,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3811, 3807])).
% 1.69/1.87 tff(3813,plain,(
% 1.69/1.87 ![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.69/1.87 inference(skolemize,[status(sab)],[3812])).
% 1.69/1.87 tff(3814,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3813, 3806])).
% 1.69/1.87 tff(3815,plain,
% 1.69/1.87 (((~hskp43) | c0_1(a557)) <=> ((~hskp43) | c0_1(a557))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3816,axiom,((~hskp43) | c0_1(a557)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.69/1.87 tff(3817,plain,
% 1.69/1.87 ((~hskp43) | c0_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3816, 3815])).
% 1.69/1.87 tff(3818,plain,
% 1.69/1.87 ((~hskp43) | c0_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3817, 3815])).
% 1.69/1.87 tff(3819,plain,
% 1.69/1.87 ((~hskp43) | c0_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3818, 3815])).
% 1.69/1.87 tff(3820,plain,
% 1.69/1.87 ((~hskp43) | c0_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3819, 3815])).
% 1.69/1.87 tff(3821,plain,
% 1.69/1.87 ((~hskp43) | c0_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3820, 3815])).
% 1.69/1.87 tff(3822,plain,
% 1.69/1.87 (c0_1(a557)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3821, 3798])).
% 1.69/1.87 tff(3823,plain,
% 1.69/1.87 (((~hskp43) | c3_1(a557)) <=> ((~hskp43) | c3_1(a557))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3824,axiom,((~hskp43) | c3_1(a557)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.69/1.87 tff(3825,plain,
% 1.69/1.87 ((~hskp43) | c3_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 1.69/1.87 tff(3826,plain,
% 1.69/1.87 ((~hskp43) | c3_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3825, 3823])).
% 1.69/1.87 tff(3827,plain,
% 1.69/1.87 ((~hskp43) | c3_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3826, 3823])).
% 1.69/1.87 tff(3828,plain,
% 1.69/1.87 ((~hskp43) | c3_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3827, 3823])).
% 1.69/1.87 tff(3829,plain,
% 1.69/1.87 ((~hskp43) | c3_1(a557)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3828, 3823])).
% 1.69/1.87 tff(3830,plain,
% 1.69/1.87 (c3_1(a557)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3829, 3798])).
% 1.69/1.87 tff(3831,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a557) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a557) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3832,plain,
% 1.69/1.87 ((hskp51 | (~ndr1_0) | c1_1(a557) | (~c3_1(a557)) | (~c0_1(a557)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (hskp51 | c1_1(a557) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3833,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a557) | (~c3_1(a557)) | (~c0_1(a557)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a557) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557))))),
% 1.69/1.87 inference(monotonicity,[status(thm)],[3832])).
% 1.69/1.87 tff(3834,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a557) | (~c3_1(a557)) | (~c0_1(a557)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a557) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)))),
% 1.69/1.87 inference(transitivity,[status(thm)],[3833, 3831])).
% 1.69/1.87 tff(3835,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a557) | (~c3_1(a557)) | (~c0_1(a557)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.69/1.87 inference(quant_inst,[status(thm)],[])).
% 1.69/1.87 tff(3836,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a557) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 1.69/1.87 tff(3837,plain,
% 1.69/1.87 (hskp51),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3836, 156, 3830, 3822, 3804, 3717, 3716, 3715, 2608])).
% 1.69/1.87 tff(3838,plain,
% 1.69/1.87 (~c2_1(a583)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[2637, 3837])).
% 1.69/1.87 tff(3839,plain,
% 1.69/1.87 (c3_1(a583)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[2645, 3837])).
% 1.69/1.87 tff(3840,plain,
% 1.69/1.87 (c0_1(a583)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[2653, 3837])).
% 1.69/1.87 tff(3841,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | c2_1(a583) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp49 | c2_1(a583) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3842,plain,
% 1.69/1.87 ((hskp49 | (~ndr1_0) | c2_1(a552) | c3_1(a552) | (~c0_1(a552)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583))) <=> (hskp49 | c2_1(a583) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3843,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | (~ndr1_0) | c2_1(a552) | c3_1(a552) | (~c0_1(a552)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | c2_1(a583) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c3_1(a583)) | (~c0_1(a583))))),
% 1.69/1.87 inference(monotonicity,[status(thm)],[3842])).
% 1.69/1.87 tff(3844,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | (~ndr1_0) | c2_1(a552) | c3_1(a552) | (~c0_1(a552)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp49 | c2_1(a583) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.87 inference(transitivity,[status(thm)],[3843, 3841])).
% 1.69/1.87 tff(3845,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | (~ndr1_0) | c2_1(a552) | c3_1(a552) | (~c0_1(a552)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.87 inference(quant_inst,[status(thm)],[])).
% 1.69/1.87 tff(3846,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp49 | c2_1(a583) | c3_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c3_1(a583)) | (~c0_1(a583))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3845, 3844])).
% 1.69/1.87 tff(3847,plain,
% 1.69/1.87 (hskp49),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3846, 156, 3840, 3839, 3838, 3717, 3715, 3814, 3793])).
% 1.69/1.87 tff(3848,plain,
% 1.69/1.87 (((~hskp49) | (~c1_1(a568))) <=> ((~hskp49) | (~c1_1(a568)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3849,plain,
% 1.69/1.87 (((~c1_1(a568)) | (~hskp49)) <=> ((~hskp49) | (~c1_1(a568)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3850,axiom,((~c1_1(a568)) | (~hskp49)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.69/1.87 tff(3851,plain,
% 1.69/1.87 ((~hskp49) | (~c1_1(a568))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3850, 3849])).
% 1.69/1.87 tff(3852,plain,
% 1.69/1.87 ((~hskp49) | (~c1_1(a568))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3851, 3848])).
% 1.69/1.87 tff(3853,plain,
% 1.69/1.87 (~c1_1(a568)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3852, 3847])).
% 1.69/1.87 tff(3854,plain,
% 1.69/1.87 (((~hskp49) | c2_1(a568)) <=> ((~hskp49) | c2_1(a568))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3855,axiom,((~hskp49) | c2_1(a568)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.69/1.87 tff(3856,plain,
% 1.69/1.87 ((~hskp49) | c2_1(a568)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3855, 3854])).
% 1.69/1.87 tff(3857,plain,
% 1.69/1.87 ((~hskp49) | c2_1(a568)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3856, 3854])).
% 1.69/1.87 tff(3858,plain,
% 1.69/1.87 ((~hskp49) | c2_1(a568)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3857, 3854])).
% 1.69/1.87 tff(3859,plain,
% 1.69/1.87 ((~hskp49) | c2_1(a568)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3858, 3854])).
% 1.69/1.87 tff(3860,plain,
% 1.69/1.87 ((~hskp49) | c2_1(a568)),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3859, 3854])).
% 1.69/1.87 tff(3861,plain,
% 1.69/1.87 (c2_1(a568)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3860, 3847])).
% 1.69/1.87 tff(3862,plain,
% 1.69/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c1_1(a568) | c1_1(a557) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a568) | c1_1(a557) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3863,plain,
% 1.69/1.87 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a557)) | c1_1(a557) | (~c3_1(a557))) <=> (c2_1(a583) | c1_1(a568) | c1_1(a557) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3864,plain,
% 1.69/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a557)) | c1_1(a557) | (~c3_1(a557)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c1_1(a568) | c1_1(a557) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583))))),
% 1.69/1.87 inference(monotonicity,[status(thm)],[3863])).
% 1.69/1.87 tff(3865,plain,
% 1.69/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a557)) | c1_1(a557) | (~c3_1(a557)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a568) | c1_1(a557) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.87 inference(transitivity,[status(thm)],[3864, 3862])).
% 1.69/1.87 tff(3866,plain,
% 1.69/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a557)) | c1_1(a557) | (~c3_1(a557)))),
% 1.69/1.87 inference(quant_inst,[status(thm)],[])).
% 1.69/1.87 tff(3867,plain,
% 1.69/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a568) | c1_1(a557) | (~ndr1_0) | (~c3_1(a557)) | (~c0_1(a557)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3866, 3865])).
% 1.69/1.87 tff(3868,plain,
% 1.69/1.87 (c3_1(a568)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3867, 156, 3840, 3839, 3861, 3830, 3822, 3838, 3853, 3804, 921])).
% 1.69/1.87 tff(3869,plain,
% 1.69/1.87 (((~hskp49) | (~c0_1(a568))) <=> ((~hskp49) | (~c0_1(a568)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3870,plain,
% 1.69/1.87 (((~c0_1(a568)) | (~hskp49)) <=> ((~hskp49) | (~c0_1(a568)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3871,axiom,((~c0_1(a568)) | (~hskp49)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.69/1.87 tff(3872,plain,
% 1.69/1.87 ((~hskp49) | (~c0_1(a568))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 1.69/1.87 tff(3873,plain,
% 1.69/1.87 ((~hskp49) | (~c0_1(a568))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3872, 3869])).
% 1.69/1.87 tff(3874,plain,
% 1.69/1.87 (~c0_1(a568)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3873, 3847])).
% 1.69/1.87 tff(3875,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a568)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3876,plain,
% 1.69/1.87 ((hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568))) <=> (hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a568)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3877,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a568))))),
% 1.69/1.87 inference(monotonicity,[status(thm)],[3876])).
% 1.69/1.87 tff(3878,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a568)))),
% 1.69/1.87 inference(transitivity,[status(thm)],[3877, 3875])).
% 1.69/1.87 tff(3879,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568)))),
% 1.69/1.87 inference(quant_inst,[status(thm)],[])).
% 1.69/1.87 tff(3880,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a568))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3879, 3878])).
% 1.69/1.87 tff(3881,plain,
% 1.69/1.87 ($false),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3880, 156, 1661, 3797, 3874, 3853, 87, 86, 1686, 3868])).
% 1.69/1.87 tff(3882,plain,((~hskp43) | hskp26 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | c3_1(a552) | c2_1(a552) | (~c0_1(a552)) | c1_1(a552)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.87 tff(3883,plain,
% 1.69/1.87 (~hskp43),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3882, 3793, 1661, 87, 86, 3717, 3715, 3797, 3716])).
% 1.69/1.87 tff(3884,plain,
% 1.69/1.87 (^[V: $i, U: $i] : refl((hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.69/1.87 inference(bind,[status(th)],[])).
% 1.69/1.87 tff(3885,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(quant_intro,[status(thm)],[3884])).
% 1.69/1.87 tff(3886,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3887,plain,
% 1.69/1.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp43) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp43))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp43) <=> (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp43) <=> (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.69/1.87 inference(bind,[status(th)],[])).
% 1.69/1.87 tff(3888,plain,
% 1.69/1.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp43) <=> ![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(quant_intro,[status(thm)],[3887])).
% 1.69/1.87 tff(3889,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause243')).
% 1.69/1.87 tff(3890,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3889, 3888])).
% 1.69/1.87 tff(3891,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3890, 3886])).
% 1.69/1.87 tff(3892,plain,(
% 1.69/1.87 ![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(skolemize,[status(sab)],[3891])).
% 1.69/1.87 tff(3893,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3892, 3885])).
% 1.69/1.87 tff(3894,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | c0_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp43 | c0_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3895,plain,
% 1.69/1.87 ((hskp43 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp43 | c0_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3896,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | c0_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.69/1.87 inference(monotonicity,[status(thm)],[3895])).
% 1.69/1.87 tff(3897,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp43 | c0_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.87 inference(transitivity,[status(thm)],[3896, 3894])).
% 1.69/1.87 tff(3898,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.87 inference(quant_inst,[status(thm)],[])).
% 1.69/1.87 tff(3899,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp43 | c0_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 1.69/1.87 tff(3900,plain,
% 1.69/1.87 (hskp43 | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3899, 156, 87, 3716, 3715, 3893])).
% 1.69/1.87 tff(3901,plain,
% 1.69/1.87 (~c2_1(a586)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3900, 3883, 3797, 3793])).
% 1.69/1.87 tff(3902,plain,
% 1.69/1.87 (c0_1(a574)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[815, 3794])).
% 1.69/1.87 tff(3903,plain,
% 1.69/1.87 ($false),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[2484, 3902, 3901, 86, 3796, 3795, 87, 35])).
% 1.69/1.87 tff(3904,plain,((~c0_1(a552)) | c3_1(a586) | c0_1(a586) | hskp33 | (~c1_1(a586)) | c1_1(a552) | c2_1(a552) | hskp19 | hskp26 | c3_1(a552)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.87 tff(3905,plain,
% 1.69/1.87 (~c0_1(a552)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3904, 3792, 87, 35, 86, 3716, 3715, 98, 1661, 3717])).
% 1.69/1.87 tff(3906,plain,
% 1.69/1.87 (hskp28),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3770, 3905, 3715])).
% 1.69/1.87 tff(3907,plain,
% 1.69/1.87 (c3_1(a589)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[185, 3906])).
% 1.69/1.87 tff(3908,plain,
% 1.69/1.87 (c2_1(a589)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[171, 3906])).
% 1.69/1.87 tff(3909,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3910,plain,
% 1.69/1.87 ((hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3911,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.69/1.87 inference(monotonicity,[status(thm)],[3910])).
% 1.69/1.87 tff(3912,plain,
% 1.69/1.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.87 inference(transitivity,[status(thm)],[3911, 3909])).
% 1.69/1.87 tff(3913,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.69/1.87 inference(quant_inst,[status(thm)],[])).
% 1.69/1.87 tff(3914,plain,
% 1.69/1.87 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3913, 3912])).
% 1.69/1.87 tff(3915,plain,
% 1.69/1.87 (~c1_1(a589)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3914, 156, 23, 3908, 3907, 3792, 87, 86, 22])).
% 1.69/1.87 tff(3916,plain,
% 1.69/1.87 (~c0_1(a589)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[177, 3906])).
% 1.69/1.87 tff(3917,plain,
% 1.69/1.87 ($false),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3164, 156, 1661, 3907, 3792, 3916, 87, 86, 1686, 3915])).
% 1.69/1.87 tff(3918,plain,(hskp4 | hskp26 | c0_1(a586) | c3_1(a586) | c2_1(a552) | c1_1(a552) | hskp33 | hskp19 | c3_1(a552) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.69/1.87 tff(3919,plain,
% 1.69/1.87 (c0_1(a586)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3918, 3789, 1661, 86, 3715, 3716, 35, 98, 3717, 1669])).
% 1.69/1.87 tff(3920,plain,
% 1.69/1.87 (((~hskp27) | (~c0_1(a586))) <=> ((~hskp27) | (~c0_1(a586)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3921,plain,
% 1.69/1.87 (((~c0_1(a586)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a586)))),
% 1.69/1.87 inference(rewrite,[status(thm)],[])).
% 1.69/1.87 tff(3922,axiom,((~c0_1(a586)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.69/1.87 tff(3923,plain,
% 1.69/1.87 ((~hskp27) | (~c0_1(a586))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 1.69/1.87 tff(3924,plain,
% 1.69/1.87 ((~hskp27) | (~c0_1(a586))),
% 1.69/1.87 inference(modus_ponens,[status(thm)],[3923, 3920])).
% 1.69/1.87 tff(3925,plain,
% 1.69/1.87 ($false),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3924, 3919, 3790])).
% 1.69/1.87 tff(3926,plain,(hskp26 | c3_1(a586) | c2_1(a552) | c1_1(a552) | hskp33 | hskp19 | c3_1(a552) | hskp6 | hskp38), inference(lemma,lemma(discharge,[]))).
% 1.69/1.87 tff(3927,plain,
% 1.69/1.87 (hskp26),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3926, 86, 3715, 3716, 35, 98, 3717, 1669, 58])).
% 1.69/1.87 tff(3928,plain,
% 1.69/1.87 (~c3_1(a584)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[1620, 3927])).
% 1.69/1.87 tff(3929,plain,
% 1.69/1.87 (c1_1(a584)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[1637, 3927])).
% 1.69/1.87 tff(3930,plain,
% 1.69/1.87 (c0_1(a584)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[1629, 3927])).
% 1.69/1.87 tff(3931,plain,
% 1.69/1.87 (c0_1(a552)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[2447, 156, 35, 3930, 3929, 3928, 3717, 3715, 85])).
% 1.69/1.87 tff(3932,plain,
% 1.69/1.87 (hskp50),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3739, 3931, 3715, 98])).
% 1.69/1.87 tff(3933,plain,
% 1.69/1.87 (~hskp4),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3737, 3932, 3716, 3715, 35, 58, 3717])).
% 1.69/1.87 tff(3934,plain,
% 1.69/1.87 (hskp27),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[205, 3933, 1669])).
% 1.69/1.87 tff(3935,plain,
% 1.69/1.87 (~c0_1(a586)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[3924, 3934])).
% 1.69/1.87 tff(3936,plain,
% 1.69/1.87 (c1_1(a586)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[95, 3934])).
% 1.69/1.87 tff(3937,plain,
% 1.69/1.87 (c0_1(a574)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[815, 3932])).
% 1.69/1.87 tff(3938,plain,
% 1.69/1.87 (~c3_1(a574)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[799, 3932])).
% 1.69/1.87 tff(3939,plain,
% 1.69/1.87 (c1_1(a574)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[807, 3932])).
% 1.69/1.87 tff(3940,plain,
% 1.69/1.87 (c2_1(a586)),
% 1.69/1.87 inference(unit_resolution,[status(thm)],[2484, 3935, 86, 3939, 3938, 3937, 35])).
% 1.69/1.87 tff(3941,plain,
% 1.69/1.87 (^[V: $i, U: $i] : refl((hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.69/1.87 inference(bind,[status(th)],[])).
% 1.69/1.87 tff(3942,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.87 inference(quant_intro,[status(thm)],[3941])).
% 1.69/1.87 tff(3943,plain,
% 1.69/1.87 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3944,plain,
% 1.69/1.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp35) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp35))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp35) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp35) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.69/1.88 inference(bind,[status(th)],[])).
% 1.69/1.88 tff(3945,plain,
% 1.69/1.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp35) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.88 inference(quant_intro,[status(thm)],[3944])).
% 1.69/1.88 tff(3946,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp35)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause238')).
% 1.69/1.88 tff(3947,plain,
% 1.69/1.88 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 1.69/1.88 tff(3948,plain,
% 1.69/1.88 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3947, 3943])).
% 1.69/1.88 tff(3949,plain,(
% 1.69/1.88 ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.88 inference(skolemize,[status(sab)],[3948])).
% 1.69/1.88 tff(3950,plain,
% 1.69/1.88 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3949, 3942])).
% 1.69/1.88 tff(3951,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3952,plain,
% 1.69/1.88 ((hskp35 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp35 | c3_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3953,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.69/1.88 inference(monotonicity,[status(thm)],[3952])).
% 1.69/1.88 tff(3954,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(transitivity,[status(thm)],[3953, 3951])).
% 1.69/1.88 tff(3955,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a552) | c1_1(a552) | (~c0_1(a552)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(quant_inst,[status(thm)],[])).
% 1.69/1.88 tff(3956,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 1.69/1.88 tff(3957,plain,
% 1.69/1.88 (hskp35 | (~c0_1(a552)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3956, 156, 86, 3716, 3715, 3950])).
% 1.69/1.88 tff(3958,plain,
% 1.69/1.88 (hskp35),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3957, 3940, 3936, 3931])).
% 1.69/1.88 tff(3959,plain,
% 1.69/1.88 (((~hskp35) | c3_1(a538)) <=> ((~hskp35) | c3_1(a538))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3960,axiom,((~hskp35) | c3_1(a538)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.69/1.88 tff(3961,plain,
% 1.69/1.88 ((~hskp35) | c3_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3960, 3959])).
% 1.69/1.88 tff(3962,plain,
% 1.69/1.88 ((~hskp35) | c3_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3961, 3959])).
% 1.69/1.88 tff(3963,plain,
% 1.69/1.88 ((~hskp35) | c3_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3962, 3959])).
% 1.69/1.88 tff(3964,plain,
% 1.69/1.88 ((~hskp35) | c3_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3963, 3959])).
% 1.69/1.88 tff(3965,plain,
% 1.69/1.88 ((~hskp35) | c3_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3964, 3959])).
% 1.69/1.88 tff(3966,plain,
% 1.69/1.88 (c3_1(a538)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3965, 3958])).
% 1.69/1.88 tff(3967,plain,
% 1.69/1.88 (((~hskp35) | c1_1(a538)) <=> ((~hskp35) | c1_1(a538))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3968,axiom,((~hskp35) | c1_1(a538)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.69/1.88 tff(3969,plain,
% 1.69/1.88 ((~hskp35) | c1_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 1.69/1.88 tff(3970,plain,
% 1.69/1.88 ((~hskp35) | c1_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3969, 3967])).
% 1.69/1.88 tff(3971,plain,
% 1.69/1.88 ((~hskp35) | c1_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3970, 3967])).
% 1.69/1.88 tff(3972,plain,
% 1.69/1.88 ((~hskp35) | c1_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3971, 3967])).
% 1.69/1.88 tff(3973,plain,
% 1.69/1.88 ((~hskp35) | c1_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3972, 3967])).
% 1.69/1.88 tff(3974,plain,
% 1.69/1.88 (c1_1(a538)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3973, 3958])).
% 1.69/1.88 tff(3975,plain,
% 1.69/1.88 (((~hskp35) | c2_1(a538)) <=> ((~hskp35) | c2_1(a538))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3976,axiom,((~hskp35) | c2_1(a538)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.69/1.88 tff(3977,plain,
% 1.69/1.88 ((~hskp35) | c2_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 1.69/1.88 tff(3978,plain,
% 1.69/1.88 ((~hskp35) | c2_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3977, 3975])).
% 1.69/1.88 tff(3979,plain,
% 1.69/1.88 ((~hskp35) | c2_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3978, 3975])).
% 1.69/1.88 tff(3980,plain,
% 1.69/1.88 ((~hskp35) | c2_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3979, 3975])).
% 1.69/1.88 tff(3981,plain,
% 1.69/1.88 ((~hskp35) | c2_1(a538)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3980, 3975])).
% 1.69/1.88 tff(3982,plain,
% 1.69/1.88 (c2_1(a538)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3981, 3958])).
% 1.69/1.88 tff(3983,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a538)) | (~c3_1(a538)) | (~c1_1(a538)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a538)) | (~c3_1(a538)) | (~c1_1(a538)) | (~c1_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3984,plain,
% 1.69/1.88 ((hskp4 | (~ndr1_0) | (~c3_1(a538)) | (~c2_1(a538)) | (~c1_1(a538)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a538)) | (~c3_1(a538)) | (~c1_1(a538)) | (~c1_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3985,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a538)) | (~c2_1(a538)) | (~c1_1(a538)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a538)) | (~c3_1(a538)) | (~c1_1(a538)) | (~c1_1(a586))))),
% 1.69/1.88 inference(monotonicity,[status(thm)],[3984])).
% 1.69/1.88 tff(3986,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a538)) | (~c2_1(a538)) | (~c1_1(a538)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a538)) | (~c3_1(a538)) | (~c1_1(a538)) | (~c1_1(a586)))),
% 1.69/1.88 inference(transitivity,[status(thm)],[3985, 3983])).
% 1.69/1.88 tff(3987,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a538)) | (~c2_1(a538)) | (~c1_1(a538)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.69/1.88 inference(quant_inst,[status(thm)],[])).
% 1.69/1.88 tff(3988,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a538)) | (~c3_1(a538)) | (~c1_1(a538)) | (~c1_1(a586))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3987, 3986])).
% 1.69/1.88 tff(3989,plain,
% 1.69/1.88 ($false),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3988, 156, 3933, 3982, 3974, 3966, 3936, 3935, 86, 22])).
% 1.69/1.88 tff(3990,plain,(c3_1(a586) | c1_1(a552) | c2_1(a552) | hskp33 | hskp6 | hskp38 | c3_1(a552) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.69/1.88 tff(3991,plain,
% 1.69/1.88 (c3_1(a586)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3990, 98, 3715, 35, 1669, 58, 3717, 3716])).
% 1.69/1.88 tff(3992,plain,
% 1.69/1.88 (((~hskp27) | (~c3_1(a586))) <=> ((~hskp27) | (~c3_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3993,plain,
% 1.69/1.88 (((~c3_1(a586)) | (~hskp27)) <=> ((~hskp27) | (~c3_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(3994,axiom,((~c3_1(a586)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.69/1.88 tff(3995,plain,
% 1.69/1.88 ((~hskp27) | (~c3_1(a586))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3994, 3993])).
% 1.69/1.88 tff(3996,plain,
% 1.69/1.88 ((~hskp27) | (~c3_1(a586))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[3995, 3992])).
% 1.69/1.88 tff(3997,plain,
% 1.69/1.88 (~hskp27),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3996, 3991])).
% 1.69/1.88 tff(3998,plain,
% 1.69/1.88 (hskp4),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[205, 3997, 1669])).
% 1.69/1.88 tff(3999,plain,
% 1.69/1.88 (~hskp50),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3737, 3998, 3716, 3715, 35, 58, 3717])).
% 1.69/1.88 tff(4000,plain,
% 1.69/1.88 (~c0_1(a552)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3739, 3999, 3715, 98])).
% 1.69/1.88 tff(4001,plain,
% 1.69/1.88 (hskp26),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3788, 3998, 1669, 3716, 3715, 35, 3717, 98, 58])).
% 1.69/1.88 tff(4002,plain,
% 1.69/1.88 (~c3_1(a584)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1620, 4001])).
% 1.69/1.88 tff(4003,plain,
% 1.69/1.88 (c1_1(a584)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1637, 4001])).
% 1.69/1.88 tff(4004,plain,
% 1.69/1.88 (c0_1(a584)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1629, 4001])).
% 1.69/1.88 tff(4005,plain,
% 1.69/1.88 ($false),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[2447, 156, 35, 4004, 4003, 4002, 3717, 3715, 85, 4000])).
% 1.69/1.88 tff(4006,plain,(hskp19 | hskp33 | c3_1(a552) | c2_1(a552) | c1_1(a552) | hskp6 | hskp38), inference(lemma,lemma(discharge,[]))).
% 1.69/1.88 tff(4007,plain,
% 1.69/1.88 (hskp19),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4006, 3726, 3717, 3715, 3716, 1669, 58])).
% 1.69/1.88 tff(4008,plain,
% 1.69/1.88 (~c2_1(a573)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1704, 4007])).
% 1.69/1.88 tff(4009,plain,
% 1.69/1.88 (~c1_1(a573)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1675, 4007])).
% 1.69/1.88 tff(4010,assumption,(c0_1(a573)), introduced(assumption)).
% 1.69/1.88 tff(4011,plain,
% 1.69/1.88 (~hskp19),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1691, 4010])).
% 1.69/1.88 tff(4012,plain,
% 1.69/1.88 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4013,plain,
% 1.69/1.88 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573))) <=> (hskp50 | hskp19 | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4014,plain,
% 1.69/1.88 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0)))),
% 1.69/1.88 inference(monotonicity,[status(thm)],[4013])).
% 1.69/1.88 tff(4015,plain,
% 1.69/1.88 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0))),
% 1.69/1.88 inference(transitivity,[status(thm)],[4014, 4012])).
% 1.69/1.88 tff(4016,plain,
% 1.69/1.88 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573)))),
% 1.69/1.88 inference(quant_inst,[status(thm)],[])).
% 1.69/1.88 tff(4017,plain,
% 1.69/1.88 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[4016, 4015])).
% 1.69/1.88 tff(4018,plain,
% 1.69/1.88 (hskp50 | hskp19 | c2_1(a573) | (~c0_1(a573))),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4017, 156, 1718, 34])).
% 1.69/1.88 tff(4019,plain,
% 1.69/1.88 (hskp50),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4018, 4011, 1719, 4010])).
% 1.69/1.88 tff(4020,plain,
% 1.69/1.88 (~c3_1(a574)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[799, 4019])).
% 1.69/1.88 tff(4021,plain,
% 1.69/1.88 (c1_1(a574)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[807, 4019])).
% 1.69/1.88 tff(4022,plain,
% 1.69/1.88 (c0_1(a574)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[815, 4019])).
% 1.69/1.88 tff(4023,plain,
% 1.69/1.88 (~hskp4),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3735, 4022, 3717, 3716, 3715, 35, 58, 4021, 4020])).
% 1.69/1.88 tff(4024,plain,
% 1.69/1.88 (hskp27),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[205, 4023, 1669])).
% 1.69/1.88 tff(4025,plain,
% 1.69/1.88 (~c3_1(a586)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3996, 4024])).
% 1.69/1.88 tff(4026,plain,
% 1.69/1.88 (~c0_1(a586)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3924, 4024])).
% 1.69/1.88 tff(4027,plain,
% 1.69/1.88 (c1_1(a586)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[95, 4024])).
% 1.69/1.88 tff(4028,plain,
% 1.69/1.88 (c2_1(a586)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[2484, 4025, 4022, 4021, 4020, 4026, 35])).
% 1.69/1.88 tff(4029,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4030,plain,
% 1.69/1.88 ((hskp35 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp35 | c3_1(a586) | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4031,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.69/1.88 inference(monotonicity,[status(thm)],[4030])).
% 1.69/1.88 tff(4032,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(transitivity,[status(thm)],[4031, 4029])).
% 1.69/1.88 tff(4033,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a573) | c1_1(a573) | (~c0_1(a573)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.69/1.88 inference(quant_inst,[status(thm)],[])).
% 1.69/1.88 tff(4034,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a573) | (~c0_1(a573)) | c1_1(a573) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[4033, 4032])).
% 1.69/1.88 tff(4035,plain,
% 1.69/1.88 (hskp35),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4034, 156, 4027, 4025, 1719, 4010, 1718, 3950, 4028])).
% 1.69/1.88 tff(4036,plain,
% 1.69/1.88 (c3_1(a538)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3965, 4035])).
% 1.69/1.88 tff(4037,plain,
% 1.69/1.88 (c1_1(a538)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3973, 4035])).
% 1.69/1.88 tff(4038,plain,
% 1.69/1.88 (c2_1(a538)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3981, 4035])).
% 1.69/1.88 tff(4039,plain,
% 1.69/1.88 ($false),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3988, 156, 4023, 4038, 4037, 4036, 4027, 4026, 4025, 22])).
% 1.69/1.88 tff(4040,plain,((~c0_1(a573)) | c2_1(a573) | c1_1(a573) | hskp33 | hskp6 | c3_1(a552) | c1_1(a552) | c2_1(a552) | hskp38), inference(lemma,lemma(discharge,[]))).
% 1.69/1.88 tff(4041,plain,
% 1.69/1.88 (~c0_1(a573)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4040, 1719, 1718, 3726, 1669, 3717, 3716, 3715, 58])).
% 1.69/1.88 tff(4042,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a573) | c0_1(a573) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c0_1(a573) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a573)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4043,plain,
% 1.69/1.88 ((hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (hskp38 | c2_1(a573) | c0_1(a573) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a573)))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4044,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a573) | c0_1(a573) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a573))))),
% 1.69/1.88 inference(monotonicity,[status(thm)],[4043])).
% 1.69/1.88 tff(4045,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c0_1(a573) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a573)))),
% 1.69/1.88 inference(transitivity,[status(thm)],[4044, 4042])).
% 1.69/1.88 tff(4046,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 1.69/1.88 inference(quant_inst,[status(thm)],[])).
% 1.69/1.88 tff(4047,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c0_1(a573) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a573))),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 1.69/1.88 tff(4048,plain,
% 1.69/1.88 (c0_1(a573) | (~c3_1(a573))),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4047, 156, 58, 1719, 3717, 3716, 3715, 663])).
% 1.69/1.88 tff(4049,plain,
% 1.69/1.88 (~c3_1(a573)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4048, 4041])).
% 1.69/1.88 tff(4050,plain,
% 1.69/1.88 (hskp28 | c2_1(a573) | c0_1(a573)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1711, 156, 1718, 122])).
% 1.69/1.88 tff(4051,plain,
% 1.69/1.88 (hskp28),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4050, 4041, 1719])).
% 1.69/1.88 tff(4052,plain,
% 1.69/1.88 (~c0_1(a589)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[177, 4051])).
% 1.69/1.88 tff(4053,plain,
% 1.69/1.88 (c2_1(a589)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[171, 4051])).
% 1.69/1.88 tff(4054,plain,
% 1.69/1.88 (c3_1(a589)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[185, 4051])).
% 1.69/1.88 tff(4055,plain,
% 1.69/1.88 (~c1_1(a589)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1751, 156, 1669, 4054, 4052, 1719, 4041, 1718, 1745])).
% 1.69/1.88 tff(4056,plain,
% 1.69/1.88 (~hskp26),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3151, 1719, 3726, 4041, 4049])).
% 1.69/1.88 tff(4057,plain,
% 1.69/1.88 (~hskp4),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1734, 4056, 4054, 4052, 4055, 4053, 1719, 1718, 4049])).
% 1.69/1.88 tff(4058,plain,
% 1.69/1.88 (hskp27),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[205, 4057, 1669])).
% 1.69/1.88 tff(4059,plain,
% 1.69/1.88 (~c0_1(a586)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3924, 4058])).
% 1.69/1.88 tff(4060,plain,
% 1.69/1.88 (~c3_1(a586)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3996, 4058])).
% 1.69/1.88 tff(4061,plain,
% 1.69/1.88 (hskp28 | c0_1(a573) | c1_1(a573)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1711, 156, 1719, 122])).
% 1.69/1.88 tff(4062,plain,
% 1.69/1.88 (hskp28),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4061, 1718, 3143])).
% 1.69/1.88 tff(4063,plain,
% 1.69/1.88 (c2_1(a589)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[171, 4062])).
% 1.69/1.88 tff(4064,plain,
% 1.69/1.88 (c3_1(a589)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[185, 4062])).
% 1.69/1.88 tff(4065,plain,
% 1.69/1.88 (c0_1(a573) | c1_1(a573) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1751, 156, 1669, 590, 1719, 1745])).
% 1.69/1.88 tff(4066,plain,
% 1.69/1.88 (~c1_1(a589)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4065, 4064, 3143, 1718])).
% 1.69/1.88 tff(4067,plain,
% 1.69/1.88 (hskp26),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3174, 4064, 590, 4066, 4063, 1719, 1718, 1717, 1669, 87, 86])).
% 1.69/1.88 tff(4068,plain,
% 1.69/1.88 (~c3_1(a584)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1620, 4067])).
% 1.69/1.88 tff(4069,plain,
% 1.69/1.88 (c1_1(a584)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1637, 4067])).
% 1.69/1.88 tff(4070,plain,
% 1.69/1.88 (c0_1(a584)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[1629, 4067])).
% 1.69/1.88 tff(4071,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a573))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4072,plain,
% 1.69/1.88 ((hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | c3_1(a573)) <=> (hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a573))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4073,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a573)))),
% 1.69/1.88 inference(monotonicity,[status(thm)],[4072])).
% 1.69/1.88 tff(4074,plain,
% 1.69/1.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a573))),
% 1.69/1.88 inference(transitivity,[status(thm)],[4073, 4071])).
% 1.69/1.88 tff(4075,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | c3_1(a573))),
% 1.69/1.88 inference(quant_inst,[status(thm)],[])).
% 1.69/1.88 tff(4076,plain,
% 1.69/1.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a573)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[4075, 4074])).
% 1.69/1.88 tff(4077,plain,
% 1.69/1.88 ($false),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4076, 156, 837, 3672, 3671, 3670, 1719, 1718, 108, 1717])).
% 1.69/1.88 tff(4078,plain,((~hskp33) | hskp0 | c2_1(a573) | c1_1(a573) | c3_1(a573)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.88 tff(4079,plain,
% 1.69/1.88 (~hskp33),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4078, 1718, 1719, 837, 1717])).
% 1.69/1.88 tff(4080,plain,
% 1.69/1.88 ($false),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[3149, 156, 4079, 4070, 4069, 4068, 1719, 3143, 85, 1717])).
% 1.69/1.88 tff(4081,plain,(c1_1(a573) | c2_1(a573) | c0_1(a573) | c3_1(a573) | c0_1(a589) | hskp6 | c0_1(a586) | c3_1(a586) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.69/1.88 tff(4082,plain,
% 1.69/1.88 ($false),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4081, 4060, 4059, 1718, 4041, 4052, 1669, 4049, 1719, 837])).
% 1.69/1.88 tff(4083,plain,(c2_1(a573) | c1_1(a573) | hskp6 | hskp0 | hskp38 | c3_1(a552) | c1_1(a552) | c2_1(a552)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.88 tff(4084,plain,
% 1.69/1.88 ($false),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4083, 4009, 4008, 1669, 837, 58, 3717, 3716, 3715])).
% 1.69/1.88 tff(4085,plain,(c2_1(a552) | hskp6 | hskp0 | hskp38 | c3_1(a552) | c1_1(a552)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.88 tff(4086,plain,
% 1.69/1.88 (hskp0),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[4085, 3714, 58, 3713, 3712, 2896])).
% 1.69/1.88 tff(4087,plain,
% 1.69/1.88 (~c2_1(a535)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[713, 4086])).
% 1.69/1.88 tff(4088,plain,
% 1.69/1.88 (c0_1(a535)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[721, 4086])).
% 1.69/1.88 tff(4089,plain,
% 1.69/1.88 (c1_1(a535)),
% 1.69/1.88 inference(unit_resolution,[status(thm)],[729, 4086])).
% 1.69/1.88 tff(4090,plain,
% 1.69/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4091,plain,
% 1.69/1.88 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))),
% 1.69/1.88 inference(rewrite,[status(thm)],[])).
% 1.69/1.88 tff(4092,plain,
% 1.69/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537)))),
% 1.69/1.88 inference(monotonicity,[status(thm)],[4091])).
% 1.69/1.88 tff(4093,plain,
% 1.69/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))),
% 1.69/1.88 inference(transitivity,[status(thm)],[4092, 4090])).
% 1.69/1.88 tff(4094,plain,
% 1.69/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.69/1.88 inference(quant_inst,[status(thm)],[])).
% 1.69/1.88 tff(4095,plain,
% 1.69/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537)),
% 1.69/1.88 inference(modus_ponens,[status(thm)],[4094, 4093])).
% 1.69/1.89 tff(4096,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4095, 156, 3702, 3428, 3427, 3426, 4089, 4088, 3701, 4087, 707, 3709])).
% 1.69/1.89 tff(4097,plain,(c3_1(a548) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | hskp38 | c1_1(a586) | c0_1(a586) | (~c2_1(a586)) | hskp15 | c2_1(a548) | (~c1_1(a548)) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4098,plain,
% 1.69/1.89 (hskp38),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4097, 3693, 3671, 3670, 3672, 88, 87, 902, 1277, 24, 3669, 56])).
% 1.69/1.89 tff(4099,plain,
% 1.69/1.89 (c0_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[677, 4098])).
% 1.69/1.89 tff(4100,plain,
% 1.69/1.89 (c1_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[685, 4098])).
% 1.69/1.89 tff(4101,plain,
% 1.69/1.89 (c2_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[693, 4098])).
% 1.69/1.89 tff(4102,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4103,plain,
% 1.69/1.89 ((hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548))) <=> (hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4104,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.69/1.89 inference(monotonicity,[status(thm)],[4103])).
% 1.69/1.89 tff(4105,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.89 inference(transitivity,[status(thm)],[4104, 4102])).
% 1.69/1.89 tff(4106,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))),
% 1.69/1.89 inference(quant_inst,[status(thm)],[])).
% 1.69/1.89 tff(4107,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.69/1.89 inference(modus_ponens,[status(thm)],[4106, 4105])).
% 1.69/1.89 tff(4108,plain,
% 1.69/1.89 (hskp34),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4107, 156, 4101, 4100, 4099, 3693, 56, 75, 3669])).
% 1.69/1.89 tff(4109,plain,
% 1.69/1.89 (~c1_1(a537)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1124, 4108])).
% 1.69/1.89 tff(4110,plain,
% 1.69/1.89 (c3_1(a537)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1132, 4108])).
% 1.69/1.89 tff(4111,plain,
% 1.69/1.89 (~c2_1(a537)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3708, 156, 1277, 4110, 3693, 4109, 24, 483, 3669])).
% 1.69/1.89 tff(4112,plain,
% 1.69/1.89 (c0_1(a537)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1147, 4108])).
% 1.69/1.89 tff(4113,plain,
% 1.69/1.89 (hskp8),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2725, 156, 4112, 4110, 88, 4109, 87, 2407, 902])).
% 1.69/1.89 tff(4114,plain,
% 1.69/1.89 (~c3_1(a552)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2430, 4113])).
% 1.69/1.89 tff(4115,plain,
% 1.69/1.89 (~c1_1(a552)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2453, 4113])).
% 1.69/1.89 tff(4116,plain,
% 1.69/1.89 (~c2_1(a552)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2424, 4113])).
% 1.69/1.89 tff(4117,plain,
% 1.69/1.89 (hskp0),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3725, 4116, 3667, 4115, 4114])).
% 1.69/1.89 tff(4118,plain,
% 1.69/1.89 (~c2_1(a535)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[713, 4117])).
% 1.69/1.89 tff(4119,plain,
% 1.69/1.89 (c0_1(a535)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[721, 4117])).
% 1.69/1.89 tff(4120,plain,
% 1.69/1.89 (c1_1(a535)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[729, 4117])).
% 1.69/1.89 tff(4121,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2754, 156, 4101, 4100, 4099, 4110, 4120, 4119, 4109, 4118, 707, 4111])).
% 1.69/1.89 tff(4122,plain,(hskp28 | (~hskp33) | c1_1(a586) | c0_1(a586) | (~c2_1(a586)) | c2_1(a548) | c0_1(a548) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4123,plain,
% 1.69/1.89 (hskp28),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4122, 56, 88, 87, 902, 24, 3667, 86])).
% 1.69/1.89 tff(4124,plain,
% 1.69/1.89 (c3_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[185, 4123])).
% 1.69/1.89 tff(4125,plain,
% 1.69/1.89 (~c0_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[177, 4123])).
% 1.69/1.89 tff(4126,plain,
% 1.69/1.89 (c2_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[171, 4123])).
% 1.69/1.89 tff(4127,plain,
% 1.69/1.89 (~hskp34),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3648, 902, 86, 88, 87])).
% 1.69/1.89 tff(4128,plain,
% 1.69/1.89 (~c1_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3699, 156, 3650, 3428, 3427, 3426, 2895, 56, 75])).
% 1.69/1.89 tff(4129,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4130,plain,
% 1.69/1.89 ((hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c3_1(a548)) <=> (hskp34 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4131,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.69/1.89 inference(monotonicity,[status(thm)],[4130])).
% 1.69/1.89 tff(4132,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.69/1.89 inference(transitivity,[status(thm)],[4131, 4129])).
% 1.69/1.89 tff(4133,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c3_1(a548))),
% 1.69/1.89 inference(quant_inst,[status(thm)],[])).
% 1.69/1.89 tff(4134,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.69/1.89 inference(modus_ponens,[status(thm)],[4133, 4132])).
% 1.69/1.89 tff(4135,plain,
% 1.69/1.89 (c3_1(a548) | c1_1(a548) | (~c1_1(a589))),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4134, 156, 3650, 625, 591, 24, 1112])).
% 1.69/1.89 tff(4136,plain,
% 1.69/1.89 (~c1_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4135, 4128, 2895])).
% 1.69/1.89 tff(4137,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c1_1(a548))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c1_1(a548))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4138,plain,
% 1.69/1.89 ((hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | c3_1(a548)) <=> (hskp0 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c1_1(a548))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4139,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c1_1(a548)))),
% 1.69/1.89 inference(monotonicity,[status(thm)],[4138])).
% 1.69/1.89 tff(4140,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c1_1(a548))),
% 1.69/1.89 inference(transitivity,[status(thm)],[4139, 4137])).
% 1.69/1.89 tff(4141,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | c3_1(a548))),
% 1.69/1.89 inference(quant_inst,[status(thm)],[])).
% 1.69/1.89 tff(4142,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a548) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c1_1(a548)),
% 1.69/1.89 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 1.69/1.89 tff(4143,plain,
% 1.69/1.89 (hskp0 | c3_1(a548) | c1_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4142, 156, 3428, 3427, 3426, 24, 108])).
% 1.69/1.89 tff(4144,plain,
% 1.69/1.89 (hskp0),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4143, 4128, 2895])).
% 1.69/1.89 tff(4145,plain,
% 1.69/1.89 (~c2_1(a535)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[713, 4144])).
% 1.69/1.89 tff(4146,plain,
% 1.69/1.89 (c0_1(a535)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[721, 4144])).
% 1.69/1.89 tff(4147,plain,
% 1.69/1.89 (c1_1(a535)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[729, 4144])).
% 1.69/1.89 tff(4148,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4149,plain,
% 1.69/1.89 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4150,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.69/1.89 inference(monotonicity,[status(thm)],[4149])).
% 1.69/1.89 tff(4151,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.69/1.89 inference(transitivity,[status(thm)],[4150, 4148])).
% 1.69/1.89 tff(4152,plain,
% 1.69/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.69/1.89 inference(quant_inst,[status(thm)],[])).
% 1.69/1.89 tff(4153,plain,
% 1.69/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589)),
% 1.69/1.89 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 1.69/1.89 tff(4154,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4153, 156, 591, 4147, 4146, 590, 87, 86, 4145, 609, 4136, 902])).
% 1.69/1.89 tff(4155,plain,(c3_1(a548) | (~c3_1(a589)) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | hskp34 | (~c2_1(a589)) | c2_1(a548) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4156,plain,
% 1.69/1.89 (c3_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4155, 591, 590, 87, 86, 902, 4127, 625, 24, 3428, 3427, 3426, 56])).
% 1.69/1.89 tff(4157,plain,
% 1.69/1.89 (~hskp46),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3658, 4127, 3428, 3427, 3426])).
% 1.69/1.89 tff(4158,plain,
% 1.69/1.89 (~hskp16),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2365, 4157, 87, 86, 902])).
% 1.69/1.89 tff(4159,plain,
% 1.69/1.89 (hskp15),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2572, 58, 4157, 87, 86, 902, 88, 625, 590, 24, 56, 591, 4156])).
% 1.69/1.89 tff(4160,plain,
% 1.69/1.89 (~c1_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1261, 4159])).
% 1.69/1.89 tff(4161,plain,
% 1.69/1.89 (~c0_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1267, 4159])).
% 1.69/1.89 tff(4162,plain,
% 1.69/1.89 (~c2_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1255, 4159])).
% 1.69/1.89 tff(4163,plain,
% 1.69/1.89 (c3_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2821, 156, 58, 4156, 4160, 4162, 24, 56, 663])).
% 1.69/1.89 tff(4164,plain,
% 1.69/1.89 (~hskp17),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2832, 4163, 86, 4161, 4160, 902, 87, 88])).
% 1.69/1.89 tff(4165,plain,
% 1.69/1.89 (hskp18),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[382, 4164, 4158])).
% 1.69/1.89 tff(4166,plain,
% 1.69/1.89 (hskp37),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2583, 4165, 58, 24, 56, 4156])).
% 1.69/1.89 tff(4167,plain,
% 1.69/1.89 (~c3_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[450, 4166])).
% 1.69/1.89 tff(4168,plain,
% 1.69/1.89 (c1_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[444, 4166])).
% 1.69/1.89 tff(4169,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a544) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c0_1(a544) | (~c1_1(a544)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4170,plain,
% 1.69/1.89 ((hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544))) <=> (hskp34 | c3_1(a544) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c0_1(a544) | (~c1_1(a544)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4171,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a544) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c0_1(a544) | (~c1_1(a544))))),
% 1.69/1.89 inference(monotonicity,[status(thm)],[4170])).
% 1.69/1.89 tff(4172,plain,
% 1.69/1.89 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c0_1(a544) | (~c1_1(a544)))),
% 1.69/1.89 inference(transitivity,[status(thm)],[4171, 4169])).
% 1.69/1.89 tff(4173,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))),
% 1.69/1.89 inference(quant_inst,[status(thm)],[])).
% 1.69/1.89 tff(4174,plain,
% 1.69/1.89 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c0_1(a544) | (~c1_1(a544))),
% 1.69/1.89 inference(modus_ponens,[status(thm)],[4173, 4172])).
% 1.69/1.89 tff(4175,plain,
% 1.69/1.89 (c0_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4174, 156, 4127, 4168, 3428, 3427, 3426, 4167, 75])).
% 1.69/1.89 tff(4176,plain,
% 1.69/1.89 (~c2_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[436, 4166])).
% 1.69/1.89 tff(4177,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4178,plain,
% 1.69/1.89 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4179,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.69/1.89 inference(monotonicity,[status(thm)],[4178])).
% 1.69/1.89 tff(4180,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.89 inference(transitivity,[status(thm)],[4179, 4177])).
% 1.69/1.89 tff(4181,plain,
% 1.69/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.89 inference(quant_inst,[status(thm)],[])).
% 1.69/1.89 tff(4182,plain,
% 1.69/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.69/1.89 inference(modus_ponens,[status(thm)],[4181, 4180])).
% 1.69/1.89 tff(4183,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4182, 156, 4168, 3428, 3427, 3426, 4176, 4160, 4162, 707, 4163, 4175])).
% 1.69/1.89 tff(4184,plain,(hskp38 | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | c2_1(a548) | c0_1(a548) | c3_1(a586) | (~c2_1(a586)) | c0_1(a586) | c1_1(a586) | (~c2_1(a589)) | c0_1(a589) | (~c3_1(a589))), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4185,plain,
% 1.69/1.89 (hskp38),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4184, 56, 3671, 3670, 24, 3672, 86, 902, 87, 88, 4126, 4125, 4124])).
% 1.69/1.89 tff(4186,plain,
% 1.69/1.89 (c2_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[693, 4185])).
% 1.69/1.89 tff(4187,plain,
% 1.69/1.89 (c1_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[685, 4185])).
% 1.69/1.89 tff(4188,plain,
% 1.69/1.89 (c3_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4155, 4124, 4125, 87, 86, 902, 4127, 4126, 24, 3672, 3671, 3670, 56])).
% 1.69/1.89 tff(4189,plain,
% 1.69/1.89 (~hskp46),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3658, 4127, 3672, 3671, 3670])).
% 1.69/1.89 tff(4190,plain,
% 1.69/1.89 (c0_1(a548) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2231, 156, 4189, 24, 12])).
% 1.69/1.89 tff(4191,plain,
% 1.69/1.89 (~c1_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4190, 4188, 56])).
% 1.69/1.89 tff(4192,plain,
% 1.69/1.89 (c0_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[677, 4185])).
% 1.69/1.89 tff(4193,plain,
% 1.69/1.89 (~hskp0),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2694, 4192, 4188, 4191, 4187, 24, 4186])).
% 1.69/1.89 tff(4194,plain,
% 1.69/1.89 (~hskp16),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2365, 4189, 87, 86, 902])).
% 1.69/1.89 tff(4195,plain,
% 1.69/1.89 (hskp15),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2711, 4192, 4189, 4188, 4186, 24, 88, 86, 902, 4187, 87, 56])).
% 1.69/1.89 tff(4196,plain,
% 1.69/1.89 (~c1_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1261, 4195])).
% 1.69/1.89 tff(4197,plain,
% 1.69/1.89 (~c0_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1267, 4195])).
% 1.69/1.89 tff(4198,plain,
% 1.69/1.89 (~c2_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1255, 4195])).
% 1.69/1.89 tff(4199,plain,
% 1.69/1.89 (c3_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2924, 156, 4193, 4186, 4187, 4192, 4196, 4198, 108])).
% 1.69/1.89 tff(4200,plain,
% 1.69/1.89 (~hskp17),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2832, 4199, 86, 4197, 4196, 902, 87, 88])).
% 1.69/1.89 tff(4201,plain,
% 1.69/1.89 (hskp18),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[382, 4200, 4194])).
% 1.69/1.89 tff(4202,plain,
% 1.69/1.89 (hskp37),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2703, 4201, 4186, 4187, 4192, 4193])).
% 1.69/1.89 tff(4203,plain,
% 1.69/1.89 (~c3_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[450, 4202])).
% 1.69/1.89 tff(4204,plain,
% 1.69/1.89 (c1_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[444, 4202])).
% 1.69/1.89 tff(4205,plain,
% 1.69/1.89 (c0_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2945, 156, 4127, 4186, 4187, 4192, 4204, 4203, 75])).
% 1.69/1.89 tff(4206,plain,
% 1.69/1.89 (~c2_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[436, 4202])).
% 1.69/1.89 tff(4207,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4208,plain,
% 1.69/1.89 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.89 inference(rewrite,[status(thm)],[])).
% 1.69/1.89 tff(4209,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.69/1.89 inference(monotonicity,[status(thm)],[4208])).
% 1.69/1.89 tff(4210,plain,
% 1.69/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.89 inference(transitivity,[status(thm)],[4209, 4207])).
% 1.69/1.89 tff(4211,plain,
% 1.69/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.89 inference(quant_inst,[status(thm)],[])).
% 1.69/1.89 tff(4212,plain,
% 1.69/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.69/1.89 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 1.69/1.89 tff(4213,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4212, 156, 4186, 4187, 4192, 4204, 4206, 4196, 4198, 707, 4199, 4205])).
% 1.69/1.89 tff(4214,plain,(c0_1(a548) | c3_1(a586) | (~c2_1(a586)) | c0_1(a586) | c1_1(a586) | c2_1(a548) | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4215,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4214, 3666, 3665, 3622, 87, 88, 86, 3386])).
% 1.69/1.89 tff(4216,plain,(c0_1(a545) | c0_1(a586) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4217,plain,
% 1.69/1.89 (c0_1(a545)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4216, 87, 88, 86])).
% 1.69/1.89 tff(4218,plain,
% 1.69/1.89 (~hskp4),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1666, 4217])).
% 1.69/1.89 tff(4219,plain,
% 1.69/1.89 (hskp6),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[205, 4218, 96])).
% 1.69/1.89 tff(4220,plain,
% 1.69/1.89 (~c0_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[211, 4219])).
% 1.69/1.89 tff(4221,plain,
% 1.69/1.89 (~c2_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[217, 4219])).
% 1.69/1.89 tff(4222,plain,
% 1.69/1.89 (c3_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[225, 4219])).
% 1.69/1.89 tff(4223,plain,
% 1.69/1.89 (~c1_1(a548)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2559, 4220, 4222, 4221, 4218])).
% 1.69/1.89 tff(4224,plain,
% 1.69/1.89 (hskp38),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2204, 653, 88, 249, 86, 24, 56])).
% 1.69/1.89 tff(4225,plain,
% 1.69/1.89 (c2_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[693, 4224])).
% 1.69/1.89 tff(4226,plain,
% 1.69/1.89 (c0_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[677, 4224])).
% 1.69/1.89 tff(4227,plain,
% 1.69/1.89 (c1_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[685, 4224])).
% 1.69/1.89 tff(4228,plain,
% 1.69/1.89 (hskp0),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[845, 4225, 653, 4227, 4226, 88, 86])).
% 1.69/1.89 tff(4229,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2694, 4228, 4227, 57, 4226, 249, 24, 4225])).
% 1.69/1.89 tff(4230,plain,(c2_1(a586) | c1_1(a548) | (~c3_1(a548)) | c2_1(a548) | c1_1(a586) | c3_1(a586) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4231,plain,
% 1.69/1.89 (c2_1(a586)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4230, 4223, 4222, 4221, 88, 86, 4220])).
% 1.69/1.89 tff(4232,plain,
% 1.69/1.89 (hskp28),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1604, 156, 4221, 4220, 122, 4223])).
% 1.69/1.89 tff(4233,plain,
% 1.69/1.89 (c3_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[185, 4232])).
% 1.69/1.89 tff(4234,plain,
% 1.69/1.89 (c2_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[171, 4232])).
% 1.69/1.89 tff(4235,plain,
% 1.69/1.89 (hskp46 | (~c2_1(a586)) | (~c1_1(a589))),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2051, 156, 4234, 4233, 87, 86, 858])).
% 1.69/1.89 tff(4236,plain,
% 1.69/1.89 (~c1_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4235, 946, 4231])).
% 1.69/1.89 tff(4237,plain,
% 1.69/1.89 (~c0_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[177, 4232])).
% 1.69/1.89 tff(4238,plain,
% 1.69/1.89 (~hskp33),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4214, 4231, 4221, 87, 88, 86, 4220])).
% 1.69/1.89 tff(4239,plain,
% 1.69/1.89 (hskp15),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2572, 946, 58, 87, 86, 4231, 88, 4234, 4237, 4221, 4220, 4233, 4222])).
% 1.69/1.89 tff(4240,plain,
% 1.69/1.89 (~c0_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1267, 4239])).
% 1.69/1.89 tff(4241,plain,
% 1.69/1.89 (~c1_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1261, 4239])).
% 1.69/1.89 tff(4242,plain,
% 1.69/1.89 (~c2_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1255, 4239])).
% 1.69/1.89 tff(4243,plain,
% 1.69/1.89 (c3_1(a569)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2821, 156, 58, 4222, 4241, 4242, 4221, 4220, 663])).
% 1.69/1.89 tff(4244,plain,
% 1.69/1.89 (~hskp17),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2832, 4243, 86, 4240, 4241, 4231, 87, 88])).
% 1.69/1.89 tff(4245,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2864, 4244, 4243, 946, 4241, 4240, 4222, 87, 86, 4220, 4231, 58, 4221, 4238])).
% 1.69/1.89 tff(4246,plain,(hskp46 | c0_1(a586) | c3_1(a586) | hskp38 | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4247,plain,
% 1.69/1.89 (hskp46),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4246, 58, 86, 87, 88])).
% 1.69/1.89 tff(4248,plain,
% 1.69/1.89 (~c0_1(a562)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[64, 4247])).
% 1.69/1.89 tff(4249,plain,
% 1.69/1.89 (~c3_1(a562)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[270, 4247])).
% 1.69/1.89 tff(4250,plain,
% 1.69/1.89 (c1_1(a562)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[288, 4247])).
% 1.69/1.89 tff(4251,plain,
% 1.69/1.89 (~c1_1(a589)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2291, 156, 4218, 4250, 4234, 4233, 4249, 4248, 22])).
% 1.69/1.89 tff(4252,plain,
% 1.69/1.89 (~hskp39),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2535, 4251, 4233, 58, 4234])).
% 1.69/1.89 tff(4253,plain,
% 1.69/1.89 (~hskp16),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2301, 4252, 4233, 58, 4234, 4250, 4248, 4249, 4251])).
% 1.69/1.89 tff(4254,plain,
% 1.69/1.89 (c1_1(a571)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[931, 156, 88, 925, 924, 86, 923, 921, 4231])).
% 1.69/1.89 tff(4255,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[615, 156, 4233, 925, 4237, 87, 86, 923, 609, 1716, 4231, 4254])).
% 1.69/1.89 tff(4256,plain,((~hskp17) | c0_1(a586) | c3_1(a586) | c1_1(a589) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4257,plain,
% 1.69/1.89 (~hskp17),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4256, 4251, 86, 87, 88])).
% 1.69/1.89 tff(4258,plain,
% 1.69/1.89 (hskp18),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[382, 4257, 4253])).
% 1.69/1.89 tff(4259,plain,
% 1.69/1.89 (hskp37),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2583, 4258, 58, 4221, 4220, 4222])).
% 1.69/1.89 tff(4260,plain,
% 1.69/1.89 (~c2_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[436, 4259])).
% 1.69/1.89 tff(4261,plain,
% 1.69/1.89 (c1_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[444, 4259])).
% 1.69/1.89 tff(4262,plain,
% 1.69/1.89 (~c0_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2937, 156, 4261, 4233, 4260, 4237, 87, 86, 609, 4251, 4231])).
% 1.69/1.89 tff(4263,plain,
% 1.69/1.89 (hskp26),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2071, 156, 4250, 4222, 4249, 4248, 4220, 1686, 4223])).
% 1.69/1.89 tff(4264,plain,
% 1.69/1.89 (~c3_1(a584)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1620, 4263])).
% 1.69/1.89 tff(4265,plain,
% 1.69/1.89 (~c3_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[450, 4259])).
% 1.69/1.89 tff(4266,plain,
% 1.69/1.89 (c1_1(a584)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1637, 4263])).
% 1.69/1.89 tff(4267,plain,
% 1.69/1.89 (c0_1(a584)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1629, 4263])).
% 1.69/1.89 tff(4268,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2862, 156, 4238, 4267, 4266, 4260, 4265, 4264, 85, 4262])).
% 1.69/1.89 tff(4269,plain,(hskp38 | c0_1(a586) | c3_1(a586) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4270,plain,
% 1.69/1.89 (hskp38),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4269, 87, 86, 88])).
% 1.69/1.89 tff(4271,plain,
% 1.69/1.89 (c2_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[693, 4270])).
% 1.69/1.89 tff(4272,plain,
% 1.69/1.89 (c0_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[677, 4270])).
% 1.69/1.89 tff(4273,plain,
% 1.69/1.89 (c1_1(a547)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[685, 4270])).
% 1.69/1.89 tff(4274,plain,
% 1.69/1.89 (~hskp0),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2694, 4273, 4223, 4272, 4222, 4221, 4271])).
% 1.69/1.89 tff(4275,plain,
% 1.69/1.89 (~hskp16),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2365, 946, 87, 86, 4231])).
% 1.69/1.89 tff(4276,plain,
% 1.69/1.89 (~hskp17),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4256, 4236, 86, 87, 88])).
% 1.69/1.89 tff(4277,plain,
% 1.69/1.89 (hskp18),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[382, 4276, 4275])).
% 1.69/1.89 tff(4278,plain,
% 1.69/1.89 (hskp37),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2703, 4277, 4271, 4273, 4272, 4274])).
% 1.69/1.89 tff(4279,plain,
% 1.69/1.89 (~c2_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[436, 4278])).
% 1.69/1.89 tff(4280,plain,
% 1.69/1.89 (c1_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[444, 4278])).
% 1.69/1.89 tff(4281,plain,
% 1.69/1.89 (~c0_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2937, 156, 4280, 4233, 4279, 4237, 87, 86, 609, 4236, 4231])).
% 1.69/1.89 tff(4282,plain,
% 1.69/1.89 (~c3_1(a544)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[450, 4278])).
% 1.69/1.89 tff(4283,plain,
% 1.69/1.89 (~hskp34),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3648, 4231, 86, 88, 87])).
% 1.69/1.89 tff(4284,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2945, 156, 4283, 4271, 4273, 4272, 4280, 4282, 75, 4281])).
% 1.69/1.89 tff(4285,plain,(hskp46 | c0_1(a586) | c3_1(a586) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4286,plain,
% 1.69/1.89 (hskp46),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4285, 87, 86, 88])).
% 1.69/1.89 tff(4287,plain,
% 1.69/1.89 (~c0_1(a562)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[64, 4286])).
% 1.69/1.89 tff(4288,plain,
% 1.69/1.89 (~c3_1(a562)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[270, 4286])).
% 1.69/1.89 tff(4289,plain,
% 1.69/1.89 (c1_1(a562)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[288, 4286])).
% 1.69/1.89 tff(4290,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[2160, 156, 4283, 4289, 4271, 4273, 4272, 4288, 4287, 75])).
% 1.69/1.89 tff(4291,plain,(c0_1(a586) | c3_1(a586) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4292,plain,
% 1.69/1.89 (c0_1(a586)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4291, 88, 86])).
% 1.69/1.89 tff(4293,plain,
% 1.69/1.89 ($false),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[3662, 3671, 3672, 1622, 3650, 3670, 1667])).
% 1.69/1.89 tff(4294,plain,((~hskp33) | (~hskp4) | hskp34), inference(lemma,lemma(discharge,[]))).
% 1.69/1.89 tff(4295,plain,
% 1.69/1.89 (~hskp33),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[4294, 3650, 2467])).
% 1.69/1.89 tff(4296,plain,
% 1.69/1.89 (~c0_1(a545)),
% 1.69/1.89 inference(unit_resolution,[status(thm)],[1666, 2467])).
% 1.69/1.90 tff(4297,plain,
% 1.69/1.90 (~hskp19),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3077, 4295, 1669, 4296, 96])).
% 1.69/1.90 tff(4298,plain,
% 1.69/1.90 (hskp50 | hskp19 | (~c0_1(a586)) | c2_1(a586)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1944, 156, 88, 34])).
% 1.69/1.90 tff(4299,plain,
% 1.69/1.90 (hskp50),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4298, 4297, 4292, 653])).
% 1.69/1.90 tff(4300,plain,
% 1.69/1.90 (c3_1(a545)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[824, 4299, 3444, 4296, 4295])).
% 1.69/1.90 tff(4301,plain,
% 1.69/1.90 (hskp46 | (~c3_1(a545))),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1163, 156, 3423, 3444, 4296, 12])).
% 1.69/1.90 tff(4302,plain,
% 1.69/1.90 (hskp46),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4301, 4300])).
% 1.69/1.90 tff(4303,plain,
% 1.69/1.90 (~c0_1(a562)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[64, 4302])).
% 1.69/1.90 tff(4304,plain,
% 1.69/1.90 (~c3_1(a562)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[270, 4302])).
% 1.69/1.90 tff(4305,plain,
% 1.69/1.90 (hskp38),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2470, 4295, 88, 1669, 86, 4296])).
% 1.69/1.90 tff(4306,plain,
% 1.69/1.90 (c0_1(a547)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[677, 4305])).
% 1.69/1.90 tff(4307,plain,
% 1.69/1.90 (c1_1(a547)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[685, 4305])).
% 1.69/1.90 tff(4308,plain,
% 1.69/1.90 (c2_1(a547)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[693, 4305])).
% 1.69/1.90 tff(4309,plain,
% 1.69/1.90 (c1_1(a562)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[288, 4302])).
% 1.69/1.90 tff(4310,plain,
% 1.69/1.90 ($false),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2160, 156, 3650, 4309, 4308, 4307, 4306, 4304, 4303, 75])).
% 1.69/1.90 tff(4311,plain,(hskp34 | c2_1(a586) | c1_1(a586) | hskp6 | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.90 tff(4312,plain,
% 1.69/1.90 (hskp34),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4311, 1669, 88, 653, 86])).
% 1.69/1.90 tff(4313,plain,
% 1.69/1.90 (~c1_1(a537)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1124, 4312])).
% 1.69/1.90 tff(4314,plain,
% 1.69/1.90 (c3_1(a537)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1132, 4312])).
% 1.69/1.90 tff(4315,plain,
% 1.69/1.90 (c0_1(a537)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1147, 4312])).
% 1.69/1.90 tff(4316,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4317,plain,
% 1.69/1.90 ((hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (hskp51 | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4318,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4317])).
% 1.69/1.90 tff(4319,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4318, 4316])).
% 1.69/1.90 tff(4320,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4321,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4320, 4319])).
% 1.69/1.90 tff(4322,plain,
% 1.69/1.90 (hskp51),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4321, 156, 4315, 4314, 88, 4313, 86, 2608, 653])).
% 1.69/1.90 tff(4323,plain,
% 1.69/1.90 (~c2_1(a583)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2637, 4322])).
% 1.69/1.90 tff(4324,plain,
% 1.69/1.90 (c3_1(a583)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2645, 4322])).
% 1.69/1.90 tff(4325,plain,
% 1.69/1.90 (c0_1(a583)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2653, 4322])).
% 1.69/1.90 tff(4326,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | c2_1(a583) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp49 | c2_1(a583) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4327,plain,
% 1.69/1.90 ((hskp49 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c0_1(a586)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583))) <=> (hskp49 | c2_1(a583) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4328,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c0_1(a586)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | c2_1(a583) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a583)) | (~c0_1(a583))))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4327])).
% 1.69/1.90 tff(4329,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c0_1(a586)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp49 | c2_1(a583) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4328, 4326])).
% 1.69/1.90 tff(4330,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp49 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c0_1(a586)) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4331,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp49 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp49 | c2_1(a583) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a583)) | (~c0_1(a583))),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 1.69/1.90 tff(4332,plain,
% 1.69/1.90 (hskp49),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4331, 156, 4325, 4324, 4323, 4292, 86, 3814, 653])).
% 1.69/1.90 tff(4333,plain,
% 1.69/1.90 (~c1_1(a568)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3852, 4332])).
% 1.69/1.90 tff(4334,plain,
% 1.69/1.90 (c2_1(a568)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3860, 4332])).
% 1.69/1.90 tff(4335,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4336,plain,
% 1.69/1.90 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c2_1(a583) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4337,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583))))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4336])).
% 1.69/1.90 tff(4338,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583)))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4337, 4335])).
% 1.69/1.90 tff(4339,plain,
% 1.69/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a568) | c3_1(a568) | (~c2_1(a568)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4340,plain,
% 1.69/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | c3_1(a568) | (~c2_1(a568)) | (~c3_1(a583)) | (~c0_1(a583))),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4339, 4338])).
% 1.69/1.90 tff(4341,plain,
% 1.69/1.90 (c3_1(a568)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4340, 156, 4325, 4324, 4334, 4315, 4314, 4323, 4333, 4313, 921])).
% 1.69/1.90 tff(4342,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c2_1(a583) | c1_1(a568) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)) | (~c3_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a583) | c1_1(a568) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4343,plain,
% 1.69/1.90 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (c1_1(a586) | c2_1(a583) | c1_1(a568) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4344,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c2_1(a583) | c1_1(a568) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)) | (~c3_1(a583)) | (~c1_1(a583))))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4343])).
% 1.69/1.90 tff(4345,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a583) | c1_1(a568) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4344, 4342])).
% 1.69/1.90 tff(4346,plain,
% 1.69/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4347,plain,
% 1.69/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a583) | c1_1(a568) | c3_1(a586) | (~ndr1_0) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)) | (~c3_1(a583)) | (~c1_1(a583))),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4346, 4345])).
% 1.69/1.90 tff(4348,plain,
% 1.69/1.90 (~c1_1(a583)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4347, 156, 4324, 4334, 88, 4323, 4333, 86, 45, 653, 4341])).
% 1.69/1.90 tff(4349,plain,
% 1.69/1.90 (~c0_1(a568)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3873, 4332])).
% 1.69/1.90 tff(4350,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a568) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a568) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | (~c2_1(a568)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4351,plain,
% 1.69/1.90 ((hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a568) | c0_1(a568) | (~c2_1(a568))) <=> (hskp8 | c0_1(a568) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | (~c2_1(a568)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4352,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a568) | c0_1(a568) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a568) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | (~c2_1(a568))))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4351])).
% 1.69/1.90 tff(4353,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a568) | c0_1(a568) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a568) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | (~c2_1(a568)))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4352, 4350])).
% 1.69/1.90 tff(4354,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a568) | c0_1(a568) | (~c2_1(a568)))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4355,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a568) | c1_1(a568) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c0_1(a537)) | (~c2_1(a568))),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4354, 4353])).
% 1.69/1.90 tff(4356,plain,
% 1.69/1.90 (hskp8),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4355, 156, 4334, 4315, 4314, 4349, 4333, 4313, 2407])).
% 1.69/1.90 tff(4357,plain,
% 1.69/1.90 (~c3_1(a552)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2430, 4356])).
% 1.69/1.90 tff(4358,plain,
% 1.69/1.90 (~c1_1(a552)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2453, 4356])).
% 1.69/1.90 tff(4359,plain,
% 1.69/1.90 (~c2_1(a552)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2424, 4356])).
% 1.69/1.90 tff(4360,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c1_1(a568) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c1_1(a568) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4361,plain,
% 1.69/1.90 (((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586)) <=> (c1_1(a586) | c1_1(a568) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4362,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c1_1(a568) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568))))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4361])).
% 1.69/1.90 tff(4363,plain,
% 1.69/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c1_1(a568) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4362, 4360])).
% 1.69/1.90 tff(4364,plain,
% 1.69/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)) | c2_1(a586) | c1_1(a586) | c3_1(a586))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4365,plain,
% 1.69/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c1_1(a568) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a586) | (~c3_1(a568)) | (~c2_1(a568))),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4364, 4363])).
% 1.69/1.90 tff(4366,plain,
% 1.69/1.90 (~c3_1(a545)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4365, 156, 4334, 88, 3423, 4333, 86, 3444, 45, 653, 4341])).
% 1.69/1.90 tff(4367,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4368,plain,
% 1.69/1.90 ((hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568))) <=> (hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4369,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568))))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4368])).
% 1.69/1.90 tff(4370,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4369, 4367])).
% 1.69/1.90 tff(4371,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | c0_1(a568) | (~c3_1(a568)))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4372,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a568) | c1_1(a568) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568))),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4371, 4370])).
% 1.69/1.90 tff(4373,plain,
% 1.69/1.90 (hskp26),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4372, 156, 3423, 4349, 4333, 4296, 1686, 4366, 4341])).
% 1.69/1.90 tff(4374,plain,
% 1.69/1.90 (~c3_1(a584)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1620, 4373])).
% 1.69/1.90 tff(4375,plain,
% 1.69/1.90 (c1_1(a584)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1637, 4373])).
% 1.69/1.90 tff(4376,plain,
% 1.69/1.90 (c0_1(a584)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1629, 4373])).
% 1.69/1.90 tff(4377,plain,
% 1.69/1.90 (hskp33),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1655, 156, 4376, 4375, 4374, 3444, 4296, 85, 4366])).
% 1.69/1.90 tff(4378,plain,
% 1.69/1.90 (hskp0),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3725, 4377, 4359, 4358, 4357])).
% 1.69/1.90 tff(4379,plain,
% 1.69/1.90 (~c2_1(a535)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[713, 4378])).
% 1.69/1.90 tff(4380,plain,
% 1.69/1.90 (c0_1(a535)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[721, 4378])).
% 1.69/1.90 tff(4381,plain,
% 1.69/1.90 (c1_1(a535)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[729, 4378])).
% 1.69/1.90 tff(4382,plain,
% 1.69/1.90 (c0_1(a536)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3393, 4377])).
% 1.69/1.90 tff(4383,plain,
% 1.69/1.90 (c2_1(a536)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3401, 4377])).
% 1.69/1.90 tff(4384,plain,
% 1.69/1.90 (c1_1(a536)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3409, 4377])).
% 1.69/1.90 tff(4385,plain,
% 1.69/1.90 ($false),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3478, 156, 4324, 4384, 4383, 4382, 4381, 4380, 4323, 4379, 707, 4348])).
% 1.69/1.90 tff(4386,plain,(hskp6 | c1_1(a586) | c3_1(a586) | c2_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.90 tff(4387,plain,
% 1.69/1.90 (hskp6),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4386, 653, 86, 88])).
% 1.69/1.90 tff(4388,plain,
% 1.69/1.90 (~c2_1(a548)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[217, 4387])).
% 1.69/1.90 tff(4389,plain,
% 1.69/1.90 (~c0_1(a548)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[211, 4387])).
% 1.69/1.90 tff(4390,plain,
% 1.69/1.90 (hskp4),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[205, 2896, 96])).
% 1.69/1.90 tff(4391,plain,
% 1.69/1.90 (~hskp33),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4294, 3650, 4390])).
% 1.69/1.90 tff(4392,plain,
% 1.69/1.90 (~c0_1(a545)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1666, 4390])).
% 1.69/1.90 tff(4393,plain,
% 1.69/1.90 (~c2_1(a545)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1643, 4390])).
% 1.69/1.90 tff(4394,plain,
% 1.69/1.90 (~hskp19),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[3077, 4391, 2896, 4392, 96])).
% 1.69/1.90 tff(4395,plain,
% 1.69/1.90 (hskp50),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4298, 4394, 4292, 653])).
% 1.69/1.90 tff(4396,plain,
% 1.69/1.90 (c3_1(a545)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[824, 4395, 4393, 4392, 4391])).
% 1.69/1.90 tff(4397,plain,
% 1.69/1.90 (c1_1(a545)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[193, 4390])).
% 1.69/1.90 tff(4398,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c2_1(a548) | c0_1(a548) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a548))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a548) | c0_1(a548) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a548))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4399,plain,
% 1.69/1.90 ((hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a548) | c1_1(a548) | c0_1(a548)) <=> (hskp6 | c2_1(a548) | c0_1(a548) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a548))),
% 1.69/1.90 inference(rewrite,[status(thm)],[])).
% 1.69/1.90 tff(4400,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a548) | c1_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c2_1(a548) | c0_1(a548) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a548)))),
% 1.69/1.90 inference(monotonicity,[status(thm)],[4399])).
% 1.69/1.90 tff(4401,plain,
% 1.69/1.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a548) | c1_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a548) | c0_1(a548) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a548))),
% 1.69/1.90 inference(transitivity,[status(thm)],[4400, 4398])).
% 1.69/1.90 tff(4402,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a548) | c1_1(a548) | c0_1(a548))),
% 1.69/1.90 inference(quant_inst,[status(thm)],[])).
% 1.69/1.90 tff(4403,plain,
% 1.69/1.90 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a548) | c0_1(a548) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a548)),
% 1.69/1.90 inference(modus_ponens,[status(thm)],[4402, 4401])).
% 1.69/1.90 tff(4404,plain,
% 1.69/1.90 ((~c3_1(a545)) | c1_1(a548)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4403, 156, 2896, 4397, 24, 56, 4392, 1745])).
% 1.69/1.90 tff(4405,plain,
% 1.69/1.90 (c1_1(a548)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4404, 4396])).
% 1.69/1.90 tff(4406,plain,
% 1.69/1.90 (hskp38),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[2470, 4391, 88, 2896, 86, 4392])).
% 1.69/1.90 tff(4407,plain,
% 1.69/1.90 (c0_1(a547)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[677, 4406])).
% 1.69/1.90 tff(4408,plain,
% 1.69/1.90 (c1_1(a547)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[685, 4406])).
% 1.69/1.90 tff(4409,plain,
% 1.69/1.90 (c2_1(a547)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[693, 4406])).
% 1.69/1.90 tff(4410,plain,
% 1.69/1.90 ($false),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4107, 156, 3650, 4409, 4408, 4407, 2895, 56, 75, 4405])).
% 1.69/1.90 tff(4411,plain,(hskp34 | c3_1(a548) | c0_1(a548) | c2_1(a548) | c2_1(a586) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.90 tff(4412,plain,
% 1.69/1.90 (hskp34),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4411, 2895, 56, 24, 653, 88, 86])).
% 1.69/1.90 tff(4413,plain,
% 1.69/1.90 (~c1_1(a537)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1124, 4412])).
% 1.69/1.90 tff(4414,plain,
% 1.69/1.90 (c3_1(a537)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1132, 4412])).
% 1.69/1.90 tff(4415,plain,
% 1.69/1.90 (c0_1(a537)),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[1147, 4412])).
% 1.69/1.90 tff(4416,plain,
% 1.69/1.90 (hskp51),
% 1.69/1.90 inference(unit_resolution,[status(thm)],[4321, 156, 4415, 4414, 88, 4413, 86, 2608, 653])).
% 1.69/1.91 tff(4417,plain,
% 1.69/1.91 (~c2_1(a583)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2637, 4416])).
% 1.69/1.91 tff(4418,plain,
% 1.69/1.91 (c3_1(a583)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2645, 4416])).
% 1.69/1.91 tff(4419,plain,
% 1.69/1.91 (c0_1(a583)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2653, 4416])).
% 1.69/1.91 tff(4420,plain,
% 1.69/1.91 (hskp49),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4331, 156, 4419, 4418, 4417, 4292, 86, 3814, 653])).
% 1.69/1.91 tff(4421,plain,
% 1.69/1.91 (~c1_1(a568)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3852, 4420])).
% 1.69/1.91 tff(4422,plain,
% 1.69/1.91 (c2_1(a568)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3860, 4420])).
% 1.69/1.91 tff(4423,plain,
% 1.69/1.91 (c3_1(a568)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4340, 156, 4419, 4418, 4422, 4415, 4414, 4417, 4421, 4413, 921])).
% 1.69/1.91 tff(4424,plain,
% 1.69/1.91 (~c1_1(a583)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4347, 156, 4418, 4422, 88, 4417, 4421, 86, 45, 653, 4423])).
% 1.69/1.91 tff(4425,plain,
% 1.69/1.91 (~c0_1(a568)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3873, 4420])).
% 1.69/1.91 tff(4426,plain,
% 1.69/1.91 (hskp8),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4355, 156, 4422, 4415, 4414, 4425, 4421, 4413, 2407])).
% 1.69/1.91 tff(4427,plain,
% 1.69/1.91 (~c3_1(a552)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2430, 4426])).
% 1.69/1.91 tff(4428,plain,
% 1.69/1.91 (~c1_1(a552)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2453, 4426])).
% 1.69/1.91 tff(4429,plain,
% 1.69/1.91 (~c3_1(a545)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4365, 156, 4422, 88, 4397, 4421, 86, 4393, 45, 653, 4423])).
% 1.69/1.91 tff(4430,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a568) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a568) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4431,plain,
% 1.69/1.91 ((hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568))) <=> (hskp15 | c1_1(a568) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4432,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a568) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)) | (~c2_1(a568))))),
% 1.69/1.91 inference(monotonicity,[status(thm)],[4431])).
% 1.69/1.91 tff(4433,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a568) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.69/1.91 inference(transitivity,[status(thm)],[4432, 4430])).
% 1.69/1.91 tff(4434,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a568) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.69/1.91 inference(quant_inst,[status(thm)],[])).
% 1.69/1.91 tff(4435,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a568) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a568)) | (~c2_1(a568))),
% 1.69/1.91 inference(modus_ponens,[status(thm)],[4434, 4433])).
% 1.69/1.91 tff(4436,plain,
% 1.69/1.91 (hskp15),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4435, 156, 4422, 4397, 4421, 4393, 483, 4429, 4423])).
% 1.69/1.91 tff(4437,plain,
% 1.69/1.91 (hskp33),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2911, 4436, 24, 2895, 56, 4392, 96])).
% 1.69/1.91 tff(4438,plain,
% 1.69/1.91 (~c2_1(a552)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2424, 4426])).
% 1.69/1.91 tff(4439,plain,
% 1.69/1.91 (hskp0),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3725, 4438, 4437, 4428, 4427])).
% 1.69/1.91 tff(4440,plain,
% 1.69/1.91 (~c2_1(a535)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[713, 4439])).
% 1.69/1.91 tff(4441,plain,
% 1.69/1.91 (c0_1(a535)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[721, 4439])).
% 1.69/1.91 tff(4442,plain,
% 1.69/1.91 (c1_1(a535)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[729, 4439])).
% 1.69/1.91 tff(4443,plain,
% 1.69/1.91 (c0_1(a536)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3393, 4437])).
% 1.69/1.91 tff(4444,plain,
% 1.69/1.91 (c2_1(a536)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3401, 4437])).
% 1.69/1.91 tff(4445,plain,
% 1.69/1.91 (c1_1(a536)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3409, 4437])).
% 1.69/1.91 tff(4446,plain,
% 1.69/1.91 ($false),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3478, 156, 4418, 4445, 4444, 4443, 4442, 4441, 4417, 4440, 707, 4424])).
% 1.69/1.91 tff(4447,plain,(c3_1(a548) | c2_1(a548) | c0_1(a548) | c1_1(a586) | c3_1(a586) | c2_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.91 tff(4448,plain,
% 1.69/1.91 (c3_1(a548)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4447, 56, 24, 88, 86, 653])).
% 1.69/1.91 tff(4449,plain,
% 1.69/1.91 (c1_1(a548)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4230, 4448, 653, 24, 88, 86, 56])).
% 1.69/1.91 tff(4450,plain,
% 1.69/1.91 (hskp46),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2834, 4448, 56, 4449])).
% 1.69/1.91 tff(4451,plain,
% 1.69/1.91 (~c0_1(a562)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[64, 4450])).
% 1.69/1.91 tff(4452,plain,
% 1.69/1.91 (~c3_1(a562)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[270, 4450])).
% 1.69/1.91 tff(4453,plain,
% 1.69/1.91 (hskp38),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2204, 4448, 88, 653, 86, 24, 56])).
% 1.69/1.91 tff(4454,plain,
% 1.69/1.91 (c0_1(a547)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[677, 4453])).
% 1.69/1.91 tff(4455,plain,
% 1.69/1.91 (c1_1(a547)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[685, 4453])).
% 1.69/1.91 tff(4456,plain,
% 1.69/1.91 (c2_1(a547)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[693, 4453])).
% 1.69/1.91 tff(4457,plain,
% 1.69/1.91 (c1_1(a562)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[288, 4450])).
% 1.69/1.91 tff(4458,plain,
% 1.69/1.91 (hskp34),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2160, 156, 4457, 4456, 4455, 4454, 4452, 4451, 75])).
% 1.69/1.91 tff(4459,plain,
% 1.69/1.91 (~c1_1(a537)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1124, 4458])).
% 1.69/1.91 tff(4460,plain,
% 1.69/1.91 (hskp42),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3196, 156, 4456, 4455, 4454, 4448, 24, 1364, 4449])).
% 1.69/1.91 tff(4461,plain,
% 1.69/1.91 (~c2_1(a556)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1385, 4460])).
% 1.69/1.91 tff(4462,plain,
% 1.69/1.91 (c3_1(a537)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1132, 4458])).
% 1.69/1.91 tff(4463,plain,
% 1.69/1.91 (c3_1(a556)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1403, 4460])).
% 1.69/1.91 tff(4464,plain,
% 1.69/1.91 (c1_1(a556)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1411, 4460])).
% 1.69/1.91 tff(4465,plain,
% 1.69/1.91 (~c2_1(a537)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3616, 156, 4464, 4463, 4462, 88, 4461, 4459, 86, 45, 653])).
% 1.69/1.91 tff(4466,plain,
% 1.69/1.91 (hskp0),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[845, 4456, 653, 4455, 4454, 88, 86])).
% 1.69/1.91 tff(4467,plain,
% 1.69/1.91 (~c2_1(a535)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[713, 4466])).
% 1.69/1.91 tff(4468,plain,
% 1.69/1.91 (c0_1(a535)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[721, 4466])).
% 1.69/1.91 tff(4469,plain,
% 1.69/1.91 (c1_1(a535)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[729, 4466])).
% 1.69/1.91 tff(4470,plain,
% 1.69/1.91 ($false),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2754, 156, 4456, 4455, 4454, 4462, 4469, 4468, 4459, 4467, 707, 4465])).
% 1.69/1.91 tff(4471,plain,(c0_1(a548) | c1_1(a586) | c3_1(a586) | c2_1(a586) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.91 tff(4472,plain,
% 1.69/1.91 ($false),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4471, 4389, 4388, 86, 653, 88])).
% 1.69/1.91 tff(4473,plain,(c2_1(a586) | c3_1(a586) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.91 tff(4474,plain,
% 1.69/1.91 (c2_1(a586)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4473, 88, 86])).
% 1.69/1.91 tff(4475,plain,
% 1.69/1.91 (hskp37),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1979, 4474, 4292])).
% 1.69/1.91 tff(4476,plain,
% 1.69/1.91 (~c3_1(a544)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[450, 4475])).
% 1.69/1.91 tff(4477,plain,
% 1.69/1.91 (c1_1(a544)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[444, 4475])).
% 1.69/1.91 tff(4478,plain,
% 1.69/1.91 (~hskp33),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4294, 4390, 3650])).
% 1.69/1.91 tff(4479,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c3_1(a544) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a544) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4480,plain,
% 1.69/1.91 ((hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a548) | c3_1(a548) | c0_1(a548)) <=> (hskp33 | c3_1(a548) | c3_1(a544) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4481,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c3_1(a544) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.69/1.91 inference(monotonicity,[status(thm)],[4480])).
% 1.69/1.91 tff(4482,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a544) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.91 inference(transitivity,[status(thm)],[4481, 4479])).
% 1.69/1.91 tff(4483,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a548) | c3_1(a548) | c0_1(a548))),
% 1.69/1.91 inference(quant_inst,[status(thm)],[])).
% 1.69/1.91 tff(4484,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c3_1(a544) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.69/1.91 inference(modus_ponens,[status(thm)],[4483, 4482])).
% 1.69/1.91 tff(4485,plain,
% 1.69/1.91 (hskp33 | c3_1(a548) | c0_1(a548) | (~c0_1(a544))),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4484, 156, 4477, 4476, 24, 85])).
% 1.69/1.91 tff(4486,plain,
% 1.69/1.91 (~c0_1(a544)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4485, 4478, 56, 2895])).
% 1.69/1.91 tff(4487,plain,
% 1.69/1.91 (hskp38),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2470, 4478, 88, 2896, 86, 97])).
% 1.69/1.91 tff(4488,plain,
% 1.69/1.91 (c0_1(a547)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[677, 4487])).
% 1.69/1.91 tff(4489,plain,
% 1.69/1.91 (c1_1(a547)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[685, 4487])).
% 1.69/1.91 tff(4490,plain,
% 1.69/1.91 (c2_1(a547)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[693, 4487])).
% 1.69/1.91 tff(4491,plain,
% 1.69/1.91 ($false),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2945, 156, 3650, 4490, 4489, 4488, 4477, 4476, 75, 4486])).
% 1.69/1.91 tff(4492,plain,(c3_1(a548) | hskp34 | c0_1(a548) | c2_1(a548) | c1_1(a586) | c3_1(a586) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.91 tff(4493,plain,
% 1.69/1.91 (c3_1(a548)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4492, 97, 56, 24, 88, 86, 3650])).
% 1.69/1.91 tff(4494,plain,
% 1.69/1.91 (hskp46),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2834, 2548, 56, 249])).
% 1.69/1.91 tff(4495,plain,
% 1.69/1.91 (~c0_1(a562)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[64, 4494])).
% 1.69/1.91 tff(4496,plain,
% 1.69/1.91 (~c3_1(a562)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[270, 4494])).
% 1.69/1.91 tff(4497,plain,
% 1.69/1.91 (c1_1(a562)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[288, 4494])).
% 1.69/1.91 tff(4498,plain,
% 1.69/1.91 (hskp39),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2063, 156, 4497, 249, 4496, 4495, 24, 281, 2548])).
% 1.69/1.91 tff(4499,plain,
% 1.69/1.91 (c1_1(a549)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[303, 4498])).
% 1.69/1.91 tff(4500,plain,
% 1.69/1.91 (c2_1(a549)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[311, 4498])).
% 1.69/1.91 tff(4501,plain,
% 1.69/1.91 (c3_1(a549)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[319, 4498])).
% 1.69/1.91 tff(4502,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a548) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a548) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4503,plain,
% 1.69/1.91 ((hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548))) <=> (hskp25 | c2_1(a548) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4504,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a548) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a548)) | (~c1_1(a548))))),
% 1.69/1.91 inference(monotonicity,[status(thm)],[4503])).
% 1.69/1.91 tff(4505,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a548) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.69/1.91 inference(transitivity,[status(thm)],[4504, 4502])).
% 1.69/1.91 tff(4506,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.69/1.91 inference(quant_inst,[status(thm)],[])).
% 1.69/1.91 tff(4507,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a548) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.69/1.91 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 1.69/1.91 tff(4508,plain,
% 1.69/1.91 (hskp25),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4507, 156, 4501, 4500, 4499, 249, 24, 55, 2548])).
% 1.69/1.91 tff(4509,plain,
% 1.69/1.91 (~c1_1(a582)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1190, 4508])).
% 1.69/1.91 tff(4510,plain,
% 1.69/1.91 (~c2_1(a582)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1196, 4508])).
% 1.69/1.91 tff(4511,plain,
% 1.69/1.91 (~c3_1(a582)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1202, 4508])).
% 1.69/1.91 tff(4512,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4513,plain,
% 1.69/1.91 ((hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (hskp34 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4514,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549))))),
% 1.69/1.91 inference(monotonicity,[status(thm)],[4513])).
% 1.69/1.91 tff(4515,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)))),
% 1.69/1.91 inference(transitivity,[status(thm)],[4514, 4512])).
% 1.69/1.91 tff(4516,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.69/1.91 inference(quant_inst,[status(thm)],[])).
% 1.69/1.91 tff(4517,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549))),
% 1.69/1.91 inference(modus_ponens,[status(thm)],[4516, 4515])).
% 1.69/1.91 tff(4518,plain,
% 1.69/1.91 ($false),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4517, 156, 3650, 4501, 4500, 4499, 4511, 4510, 4509, 1112])).
% 1.69/1.91 tff(4519,plain,((~c1_1(a548)) | hskp34 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.91 tff(4520,plain,
% 1.69/1.91 (~c1_1(a548)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4519, 4493, 3650, 24, 56])).
% 1.69/1.91 tff(4521,plain,
% 1.69/1.91 (~c2_1(a544)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[436, 4475])).
% 1.69/1.91 tff(4522,plain,
% 1.69/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4523,plain,
% 1.69/1.91 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4524,plain,
% 1.69/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.69/1.91 inference(monotonicity,[status(thm)],[4523])).
% 1.69/1.91 tff(4525,plain,
% 1.69/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.69/1.91 inference(transitivity,[status(thm)],[4524, 4522])).
% 1.69/1.91 tff(4526,plain,
% 1.69/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.91 inference(quant_inst,[status(thm)],[])).
% 1.69/1.91 tff(4527,plain,
% 1.69/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.69/1.91 inference(modus_ponens,[status(thm)],[4526, 4525])).
% 1.69/1.91 tff(4528,plain,
% 1.69/1.91 (~c0_1(a544)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4527, 156, 2771, 2770, 2769, 494, 249, 485, 24, 707, 57])).
% 1.69/1.91 tff(4529,plain,
% 1.69/1.91 ($false),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2945, 156, 3650, 2771, 2770, 2769, 494, 484, 75, 4528])).
% 1.69/1.91 tff(4530,plain,((~hskp38) | hskp34 | (~c1_1(a544)) | c3_1(a544) | (~c3_1(a548)) | c2_1(a544) | c2_1(a548) | c1_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.91 tff(4531,plain,
% 1.69/1.91 (~hskp38),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4530, 4493, 4477, 4476, 3650, 4521, 24, 4520])).
% 1.69/1.91 tff(4532,plain,
% 1.69/1.91 (hskp28),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[3668, 57, 56])).
% 1.69/1.91 tff(4533,plain,
% 1.69/1.91 (c2_1(a589)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[171, 4532])).
% 1.69/1.91 tff(4534,plain,
% 1.69/1.91 (c3_1(a589)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[185, 4532])).
% 1.69/1.91 tff(4535,plain,
% 1.69/1.91 (~c0_1(a589)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[177, 4532])).
% 1.69/1.91 tff(4536,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a586) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a586) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c1_1(a589)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4537,plain,
% 1.69/1.91 ((hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589))) <=> (hskp46 | c1_1(a586) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c1_1(a589)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4538,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a586) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c1_1(a589))))),
% 1.69/1.91 inference(monotonicity,[status(thm)],[4537])).
% 1.69/1.91 tff(4539,plain,
% 1.69/1.91 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a586) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c1_1(a589)))),
% 1.69/1.91 inference(transitivity,[status(thm)],[4538, 4536])).
% 1.69/1.91 tff(4540,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))),
% 1.69/1.91 inference(quant_inst,[status(thm)],[])).
% 1.69/1.91 tff(4541,plain,
% 1.69/1.91 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a586) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c1_1(a589))),
% 1.69/1.91 inference(modus_ponens,[status(thm)],[4540, 4539])).
% 1.69/1.91 tff(4542,plain,
% 1.69/1.91 (hskp46 | (~c1_1(a589))),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4541, 156, 4533, 88, 4535, 1996, 2215, 902])).
% 1.69/1.91 tff(4543,plain,
% 1.69/1.91 (~c1_1(a589)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4542, 946])).
% 1.69/1.91 tff(4544,plain,
% 1.69/1.91 (hskp15),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2512, 4543, 2501, 4534, 4533])).
% 1.69/1.91 tff(4545,plain,
% 1.69/1.91 (~c2_1(a569)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1255, 4544])).
% 1.69/1.91 tff(4546,plain,
% 1.69/1.91 (~c1_1(a569)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1261, 4544])).
% 1.69/1.91 tff(4547,plain,
% 1.69/1.91 (c3_1(a569)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2821, 156, 58, 249, 4546, 4545, 24, 56, 663])).
% 1.69/1.91 tff(4548,plain,
% 1.69/1.91 (~c0_1(a569)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1267, 4544])).
% 1.69/1.91 tff(4549,assumption,(~c0_1(a544)), introduced(assumption)).
% 1.69/1.91 tff(4550,plain,
% 1.69/1.91 (hskp26),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2852, 156, 494, 484, 2785, 2775, 1686, 2824, 4549])).
% 1.69/1.91 tff(4551,plain,
% 1.69/1.91 (~c3_1(a584)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1620, 4550])).
% 1.69/1.91 tff(4552,plain,
% 1.69/1.91 (c1_1(a584)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1637, 4550])).
% 1.69/1.91 tff(4553,plain,
% 1.69/1.91 (c0_1(a584)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[1629, 4550])).
% 1.69/1.91 tff(4554,plain,
% 1.69/1.91 ($false),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[2862, 156, 35, 4553, 4552, 485, 484, 4551, 85, 4549])).
% 1.69/1.91 tff(4555,plain,(c0_1(a544) | hskp33 | c2_1(a544) | c3_1(a544) | (~c1_1(a544)) | c0_1(a569) | c1_1(a569) | (~c3_1(a569))), inference(lemma,lemma(discharge,[]))).
% 1.69/1.91 tff(4556,plain,
% 1.69/1.91 (c0_1(a544)),
% 1.69/1.91 inference(unit_resolution,[status(thm)],[4555, 4548, 2503, 2502, 2504, 35, 4546, 4547])).
% 1.69/1.91 tff(4557,assumption,(c0_1(a544)), introduced(assumption)).
% 1.69/1.91 tff(4558,plain,
% 1.69/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a548) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a548) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4559,plain,
% 1.69/1.91 (((~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c2_1(a545)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c0_1(a548) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.69/1.91 inference(rewrite,[status(thm)],[])).
% 1.69/1.91 tff(4560,plain,
% 1.69/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c2_1(a545)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a548) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.69/1.91 inference(monotonicity,[status(thm)],[4559])).
% 1.69/1.91 tff(4561,plain,
% 1.69/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c2_1(a545)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a548) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.91 inference(transitivity,[status(thm)],[4560, 4558])).
% 1.77/1.91 tff(4562,plain,
% 1.77/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c2_1(a545)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.91 inference(quant_inst,[status(thm)],[])).
% 1.77/1.91 tff(4563,plain,
% 1.77/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a548) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.77/1.91 inference(modus_ponens,[status(thm)],[4562, 4561])).
% 1.77/1.91 tff(4564,plain,
% 1.77/1.91 ((~c2_1(a545)) | c3_1(a545) | (~c0_1(a544))),
% 1.77/1.91 inference(unit_resolution,[status(thm)],[4563, 156, 494, 249, 485, 56, 97, 609, 57])).
% 1.77/1.91 tff(4565,plain,
% 1.77/1.91 (~c2_1(a545)),
% 1.77/1.91 inference(unit_resolution,[status(thm)],[4564, 765, 4557])).
% 1.77/1.91 tff(4566,plain,
% 1.77/1.91 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.91 inference(rewrite,[status(thm)],[])).
% 1.77/1.91 tff(4567,plain,
% 1.77/1.91 ((hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | c3_1(a544) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.91 inference(rewrite,[status(thm)],[])).
% 1.77/1.91 tff(4568,plain,
% 1.77/1.91 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.77/1.91 inference(monotonicity,[status(thm)],[4567])).
% 1.77/1.91 tff(4569,plain,
% 1.77/1.91 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.91 inference(transitivity,[status(thm)],[4568, 4566])).
% 1.77/1.91 tff(4570,plain,
% 1.77/1.91 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.77/1.91 inference(quant_inst,[status(thm)],[])).
% 1.77/1.91 tff(4571,plain,
% 1.77/1.91 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.77/1.91 inference(modus_ponens,[status(thm)],[4570, 4569])).
% 1.77/1.91 tff(4572,plain,
% 1.77/1.91 ($false),
% 1.77/1.91 inference(unit_resolution,[status(thm)],[4571, 156, 35, 494, 484, 4565, 97, 85, 765, 4557])).
% 1.77/1.91 tff(4573,plain,(c3_1(a545) | hskp33 | (~c1_1(a544)) | c3_1(a544) | c0_1(a545) | (~c0_1(a544)) | (~c3_1(a548)) | c2_1(a544) | c0_1(a548) | c1_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.91 tff(4574,plain,
% 1.77/1.91 (c3_1(a545)),
% 1.77/1.91 inference(unit_resolution,[status(thm)],[4573, 4556, 2504, 2502, 97, 35, 249, 2503, 56, 57])).
% 1.77/1.92 tff(4575,assumption,(hskp29), introduced(assumption)).
% 1.77/1.92 tff(4576,plain,
% 1.77/1.92 (((~hskp29) | (~c0_1(a590))) <=> ((~hskp29) | (~c0_1(a590)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4577,plain,
% 1.77/1.92 (((~c0_1(a590)) | (~hskp29)) <=> ((~hskp29) | (~c0_1(a590)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4578,axiom,((~c0_1(a590)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.77/1.92 tff(4579,plain,
% 1.77/1.92 ((~hskp29) | (~c0_1(a590))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4578, 4577])).
% 1.77/1.92 tff(4580,plain,
% 1.77/1.92 ((~hskp29) | (~c0_1(a590))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4579, 4576])).
% 1.77/1.92 tff(4581,plain,
% 1.77/1.92 (~c0_1(a590)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4580, 4575])).
% 1.77/1.92 tff(4582,plain,
% 1.77/1.92 (((~hskp29) | (~c3_1(a590))) <=> ((~hskp29) | (~c3_1(a590)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4583,plain,
% 1.77/1.92 (((~c3_1(a590)) | (~hskp29)) <=> ((~hskp29) | (~c3_1(a590)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4584,axiom,((~c3_1(a590)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.77/1.92 tff(4585,plain,
% 1.77/1.92 ((~hskp29) | (~c3_1(a590))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4584, 4583])).
% 1.77/1.92 tff(4586,plain,
% 1.77/1.92 ((~hskp29) | (~c3_1(a590))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4585, 4582])).
% 1.77/1.92 tff(4587,plain,
% 1.77/1.92 (~c3_1(a590)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4586, 4575])).
% 1.77/1.92 tff(4588,plain,
% 1.77/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4589,plain,
% 1.77/1.92 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c1_1(a545) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4590,plain,
% 1.77/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[4589])).
% 1.77/1.92 tff(4591,plain,
% 1.77/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(transitivity,[status(thm)],[4590, 4588])).
% 1.77/1.92 tff(4592,plain,
% 1.77/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(quant_inst,[status(thm)],[])).
% 1.77/1.92 tff(4593,plain,
% 1.77/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4592, 4591])).
% 1.77/1.92 tff(4594,plain,
% 1.77/1.92 (~c2_1(a590)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4593, 156, 494, 112, 485, 4587, 4581, 97, 609, 2, 4557])).
% 1.77/1.92 tff(4595,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4596,plain,
% 1.77/1.92 ((hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a590) | c3_1(a590) | c0_1(a590)) <=> (hskp33 | c3_1(a544) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4597,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a590) | c3_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[4596])).
% 1.77/1.92 tff(4598,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a590) | c3_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(transitivity,[status(thm)],[4597, 4595])).
% 1.77/1.92 tff(4599,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a590) | c3_1(a590) | c0_1(a590))),
% 1.77/1.92 inference(quant_inst,[status(thm)],[])).
% 1.77/1.92 tff(4600,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4599, 4598])).
% 1.77/1.92 tff(4601,plain,
% 1.77/1.92 ($false),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4600, 156, 35, 494, 484, 4587, 4581, 85, 4557, 4594])).
% 1.77/1.92 tff(4602,plain,((~hskp29) | hskp33 | (~c1_1(a544)) | c3_1(a544) | (~c0_1(a544)) | c1_1(a545) | c2_1(a544) | c0_1(a545) | (~c3_1(a545))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.92 tff(4603,plain,
% 1.77/1.92 (~hskp29),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4602, 4557, 494, 484, 35, 112, 485, 97, 2])).
% 1.77/1.92 tff(4604,plain,
% 1.77/1.92 (^[U: $i] : refl((hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(4605,plain,
% 1.77/1.92 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[4604])).
% 1.77/1.92 tff(4606,plain,
% 1.77/1.92 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4607,plain,
% 1.77/1.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp29) | hskp30) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp30))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp30) <=> (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp29) | hskp30) <=> (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.77/1.92 inference(bind,[status(th)],[])).
% 1.77/1.92 tff(4608,plain,
% 1.77/1.92 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp29) | hskp30) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.77/1.92 inference(quant_intro,[status(thm)],[4607])).
% 1.77/1.92 tff(4609,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c1_1(U)) | hskp29) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause222')).
% 1.77/1.92 tff(4610,plain,
% 1.77/1.92 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4609, 4608])).
% 1.77/1.92 tff(4611,plain,
% 1.77/1.92 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4610, 4606])).
% 1.77/1.92 tff(4612,plain,(
% 1.77/1.92 ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.77/1.92 inference(skolemize,[status(sab)],[4611])).
% 1.77/1.92 tff(4613,plain,
% 1.77/1.92 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4612, 4605])).
% 1.77/1.92 tff(4614,plain,
% 1.77/1.92 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp30 | hskp29 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4615,plain,
% 1.77/1.92 ((hskp30 | hskp29 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c3_1(a548))) <=> (hskp30 | hskp29 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4616,plain,
% 1.77/1.92 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548)))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[4615])).
% 1.77/1.92 tff(4617,plain,
% 1.77/1.92 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp30 | hskp29 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548))),
% 1.77/1.92 inference(transitivity,[status(thm)],[4616, 4614])).
% 1.77/1.92 tff(4618,plain,
% 1.77/1.92 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)))),
% 1.77/1.92 inference(quant_inst,[status(thm)],[])).
% 1.77/1.92 tff(4619,plain,
% 1.77/1.92 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp30 | hskp29 | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548)),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 1.77/1.92 tff(4620,plain,
% 1.77/1.92 (hskp30 | hskp29 | (~c3_1(a548)) | c1_1(a548)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4619, 156, 24, 4613])).
% 1.77/1.92 tff(4621,plain,
% 1.77/1.92 (hskp30),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4620, 4603, 249, 57])).
% 1.77/1.92 tff(4622,plain,
% 1.77/1.92 (((~hskp30) | (~c0_1(a591))) <=> ((~hskp30) | (~c0_1(a591)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4623,plain,
% 1.77/1.92 (((~c0_1(a591)) | (~hskp30)) <=> ((~hskp30) | (~c0_1(a591)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4624,axiom,((~c0_1(a591)) | (~hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.77/1.92 tff(4625,plain,
% 1.77/1.92 ((~hskp30) | (~c0_1(a591))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4624, 4623])).
% 1.77/1.92 tff(4626,plain,
% 1.77/1.92 ((~hskp30) | (~c0_1(a591))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4625, 4622])).
% 1.77/1.92 tff(4627,plain,
% 1.77/1.92 (~c0_1(a591)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4626, 4621])).
% 1.77/1.92 tff(4628,plain,
% 1.77/1.92 (((~hskp30) | (~c2_1(a591))) <=> ((~hskp30) | (~c2_1(a591)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4629,plain,
% 1.77/1.92 (((~c2_1(a591)) | (~hskp30)) <=> ((~hskp30) | (~c2_1(a591)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4630,axiom,((~c2_1(a591)) | (~hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.77/1.92 tff(4631,plain,
% 1.77/1.92 ((~hskp30) | (~c2_1(a591))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4630, 4629])).
% 1.77/1.92 tff(4632,plain,
% 1.77/1.92 ((~hskp30) | (~c2_1(a591))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4631, 4628])).
% 1.77/1.92 tff(4633,plain,
% 1.77/1.92 (~c2_1(a591)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4632, 4621])).
% 1.77/1.92 tff(4634,plain,
% 1.77/1.92 (((~hskp30) | c1_1(a591)) <=> ((~hskp30) | c1_1(a591))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4635,axiom,((~hskp30) | c1_1(a591)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.77/1.92 tff(4636,plain,
% 1.77/1.92 ((~hskp30) | c1_1(a591)),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4635, 4634])).
% 1.77/1.92 tff(4637,plain,
% 1.77/1.92 ((~hskp30) | c1_1(a591)),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4636, 4634])).
% 1.77/1.92 tff(4638,plain,
% 1.77/1.92 ((~hskp30) | c1_1(a591)),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4637, 4634])).
% 1.77/1.92 tff(4639,plain,
% 1.77/1.92 ((~hskp30) | c1_1(a591)),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4638, 4634])).
% 1.77/1.92 tff(4640,plain,
% 1.77/1.92 ((~hskp30) | c1_1(a591)),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4639, 4634])).
% 1.77/1.92 tff(4641,plain,
% 1.77/1.92 (c1_1(a591)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4640, 4621])).
% 1.77/1.92 tff(4642,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a591) | c0_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a591) | c0_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4643,plain,
% 1.77/1.92 ((hskp46 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c2_1(a591) | c0_1(a591) | (~c3_1(a591))) <=> (hskp46 | c2_1(a591) | c0_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4644,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c2_1(a591) | c0_1(a591) | (~c3_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a591) | c0_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591))))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[4643])).
% 1.77/1.92 tff(4645,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c2_1(a591) | c0_1(a591) | (~c3_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a591) | c0_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.77/1.92 inference(transitivity,[status(thm)],[4644, 4642])).
% 1.77/1.92 tff(4646,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c2_1(a591) | c0_1(a591) | (~c3_1(a591)))),
% 1.77/1.92 inference(quant_inst,[status(thm)],[])).
% 1.77/1.92 tff(4647,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a591) | c0_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4646, 4645])).
% 1.77/1.92 tff(4648,plain,
% 1.77/1.92 (~c3_1(a591)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4647, 156, 946, 4641, 4633, 4627, 12])).
% 1.77/1.92 tff(4649,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c2_1(a591) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c2_1(a591) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4650,plain,
% 1.77/1.92 ((hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a591) | c3_1(a591) | c0_1(a591)) <=> (hskp33 | c3_1(a544) | c2_1(a591) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4651,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a544) | c2_1(a591) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[4650])).
% 1.77/1.92 tff(4652,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c2_1(a591) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(transitivity,[status(thm)],[4651, 4649])).
% 1.77/1.92 tff(4653,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a591) | c3_1(a591) | c0_1(a591))),
% 1.77/1.92 inference(quant_inst,[status(thm)],[])).
% 1.77/1.92 tff(4654,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a544) | c2_1(a591) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4653, 4652])).
% 1.77/1.92 tff(4655,plain,
% 1.77/1.92 ($false),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4654, 156, 35, 494, 484, 4633, 4627, 85, 4557, 4648])).
% 1.77/1.92 tff(4656,plain,((~c0_1(a544)) | hskp33 | (~c1_1(a544)) | c3_1(a544) | hskp46 | (~c3_1(a548)) | c1_1(a548) | c2_1(a548) | c1_1(a545) | c2_1(a544) | c0_1(a545) | (~c3_1(a545))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.92 tff(4657,plain,
% 1.77/1.92 (c1_1(a545)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4656, 4574, 2504, 2502, 946, 249, 57, 24, 4556, 2503, 97, 35])).
% 1.77/1.92 tff(4658,plain,
% 1.77/1.92 (c2_1(a545)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[1211, 4657, 58, 97, 4574])).
% 1.77/1.92 tff(4659,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | (~c2_1(a586)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4660,plain,
% 1.77/1.92 ((hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a545) | (~c1_1(a545)) | (~c2_1(a545))) <=> (hskp46 | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | (~c2_1(a586)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4661,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a545) | (~c1_1(a545)) | (~c2_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | (~c2_1(a586))))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[4660])).
% 1.77/1.92 tff(4662,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a545) | (~c1_1(a545)) | (~c2_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | (~c2_1(a586)))),
% 1.77/1.92 inference(transitivity,[status(thm)],[4661, 4659])).
% 1.77/1.92 tff(4663,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c0_1(a545) | (~c1_1(a545)) | (~c2_1(a545)))),
% 1.77/1.92 inference(quant_inst,[status(thm)],[])).
% 1.77/1.92 tff(4664,plain,
% 1.77/1.92 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a545)) | c0_1(a545) | (~ndr1_0) | (~c1_1(a545)) | (~c2_1(a586))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4663, 4662])).
% 1.77/1.92 tff(4665,plain,
% 1.77/1.92 (hskp46 | (~c2_1(a545)) | (~c1_1(a545))),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4664, 156, 88, 1996, 97, 2215, 902])).
% 1.77/1.92 tff(4666,plain,
% 1.77/1.92 ($false),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4665, 4658, 4657, 946])).
% 1.77/1.92 tff(4667,plain,(hskp46 | c1_1(a586) | (~c0_1(a586)) | c0_1(a545) | (~c2_1(a586)) | hskp38 | (~c3_1(a548)) | c1_1(a548) | c2_1(a548) | hskp33 | c0_1(a548) | (~hskp37)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.92 tff(4668,plain,
% 1.77/1.92 (hskp46),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4667, 57, 1996, 97, 902, 58, 249, 88, 24, 35, 56, 2501])).
% 1.77/1.92 tff(4669,plain,
% 1.77/1.92 (~c0_1(a562)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[64, 4668])).
% 1.77/1.92 tff(4670,plain,
% 1.77/1.92 (~c3_1(a562)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[270, 4668])).
% 1.77/1.92 tff(4671,plain,
% 1.77/1.92 (c1_1(a562)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[288, 4668])).
% 1.77/1.92 tff(4672,plain,
% 1.77/1.92 (hskp26),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[2071, 156, 4671, 249, 4670, 4669, 56, 1686, 57])).
% 1.77/1.92 tff(4673,plain,
% 1.77/1.92 (~c3_1(a584)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[1620, 4672])).
% 1.77/1.92 tff(4674,plain,
% 1.77/1.92 (c1_1(a584)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[1637, 4672])).
% 1.77/1.92 tff(4675,plain,
% 1.77/1.92 (c0_1(a584)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[1629, 4672])).
% 1.77/1.92 tff(4676,plain,
% 1.77/1.92 (c0_1(a544)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[2862, 156, 35, 4675, 4674, 2503, 2502, 4673, 85])).
% 1.77/1.92 tff(4677,plain,
% 1.77/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4678,plain,
% 1.77/1.92 (((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4679,plain,
% 1.77/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562))))),
% 1.77/1.92 inference(monotonicity,[status(thm)],[4678])).
% 1.77/1.92 tff(4680,plain,
% 1.77/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))),
% 1.77/1.92 inference(transitivity,[status(thm)],[4679, 4677])).
% 1.77/1.92 tff(4681,plain,
% 1.77/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.92 inference(quant_inst,[status(thm)],[])).
% 1.77/1.92 tff(4682,plain,
% 1.77/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562))),
% 1.77/1.92 inference(modus_ponens,[status(thm)],[4681, 4680])).
% 1.77/1.92 tff(4683,plain,
% 1.77/1.92 ((~c0_1(a544)) | (~c2_1(a562))),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4682, 156, 2504, 249, 4670, 4669, 2503, 56, 609, 57])).
% 1.77/1.92 tff(4684,plain,
% 1.77/1.92 (~c2_1(a562)),
% 1.77/1.92 inference(unit_resolution,[status(thm)],[4683, 4676])).
% 1.77/1.92 tff(4685,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a544) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a544) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4686,plain,
% 1.77/1.92 ((hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562) | c3_1(a562) | c0_1(a562)) <=> (hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a544) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562))),
% 1.77/1.92 inference(rewrite,[status(thm)],[])).
% 1.77/1.92 tff(4687,plain,
% 1.77/1.92 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562) | c3_1(a562) | c0_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a544) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562)))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4686])).
% 1.77/1.93 tff(4688,plain,
% 1.77/1.93 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562) | c3_1(a562) | c0_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a544) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4687, 4685])).
% 1.77/1.93 tff(4689,plain,
% 1.77/1.93 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a544) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562) | c3_1(a562) | c0_1(a562))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4690,plain,
% 1.77/1.93 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a544) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | c2_1(a562)),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[4689, 4688])).
% 1.77/1.93 tff(4691,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4690, 156, 35, 2504, 4670, 4669, 2502, 85, 4676, 4684])).
% 1.77/1.93 tff(4692,plain,(c1_1(a548) | hskp33 | (~c3_1(a548)) | c0_1(a548) | (~c0_1(a586)) | c0_1(a545) | (~c2_1(a586)) | hskp38 | c1_1(a586) | c2_1(a548) | (~hskp37)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4693,plain,
% 1.77/1.93 (hskp33),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4692, 4531, 4493, 56, 4292, 97, 4474, 4520, 88, 24, 4475])).
% 1.77/1.93 tff(4694,plain,
% 1.77/1.93 (c0_1(a536)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3393, 4693])).
% 1.77/1.93 tff(4695,plain,
% 1.77/1.93 (c2_1(a536)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3401, 4693])).
% 1.77/1.93 tff(4696,plain,
% 1.77/1.93 (c1_1(a536)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3409, 4693])).
% 1.77/1.93 tff(4697,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4698,plain,
% 1.77/1.93 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4699,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4698])).
% 1.77/1.93 tff(4700,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4699, 4697])).
% 1.77/1.93 tff(4701,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4702,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[4701, 4700])).
% 1.77/1.93 tff(4703,plain,
% 1.77/1.93 (~c0_1(a544)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4702, 156, 4477, 4696, 4695, 4694, 4493, 4521, 24, 707, 4520])).
% 1.77/1.93 tff(4704,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4174, 156, 3650, 4477, 4696, 4695, 4694, 4476, 75, 4703])).
% 1.77/1.93 tff(4705,plain,(c0_1(a545) | hskp34 | c2_1(a548) | c0_1(a548) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4706,plain,
% 1.77/1.93 (c0_1(a545)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4705, 56, 24, 3650, 88, 86])).
% 1.77/1.93 tff(4707,plain,
% 1.77/1.93 (~hskp4),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1666, 4706])).
% 1.77/1.93 tff(4708,plain,
% 1.77/1.93 (hskp6),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[205, 4707, 96])).
% 1.77/1.93 tff(4709,plain,
% 1.77/1.93 (c3_1(a548)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[225, 4708])).
% 1.77/1.93 tff(4710,plain,
% 1.77/1.93 (~c1_1(a548)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4519, 4709, 3650, 24, 56])).
% 1.77/1.93 tff(4711,plain,
% 1.77/1.93 (~hskp38),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4530, 4709, 4477, 4476, 3650, 4521, 24, 4710])).
% 1.77/1.93 tff(4712,plain,
% 1.77/1.93 (c0_1(a544)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4555, 4547, 2503, 2502, 2504, 35, 4546, 4548])).
% 1.77/1.93 tff(4713,assumption,(hskp30), introduced(assumption)).
% 1.77/1.93 tff(4714,plain,
% 1.77/1.93 (~c0_1(a591)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4626, 4713])).
% 1.77/1.93 tff(4715,plain,
% 1.77/1.93 (~c2_1(a591)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4632, 4713])).
% 1.77/1.93 tff(4716,plain,
% 1.77/1.93 (c1_1(a591)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4640, 4713])).
% 1.77/1.93 tff(4717,plain,
% 1.77/1.93 (~c3_1(a591)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4647, 156, 946, 4716, 4715, 4714, 12])).
% 1.77/1.93 tff(4718,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4654, 156, 35, 494, 484, 4715, 4714, 85, 4557, 4717])).
% 1.77/1.93 tff(4719,plain,((~hskp30) | hskp33 | (~c1_1(a544)) | c3_1(a544) | (~c0_1(a544)) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4720,plain,
% 1.77/1.93 (~hskp30),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4719, 4712, 2504, 2502, 35, 946])).
% 1.77/1.93 tff(4721,plain,
% 1.77/1.93 (hskp29),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4620, 4720, 249, 57])).
% 1.77/1.93 tff(4722,plain,
% 1.77/1.93 (~c0_1(a590)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4580, 4721])).
% 1.77/1.93 tff(4723,plain,
% 1.77/1.93 (~c3_1(a590)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4586, 4721])).
% 1.77/1.93 tff(4724,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4725,plain,
% 1.77/1.93 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4726,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4725])).
% 1.77/1.93 tff(4727,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4726, 4724])).
% 1.77/1.93 tff(4728,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4729,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[4728, 4727])).
% 1.77/1.93 tff(4730,plain,
% 1.77/1.93 (~c2_1(a590)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4729, 156, 2504, 2503, 4723, 4722, 4548, 4546, 609, 4547, 4712])).
% 1.77/1.93 tff(4731,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4600, 156, 35, 2504, 2502, 4723, 4722, 85, 4712, 4730])).
% 1.77/1.93 tff(4732,plain,(hskp46 | hskp33 | (~c3_1(a548)) | c1_1(a548) | c2_1(a548) | hskp38 | c0_1(a548) | (~hskp37) | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4733,plain,
% 1.77/1.93 (hskp46),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4732, 35, 249, 57, 24, 58, 56, 2501, 88, 1996, 902])).
% 1.77/1.93 tff(4734,plain,
% 1.77/1.93 (~c0_1(a562)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[64, 4733])).
% 1.77/1.93 tff(4735,plain,
% 1.77/1.93 (~c3_1(a562)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[270, 4733])).
% 1.77/1.93 tff(4736,plain,
% 1.77/1.93 (c1_1(a562)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[288, 4733])).
% 1.77/1.93 tff(4737,plain,
% 1.77/1.93 (hskp26),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2071, 156, 4736, 249, 4735, 4734, 56, 1686, 57])).
% 1.77/1.93 tff(4738,plain,
% 1.77/1.93 (~c3_1(a584)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1620, 4737])).
% 1.77/1.93 tff(4739,plain,
% 1.77/1.93 (c1_1(a584)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1637, 4737])).
% 1.77/1.93 tff(4740,plain,
% 1.77/1.93 (c0_1(a584)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1629, 4737])).
% 1.77/1.93 tff(4741,plain,
% 1.77/1.93 (c0_1(a544)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2862, 156, 35, 4740, 4739, 2503, 2502, 4738, 85])).
% 1.77/1.93 tff(4742,plain,
% 1.77/1.93 ((~c0_1(a544)) | (~c2_1(a562))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4682, 156, 2504, 249, 4735, 4734, 2503, 56, 609, 57])).
% 1.77/1.93 tff(4743,plain,
% 1.77/1.93 (~c2_1(a562)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4742, 4741])).
% 1.77/1.93 tff(4744,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4690, 156, 35, 2504, 4735, 4734, 2502, 85, 4741, 4743])).
% 1.77/1.93 tff(4745,plain,(hskp33 | (~c3_1(a548)) | c0_1(a548) | c1_1(a548) | c2_1(a548) | hskp38 | (~hskp37) | c1_1(a586) | (~c0_1(a586)) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4746,plain,
% 1.77/1.93 (hskp33),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4745, 4709, 56, 4710, 24, 4711, 4475, 88, 4292, 4474])).
% 1.77/1.93 tff(4747,plain,
% 1.77/1.93 (c0_1(a536)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3393, 4746])).
% 1.77/1.93 tff(4748,plain,
% 1.77/1.93 (c2_1(a536)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3401, 4746])).
% 1.77/1.93 tff(4749,plain,
% 1.77/1.93 (c1_1(a536)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3409, 4746])).
% 1.77/1.93 tff(4750,plain,
% 1.77/1.93 (~c0_1(a544)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4702, 156, 4477, 4749, 4748, 4747, 4709, 4521, 24, 707, 4710])).
% 1.77/1.93 tff(4751,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4174, 156, 3650, 4477, 4749, 4748, 4747, 4476, 75, 4750])).
% 1.77/1.93 tff(4752,plain,(c0_1(a548) | hskp34 | c2_1(a548) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4753,plain,
% 1.77/1.93 (c0_1(a548)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4752, 3650, 24, 88, 86])).
% 1.77/1.93 tff(4754,plain,
% 1.77/1.93 (~hskp6),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[211, 4753])).
% 1.77/1.93 tff(4755,plain,
% 1.77/1.93 (hskp4),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[205, 4754, 96])).
% 1.77/1.93 tff(4756,plain,
% 1.77/1.93 (~c0_1(a545)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1666, 4755])).
% 1.77/1.93 tff(4757,plain,
% 1.77/1.93 (~hskp33),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4294, 4755, 3650])).
% 1.77/1.93 tff(4758,plain,
% 1.77/1.93 (hskp38),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2470, 4757, 88, 4754, 86, 4756])).
% 1.77/1.93 tff(4759,plain,
% 1.77/1.93 (c0_1(a547)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[677, 4758])).
% 1.77/1.93 tff(4760,plain,
% 1.77/1.93 (c1_1(a547)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[685, 4758])).
% 1.77/1.93 tff(4761,plain,
% 1.77/1.93 (c2_1(a547)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[693, 4758])).
% 1.77/1.93 tff(4762,plain,
% 1.77/1.93 (c0_1(a544)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2945, 156, 3650, 4761, 4760, 4759, 4477, 4476, 75])).
% 1.77/1.93 tff(4763,plain,
% 1.77/1.93 (~c2_1(a545)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1643, 4755])).
% 1.77/1.93 tff(4764,plain,
% 1.77/1.93 (c3_1(a545)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4571, 156, 4757, 4477, 4476, 4763, 4756, 85, 4762])).
% 1.77/1.93 tff(4765,plain,
% 1.77/1.93 (c1_1(a545)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[193, 4755])).
% 1.77/1.93 tff(4766,plain,
% 1.77/1.93 (hskp46 | (~c3_1(a545))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1163, 156, 4765, 4763, 4756, 12])).
% 1.77/1.93 tff(4767,plain,
% 1.77/1.93 (hskp46),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4766, 4764])).
% 1.77/1.93 tff(4768,plain,
% 1.77/1.93 (~c0_1(a562)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[64, 4767])).
% 1.77/1.93 tff(4769,plain,
% 1.77/1.93 (~c3_1(a562)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[270, 4767])).
% 1.77/1.93 tff(4770,plain,
% 1.77/1.93 (c1_1(a562)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[288, 4767])).
% 1.77/1.93 tff(4771,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2160, 156, 3650, 4770, 4761, 4760, 4759, 4769, 4768, 75])).
% 1.77/1.93 tff(4772,plain,(hskp34 | c1_1(a586) | c3_1(a586) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4773,plain,
% 1.77/1.93 (hskp34),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4772, 24, 86, 88])).
% 1.77/1.93 tff(4774,plain,
% 1.77/1.93 (~c1_1(a537)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1124, 4773])).
% 1.77/1.93 tff(4775,plain,
% 1.77/1.93 (c3_1(a537)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1132, 4773])).
% 1.77/1.93 tff(4776,plain,
% 1.77/1.93 (c0_1(a537)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1147, 4773])).
% 1.77/1.93 tff(4777,assumption,(~c2_1(a537)), introduced(assumption)).
% 1.77/1.93 tff(4778,assumption,(~c1_1(a537)), introduced(assumption)).
% 1.77/1.93 tff(4779,assumption,(c3_1(a537)), introduced(assumption)).
% 1.77/1.93 tff(4780,assumption,(c0_1(a537)), introduced(assumption)).
% 1.77/1.93 tff(4781,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4782,plain,
% 1.77/1.93 (((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4783,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4782])).
% 1.77/1.93 tff(4784,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4783, 4781])).
% 1.77/1.93 tff(4785,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4786,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[4785, 4784])).
% 1.77/1.93 tff(4787,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4786, 156, 4780, 4779, 88, 4778, 86, 921, 4474, 4777])).
% 1.77/1.93 tff(4788,plain,(c2_1(a537) | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a586) | c1_1(a537) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4789,plain,
% 1.77/1.93 (c2_1(a537)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4788, 4776, 4775, 88, 4774, 86])).
% 1.77/1.93 tff(4790,plain,
% 1.77/1.93 (hskp15 | (~c2_1(a537))),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1139, 156, 4477, 4775, 4521, 4476, 4774, 483])).
% 1.77/1.93 tff(4791,plain,
% 1.77/1.93 (hskp15),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4790, 4789])).
% 1.77/1.93 tff(4792,plain,
% 1.77/1.93 (~c2_1(a569)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1255, 4791])).
% 1.77/1.93 tff(4793,plain,
% 1.77/1.93 (~hskp19),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3077, 4392, 35, 2896, 96])).
% 1.77/1.93 tff(4794,plain,
% 1.77/1.93 (hskp38),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2470, 4392, 88, 35, 86, 2896])).
% 1.77/1.93 tff(4795,plain,
% 1.77/1.93 (c0_1(a547)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[677, 4794])).
% 1.77/1.93 tff(4796,plain,
% 1.77/1.93 (c1_1(a547)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[685, 4794])).
% 1.77/1.93 tff(4797,plain,
% 1.77/1.93 (c2_1(a547)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[693, 4794])).
% 1.77/1.93 tff(4798,plain,
% 1.77/1.93 (~hskp50),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2674, 4797, 4474, 4390, 88, 86, 35, 4392, 4796, 4795])).
% 1.77/1.93 tff(4799,plain,
% 1.77/1.93 (hskp50 | hskp19 | c2_1(a537)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1154, 156, 4776, 4774, 34])).
% 1.77/1.93 tff(4800,plain,
% 1.77/1.93 (c2_1(a537)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4799, 4798, 4793])).
% 1.77/1.93 tff(4801,plain,
% 1.77/1.93 (hskp15),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4790, 4800])).
% 1.77/1.93 tff(4802,plain,
% 1.77/1.93 (c0_1(a548)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[2911, 4801, 24, 35, 2895, 4392, 96])).
% 1.77/1.93 tff(4803,plain,
% 1.77/1.93 (hskp50 | hskp19 | (~c0_1(a548)) | c1_1(a548)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[3021, 156, 24, 34])).
% 1.77/1.93 tff(4804,plain,
% 1.77/1.93 (c1_1(a548)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4803, 4802, 4798, 4793])).
% 1.77/1.93 tff(4805,plain,
% 1.77/1.93 (~c2_1(a569)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1255, 4801])).
% 1.77/1.93 tff(4806,plain,
% 1.77/1.93 (~c1_1(a569)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[1261, 4801])).
% 1.77/1.93 tff(4807,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4808,plain,
% 1.77/1.93 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))) <=> (c1_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4809,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4808])).
% 1.77/1.93 tff(4810,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4809, 4807])).
% 1.77/1.93 tff(4811,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4812,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[4811, 4810])).
% 1.77/1.93 tff(4813,plain,
% 1.77/1.93 (~c3_1(a569)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4812, 156, 4797, 4796, 4795, 4806, 4805, 24, 4802, 707, 4804])).
% 1.77/1.93 tff(4814,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4815,plain,
% 1.77/1.93 (((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4816,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4815])).
% 1.77/1.93 tff(4817,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4816, 4814])).
% 1.77/1.93 tff(4818,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4819,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[4818, 4817])).
% 1.77/1.93 tff(4820,plain,
% 1.77/1.93 (~c3_1(a545)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4819, 156, 4775, 4397, 4774, 4806, 4805, 4393, 45, 4813, 4800])).
% 1.77/1.93 tff(4821,plain,
% 1.77/1.93 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4822,plain,
% 1.77/1.93 ((hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | c3_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4823,plain,
% 1.77/1.93 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4822])).
% 1.77/1.93 tff(4824,plain,
% 1.77/1.93 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4823, 4821])).
% 1.77/1.93 tff(4825,plain,
% 1.77/1.93 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4826,plain,
% 1.77/1.93 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548))),
% 1.77/1.93 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 1.77/1.93 tff(4827,plain,
% 1.77/1.93 ($false),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4826, 156, 35, 2895, 4802, 4393, 4392, 85, 4820, 4804])).
% 1.77/1.93 tff(4828,plain,(c3_1(a548) | hskp33 | c2_1(a548) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.93 tff(4829,plain,
% 1.77/1.93 (c3_1(a548)),
% 1.77/1.93 inference(unit_resolution,[status(thm)],[4828, 35, 24, 88, 86])).
% 1.77/1.93 tff(4830,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c1_1(a537) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c1_1(a537) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4831,plain,
% 1.77/1.93 (((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c1_1(a586) | c1_1(a537) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.77/1.93 inference(rewrite,[status(thm)],[])).
% 1.77/1.93 tff(4832,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c1_1(a537) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.77/1.93 inference(monotonicity,[status(thm)],[4831])).
% 1.77/1.93 tff(4833,plain,
% 1.77/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c1_1(a537) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.77/1.93 inference(transitivity,[status(thm)],[4832, 4830])).
% 1.77/1.93 tff(4834,plain,
% 1.77/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 1.77/1.93 inference(quant_inst,[status(thm)],[])).
% 1.77/1.93 tff(4835,plain,
% 1.77/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c1_1(a537) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4834, 4833])).
% 1.77/1.94 tff(4836,plain,
% 1.77/1.94 ((~c0_1(a548)) | (~c3_1(a548))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4835, 156, 4776, 4775, 88, 4774, 86, 24, 921, 4474])).
% 1.77/1.94 tff(4837,plain,
% 1.77/1.94 (~c0_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4836, 4829])).
% 1.77/1.94 tff(4838,plain,
% 1.77/1.94 (~c0_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1267, 4791])).
% 1.77/1.94 tff(4839,plain,
% 1.77/1.94 (~c1_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1261, 4791])).
% 1.77/1.94 tff(4840,plain,
% 1.77/1.94 (hskp15 | (~c2_1(a537))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1139, 156, 494, 4779, 485, 484, 4778, 483])).
% 1.77/1.94 tff(4841,plain,
% 1.77/1.94 (hskp15),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4840, 1])).
% 1.77/1.94 tff(4842,plain,
% 1.77/1.94 (~c2_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1255, 4841])).
% 1.77/1.94 tff(4843,plain,
% 1.77/1.94 (~c1_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1261, 4841])).
% 1.77/1.94 tff(4844,assumption,(~c3_1(a569)), introduced(assumption)).
% 1.77/1.94 tff(4845,plain,
% 1.77/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4846,plain,
% 1.77/1.94 (((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4847,plain,
% 1.77/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[4846])).
% 1.77/1.94 tff(4848,plain,
% 1.77/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.77/1.94 inference(transitivity,[status(thm)],[4847, 4845])).
% 1.77/1.94 tff(4849,plain,
% 1.77/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(4850,plain,
% 1.77/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c1_1(a569) | c2_1(a569) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4849, 4848])).
% 1.77/1.94 tff(4851,plain,
% 1.77/1.94 ((~c3_1(a548)) | (~c1_1(a548)) | c3_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4850, 156, 4779, 4778, 2775, 2774, 24, 45, 1])).
% 1.77/1.94 tff(4852,plain,
% 1.77/1.94 (~c1_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4851, 4844, 249])).
% 1.77/1.94 tff(4853,plain,
% 1.77/1.94 (hskp0),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2925, 4844])).
% 1.77/1.94 tff(4854,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2694, 4853, 4852, 249, 731, 732, 24, 733])).
% 1.77/1.94 tff(4855,plain,(c3_1(a569) | (~c3_1(a548)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | (~c2_1(a547)) | c1_1(a569) | c2_1(a569) | (~c3_1(a537)) | c1_1(a537) | (~c2_1(a537))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4856,plain,
% 1.77/1.94 (c3_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4855, 2769, 249, 2770, 24, 2771, 4843, 4842, 4779, 4778, 1])).
% 1.77/1.94 tff(4857,plain,
% 1.77/1.94 (~c0_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1267, 4841])).
% 1.77/1.94 tff(4858,plain,
% 1.77/1.94 (c0_1(a544)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4555, 4856, 485, 484, 494, 4843, 35, 4857])).
% 1.77/1.94 tff(4859,plain,
% 1.77/1.94 ((~c3_1(a569)) | (~c0_1(a544))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4212, 156, 2771, 2770, 2769, 494, 485, 4843, 4842, 707])).
% 1.77/1.94 tff(4860,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4859, 4858, 4856])).
% 1.77/1.94 tff(4861,plain,((~hskp38) | (~c1_1(a544)) | c2_1(a544) | c3_1(a544) | hskp33 | (~c3_1(a548)) | c2_1(a548) | (~c3_1(a537)) | c1_1(a537) | (~c2_1(a537))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4862,plain,
% 1.77/1.94 (~hskp38),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4861, 35, 4521, 4476, 4477, 4829, 24, 4775, 4774, 4789])).
% 1.77/1.94 tff(4863,plain,
% 1.77/1.94 (c3_1(a569)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2822, 58, 56, 249])).
% 1.77/1.94 tff(4864,plain,
% 1.77/1.94 (c1_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4692, 58, 249, 35, 1996, 56, 902, 97, 88, 24, 2501])).
% 1.77/1.94 tff(4865,plain,
% 1.77/1.94 (hskp4),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2559, 4864, 249, 24, 56])).
% 1.77/1.94 tff(4866,plain,
% 1.77/1.94 (c1_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[193, 4865])).
% 1.77/1.94 tff(4867,plain,
% 1.77/1.94 (~hskp26),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1659, 4865, 35, 58, 97])).
% 1.77/1.94 tff(4868,plain,
% 1.77/1.94 (~c2_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1643, 4865])).
% 1.77/1.94 tff(4869,plain,
% 1.77/1.94 (~c3_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1211, 4868, 58, 97, 4866])).
% 1.77/1.94 tff(4870,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a569) | c1_1(a569) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a569)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a569) | c1_1(a569) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a569)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4871,plain,
% 1.77/1.94 ((hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569))) <=> (hskp26 | c0_1(a569) | c1_1(a569) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a569)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4872,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a569) | c1_1(a569) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a569))))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[4871])).
% 1.77/1.94 tff(4873,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a569) | c1_1(a569) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a569)))),
% 1.77/1.94 inference(transitivity,[status(thm)],[4872, 4870])).
% 1.77/1.94 tff(4874,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(4875,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a569) | c1_1(a569) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a569))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4874, 4873])).
% 1.77/1.94 tff(4876,plain,
% 1.77/1.94 (hskp26 | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a569))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4875, 156, 2785, 2775, 97, 1686])).
% 1.77/1.94 tff(4877,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4876, 4869, 4867, 4866, 4863])).
% 1.77/1.94 tff(4878,plain,(hskp38 | c0_1(a569) | c1_1(a569) | c0_1(a545) | hskp33 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | c2_1(a569) | (~c0_1(a586)) | (~c2_1(a586)) | c1_1(a586) | (~hskp37)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4879,plain,
% 1.77/1.94 (c0_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4878, 4862, 4839, 4838, 35, 4829, 24, 4837, 4792, 4292, 4474, 88, 4475])).
% 1.77/1.94 tff(4880,plain,
% 1.77/1.94 (c1_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4745, 4862, 35, 4829, 24, 4837, 4475, 88, 4292, 4474])).
% 1.77/1.94 tff(4881,plain,
% 1.77/1.94 (hskp4),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2559, 4880, 4829, 24, 4837])).
% 1.77/1.94 tff(4882,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1666, 4881, 4879])).
% 1.77/1.94 tff(4883,plain,(hskp33 | c2_1(a548) | c1_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4884,plain,
% 1.77/1.94 (c1_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4883, 86, 24, 35])).
% 1.77/1.94 tff(4885,plain,
% 1.77/1.94 (^[V: $i, U: $i] : refl((hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(4886,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[4885])).
% 1.77/1.94 tff(4887,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4888,plain,
% 1.77/1.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))))), (((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp32) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp32))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp32) <=> (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp32) <=> (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.77/1.94 inference(bind,[status(th)],[])).
% 1.77/1.94 tff(4889,plain,
% 1.77/1.94 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp32) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.77/1.94 inference(quant_intro,[status(thm)],[4888])).
% 1.77/1.94 tff(4890,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause252')).
% 1.77/1.94 tff(4891,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4890, 4889])).
% 1.77/1.94 tff(4892,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4891, 4887])).
% 1.77/1.94 tff(4893,plain,(
% 1.77/1.94 ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.77/1.94 inference(skolemize,[status(sab)],[4892])).
% 1.77/1.94 tff(4894,plain,
% 1.77/1.94 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4893, 4886])).
% 1.77/1.94 tff(4895,plain,
% 1.77/1.94 (c3_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[824, 1644, 35, 794, 97])).
% 1.77/1.94 tff(4896,plain,
% 1.77/1.94 (hskp38),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1211, 1644, 1645, 97, 4895])).
% 1.77/1.94 tff(4897,plain,
% 1.77/1.94 (c0_1(a547)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[677, 4896])).
% 1.77/1.94 tff(4898,plain,
% 1.77/1.94 (c2_1(a547)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[693, 4896])).
% 1.77/1.94 tff(4899,plain,
% 1.77/1.94 (c1_1(a547)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[685, 4896])).
% 1.77/1.94 tff(4900,plain,
% 1.77/1.94 (hskp39),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1586, 4899, 4898, 4895, 4897, 1645, 1644, 97])).
% 1.77/1.94 tff(4901,plain,
% 1.77/1.94 (c1_1(a549)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[303, 4900])).
% 1.77/1.94 tff(4902,plain,
% 1.77/1.94 (c2_1(a549)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[311, 4900])).
% 1.77/1.94 tff(4903,plain,
% 1.77/1.94 (c3_1(a549)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[319, 4900])).
% 1.77/1.94 tff(4904,plain,
% 1.77/1.94 (hskp25),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1184, 156, 4903, 4902, 4901, 1645, 1644, 55, 4895])).
% 1.77/1.94 tff(4905,plain,
% 1.77/1.94 (~c1_1(a582)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1190, 4904])).
% 1.77/1.94 tff(4906,plain,
% 1.77/1.94 (~c2_1(a582)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1196, 4904])).
% 1.77/1.94 tff(4907,plain,
% 1.77/1.94 (~c3_1(a582)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1202, 4904])).
% 1.77/1.94 tff(4908,plain,
% 1.77/1.94 (hskp46),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1163, 156, 1645, 1644, 97, 12, 4895])).
% 1.77/1.94 tff(4909,plain,
% 1.77/1.94 (~c0_1(a562)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[64, 4908])).
% 1.77/1.94 tff(4910,plain,
% 1.77/1.94 (~c3_1(a562)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[270, 4908])).
% 1.77/1.94 tff(4911,plain,
% 1.77/1.94 (c1_1(a562)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[288, 4908])).
% 1.77/1.94 tff(4912,plain,
% 1.77/1.94 (hskp34),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2160, 156, 4911, 4898, 4899, 4897, 4910, 4909, 75])).
% 1.77/1.94 tff(4913,plain,
% 1.77/1.94 (~c1_1(a537)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1124, 4912])).
% 1.77/1.94 tff(4914,plain,
% 1.77/1.94 (hskp42),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1574, 156, 4898, 4899, 4897, 1645, 1644, 1364, 4895])).
% 1.77/1.94 tff(4915,plain,
% 1.77/1.94 (~c2_1(a556)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1385, 4914])).
% 1.77/1.94 tff(4916,plain,
% 1.77/1.94 (c3_1(a537)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1132, 4912])).
% 1.77/1.94 tff(4917,plain,
% 1.77/1.94 (c3_1(a556)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1403, 4914])).
% 1.77/1.94 tff(4918,plain,
% 1.77/1.94 (c1_1(a556)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1411, 4914])).
% 1.77/1.94 tff(4919,plain,
% 1.77/1.94 (~c2_1(a537)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2192, 156, 4918, 4917, 4916, 4915, 4913, 4907, 4906, 4905, 45])).
% 1.77/1.94 tff(4920,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4921,plain,
% 1.77/1.94 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (hskp0 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4922,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[4921])).
% 1.77/1.94 tff(4923,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.77/1.94 inference(transitivity,[status(thm)],[4922, 4920])).
% 1.77/1.94 tff(4924,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(4925,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4924, 4923])).
% 1.77/1.94 tff(4926,plain,
% 1.77/1.94 (hskp0),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4925, 156, 4898, 4899, 4897, 4907, 4906, 4905, 108])).
% 1.77/1.94 tff(4927,plain,
% 1.77/1.94 (~c2_1(a535)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[713, 4926])).
% 1.77/1.94 tff(4928,plain,
% 1.77/1.94 (c0_1(a535)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[721, 4926])).
% 1.77/1.94 tff(4929,plain,
% 1.77/1.94 (c1_1(a535)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[729, 4926])).
% 1.77/1.94 tff(4930,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2754, 156, 4898, 4899, 4897, 4916, 4929, 4928, 4913, 4927, 707, 4919])).
% 1.77/1.94 tff(4931,plain,((~hskp4) | c0_1(a545) | hskp33 | (~hskp50)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4932,plain,
% 1.77/1.94 (~hskp4),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4931, 794, 35, 97])).
% 1.77/1.94 tff(4933,plain,
% 1.77/1.94 (hskp27),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[205, 4932, 2896])).
% 1.77/1.94 tff(4934,plain,
% 1.77/1.94 (~c0_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[3924, 4933])).
% 1.77/1.94 tff(4935,plain,
% 1.77/1.94 (~c3_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[3996, 4933])).
% 1.77/1.94 tff(4936,plain,
% 1.77/1.94 (hskp4),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[205, 96, 2896])).
% 1.77/1.94 tff(4937,plain,
% 1.77/1.94 (~c0_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1666, 4936])).
% 1.77/1.94 tff(4938,plain,
% 1.77/1.94 (~c2_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1643, 4936])).
% 1.77/1.94 tff(4939,plain,
% 1.77/1.94 (c3_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4883, 88, 24, 35])).
% 1.77/1.94 tff(4940,plain,
% 1.77/1.94 (hskp4),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[205, 96, 1669])).
% 1.77/1.94 tff(4941,plain,
% 1.77/1.94 (c1_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[193, 4940])).
% 1.77/1.94 tff(4942,plain,
% 1.77/1.94 (~c0_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1666, 4940])).
% 1.77/1.94 tff(4943,plain,
% 1.77/1.94 (~hskp26),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1659, 58, 35, 4940, 4942])).
% 1.77/1.94 tff(4944,plain,
% 1.77/1.94 (~c2_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1643, 4940])).
% 1.77/1.94 tff(4945,plain,
% 1.77/1.94 (~c3_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1211, 58, 4944, 4942, 4941])).
% 1.77/1.94 tff(4946,plain,
% 1.77/1.94 (~hskp50),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[824, 4945, 35, 4944, 4942])).
% 1.77/1.94 tff(4947,plain,
% 1.77/1.94 (~hskp19),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[3077, 4942, 35, 1669, 96])).
% 1.77/1.94 tff(4948,assumption,(c3_1(a586)), introduced(assumption)).
% 1.77/1.94 tff(4949,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a586) | (~c3_1(a586)) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a586) | (~c3_1(a586)) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a586)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4950,plain,
% 1.77/1.94 ((hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586))) <=> (hskp15 | c1_1(a586) | (~c3_1(a586)) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a586)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4951,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a586) | (~c3_1(a586)) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a586))))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[4950])).
% 1.77/1.94 tff(4952,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a586) | (~c3_1(a586)) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a586)))),
% 1.77/1.94 inference(transitivity,[status(thm)],[4951, 4949])).
% 1.77/1.94 tff(4953,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(4954,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a586) | (~c3_1(a586)) | c2_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a586))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4953, 4952])).
% 1.77/1.94 tff(4955,plain,
% 1.77/1.94 (~c2_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4954, 156, 109, 88, 1046, 4948, 111, 483, 765])).
% 1.77/1.94 tff(4956,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4957,plain,
% 1.77/1.94 ((hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586))) <=> (hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4958,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545))))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[4957])).
% 1.77/1.94 tff(4959,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)))),
% 1.77/1.94 inference(transitivity,[status(thm)],[4958, 4956])).
% 1.77/1.94 tff(4960,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a545) | c3_1(a545) | (~c1_1(a545)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(4961,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4960, 4959])).
% 1.77/1.94 tff(4962,plain,
% 1.77/1.94 (c0_1(a586)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4961, 156, 1661, 88, 1046, 4948, 97, 1686, 765])).
% 1.77/1.94 tff(4963,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1944, 156, 110, 98, 88, 4962, 34, 4955])).
% 1.77/1.94 tff(4964,plain,(c1_1(a586) | hskp50 | hskp19 | hskp26 | (~c1_1(a545)) | (~c3_1(a586)) | c0_1(a545) | c3_1(a545) | hskp15 | c2_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4965,plain,
% 1.77/1.94 (hskp15),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4964, 4943, 88, 4948, 4944, 4941, 4942, 4947, 4945, 4946])).
% 1.77/1.94 tff(4966,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1971, 4965, 4943, 4942, 1669, 4941])).
% 1.77/1.94 tff(4967,plain,(hskp38 | hskp6 | c1_1(a586) | (~c3_1(a586)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4968,plain,
% 1.77/1.94 (hskp38),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4967, 88, 2896, 4939, 35])).
% 1.77/1.94 tff(4969,plain,
% 1.77/1.94 (c0_1(a547)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[677, 4968])).
% 1.77/1.94 tff(4970,plain,
% 1.77/1.94 (c1_1(a547)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[685, 4968])).
% 1.77/1.94 tff(4971,plain,
% 1.77/1.94 (c2_1(a547)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[693, 4968])).
% 1.77/1.94 tff(4972,plain,
% 1.77/1.94 (hskp4),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[205, 2897, 2896])).
% 1.77/1.94 tff(4973,plain,
% 1.77/1.94 (~c0_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1666, 4972])).
% 1.77/1.94 tff(4974,plain,
% 1.77/1.94 (~c2_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1643, 4972])).
% 1.77/1.94 tff(4975,plain,
% 1.77/1.94 (~hskp15),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2911, 56, 24, 35, 2895, 4973, 2897])).
% 1.77/1.94 tff(4976,plain,
% 1.77/1.94 (c1_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[193, 4972])).
% 1.77/1.94 tff(4977,plain,
% 1.77/1.94 (c0_1(a548) | (~c3_1(a545)) | c1_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4403, 156, 1669, 1046, 24, 97, 1745])).
% 1.77/1.94 tff(4978,plain,
% 1.77/1.94 (~c3_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4977, 57, 56])).
% 1.77/1.94 tff(4979,plain,
% 1.77/1.94 (c1_1(a589)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2044, 4978, 1046, 109, 4534, 111, 4533])).
% 1.77/1.94 tff(4980,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4981,plain,
% 1.77/1.94 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c0_1(a548)) <=> (hskp6 | c0_1(a589) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(4982,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.77/1.94 inference(monotonicity,[status(thm)],[4981])).
% 1.77/1.94 tff(4983,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.77/1.94 inference(transitivity,[status(thm)],[4982, 4980])).
% 1.77/1.94 tff(4984,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a548) | c1_1(a548) | c0_1(a548))),
% 1.77/1.94 inference(quant_inst,[status(thm)],[])).
% 1.77/1.94 tff(4985,plain,
% 1.77/1.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.77/1.94 inference(modus_ponens,[status(thm)],[4984, 4983])).
% 1.77/1.94 tff(4986,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4985, 156, 1669, 4534, 4535, 24, 56, 1745, 4979, 57])).
% 1.77/1.94 tff(4987,plain,(c1_1(a548) | hskp6 | c2_1(a548) | c0_1(a548) | (~c1_1(a545)) | hskp15 | c2_1(a545) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(4988,plain,
% 1.77/1.94 (c1_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4987, 56, 24, 2896, 4976, 4975, 4974, 4973])).
% 1.77/1.94 tff(4989,plain,
% 1.77/1.94 (hskp34 | c0_1(a548) | (~c1_1(a548))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4107, 156, 733, 732, 731, 2895, 75])).
% 1.77/1.94 tff(4990,plain,
% 1.77/1.94 (hskp34),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4989, 4988, 56])).
% 1.77/1.94 tff(4991,plain,
% 1.77/1.94 (~c1_1(a537)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1124, 4990])).
% 1.77/1.94 tff(4992,plain,
% 1.77/1.94 (c3_1(a537)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1132, 4990])).
% 1.77/1.94 tff(4993,plain,
% 1.77/1.94 (~c2_1(a537)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[3708, 156, 4975, 4992, 2895, 4991, 24, 483, 4988])).
% 1.77/1.94 tff(4994,plain,
% 1.77/1.94 (c0_1(a537)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1147, 4990])).
% 1.77/1.94 tff(4995,plain,
% 1.77/1.94 (~hskp19),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[3077, 4973, 35, 2896, 2897])).
% 1.77/1.94 tff(4996,plain,
% 1.77/1.94 (hskp50),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1154, 156, 4995, 4994, 4991, 34, 4993])).
% 1.77/1.94 tff(4997,plain,
% 1.77/1.94 (~c3_1(a574)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[799, 4996])).
% 1.77/1.94 tff(4998,plain,
% 1.77/1.94 (c1_1(a574)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[807, 4996])).
% 1.77/1.94 tff(4999,plain,
% 1.77/1.94 (c0_1(a574)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[815, 4996])).
% 1.77/1.94 tff(5000,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[2491, 156, 35, 4999, 4998, 2895, 4997, 24, 56, 85])).
% 1.77/1.94 tff(5001,plain,(c0_1(a548) | hskp33 | c3_1(a548) | c2_1(a548) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(5002,plain,
% 1.77/1.94 (c0_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[5001, 4971, 2895, 24, 35, 4970, 4969, 96])).
% 1.77/1.94 tff(5003,plain,
% 1.77/1.94 (~hskp19),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[3077, 4937, 35, 2896, 96])).
% 1.77/1.94 tff(5004,assumption,(c0_1(a548)), introduced(assumption)).
% 1.77/1.94 tff(5005,plain,
% 1.77/1.94 (~hskp50),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[824, 765, 35, 111, 97])).
% 1.77/1.94 tff(5006,plain,
% 1.77/1.94 ((~c0_1(a548)) | c3_1(a545) | (~c1_1(a548))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4826, 156, 35, 2895, 111, 97, 85])).
% 1.77/1.94 tff(5007,plain,
% 1.77/1.94 (~c1_1(a548)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[5006, 765, 5004])).
% 1.77/1.94 tff(5008,plain,
% 1.77/1.94 ($false),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[4803, 5007, 5005, 98, 5004])).
% 1.77/1.94 tff(5009,plain,(c3_1(a545) | hskp19 | (~c0_1(a548)) | c2_1(a548) | hskp33 | c3_1(a548) | c2_1(a545) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.94 tff(5010,plain,
% 1.77/1.94 (c3_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[5009, 5003, 5002, 24, 35, 2895, 4938, 4937])).
% 1.77/1.94 tff(5011,plain,
% 1.77/1.94 (c1_1(a545)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[193, 4936])).
% 1.77/1.94 tff(5012,plain,
% 1.77/1.94 (hskp42 | (~c3_1(a545))),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1574, 156, 4971, 4970, 4969, 5011, 4938, 1364])).
% 1.77/1.94 tff(5013,plain,
% 1.77/1.94 (hskp42),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[5012, 5010])).
% 1.77/1.94 tff(5014,plain,
% 1.77/1.94 (~c2_1(a556)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1385, 5013])).
% 1.77/1.94 tff(5015,plain,
% 1.77/1.94 (hskp39),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1586, 5010, 4971, 4970, 4969, 5011, 4938, 4937])).
% 1.77/1.94 tff(5016,plain,
% 1.77/1.94 (c1_1(a549)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[303, 5015])).
% 1.77/1.94 tff(5017,plain,
% 1.77/1.94 (c2_1(a549)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[311, 5015])).
% 1.77/1.94 tff(5018,plain,
% 1.77/1.94 (c3_1(a549)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[319, 5015])).
% 1.77/1.94 tff(5019,plain,
% 1.77/1.94 (c3_1(a556)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1403, 5013])).
% 1.77/1.94 tff(5020,plain,
% 1.77/1.94 (c1_1(a556)),
% 1.77/1.94 inference(unit_resolution,[status(thm)],[1411, 5013])).
% 1.77/1.94 tff(5021,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a556) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a556) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(5022,plain,
% 1.77/1.94 ((hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556))) <=> (hskp25 | c2_1(a556) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.77/1.94 inference(rewrite,[status(thm)],[])).
% 1.77/1.94 tff(5023,plain,
% 1.77/1.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a556) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5022])).
% 1.77/1.95 tff(5024,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a556) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5023, 5021])).
% 1.77/1.95 tff(5025,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5026,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a556) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c3_1(a556)) | (~c1_1(a556))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.77/1.95 tff(5027,plain,
% 1.77/1.95 (hskp25),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5026, 156, 5020, 5019, 5018, 5017, 5016, 5014, 55])).
% 1.77/1.95 tff(5028,plain,
% 1.77/1.95 (~c1_1(a582)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1190, 5027])).
% 1.77/1.95 tff(5029,plain,
% 1.77/1.95 (~c2_1(a582)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1196, 5027])).
% 1.77/1.95 tff(5030,plain,
% 1.77/1.95 (~c3_1(a582)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1202, 5027])).
% 1.77/1.95 tff(5031,plain,
% 1.77/1.95 (hskp46 | (~c3_1(a545))),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1163, 156, 5011, 4938, 4937, 12])).
% 1.77/1.95 tff(5032,plain,
% 1.77/1.95 (hskp46),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5031, 5010])).
% 1.77/1.95 tff(5033,plain,
% 1.77/1.95 (~c0_1(a562)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[64, 5032])).
% 1.77/1.95 tff(5034,plain,
% 1.77/1.95 (~c3_1(a562)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[270, 5032])).
% 1.77/1.95 tff(5035,plain,
% 1.77/1.95 (c1_1(a562)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[288, 5032])).
% 1.77/1.95 tff(5036,plain,
% 1.77/1.95 (hskp34),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[2160, 156, 5035, 4971, 4970, 4969, 5034, 5033, 75])).
% 1.77/1.95 tff(5037,plain,
% 1.77/1.95 (~c1_1(a537)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1124, 5036])).
% 1.77/1.95 tff(5038,plain,
% 1.77/1.95 (c3_1(a537)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1132, 5036])).
% 1.77/1.95 tff(5039,plain,
% 1.77/1.95 (~c2_1(a537)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[2192, 156, 5020, 5019, 5038, 5014, 5037, 5030, 5029, 5028, 45])).
% 1.77/1.95 tff(5040,plain,
% 1.77/1.95 (hskp0),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[4925, 156, 4971, 4970, 4969, 5030, 5029, 5028, 108])).
% 1.77/1.95 tff(5041,plain,
% 1.77/1.95 (~c2_1(a535)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[713, 5040])).
% 1.77/1.95 tff(5042,plain,
% 1.77/1.95 (c0_1(a535)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[721, 5040])).
% 1.77/1.95 tff(5043,plain,
% 1.77/1.95 (c1_1(a535)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[729, 5040])).
% 1.77/1.95 tff(5044,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[2754, 156, 4971, 4970, 4969, 5038, 5043, 5042, 5037, 5041, 707, 5039])).
% 1.77/1.95 tff(5045,plain,(c1_1(a586) | c2_1(a548) | hskp33 | c3_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5046,plain,
% 1.77/1.95 (c1_1(a586)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5045, 2895, 35, 24])).
% 1.77/1.95 tff(5047,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | (~c0_1(a586)) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | (~c0_1(a586)) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5048,plain,
% 1.77/1.95 ((hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c3_1(a548) | c0_1(a548)) <=> (hskp33 | c3_1(a548) | (~c0_1(a586)) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5049,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | (~c0_1(a586)) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a586))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5048])).
% 1.77/1.95 tff(5050,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | (~c0_1(a586)) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a586)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5049, 5047])).
% 1.77/1.95 tff(5051,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c3_1(a548) | c0_1(a548))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5052,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | (~c0_1(a586)) | c3_1(a586) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a586))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5051, 5050])).
% 1.77/1.95 tff(5053,plain,
% 1.77/1.95 (~c0_1(a586)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5052, 156, 35, 5046, 2895, 86, 24, 56, 85])).
% 1.77/1.95 tff(5054,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[2909, 156, 35, 1630, 1638, 2895, 1621, 24, 56, 85])).
% 1.77/1.95 tff(5055,plain,((~hskp26) | hskp33 | c3_1(a548) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5056,plain,
% 1.77/1.95 (~hskp26),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5055, 56, 2895, 24, 35])).
% 1.77/1.95 tff(5057,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[2491, 156, 35, 816, 808, 2895, 800, 24, 56, 85])).
% 1.77/1.95 tff(5058,plain,((~hskp50) | hskp33 | c3_1(a548) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5059,plain,
% 1.77/1.95 (~hskp50),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5058, 56, 2895, 24, 35])).
% 1.77/1.95 tff(5060,assumption,(hskp28), introduced(assumption)).
% 1.77/1.95 tff(5061,plain,
% 1.77/1.95 (c3_1(a589)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[185, 5060])).
% 1.77/1.95 tff(5062,plain,
% 1.77/1.95 (c2_1(a589)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[171, 5060])).
% 1.77/1.95 tff(5063,plain,
% 1.77/1.95 (~c1_1(a589)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[3914, 156, 23, 5062, 5061, 3797, 87, 86, 22])).
% 1.77/1.95 tff(5064,plain,
% 1.77/1.95 (~c0_1(a589)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[177, 5060])).
% 1.77/1.95 tff(5065,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[3164, 156, 1661, 5061, 3797, 5064, 87, 86, 1686, 5063])).
% 1.77/1.95 tff(5066,plain,((~hskp28) | hskp26 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5067,plain,
% 1.77/1.95 (~hskp28),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5066, 194, 3797, 1661, 86, 87])).
% 1.77/1.95 tff(5068,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1711, 156, 1213, 1705, 1692, 1676, 122])).
% 1.77/1.95 tff(5069,plain,((~hskp19) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5070,plain,
% 1.77/1.95 (~hskp19),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5069, 5067])).
% 1.77/1.95 tff(5071,plain,
% 1.77/1.95 (c2_1(a545)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[163, 5067, 112])).
% 1.77/1.95 tff(5072,plain,
% 1.77/1.95 (c1_1(a548)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[3668, 5067, 56])).
% 1.77/1.95 tff(5073,plain,
% 1.77/1.95 (~hskp15),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1276, 5067])).
% 1.77/1.95 tff(5074,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c3_1(a548) | c1_1(a545) | c2_1(a548) | (~c2_1(a545)) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a548) | c1_1(a545) | c2_1(a548) | (~c2_1(a545)) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5075,plain,
% 1.77/1.95 ((hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a545) | (~c3_1(a545)) | (~c2_1(a545))) <=> (hskp15 | c3_1(a548) | c1_1(a545) | c2_1(a548) | (~c2_1(a545)) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5076,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a545) | (~c3_1(a545)) | (~c2_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c3_1(a548) | c1_1(a545) | c2_1(a548) | (~c2_1(a545)) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5075])).
% 1.77/1.95 tff(5077,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a545) | (~c3_1(a545)) | (~c2_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a548) | c1_1(a545) | c2_1(a548) | (~c2_1(a545)) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5076, 5074])).
% 1.77/1.95 tff(5078,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c1_1(a548)) | c1_1(a545) | (~c3_1(a545)) | (~c2_1(a545)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5079,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a548) | c1_1(a545) | c2_1(a548) | (~c2_1(a545)) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5078, 5077])).
% 1.77/1.95 tff(5080,plain,
% 1.77/1.95 (~c3_1(a545)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5079, 156, 5073, 2895, 112, 24, 5071, 483, 5072])).
% 1.77/1.95 tff(5081,assumption,(c2_1(a545)), introduced(assumption)).
% 1.77/1.95 tff(5082,plain,
% 1.77/1.95 (~hskp25),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[1301, 1213, 110, 98])).
% 1.77/1.95 tff(5083,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5084,plain,
% 1.77/1.95 ((hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5085,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5084])).
% 1.77/1.95 tff(5086,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5085, 5083])).
% 1.77/1.95 tff(5087,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5088,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5087, 5086])).
% 1.77/1.95 tff(5089,plain,
% 1.77/1.95 (~c2_1(a570)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5088, 156, 23, 3797, 365, 357, 87, 86, 22])).
% 1.77/1.95 tff(5090,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5091,plain,
% 1.77/1.95 ((hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp39 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5092,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5091])).
% 1.77/1.95 tff(5093,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5092, 5090])).
% 1.77/1.95 tff(5094,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5095,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a586))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5094, 5093])).
% 1.77/1.95 tff(5096,plain,
% 1.77/1.95 (hskp39),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5095, 156, 3797, 365, 357, 87, 86, 281, 5089])).
% 1.77/1.95 tff(5097,plain,
% 1.77/1.95 (c1_1(a549)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[303, 5096])).
% 1.77/1.95 tff(5098,plain,
% 1.77/1.95 (c2_1(a549)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[311, 5096])).
% 1.77/1.95 tff(5099,plain,
% 1.77/1.95 (c3_1(a549)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[319, 5096])).
% 1.77/1.95 tff(5100,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5101,plain,
% 1.77/1.95 ((hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570))) <=> (hskp25 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5102,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5101])).
% 1.77/1.95 tff(5103,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5102, 5100])).
% 1.77/1.95 tff(5104,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5105,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5104, 5103])).
% 1.77/1.95 tff(5106,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5105, 156, 1423, 5099, 5098, 5097, 365, 357, 55, 5089])).
% 1.77/1.95 tff(5107,plain,((~hskp16) | hskp25 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5108,plain,
% 1.77/1.95 (~hskp16),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5107, 5082, 3797, 194, 86, 87])).
% 1.77/1.95 tff(5109,plain,
% 1.77/1.95 (hskp17),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[382, 5108, 1795])).
% 1.77/1.95 tff(5110,plain,
% 1.77/1.95 (~c2_1(a571)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[573, 5109])).
% 1.77/1.95 tff(5111,plain,
% 1.77/1.95 (c3_1(a571)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[623, 5109])).
% 1.77/1.95 tff(5112,plain,
% 1.77/1.95 (c0_1(a571)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[581, 5109])).
% 1.77/1.95 tff(5113,plain,
% 1.77/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a545) | c2_1(a571) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a545) | c2_1(a571) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5114,plain,
% 1.77/1.95 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571))) <=> (c1_1(a545) | c2_1(a571) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5115,plain,
% 1.77/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a545) | c2_1(a571) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5114])).
% 1.77/1.95 tff(5116,plain,
% 1.77/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a545) | c2_1(a571) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5115, 5113])).
% 1.77/1.95 tff(5117,plain,
% 1.77/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5118,plain,
% 1.77/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a545) | c2_1(a571) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5117, 5116])).
% 1.77/1.95 tff(5119,plain,
% 1.77/1.95 (c1_1(a571)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5118, 156, 5112, 5111, 112, 5110, 5081, 921, 765])).
% 1.77/1.95 tff(5120,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5121,plain,
% 1.77/1.95 ((hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a586)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5122,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a586))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5121])).
% 1.77/1.95 tff(5123,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a586)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5122, 5120])).
% 1.77/1.95 tff(5124,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5125,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c1_1(a586))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5124, 5123])).
% 1.77/1.95 tff(5126,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5125, 156, 23, 1876, 1875, 1874, 3797, 87, 86, 22])).
% 1.77/1.95 tff(5127,plain,((~hskp39) | hskp4 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5128,plain,
% 1.77/1.95 (~hskp39),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5127, 194, 3797, 87, 86])).
% 1.77/1.95 tff(5129,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a548) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a548) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5130,plain,
% 1.77/1.95 ((hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548))) <=> (hskp39 | c3_1(a548) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.77/1.95 inference(rewrite,[status(thm)],[])).
% 1.77/1.95 tff(5131,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a548) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a571)) | (~c1_1(a571))))),
% 1.77/1.95 inference(monotonicity,[status(thm)],[5130])).
% 1.77/1.95 tff(5132,plain,
% 1.77/1.95 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a548) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.77/1.95 inference(transitivity,[status(thm)],[5131, 5129])).
% 1.77/1.95 tff(5133,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))),
% 1.77/1.95 inference(quant_inst,[status(thm)],[])).
% 1.77/1.95 tff(5134,plain,
% 1.77/1.95 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a548) | c2_1(a571) | c0_1(a548) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a571)) | (~c1_1(a571))),
% 1.77/1.95 inference(modus_ponens,[status(thm)],[5133, 5132])).
% 1.77/1.95 tff(5135,plain,
% 1.77/1.95 ($false),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5134, 156, 5128, 5111, 2895, 5110, 56, 281, 3669, 5119])).
% 1.77/1.95 tff(5136,plain,(hskp28 | c3_1(a548) | c0_1(a548) | c1_1(a545) | (~c2_1(a545)) | c3_1(a545) | hskp18 | (~c1_1(a586)) | c3_1(a586) | c0_1(a586) | hskp50 | hskp19 | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.95 tff(5137,plain,
% 1.77/1.95 (hskp18),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[5136, 5080, 56, 112, 5071, 5067, 2895, 3797, 86, 87, 110, 5070, 24])).
% 1.77/1.95 tff(5138,plain,
% 1.77/1.95 (hskp37),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[430, 5137, 110, 5070])).
% 1.77/1.95 tff(5139,plain,
% 1.77/1.95 (~c2_1(a544)),
% 1.77/1.95 inference(unit_resolution,[status(thm)],[436, 5138])).
% 1.77/1.96 tff(5140,plain,
% 1.77/1.96 (~c3_1(a544)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[450, 5138])).
% 1.77/1.96 tff(5141,assumption,(hskp40), introduced(assumption)).
% 1.77/1.96 tff(5142,plain,
% 1.77/1.96 (c2_1(a551)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[532, 5141])).
% 1.77/1.96 tff(5143,plain,
% 1.77/1.96 (c3_1(a551)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[540, 5141])).
% 1.77/1.96 tff(5144,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5145,plain,
% 1.77/1.96 ((hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5146,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5145])).
% 1.77/1.96 tff(5147,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5146, 5144])).
% 1.77/1.96 tff(5148,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5149,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5148, 5147])).
% 1.77/1.96 tff(5150,plain,
% 1.77/1.96 (~c1_1(a551)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5149, 156, 23, 5143, 5142, 3797, 87, 86, 22])).
% 1.77/1.96 tff(5151,plain,
% 1.77/1.96 (~c0_1(a551)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[558, 5141])).
% 1.77/1.96 tff(5152,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a551) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a551)) | c1_1(a551))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a551) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a551)) | c1_1(a551))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5153,plain,
% 1.77/1.96 ((hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a551) | c0_1(a551) | (~c3_1(a551))) <=> (hskp26 | c0_1(a551) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a551)) | c1_1(a551))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5154,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a551) | c0_1(a551) | (~c3_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a551) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a551)) | c1_1(a551)))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5153])).
% 1.77/1.96 tff(5155,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a551) | c0_1(a551) | (~c3_1(a551)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a551) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a551)) | c1_1(a551))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5154, 5152])).
% 1.77/1.96 tff(5156,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a551) | c0_1(a551) | (~c3_1(a551)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5157,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a551) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a551)) | c1_1(a551)),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5156, 5155])).
% 1.77/1.96 tff(5158,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5157, 156, 1661, 5143, 3797, 5151, 87, 86, 1686, 5150])).
% 1.77/1.96 tff(5159,plain,((~hskp40) | hskp26 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5160,plain,
% 1.77/1.96 (~hskp40),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5159, 194, 3797, 1661, 86, 87])).
% 1.77/1.96 tff(5161,plain,
% 1.77/1.96 (hskp7),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[524, 5137, 110, 5160, 5070])).
% 1.77/1.96 tff(5162,plain,
% 1.77/1.96 (c1_1(a544)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[444, 5138])).
% 1.77/1.96 tff(5163,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[502, 5162, 5161, 5070, 5073, 5140, 110, 5139])).
% 1.77/1.96 tff(5164,plain,(c1_1(a545) | hskp50 | c0_1(a548) | c3_1(a548) | (~c1_1(a586)) | c3_1(a586) | c0_1(a586) | c2_1(a548) | c0_1(a545) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5165,plain,
% 1.77/1.96 (c1_1(a545)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5164, 86, 56, 2895, 5046, 5059, 5053, 24, 97, 5056])).
% 1.77/1.96 tff(5166,plain,
% 1.77/1.96 (~hskp15),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1971, 1046, 97, 2896, 5056])).
% 1.77/1.96 tff(5167,plain,
% 1.77/1.96 (hskp28),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1314, 1303])).
% 1.77/1.96 tff(5168,plain,
% 1.77/1.96 (~c0_1(a589)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[177, 5167])).
% 1.77/1.96 tff(5169,plain,
% 1.77/1.96 (c3_1(a589)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[185, 5167])).
% 1.77/1.96 tff(5170,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5171,plain,
% 1.77/1.96 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a554) | c1_1(a554) | c0_1(a554)) <=> (hskp6 | c0_1(a589) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5172,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a554) | c1_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a589) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5171])).
% 1.77/1.96 tff(5173,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a554) | c1_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5172, 5170])).
% 1.77/1.96 tff(5174,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a554) | c1_1(a554) | c0_1(a554))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5175,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a589) | c0_1(a554) | c2_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5174, 5173])).
% 1.77/1.96 tff(5176,plain,
% 1.77/1.96 (~c1_1(a589)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5175, 156, 1669, 5169, 5168, 1306, 1305, 1304, 1745])).
% 1.77/1.96 tff(5177,plain,
% 1.77/1.96 (c2_1(a589)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[171, 5167])).
% 1.77/1.96 tff(5178,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1562, 156, 109, 5177, 5169, 1046, 111, 483, 5176, 765])).
% 1.77/1.96 tff(5179,plain,((~hskp9) | hskp15 | (~c1_1(a545)) | c2_1(a545) | c3_1(a545) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5180,plain,
% 1.77/1.96 (~hskp9),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5179, 765, 2896, 5166, 1046, 111])).
% 1.77/1.96 tff(5181,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c3_1(a548) | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a555)) | (~c0_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c3_1(a548) | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a555)) | (~c0_1(a555)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5182,plain,
% 1.77/1.96 ((hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c3_1(a548) | c0_1(a548)) <=> (hskp45 | c3_1(a548) | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a555)) | (~c0_1(a555)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5183,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c3_1(a548) | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a555)) | (~c0_1(a555))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5182])).
% 1.77/1.96 tff(5184,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c3_1(a548) | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a555)) | (~c0_1(a555)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5183, 5181])).
% 1.77/1.96 tff(5185,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a548) | c3_1(a548) | c0_1(a548))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5186,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c3_1(a548) | c2_1(a555) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a555)) | (~c0_1(a555))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5185, 5184])).
% 1.77/1.96 tff(5187,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5186, 156, 2117, 241, 2895, 233, 24, 56, 757, 248])).
% 1.77/1.96 tff(5188,plain,((~hskp41) | hskp45 | c3_1(a548) | c2_1(a548) | c0_1(a548) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5189,plain,
% 1.77/1.96 (~hskp41),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5188, 2111, 2895, 24, 56, 5059, 98])).
% 1.77/1.96 tff(5190,plain,
% 1.77/1.96 (hskp17),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[567, 5189, 5166, 5059, 98, 5180])).
% 1.77/1.96 tff(5191,plain,
% 1.77/1.96 (~c2_1(a571)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[573, 5190])).
% 1.77/1.96 tff(5192,plain,
% 1.77/1.96 (c0_1(a571)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[581, 5190])).
% 1.77/1.96 tff(5193,plain,
% 1.77/1.96 (c1_1(a571)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[588, 156, 5059, 98, 5192, 5191, 34])).
% 1.77/1.96 tff(5194,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c3_1(a548) | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c3_1(a548) | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5195,plain,
% 1.77/1.96 ((hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c3_1(a548) | c0_1(a548)) <=> (hskp45 | c3_1(a548) | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5196,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c3_1(a548) | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5195])).
% 1.77/1.96 tff(5197,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c3_1(a548) | c0_1(a548))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c3_1(a548) | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5196, 5194])).
% 1.77/1.96 tff(5198,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c3_1(a548) | c0_1(a548))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5199,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c3_1(a548) | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5198, 5197])).
% 1.77/1.96 tff(5200,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5199, 156, 2111, 5192, 2895, 5191, 24, 56, 757, 5193])).
% 1.77/1.96 tff(5201,plain,(c3_1(a545) | c3_1(a548) | c2_1(a548) | c0_1(a548) | hskp19 | hskp33 | c2_1(a545) | c0_1(a545) | (~c1_1(a545))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5202,plain,
% 1.77/1.96 (c3_1(a545)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5201, 98, 24, 56, 2895, 35, 111, 97, 1046])).
% 1.77/1.96 tff(5203,plain,
% 1.77/1.96 (hskp46),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1164, 5202])).
% 1.77/1.96 tff(5204,plain,
% 1.77/1.96 (~c0_1(a562)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[64, 5203])).
% 1.77/1.96 tff(5205,plain,
% 1.77/1.96 (~c3_1(a562)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[270, 5203])).
% 1.77/1.96 tff(5206,plain,
% 1.77/1.96 (hskp38),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1211, 5202, 111, 97, 1046])).
% 1.77/1.96 tff(5207,plain,
% 1.77/1.96 (c0_1(a547)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[677, 5206])).
% 1.77/1.96 tff(5208,plain,
% 1.77/1.96 (c1_1(a547)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[685, 5206])).
% 1.77/1.96 tff(5209,plain,
% 1.77/1.96 (c2_1(a547)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[693, 5206])).
% 1.77/1.96 tff(5210,plain,
% 1.77/1.96 (c1_1(a562)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[288, 5203])).
% 1.77/1.96 tff(5211,plain,
% 1.77/1.96 (hskp34),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[2160, 156, 5210, 5209, 5208, 5207, 5205, 5204, 75])).
% 1.77/1.96 tff(5212,plain,
% 1.77/1.96 (~c1_1(a537)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1124, 5211])).
% 1.77/1.96 tff(5213,plain,
% 1.77/1.96 (c0_1(a537)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1147, 5211])).
% 1.77/1.96 tff(5214,plain,
% 1.77/1.96 (c2_1(a537)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1154, 156, 5059, 98, 5213, 5212, 34])).
% 1.77/1.96 tff(5215,plain,
% 1.77/1.96 (c1_1(a548)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[4987, 111, 24, 2896, 56, 1046, 5166, 97])).
% 1.77/1.96 tff(5216,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a548)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5217,plain,
% 1.77/1.96 ((hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548))) <=> (hskp39 | c3_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a548)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5218,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a548))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5217])).
% 1.77/1.96 tff(5219,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a548)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5218, 5216])).
% 1.77/1.96 tff(5220,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a548) | c0_1(a548) | (~c1_1(a548)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5221,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a548) | c0_1(a548) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a548))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5220, 5219])).
% 1.77/1.96 tff(5222,plain,
% 1.77/1.96 (hskp39 | (~c3_1(a545))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5221, 156, 2895, 1046, 56, 111, 281, 5215])).
% 1.77/1.96 tff(5223,plain,
% 1.77/1.96 (hskp39),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5222, 5202])).
% 1.77/1.96 tff(5224,plain,
% 1.77/1.96 (c1_1(a549)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[303, 5223])).
% 1.77/1.96 tff(5225,plain,
% 1.77/1.96 (c2_1(a549)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[311, 5223])).
% 1.77/1.96 tff(5226,plain,
% 1.77/1.96 (c3_1(a549)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[319, 5223])).
% 1.77/1.96 tff(5227,plain,
% 1.77/1.96 (hskp25),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1184, 156, 5226, 5225, 5224, 1046, 111, 55, 5202])).
% 1.77/1.96 tff(5228,plain,
% 1.77/1.96 (~c1_1(a582)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1190, 5227])).
% 1.77/1.96 tff(5229,plain,
% 1.77/1.96 (~c2_1(a582)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1196, 5227])).
% 1.77/1.96 tff(5230,plain,
% 1.77/1.96 (~c3_1(a582)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1202, 5227])).
% 1.77/1.96 tff(5231,plain,
% 1.77/1.96 (hskp42),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1574, 156, 5209, 5208, 5207, 1046, 111, 1364, 5202])).
% 1.77/1.96 tff(5232,plain,
% 1.77/1.96 (~c2_1(a556)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1385, 5231])).
% 1.77/1.96 tff(5233,plain,
% 1.77/1.96 (c3_1(a537)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1132, 5211])).
% 1.77/1.96 tff(5234,plain,
% 1.77/1.96 (c3_1(a556)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1403, 5231])).
% 1.77/1.96 tff(5235,plain,
% 1.77/1.96 (c1_1(a556)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1411, 5231])).
% 1.77/1.96 tff(5236,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[2192, 156, 5235, 5234, 5233, 5232, 5212, 5230, 5229, 5228, 45, 5214])).
% 1.77/1.96 tff(5237,plain,(hskp19 | (~c1_1(a545)) | c2_1(a545) | c3_1(a548) | c0_1(a548) | c0_1(a545) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5238,plain,
% 1.77/1.96 (hskp19),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5237, 111, 5165, 2895, 56, 97, 24, 35])).
% 1.77/1.96 tff(5239,plain,
% 1.77/1.96 (~c0_1(a573)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1691, 5238])).
% 1.77/1.96 tff(5240,plain,
% 1.77/1.96 (~c1_1(a573)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1675, 5238])).
% 1.77/1.96 tff(5241,plain,
% 1.77/1.96 (~c2_1(a573)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1704, 5238])).
% 1.77/1.96 tff(5242,plain,
% 1.77/1.96 (c3_1(a573)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[3176, 5241, 2896, 5240, 86, 5056, 5053, 5239])).
% 1.77/1.96 tff(5243,plain,
% 1.77/1.96 (~hskp15),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1971, 5165, 97, 2896, 5056])).
% 1.77/1.96 tff(5244,plain,
% 1.77/1.96 (c1_1(a548)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[4987, 111, 24, 2896, 56, 5165, 5243, 97])).
% 1.77/1.96 tff(5245,plain,
% 1.77/1.96 (~hskp28),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5066, 23, 3797, 1661, 86, 87])).
% 1.77/1.96 tff(5246,plain,
% 1.77/1.96 (~hskp19),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5069, 5245])).
% 1.77/1.96 tff(5247,plain,
% 1.77/1.96 (~hskp25),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1301, 5245, 110, 5246])).
% 1.77/1.96 tff(5248,plain,
% 1.77/1.96 (~hskp16),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5107, 5247, 3797, 23, 86, 87])).
% 1.77/1.96 tff(5249,plain,
% 1.77/1.96 (~hskp39),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5127, 23, 3797, 87, 86])).
% 1.77/1.96 tff(5250,plain,
% 1.77/1.96 (c1_1(a571)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[588, 156, 110, 98, 925, 923, 34])).
% 1.77/1.96 tff(5251,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5134, 156, 859, 924, 2895, 923, 56, 281, 2548, 5250])).
% 1.77/1.96 tff(5252,plain,((~hskp17) | hskp39 | c3_1(a548) | c0_1(a548) | (~c1_1(a548)) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5253,plain,
% 1.77/1.96 (~hskp17),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5252, 5249, 2895, 56, 2548, 110, 5246])).
% 1.77/1.96 tff(5254,plain,
% 1.77/1.96 (hskp18),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[382, 5253, 5248])).
% 1.77/1.96 tff(5255,plain,
% 1.77/1.96 (hskp37),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[430, 5254, 110, 5246])).
% 1.77/1.96 tff(5256,plain,
% 1.77/1.96 (~c2_1(a544)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[436, 5255])).
% 1.77/1.96 tff(5257,plain,
% 1.77/1.96 (~c3_1(a544)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[450, 5255])).
% 1.77/1.96 tff(5258,plain,
% 1.77/1.96 (~hskp40),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5159, 23, 3797, 1661, 86, 87])).
% 1.77/1.96 tff(5259,plain,
% 1.77/1.96 (hskp7),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[524, 5254, 110, 5258, 5246])).
% 1.77/1.96 tff(5260,plain,
% 1.77/1.96 (c1_1(a544)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[444, 5255])).
% 1.77/1.96 tff(5261,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[502, 5260, 5259, 5246, 109, 5257, 110, 5256])).
% 1.77/1.96 tff(5262,plain,(hskp4 | hskp15 | hskp50 | c3_1(a548) | c0_1(a548) | (~c1_1(a548)) | (~c1_1(a586)) | c3_1(a586) | c0_1(a586) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5263,plain,
% 1.77/1.96 (hskp4),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5262, 5244, 5059, 2895, 56, 5243, 5046, 86, 5053, 5056])).
% 1.77/1.96 tff(5264,plain,
% 1.77/1.96 (c3_1(a545)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1753, 5238, 2896, 5263, 5056])).
% 1.77/1.96 tff(5265,plain,
% 1.77/1.96 (hskp46 | (~c3_1(a545))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1163, 156, 5165, 111, 97, 12])).
% 1.77/1.96 tff(5266,plain,
% 1.77/1.96 (hskp46),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5265, 5264])).
% 1.77/1.96 tff(5267,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[3247, 5266, 5242, 5056, 5240, 5239])).
% 1.77/1.96 tff(5268,plain,(c2_1(a545) | c0_1(a545) | c3_1(a586) | c3_1(a548) | c0_1(a548) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5269,plain,
% 1.77/1.96 (c2_1(a545)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5268, 86, 97, 2895, 56, 24, 35])).
% 1.77/1.96 tff(5270,plain,
% 1.77/1.96 (~hskp4),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1643, 5269])).
% 1.77/1.96 tff(5271,plain,
% 1.77/1.96 (~hskp28),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5066, 5270, 5046, 5056, 86, 5053])).
% 1.77/1.96 tff(5272,plain,
% 1.77/1.96 (~c1_1(a548)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5262, 5270, 5059, 2895, 56, 5243, 5046, 86, 5053, 5056])).
% 1.77/1.96 tff(5273,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[3668, 5272, 5271, 56])).
% 1.77/1.96 tff(5274,plain,(c3_1(a586) | c0_1(a548) | c2_1(a548) | c3_1(a548) | c0_1(a545) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5275,plain,
% 1.77/1.96 (c3_1(a586)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5274, 56, 24, 2895, 97, 35])).
% 1.77/1.96 tff(5276,plain,
% 1.77/1.96 (~hskp27),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[3996, 5275])).
% 1.77/1.96 tff(5277,plain,
% 1.77/1.96 (hskp4),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[205, 5276, 2896])).
% 1.77/1.96 tff(5278,plain,
% 1.77/1.96 (c1_1(a545)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[193, 5277])).
% 1.77/1.96 tff(5279,plain,
% 1.77/1.96 (~hskp19),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[3077, 5276, 35, 2896, 97])).
% 1.77/1.96 tff(5280,plain,
% 1.77/1.96 (~c2_1(a545)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[1643, 5277])).
% 1.77/1.96 tff(5281,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5237, 5280, 5279, 5278, 2895, 56, 97, 24, 35])).
% 1.77/1.96 tff(5282,plain,(c0_1(a548) | c3_1(a548) | c0_1(a545) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5283,plain,
% 1.77/1.96 (c0_1(a548)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5282, 97, 2895, 24, 35])).
% 1.77/1.96 tff(5284,plain,
% 1.77/1.96 (c3_1(a545)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[824, 111, 35, 794, 97])).
% 1.77/1.96 tff(5285,plain,
% 1.77/1.96 (c2_1(a586)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[2766, 87, 794, 86, 35])).
% 1.77/1.96 tff(5286,plain,
% 1.77/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)) | (~c2_1(a586)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5287,plain,
% 1.77/1.96 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))) <=> (c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)) | (~c2_1(a586)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5288,plain,
% 1.77/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)) | (~c2_1(a586))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5287])).
% 1.77/1.96 tff(5289,plain,
% 1.77/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)) | (~c2_1(a586)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5288, 5286])).
% 1.77/1.96 tff(5290,plain,
% 1.77/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5291,plain,
% 1.77/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a545) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a548)) | (~c2_1(a586))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 1.77/1.96 tff(5292,plain,
% 1.77/1.96 ((~c3_1(a545)) | (~c2_1(a586))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5291, 156, 112, 87, 86, 24, 5004, 97, 609, 2548])).
% 1.77/1.96 tff(5293,plain,
% 1.77/1.96 (~c2_1(a586)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5292, 2])).
% 1.77/1.96 tff(5294,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a586)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5295,plain,
% 1.77/1.96 ((hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545))) <=> (hskp26 | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a586)))),
% 1.77/1.96 inference(rewrite,[status(thm)],[])).
% 1.77/1.96 tff(5296,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a586))))),
% 1.77/1.96 inference(monotonicity,[status(thm)],[5295])).
% 1.77/1.96 tff(5297,plain,
% 1.77/1.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a586)))),
% 1.77/1.96 inference(transitivity,[status(thm)],[5296, 5294])).
% 1.77/1.96 tff(5298,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a545) | c0_1(a545) | (~c3_1(a545)))),
% 1.77/1.96 inference(quant_inst,[status(thm)],[])).
% 1.77/1.96 tff(5299,plain,
% 1.77/1.96 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a545) | c0_1(a586) | c3_1(a586) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a586))),
% 1.77/1.96 inference(modus_ponens,[status(thm)],[5298, 5297])).
% 1.77/1.96 tff(5300,plain,
% 1.77/1.96 (hskp26 | (~c3_1(a545))),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5299, 156, 3797, 112, 87, 86, 97, 1686])).
% 1.77/1.96 tff(5301,plain,
% 1.77/1.96 (hskp26),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5300, 2])).
% 1.77/1.96 tff(5302,plain,
% 1.77/1.96 ($false),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[3104, 5301, 5293, 87, 86, 35])).
% 1.77/1.96 tff(5303,plain,((~c3_1(a545)) | c0_1(a586) | c3_1(a586) | hskp33 | (~c1_1(a586)) | c1_1(a545) | c0_1(a545) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.96 tff(5304,plain,
% 1.77/1.96 (~c1_1(a548)),
% 1.77/1.96 inference(unit_resolution,[status(thm)],[5303, 112, 86, 35, 3797, 87, 97, 24, 5004, 2])).
% 1.77/1.97 tff(5305,assumption,(hskp35), introduced(assumption)).
% 1.77/1.97 tff(5306,plain,
% 1.77/1.97 (c3_1(a538)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[3965, 5305])).
% 1.77/1.97 tff(5307,plain,
% 1.77/1.97 (c1_1(a538)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[3973, 5305])).
% 1.77/1.97 tff(5308,plain,
% 1.77/1.97 (c2_1(a538)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[3981, 5305])).
% 1.77/1.97 tff(5309,plain,
% 1.77/1.97 ($false),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[3988, 156, 23, 5308, 5307, 5306, 3797, 87, 86, 22])).
% 1.77/1.97 tff(5310,plain,((~hskp35) | hskp4 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.97 tff(5311,plain,
% 1.77/1.97 (~hskp35),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5310, 194, 3797, 87, 86])).
% 1.77/1.97 tff(5312,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(5313,plain,
% 1.77/1.97 ((hskp35 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp35 | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(5314,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[5313])).
% 1.77/1.97 tff(5315,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(transitivity,[status(thm)],[5314, 5312])).
% 1.77/1.97 tff(5316,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a548) | c1_1(a548) | (~c0_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(5317,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[5316, 5315])).
% 1.77/1.97 tff(5318,plain,
% 1.77/1.97 (hskp35 | c1_1(a548) | (~c2_1(a586))),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5317, 156, 3797, 86, 24, 5004, 3950])).
% 1.77/1.97 tff(5319,plain,
% 1.77/1.97 ($false),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5318, 5311, 5304, 902])).
% 1.77/1.97 tff(5320,plain,(c1_1(a545) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | c0_1(a586) | hskp33 | c0_1(a545) | (~c3_1(a545))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.97 tff(5321,plain,
% 1.77/1.97 (c1_1(a545)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5320, 5284, 3797, 86, 24, 5004, 87, 35, 97, 5285])).
% 1.77/1.97 tff(5322,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a586)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(5323,plain,
% 1.77/1.97 ((hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a586)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(5324,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a586))))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[5323])).
% 1.77/1.97 tff(5325,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a586)))),
% 1.77/1.97 inference(transitivity,[status(thm)],[5324, 5322])).
% 1.77/1.97 tff(5326,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(5327,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a586))),
% 1.77/1.97 inference(modus_ponens,[status(thm)],[5326, 5325])).
% 1.77/1.97 tff(5328,plain,
% 1.77/1.97 (hskp39 | (~c1_1(a545))),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5327, 156, 3797, 87, 86, 111, 281, 5284])).
% 1.77/1.97 tff(5329,plain,
% 1.77/1.97 (hskp39),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5328, 5321])).
% 1.77/1.97 tff(5330,plain,
% 1.77/1.97 (c1_1(a549)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[303, 5329])).
% 1.77/1.97 tff(5331,plain,
% 1.77/1.97 (c2_1(a549)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[311, 5329])).
% 1.77/1.97 tff(5332,plain,
% 1.77/1.97 (c3_1(a549)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[319, 5329])).
% 1.77/1.97 tff(5333,plain,
% 1.77/1.97 (hskp25),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1184, 156, 5332, 5331, 5330, 5321, 111, 55, 5284])).
% 1.77/1.97 tff(5334,plain,
% 1.77/1.97 (~c1_1(a582)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1190, 5333])).
% 1.77/1.97 tff(5335,plain,
% 1.77/1.97 (~c2_1(a582)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1196, 5333])).
% 1.77/1.97 tff(5336,plain,
% 1.77/1.97 (~c3_1(a582)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1202, 5333])).
% 1.77/1.97 tff(5337,plain,
% 1.77/1.97 (hskp46 | (~c1_1(a545))),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1163, 156, 111, 97, 12, 5284])).
% 1.77/1.97 tff(5338,plain,
% 1.77/1.97 (hskp46),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5337, 5321])).
% 1.77/1.97 tff(5339,plain,
% 1.77/1.97 (~c0_1(a562)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[64, 5338])).
% 1.77/1.97 tff(5340,plain,
% 1.77/1.97 (~c3_1(a562)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[270, 5338])).
% 1.77/1.97 tff(5341,plain,
% 1.77/1.97 (hskp38),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1211, 5321, 111, 97, 5284])).
% 1.77/1.97 tff(5342,plain,
% 1.77/1.97 (c0_1(a547)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[677, 5341])).
% 1.77/1.97 tff(5343,plain,
% 1.77/1.97 (c1_1(a547)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[685, 5341])).
% 1.77/1.97 tff(5344,plain,
% 1.77/1.97 (c2_1(a547)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[693, 5341])).
% 1.77/1.97 tff(5345,plain,
% 1.77/1.97 (c1_1(a562)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[288, 5338])).
% 1.77/1.97 tff(5346,plain,
% 1.77/1.97 (hskp34),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[2160, 156, 5345, 5344, 5343, 5342, 5340, 5339, 75])).
% 1.77/1.97 tff(5347,plain,
% 1.77/1.97 (~c1_1(a537)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1124, 5346])).
% 1.77/1.97 tff(5348,plain,
% 1.77/1.97 (hskp42),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1574, 156, 5344, 5343, 5342, 5321, 111, 1364, 5284])).
% 1.77/1.97 tff(5349,plain,
% 1.77/1.97 (~c2_1(a556)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1385, 5348])).
% 1.77/1.97 tff(5350,plain,
% 1.77/1.97 (c3_1(a537)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1132, 5346])).
% 1.77/1.97 tff(5351,plain,
% 1.77/1.97 (c3_1(a556)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1403, 5348])).
% 1.77/1.97 tff(5352,plain,
% 1.77/1.97 (c1_1(a556)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1411, 5348])).
% 1.77/1.97 tff(5353,plain,
% 1.77/1.97 (~c2_1(a537)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[2192, 156, 5352, 5351, 5350, 5349, 5347, 5336, 5335, 5334, 45])).
% 1.77/1.97 tff(5354,plain,
% 1.77/1.97 (hskp0),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[4925, 156, 5344, 5343, 5342, 5336, 5335, 5334, 108])).
% 1.77/1.97 tff(5355,plain,
% 1.77/1.97 (~c2_1(a535)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[713, 5354])).
% 1.77/1.97 tff(5356,plain,
% 1.77/1.97 (c0_1(a535)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[721, 5354])).
% 1.77/1.97 tff(5357,plain,
% 1.77/1.97 (c1_1(a535)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[729, 5354])).
% 1.77/1.97 tff(5358,plain,
% 1.77/1.97 ($false),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[2754, 156, 5344, 5343, 5342, 5350, 5357, 5356, 5347, 5355, 707, 5353])).
% 1.77/1.97 tff(5359,plain,(c2_1(a545) | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | c0_1(a545) | c2_1(a548) | (~c0_1(a548)) | hskp33 | (~hskp50)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.97 tff(5360,plain,
% 1.77/1.97 (c2_1(a545)),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5359, 87, 5046, 86, 97, 24, 5283, 35, 794])).
% 1.77/1.97 tff(5361,plain,
% 1.77/1.97 (~hskp4),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[1643, 5360])).
% 1.77/1.97 tff(5362,plain,
% 1.77/1.97 (~hskp35),
% 1.77/1.97 inference(unit_resolution,[status(thm)],[5310, 5361, 5046, 87, 86])).
% 1.77/1.97 tff(5363,assumption,(~hskp35), introduced(assumption)).
% 1.77/1.97 tff(5364,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(5365,plain,
% 1.77/1.97 ((hskp35 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp35 | c3_1(a586) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(rewrite,[status(thm)],[])).
% 1.77/1.97 tff(5366,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.77/1.97 inference(monotonicity,[status(thm)],[5365])).
% 1.77/1.97 tff(5367,plain,
% 1.77/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(transitivity,[status(thm)],[5366, 5364])).
% 1.77/1.97 tff(5368,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a582) | c1_1(a582) | (~c0_1(a582)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.77/1.97 inference(quant_inst,[status(thm)],[])).
% 1.77/1.97 tff(5369,plain,
% 1.77/1.97 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c0_1(a582)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 1.82/1.97 tff(5370,plain,
% 1.82/1.97 (~c0_1(a582)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5369, 156, 5363, 3797, 86, 1279, 1280, 3950, 902])).
% 1.82/1.97 tff(5371,plain,
% 1.82/1.97 (~c3_1(a582)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[1202, 1278])).
% 1.82/1.97 tff(5372,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5373,plain,
% 1.82/1.97 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a582) | c3_1(a582) | c0_1(a582)) <=> (hskp33 | c3_1(a574) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5374,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a582) | c3_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c0_1(a574)) | (~c1_1(a574))))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[5373])).
% 1.82/1.97 tff(5375,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a582) | c3_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.82/1.97 inference(transitivity,[status(thm)],[5374, 5372])).
% 1.82/1.97 tff(5376,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a582) | c3_1(a582) | c0_1(a582))),
% 1.82/1.97 inference(quant_inst,[status(thm)],[])).
% 1.82/1.97 tff(5377,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a582) | c2_1(a582) | (~ndr1_0) | c0_1(a582) | (~c0_1(a574)) | (~c1_1(a574))),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[5376, 5375])).
% 1.82/1.97 tff(5378,plain,
% 1.82/1.97 ($false),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5377, 156, 35, 2476, 2475, 2474, 5371, 1279, 85, 5370])).
% 1.82/1.97 tff(5379,plain,((~hskp25) | hskp33 | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | hskp35 | (~c1_1(a586)) | c3_1(a586) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.97 tff(5380,plain,
% 1.82/1.97 (~hskp25),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5379, 5362, 5046, 808, 800, 5285, 816, 86, 35])).
% 1.82/1.97 tff(5381,plain,
% 1.82/1.97 (~hskp16),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5107, 5380, 5046, 5361, 86, 87])).
% 1.82/1.97 tff(5382,plain,
% 1.82/1.97 (~hskp39),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5127, 5361, 5046, 87, 86])).
% 1.82/1.97 tff(5383,plain,
% 1.82/1.97 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a548) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a548) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5384,plain,
% 1.82/1.97 ((hskp39 | hskp24 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c0_1(a548))) <=> (hskp39 | hskp24 | c3_1(a548) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5385,plain,
% 1.82/1.97 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c0_1(a548)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a548) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0)))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[5384])).
% 1.82/1.97 tff(5386,plain,
% 1.82/1.97 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c0_1(a548)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a548) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0))),
% 1.82/1.97 inference(transitivity,[status(thm)],[5385, 5383])).
% 1.82/1.97 tff(5387,plain,
% 1.82/1.97 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a548) | c3_1(a548) | (~c0_1(a548)))),
% 1.82/1.97 inference(quant_inst,[status(thm)],[])).
% 1.82/1.97 tff(5388,plain,
% 1.82/1.97 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a548) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[5387, 5386])).
% 1.82/1.97 tff(5389,plain,
% 1.82/1.97 (hskp39 | hskp24 | c3_1(a548) | (~c0_1(a548))),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5388, 156, 24, 3496])).
% 1.82/1.97 tff(5390,plain,
% 1.82/1.97 (hskp24),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5389, 5382, 2895, 5283])).
% 1.82/1.97 tff(5391,plain,
% 1.82/1.97 (~c3_1(a581)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[3513, 5390])).
% 1.82/1.97 tff(5392,plain,
% 1.82/1.97 (~c1_1(a581)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[3519, 5390])).
% 1.82/1.97 tff(5393,plain,
% 1.82/1.97 (c2_1(a581)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[3541, 5390])).
% 1.82/1.97 tff(5394,assumption,(~c3_1(a581)), introduced(assumption)).
% 1.82/1.97 tff(5395,assumption,(~c1_1(a581)), introduced(assumption)).
% 1.82/1.97 tff(5396,assumption,(c2_1(a581)), introduced(assumption)).
% 1.82/1.97 tff(5397,plain,
% 1.82/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a581) | c3_1(a581) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a581)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a581) | c3_1(a581) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a581)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5398,plain,
% 1.82/1.97 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571))) <=> (c1_1(a581) | c3_1(a581) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a581)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5399,plain,
% 1.82/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a581) | c3_1(a581) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a581))))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[5398])).
% 1.82/1.97 tff(5400,plain,
% 1.82/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a581) | c3_1(a581) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a581)))),
% 1.82/1.97 inference(transitivity,[status(thm)],[5399, 5397])).
% 1.82/1.97 tff(5401,plain,
% 1.82/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))),
% 1.82/1.97 inference(quant_inst,[status(thm)],[])).
% 1.82/1.97 tff(5402,plain,
% 1.82/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a581) | c3_1(a581) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a581))),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[5401, 5400])).
% 1.82/1.97 tff(5403,plain,
% 1.82/1.97 (c1_1(a571)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5402, 156, 5396, 925, 924, 5395, 5394, 923, 921])).
% 1.82/1.97 tff(5404,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a586)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5405,plain,
% 1.82/1.97 ((hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a586)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5406,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a586))))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[5405])).
% 1.82/1.97 tff(5407,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a586)))),
% 1.82/1.97 inference(transitivity,[status(thm)],[5406, 5404])).
% 1.82/1.97 tff(5408,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.82/1.97 inference(quant_inst,[status(thm)],[])).
% 1.82/1.97 tff(5409,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c1_1(a586))),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[5408, 5407])).
% 1.82/1.97 tff(5410,plain,
% 1.82/1.97 ($false),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5409, 156, 859, 3797, 924, 87, 86, 923, 281, 5403])).
% 1.82/1.97 tff(5411,plain,((~hskp17) | hskp39 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | (~c2_1(a581)) | c1_1(a581) | c3_1(a581)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.97 tff(5412,plain,
% 1.82/1.97 (~hskp17),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5411, 5393, 5046, 87, 86, 5382, 5392, 5391])).
% 1.82/1.97 tff(5413,plain,
% 1.82/1.97 (hskp18),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[382, 5412, 5381])).
% 1.82/1.97 tff(5414,plain,
% 1.82/1.97 (~c1_1(a572)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[389, 5413])).
% 1.82/1.97 tff(5415,plain,
% 1.82/1.97 (c0_1(a572)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[397, 5413])).
% 1.82/1.97 tff(5416,assumption,(~c2_1(a572)), introduced(assumption)).
% 1.82/1.97 tff(5417,assumption,(~c1_1(a572)), introduced(assumption)).
% 1.82/1.97 tff(5418,assumption,(c0_1(a572)), introduced(assumption)).
% 1.82/1.97 tff(5419,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5420,plain,
% 1.82/1.97 ((hskp35 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp35 | c3_1(a586) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5421,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a586) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[5420])).
% 1.82/1.97 tff(5422,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.97 inference(transitivity,[status(thm)],[5421, 5419])).
% 1.82/1.97 tff(5423,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a572) | c1_1(a572) | (~c0_1(a572)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.97 inference(quant_inst,[status(thm)],[])).
% 1.82/1.97 tff(5424,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a586) | c1_1(a572) | (~ndr1_0) | c2_1(a572) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 1.82/1.97 tff(5425,plain,
% 1.82/1.97 ($false),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5424, 156, 5363, 3797, 5418, 86, 5417, 3950, 902, 5416])).
% 1.82/1.97 tff(5426,plain,(c2_1(a572) | hskp35 | (~c1_1(a586)) | (~c0_1(a572)) | c3_1(a586) | c1_1(a572) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.97 tff(5427,plain,
% 1.82/1.97 (c2_1(a572)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5426, 5415, 5046, 5285, 86, 5414, 5362])).
% 1.82/1.97 tff(5428,plain,
% 1.82/1.97 (~c3_1(a572)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[420, 5413])).
% 1.82/1.97 tff(5429,plain,
% 1.82/1.97 (hskp37),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[428, 156, 5415, 5428, 5414, 415, 5427])).
% 1.82/1.97 tff(5430,plain,
% 1.82/1.97 (~c3_1(a544)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[450, 5429])).
% 1.82/1.97 tff(5431,plain,
% 1.82/1.97 (~c2_1(a544)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[436, 5429])).
% 1.82/1.97 tff(5432,plain,
% 1.82/1.97 (c1_1(a544)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[444, 5429])).
% 1.82/1.97 tff(5433,plain,
% 1.82/1.97 (hskp35 | c1_1(a548) | (~c2_1(a586))),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5317, 156, 5046, 86, 24, 5283, 3950])).
% 1.82/1.97 tff(5434,plain,
% 1.82/1.97 (c1_1(a548)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5433, 5362, 5285])).
% 1.82/1.97 tff(5435,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c2_1(a544) | c3_1(a544) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c2_1(a544) | c3_1(a544) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c0_1(a544))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5436,plain,
% 1.82/1.97 ((hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a544) | c3_1(a544) | c0_1(a544)) <=> (hskp33 | c3_1(a548) | c2_1(a544) | c3_1(a544) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c0_1(a544))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5437,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c2_1(a544) | c3_1(a544) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c0_1(a544)))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[5436])).
% 1.82/1.97 tff(5438,plain,
% 1.82/1.97 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c2_1(a544) | c3_1(a544) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c0_1(a544))),
% 1.82/1.97 inference(transitivity,[status(thm)],[5437, 5435])).
% 1.82/1.97 tff(5439,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a544) | c3_1(a544) | c0_1(a544))),
% 1.82/1.97 inference(quant_inst,[status(thm)],[])).
% 1.82/1.97 tff(5440,plain,
% 1.82/1.97 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c2_1(a544) | c3_1(a544) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c0_1(a544)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[5439, 5438])).
% 1.82/1.97 tff(5441,plain,
% 1.82/1.97 (c0_1(a544)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5440, 156, 35, 2895, 5431, 5430, 5283, 85, 5434])).
% 1.82/1.97 tff(5442,plain,
% 1.82/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5443,plain,
% 1.82/1.97 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.82/1.97 inference(rewrite,[status(thm)],[])).
% 1.82/1.97 tff(5444,plain,
% 1.82/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[5443])).
% 1.82/1.97 tff(5445,plain,
% 1.82/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5444, 5442])).
% 1.82/1.98 tff(5446,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5447,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a544) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5446, 5445])).
% 1.82/1.98 tff(5448,plain,
% 1.82/1.98 (~c3_1(a569)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5447, 156, 494, 485, 87, 86, 1268, 1262, 609, 902, 4557])).
% 1.82/1.98 tff(5449,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c0_1(a569) | c2_1(a569) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c0_1(a569) | c2_1(a569) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5450,plain,
% 1.82/1.98 ((hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569)) <=> (hskp33 | c3_1(a548) | c0_1(a569) | c2_1(a569) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5451,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c0_1(a569) | c2_1(a569) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569)))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5450])).
% 1.82/1.98 tff(5452,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c0_1(a569) | c2_1(a569) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5451, 5449])).
% 1.82/1.98 tff(5453,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a569) | c3_1(a569) | c0_1(a569))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5454,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c0_1(a569) | c2_1(a569) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c3_1(a569)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5453, 5452])).
% 1.82/1.98 tff(5455,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5454, 156, 35, 2895, 1268, 1256, 5004, 85, 2548, 5448])).
% 1.82/1.98 tff(5456,plain,((~hskp15) | hskp33 | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | (~c1_1(a544)) | c2_1(a544) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a544))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(5457,plain,
% 1.82/1.98 (~hskp15),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5456, 5434, 2895, 5283, 35, 5432, 5431, 87, 86, 5285, 5441])).
% 1.82/1.98 tff(5458,plain,
% 1.82/1.98 (~c2_1(a550)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[500, 156, 109, 494, 493, 485, 484, 458, 483])).
% 1.82/1.98 tff(5459,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a581) | c3_1(a581) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | c2_1(a550) | (~c0_1(a550)) | (~c2_1(a581)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a581) | c3_1(a581) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | c2_1(a550) | (~c0_1(a550)) | (~c2_1(a581)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5460,plain,
% 1.82/1.98 (((~ndr1_0) | c2_1(a550) | (~c3_1(a550)) | (~c0_1(a550)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a550)) | c1_1(a550) | (~c3_1(a550))) <=> (c1_1(a581) | c3_1(a581) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | c2_1(a550) | (~c0_1(a550)) | (~c2_1(a581)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5461,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a550) | (~c3_1(a550)) | (~c0_1(a550)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a550)) | c1_1(a550) | (~c3_1(a550)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a581) | c3_1(a581) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | c2_1(a550) | (~c0_1(a550)) | (~c2_1(a581))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5460])).
% 1.82/1.98 tff(5462,plain,
% 1.82/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a550) | (~c3_1(a550)) | (~c0_1(a550)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a550)) | c1_1(a550) | (~c3_1(a550)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a581) | c3_1(a581) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | c2_1(a550) | (~c0_1(a550)) | (~c2_1(a581)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5461, 5459])).
% 1.82/1.98 tff(5463,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a550) | (~c3_1(a550)) | (~c0_1(a550)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a550)) | c1_1(a550) | (~c3_1(a550)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5464,plain,
% 1.82/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a581) | c3_1(a581) | c1_1(a550) | (~ndr1_0) | (~c3_1(a550)) | c2_1(a550) | (~c0_1(a550)) | (~c2_1(a581))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5463, 5462])).
% 1.82/1.98 tff(5465,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5464, 156, 5396, 466, 493, 5395, 5394, 458, 921, 5458])).
% 1.82/1.98 tff(5466,plain,((~hskp7) | (~c2_1(a581)) | c1_1(a581) | c3_1(a581) | hskp15 | (~c1_1(a544)) | c2_1(a544) | c3_1(a544)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(5467,plain,
% 1.82/1.98 (~hskp7),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5466, 5393, 5392, 5391, 5457, 5432, 5431, 5430])).
% 1.82/1.98 tff(5468,plain,
% 1.82/1.98 (hskp40 | hskp7),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[521, 156, 5415, 5414, 513, 5427])).
% 1.82/1.98 tff(5469,plain,
% 1.82/1.98 (hskp40),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5468, 5467])).
% 1.82/1.98 tff(5470,plain,
% 1.82/1.98 (c3_1(a551)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[540, 5469])).
% 1.82/1.98 tff(5471,plain,
% 1.82/1.98 (c2_1(a551)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[532, 5469])).
% 1.82/1.98 tff(5472,plain,
% 1.82/1.98 (c1_1(a551)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[552, 5471, 5430, 5457, 5432, 5431, 5470])).
% 1.82/1.98 tff(5473,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5474,plain,
% 1.82/1.98 ((hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp46 | c0_1(a586) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5475,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c0_1(a586) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5474])).
% 1.82/1.98 tff(5476,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5475, 5473])).
% 1.82/1.98 tff(5477,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a572) | (~c2_1(a572)) | (~c0_1(a572)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5478,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a586) | c1_1(a572) | (~ndr1_0) | (~c2_1(a572)) | (~c0_1(a572)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5477, 5476])).
% 1.82/1.98 tff(5479,plain,
% 1.82/1.98 (hskp46),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5478, 156, 5046, 5415, 87, 5414, 2215, 5285, 5427])).
% 1.82/1.98 tff(5480,plain,
% 1.82/1.98 (~c0_1(a562)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[64, 5479])).
% 1.82/1.98 tff(5481,plain,
% 1.82/1.98 (~c3_1(a562)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[270, 5479])).
% 1.82/1.98 tff(5482,plain,
% 1.82/1.98 (c1_1(a562)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[288, 5479])).
% 1.82/1.98 tff(5483,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c1_1(a562)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5484,plain,
% 1.82/1.98 ((hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c1_1(a562)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5485,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c1_1(a562))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5484])).
% 1.82/1.98 tff(5486,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c1_1(a562)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5485, 5483])).
% 1.82/1.98 tff(5487,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a551)) | (~c2_1(a551)) | (~c1_1(a551)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5488,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)) | (~c1_1(a551)) | (~c1_1(a562))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5487, 5486])).
% 1.82/1.98 tff(5489,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5488, 156, 5361, 5482, 5470, 5471, 5481, 5480, 22, 5472])).
% 1.82/1.98 tff(5490,plain,(c0_1(a586) | c3_1(a548) | hskp33 | c3_1(a586) | c2_1(a548) | c0_1(a545) | (~hskp50)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(5491,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5490, 4935, 4934, 35, 2895, 24, 97, 794])).
% 1.82/1.98 tff(5492,plain,((~hskp50) | hskp33 | c3_1(a548) | c2_1(a548) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(5493,plain,
% 1.82/1.98 (~hskp50),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5492, 97, 2895, 24, 35])).
% 1.82/1.98 tff(5494,plain,
% 1.82/1.98 (c1_1(a548)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[4803, 110, 5283, 98])).
% 1.82/1.98 tff(5495,plain,
% 1.82/1.98 (c3_1(a545)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5009, 111, 5283, 24, 35, 2895, 98, 97])).
% 1.82/1.98 tff(5496,plain,
% 1.82/1.98 (hskp27),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[205, 194, 2896])).
% 1.82/1.98 tff(5497,plain,
% 1.82/1.98 (~c3_1(a586)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3996, 5496])).
% 1.82/1.98 tff(5498,plain,
% 1.82/1.98 (~c0_1(a586)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[3924, 5496])).
% 1.82/1.98 tff(5499,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c0_1(a586) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c0_1(a586) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c2_1(a586))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5500,plain,
% 1.82/1.98 ((hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a586) | c3_1(a586) | c0_1(a586)) <=> (hskp33 | c3_1(a548) | c0_1(a586) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c2_1(a586))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5501,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a548) | c0_1(a586) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c2_1(a586)))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5500])).
% 1.82/1.98 tff(5502,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a586) | c3_1(a586) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c0_1(a586) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c2_1(a586))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5501, 5499])).
% 1.82/1.98 tff(5503,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a586) | c3_1(a586) | c0_1(a586))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5504,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a548) | c0_1(a586) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | c2_1(a586)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5503, 5502])).
% 1.82/1.98 tff(5505,plain,
% 1.82/1.98 ($false),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5504, 156, 35, 2895, 87, 86, 5004, 85, 653, 2548])).
% 1.82/1.98 tff(5506,plain,(c2_1(a586) | hskp33 | c3_1(a548) | c0_1(a586) | c3_1(a586) | (~c0_1(a548)) | (~c1_1(a548))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.98 tff(5507,plain,
% 1.82/1.98 (c2_1(a586)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5506, 5498, 2895, 35, 5497, 5283, 5494])).
% 1.82/1.98 tff(5508,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a548) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a548) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5509,plain,
% 1.82/1.98 ((hskp32 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp32 | c3_1(a548) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5510,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a548) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5509])).
% 1.82/1.98 tff(5511,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a548) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5510, 5508])).
% 1.82/1.98 tff(5512,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5513,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a548) | c3_1(a586) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5512, 5511])).
% 1.82/1.98 tff(5514,plain,
% 1.82/1.98 (hskp32 | (~c2_1(a586))),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5513, 156, 5046, 2895, 5497, 5283, 4894, 5494])).
% 1.82/1.98 tff(5515,plain,
% 1.82/1.98 (hskp32),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5514, 5507])).
% 1.82/1.98 tff(5516,plain,
% 1.82/1.98 (((~hskp32) | c0_1(a596)) <=> ((~hskp32) | c0_1(a596))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5517,axiom,((~hskp32) | c0_1(a596)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.82/1.98 tff(5518,plain,
% 1.82/1.98 ((~hskp32) | c0_1(a596)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5517, 5516])).
% 1.82/1.98 tff(5519,plain,
% 1.82/1.98 ((~hskp32) | c0_1(a596)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5518, 5516])).
% 1.82/1.98 tff(5520,plain,
% 1.82/1.98 ((~hskp32) | c0_1(a596)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5519, 5516])).
% 1.82/1.98 tff(5521,plain,
% 1.82/1.98 ((~hskp32) | c0_1(a596)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5520, 5516])).
% 1.82/1.98 tff(5522,plain,
% 1.82/1.98 ((~hskp32) | c0_1(a596)),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5521, 5516])).
% 1.82/1.98 tff(5523,plain,
% 1.82/1.98 (c0_1(a596)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5522, 5515])).
% 1.82/1.98 tff(5524,plain,
% 1.82/1.98 (((~hskp32) | (~c3_1(a596))) <=> ((~hskp32) | (~c3_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5525,plain,
% 1.82/1.98 (((~c3_1(a596)) | (~hskp32)) <=> ((~hskp32) | (~c3_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5526,axiom,((~c3_1(a596)) | (~hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 1.82/1.98 tff(5527,plain,
% 1.82/1.98 ((~hskp32) | (~c3_1(a596))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5526, 5525])).
% 1.82/1.98 tff(5528,plain,
% 1.82/1.98 ((~hskp32) | (~c3_1(a596))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5527, 5524])).
% 1.82/1.98 tff(5529,plain,
% 1.82/1.98 (~c3_1(a596)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5528, 5515])).
% 1.82/1.98 tff(5530,plain,
% 1.82/1.98 (((~hskp32) | (~c2_1(a596))) <=> ((~hskp32) | (~c2_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5531,plain,
% 1.82/1.98 (((~c2_1(a596)) | (~hskp32)) <=> ((~hskp32) | (~c2_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5532,axiom,((~c2_1(a596)) | (~hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.82/1.98 tff(5533,plain,
% 1.82/1.98 ((~hskp32) | (~c2_1(a596))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 1.82/1.98 tff(5534,plain,
% 1.82/1.98 ((~hskp32) | (~c2_1(a596))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5533, 5530])).
% 1.82/1.98 tff(5535,plain,
% 1.82/1.98 (~c2_1(a596)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5534, 5515])).
% 1.82/1.98 tff(5536,plain,
% 1.82/1.98 (~hskp35),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5310, 5498, 5046, 194, 5497])).
% 1.82/1.98 tff(5537,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a596) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | c1_1(a596) | (~c0_1(a596)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a596) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | c1_1(a596) | (~c0_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5538,plain,
% 1.82/1.98 ((hskp35 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp35 | c2_1(a596) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | c1_1(a596) | (~c0_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5539,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a596) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | c1_1(a596) | (~c0_1(a596))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5538])).
% 1.82/1.98 tff(5540,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a596) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | c1_1(a596) | (~c0_1(a596)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5539, 5537])).
% 1.82/1.98 tff(5541,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/1.98 inference(quant_inst,[status(thm)],[])).
% 1.82/1.98 tff(5542,plain,
% 1.82/1.98 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a596) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | c1_1(a596) | (~c0_1(a596))),
% 1.82/1.98 inference(modus_ponens,[status(thm)],[5541, 5540])).
% 1.82/1.98 tff(5543,plain,
% 1.82/1.98 (c1_1(a596)),
% 1.82/1.98 inference(unit_resolution,[status(thm)],[5542, 156, 5536, 5523, 5046, 5535, 5497, 3950, 5507])).
% 1.82/1.98 tff(5544,assumption,(c1_1(a596)), introduced(assumption)).
% 1.82/1.98 tff(5545,assumption,(~c3_1(a596)), introduced(assumption)).
% 1.82/1.98 tff(5546,assumption,(c0_1(a596)), introduced(assumption)).
% 1.82/1.98 tff(5547,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a596) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a596)) | (~c0_1(a596)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a596) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5548,plain,
% 1.82/1.98 ((hskp33 | (~ndr1_0) | c3_1(a596) | (~c0_1(a596)) | (~c1_1(a596)) | c2_1(a554) | c3_1(a554) | c0_1(a554)) <=> (hskp33 | c3_1(a596) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/1.98 inference(rewrite,[status(thm)],[])).
% 1.82/1.98 tff(5549,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a596) | (~c0_1(a596)) | (~c1_1(a596)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a596) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a596)) | (~c0_1(a596))))),
% 1.82/1.98 inference(monotonicity,[status(thm)],[5548])).
% 1.82/1.98 tff(5550,plain,
% 1.82/1.98 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a596) | (~c0_1(a596)) | (~c1_1(a596)) | c2_1(a554) | c3_1(a554) | c0_1(a554))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a596) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/1.98 inference(transitivity,[status(thm)],[5549, 5547])).
% 1.82/1.99 tff(5551,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a596) | (~c0_1(a596)) | (~c1_1(a596)) | c2_1(a554) | c3_1(a554) | c0_1(a554))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5552,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a596) | c0_1(a554) | c2_1(a554) | (~ndr1_0) | c3_1(a554) | (~c1_1(a596)) | (~c0_1(a596))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5551, 5550])).
% 1.82/1.99 tff(5553,plain,
% 1.82/1.99 (c3_1(a554)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5552, 156, 35, 5546, 5545, 1306, 1305, 85, 5544])).
% 1.82/1.99 tff(5554,assumption,(~c2_1(a596)), introduced(assumption)).
% 1.82/1.99 tff(5555,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5556,plain,
% 1.82/1.99 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596))) <=> (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5557,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[5556])).
% 1.82/1.99 tff(5558,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[5557, 5555])).
% 1.82/1.99 tff(5559,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a554) | c0_1(a554) | (~c3_1(a554)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5560,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a554) | c1_1(a554) | (~ndr1_0) | (~c3_1(a554)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5559, 5558])).
% 1.82/1.99 tff(5561,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5560, 156, 5546, 5554, 87, 86, 1306, 1304, 609, 902, 5544, 5553])).
% 1.82/1.99 tff(5562,plain,((~hskp9) | (~c0_1(a596)) | c2_1(a596) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a596)) | hskp33 | c3_1(a596)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(5563,plain,
% 1.82/1.99 (~hskp9),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5562, 5543, 5498, 5535, 5497, 5507, 5529, 35, 5523])).
% 1.82/1.99 tff(5564,plain,
% 1.82/1.99 (~c3_1(a545)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5303, 5498, 5497, 35, 5046, 112, 97, 24, 5283, 5494])).
% 1.82/1.99 tff(5565,plain,
% 1.82/1.99 (c2_1(a545)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5009, 5564, 5283, 24, 35, 2895, 98, 97])).
% 1.82/1.99 tff(5566,plain,
% 1.82/1.99 (c1_1(a571)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5118, 156, 925, 924, 112, 923, 5081, 921, 765])).
% 1.82/1.99 tff(5567,plain,
% 1.82/1.99 (~hskp39),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5127, 87, 3797, 194, 86])).
% 1.82/1.99 tff(5568,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5409, 156, 5567, 3797, 924, 87, 86, 923, 281, 5566])).
% 1.82/1.99 tff(5569,plain,((~hskp17) | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | c1_1(a545) | (~c2_1(a545)) | c3_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(5570,plain,
% 1.82/1.99 (~hskp17),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5569, 5498, 5046, 5497, 112, 5565, 5564])).
% 1.82/1.99 tff(5571,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a545) | c2_1(a555) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a545) | c2_1(a555) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5572,plain,
% 1.82/1.99 (((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555))) <=> (c1_1(a545) | c2_1(a555) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5573,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a545) | c2_1(a555) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[5572])).
% 1.82/1.99 tff(5574,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a545) | c2_1(a555) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[5573, 5571])).
% 1.82/1.99 tff(5575,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a545) | c3_1(a545) | (~c2_1(a545)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5576,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a545) | c2_1(a555) | (~c2_1(a545)) | (~ndr1_0) | c3_1(a545) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5575, 5574])).
% 1.82/1.99 tff(5577,plain,
% 1.82/1.99 (c1_1(a555)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5576, 156, 257, 241, 112, 233, 5081, 921, 765])).
% 1.82/1.99 tff(5578,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a555) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a555) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5579,plain,
% 1.82/1.99 ((hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp39 | c2_1(a555) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5580,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a555) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a555)) | (~c1_1(a555))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[5579])).
% 1.82/1.99 tff(5581,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a555) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a555)) | (~c1_1(a555)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[5580, 5578])).
% 1.82/1.99 tff(5582,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5583,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a555) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a555)) | (~c1_1(a555))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5582, 5581])).
% 1.82/1.99 tff(5584,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5583, 156, 5567, 257, 3797, 233, 87, 86, 281, 5577])).
% 1.82/1.99 tff(5585,plain,((~hskp41) | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | c1_1(a545) | (~c2_1(a545)) | c3_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(5586,plain,
% 1.82/1.99 (~hskp41),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5585, 5498, 5046, 5497, 112, 5565, 5564])).
% 1.82/1.99 tff(5587,plain,
% 1.82/1.99 (hskp15),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[567, 5586, 5570, 110, 98, 5563])).
% 1.82/1.99 tff(5588,plain,
% 1.82/1.99 (~c2_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1255, 5587])).
% 1.82/1.99 tff(5589,plain,
% 1.82/1.99 (~c0_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1267, 5587])).
% 1.82/1.99 tff(5590,plain,
% 1.82/1.99 (c3_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5454, 156, 35, 2895, 5589, 5588, 5283, 85, 5494])).
% 1.82/1.99 tff(5591,plain,
% 1.82/1.99 (~c1_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1261, 5587])).
% 1.82/1.99 tff(5592,plain,
% 1.82/1.99 (~hskp16),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[373, 5586, 5563])).
% 1.82/1.99 tff(5593,plain,
% 1.82/1.99 (hskp18),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[382, 5592, 5570])).
% 1.82/1.99 tff(5594,plain,
% 1.82/1.99 (hskp37),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[430, 5593, 110, 98])).
% 1.82/1.99 tff(5595,plain,
% 1.82/1.99 (~c2_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[436, 5594])).
% 1.82/1.99 tff(5596,plain,
% 1.82/1.99 (c1_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[444, 5594])).
% 1.82/1.99 tff(5597,plain,
% 1.82/1.99 (~c0_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5447, 156, 5596, 5595, 5498, 5497, 5589, 5591, 609, 5507, 5590])).
% 1.82/1.99 tff(5598,plain,
% 1.82/1.99 (~c3_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[450, 5594])).
% 1.82/1.99 tff(5599,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5440, 156, 35, 2895, 5595, 5598, 5283, 85, 5494, 5597])).
% 1.82/1.99 tff(5600,plain,(c1_1(a545) | hskp33 | c3_1(a548) | hskp50 | hskp19 | c2_1(a548) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(5601,plain,
% 1.82/1.99 (c1_1(a545)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5600, 110, 2895, 35, 98, 24, 97])).
% 1.82/1.99 tff(5602,plain,
% 1.82/1.99 (hskp38),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1211, 5495, 111, 97, 5601])).
% 1.82/1.99 tff(5603,plain,
% 1.82/1.99 (c0_1(a547)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[677, 5602])).
% 1.82/1.99 tff(5604,plain,
% 1.82/1.99 (c2_1(a547)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[693, 5602])).
% 1.82/1.99 tff(5605,plain,
% 1.82/1.99 (c1_1(a547)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[685, 5602])).
% 1.82/1.99 tff(5606,plain,
% 1.82/1.99 (hskp39),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1586, 5605, 5604, 5495, 5603, 5601, 111, 97])).
% 1.82/1.99 tff(5607,plain,
% 1.82/1.99 (c1_1(a549)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[303, 5606])).
% 1.82/1.99 tff(5608,plain,
% 1.82/1.99 (c2_1(a549)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[311, 5606])).
% 1.82/1.99 tff(5609,plain,
% 1.82/1.99 (c3_1(a549)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[319, 5606])).
% 1.82/1.99 tff(5610,plain,
% 1.82/1.99 (hskp25),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1184, 156, 5609, 5608, 5607, 5601, 111, 55, 5495])).
% 1.82/1.99 tff(5611,plain,
% 1.82/1.99 (~c1_1(a582)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1190, 5610])).
% 1.82/1.99 tff(5612,plain,
% 1.82/1.99 (~c2_1(a582)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1196, 5610])).
% 1.82/1.99 tff(5613,plain,
% 1.82/1.99 (~c0_1(a582)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1288, 156, 110, 98, 5612, 5611, 34])).
% 1.82/1.99 tff(5614,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c2_1(a582) | c1_1(a582) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a582) | c1_1(a582) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c0_1(a582))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5615,plain,
% 1.82/1.99 ((hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a582) | c1_1(a582) | c0_1(a582)) <=> (hskp6 | c2_1(a582) | c1_1(a582) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c0_1(a582))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5616,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c2_1(a582) | c1_1(a582) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c0_1(a582)))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[5615])).
% 1.82/1.99 tff(5617,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a582) | c1_1(a582) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c0_1(a582))),
% 1.82/1.99 inference(transitivity,[status(thm)],[5616, 5614])).
% 1.82/1.99 tff(5618,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | c2_1(a582) | c1_1(a582) | c0_1(a582))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5619,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c2_1(a582) | c1_1(a582) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | c0_1(a582)),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 1.82/1.99 tff(5620,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5619, 156, 2896, 5601, 5612, 5611, 97, 1745, 5495, 5613])).
% 1.82/1.99 tff(5621,plain,(c2_1(a545) | c0_1(a545) | hskp50 | hskp19 | c2_1(a548) | hskp33 | c3_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(5622,plain,
% 1.82/1.99 (c2_1(a545)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5621, 110, 97, 98, 24, 35, 2895])).
% 1.82/1.99 tff(5623,plain,
% 1.82/1.99 (~hskp4),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1643, 5622])).
% 1.82/1.99 tff(5624,plain,
% 1.82/1.99 (hskp27),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[205, 5623, 2896])).
% 1.82/1.99 tff(5625,plain,
% 1.82/1.99 (~c3_1(a586)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3996, 5624])).
% 1.82/1.99 tff(5626,plain,
% 1.82/1.99 (~c0_1(a586)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3924, 5624])).
% 1.82/1.99 tff(5627,plain,
% 1.82/1.99 (c2_1(a586)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5506, 5626, 2895, 35, 5625, 5283, 5494])).
% 1.82/1.99 tff(5628,plain,
% 1.82/1.99 (hskp32),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5513, 156, 5046, 2895, 5625, 5283, 4894, 5627, 5494])).
% 1.82/1.99 tff(5629,plain,
% 1.82/1.99 (c0_1(a596)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5522, 5628])).
% 1.82/1.99 tff(5630,plain,
% 1.82/1.99 (~c3_1(a596)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5528, 5628])).
% 1.82/1.99 tff(5631,plain,
% 1.82/1.99 (~c2_1(a596)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5534, 5628])).
% 1.82/1.99 tff(5632,plain,
% 1.82/1.99 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a596)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a596)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5633,plain,
% 1.82/1.99 ((hskp50 | hskp19 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596))) <=> (hskp50 | hskp19 | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a596)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5634,plain,
% 1.82/1.99 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a596))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[5633])).
% 1.82/1.99 tff(5635,plain,
% 1.82/1.99 (((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596)))) <=> ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a596)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[5634, 5632])).
% 1.82/1.99 tff(5636,plain,
% 1.82/1.99 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp50 | hskp19 | (~ndr1_0) | c2_1(a596) | c1_1(a596) | (~c0_1(a596)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5637,plain,
% 1.82/1.99 ((~![U: $i] : (hskp50 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp50 | hskp19 | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a596))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5636, 5635])).
% 1.82/1.99 tff(5638,plain,
% 1.82/1.99 (c1_1(a596)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5637, 156, 110, 98, 5629, 5631, 34])).
% 1.82/1.99 tff(5639,plain,
% 1.82/1.99 (~hskp9),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5562, 5638, 5626, 5631, 5625, 5627, 5630, 35, 5629])).
% 1.82/1.99 tff(5640,plain,
% 1.82/1.99 (~hskp39),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5127, 5626, 5046, 5623, 5625])).
% 1.82/1.99 tff(5641,plain,
% 1.82/1.99 (hskp24),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5389, 5640, 2895, 5283])).
% 1.82/1.99 tff(5642,plain,
% 1.82/1.99 (~c3_1(a581)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3513, 5641])).
% 1.82/1.99 tff(5643,plain,
% 1.82/1.99 (~c1_1(a581)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3519, 5641])).
% 1.82/1.99 tff(5644,plain,
% 1.82/1.99 (c2_1(a581)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3541, 5641])).
% 1.82/1.99 tff(5645,plain,
% 1.82/1.99 (~hskp17),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5411, 5640, 5046, 5626, 5625, 5644, 5643, 5642])).
% 1.82/1.99 tff(5646,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a555) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a555) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5647,plain,
% 1.82/1.99 (((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555))) <=> (c2_1(a555) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5648,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a555) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[5647])).
% 1.82/1.99 tff(5649,plain,
% 1.82/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a555) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[5648, 5646])).
% 1.82/1.99 tff(5650,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5651,plain,
% 1.82/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a555) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5650, 5649])).
% 1.82/1.99 tff(5652,plain,
% 1.82/1.99 (c1_1(a555)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5651, 156, 257, 241, 5396, 233, 5395, 5394, 921])).
% 1.82/1.99 tff(5653,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5583, 156, 859, 257, 3797, 233, 87, 86, 281, 5652])).
% 1.82/1.99 tff(5654,plain,((~hskp41) | hskp39 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | (~c2_1(a581)) | c1_1(a581) | c3_1(a581)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(5655,plain,
% 1.82/1.99 (~hskp41),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5654, 5640, 5046, 5626, 5625, 5644, 5643, 5642])).
% 1.82/1.99 tff(5656,plain,
% 1.82/1.99 (hskp15),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[567, 5655, 5645, 110, 98, 5639])).
% 1.82/1.99 tff(5657,plain,
% 1.82/1.99 (~c2_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1255, 5656])).
% 1.82/1.99 tff(5658,plain,
% 1.82/1.99 (~c0_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1267, 5656])).
% 1.82/1.99 tff(5659,plain,
% 1.82/1.99 (c3_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5454, 156, 35, 2895, 5658, 5657, 5283, 85, 5494])).
% 1.82/1.99 tff(5660,plain,
% 1.82/1.99 (~c1_1(a569)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1261, 5656])).
% 1.82/1.99 tff(5661,plain,
% 1.82/1.99 (~hskp16),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[373, 5655, 5639])).
% 1.82/1.99 tff(5662,plain,
% 1.82/1.99 (hskp18),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[382, 5661, 5645])).
% 1.82/1.99 tff(5663,plain,
% 1.82/1.99 (hskp37),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[430, 5662, 110, 98])).
% 1.82/1.99 tff(5664,plain,
% 1.82/1.99 (~c2_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[436, 5663])).
% 1.82/1.99 tff(5665,plain,
% 1.82/1.99 (c1_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[444, 5663])).
% 1.82/1.99 tff(5666,plain,
% 1.82/1.99 (~c0_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5447, 156, 5665, 5664, 5626, 5625, 5658, 5660, 609, 5627, 5659])).
% 1.82/1.99 tff(5667,plain,
% 1.82/1.99 (~c3_1(a544)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[450, 5663])).
% 1.82/1.99 tff(5668,plain,
% 1.82/1.99 ($false),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5440, 156, 35, 2895, 5664, 5667, 5283, 85, 5494, 5666])).
% 1.82/1.99 tff(5669,plain,(hskp50 | hskp33 | c3_1(a548) | hskp19 | c2_1(a548) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.99 tff(5670,plain,
% 1.82/1.99 (hskp19),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5669, 5493, 2895, 35, 24, 97])).
% 1.82/1.99 tff(5671,plain,
% 1.82/1.99 (~c0_1(a573)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1691, 5670])).
% 1.82/1.99 tff(5672,plain,
% 1.82/1.99 (~c2_1(a573)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1704, 5670])).
% 1.82/1.99 tff(5673,plain,
% 1.82/1.99 (~c1_1(a573)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1675, 5670])).
% 1.82/1.99 tff(5674,plain,
% 1.82/1.99 (hskp28),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5069, 5670])).
% 1.82/1.99 tff(5675,plain,
% 1.82/1.99 (~c0_1(a589)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[177, 5674])).
% 1.82/1.99 tff(5676,plain,
% 1.82/1.99 (c3_1(a589)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[185, 5674])).
% 1.82/1.99 tff(5677,plain,
% 1.82/1.99 (~c1_1(a589)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[1751, 156, 2896, 5676, 5675, 5672, 5671, 5673, 1745])).
% 1.82/1.99 tff(5678,plain,
% 1.82/1.99 (hskp27),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3077, 5670, 35, 2896, 97])).
% 1.82/1.99 tff(5679,plain,
% 1.82/1.99 (~c3_1(a586)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3996, 5678])).
% 1.82/1.99 tff(5680,plain,
% 1.82/1.99 (~c0_1(a586)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3924, 5678])).
% 1.82/1.99 tff(5681,plain,
% 1.82/1.99 (hskp26),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3164, 156, 5676, 5046, 5675, 5680, 5679, 1686, 5677])).
% 1.82/1.99 tff(5682,plain,
% 1.82/1.99 (c3_1(a573)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3151, 5681, 5672, 5671, 35])).
% 1.82/1.99 tff(5683,plain,
% 1.82/1.99 (c2_1(a586)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[3104, 5681, 5680, 5679, 35])).
% 1.82/1.99 tff(5684,plain,
% 1.82/1.99 (^[V: $i, U: $i] : refl((hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.82/1.99 inference(bind,[status(th)],[])).
% 1.82/1.99 tff(5685,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.82/1.99 inference(quant_intro,[status(thm)],[5684])).
% 1.82/1.99 tff(5686,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5687,plain,
% 1.82/1.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp47) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp47))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.82/1.99 inference(bind,[status(th)],[])).
% 1.82/1.99 tff(5688,plain,
% 1.82/1.99 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp47) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.82/1.99 inference(quant_intro,[status(thm)],[5687])).
% 1.82/1.99 tff(5689,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause249')).
% 1.82/1.99 tff(5690,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5689, 5688])).
% 1.82/1.99 tff(5691,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5690, 5686])).
% 1.82/1.99 tff(5692,plain,(
% 1.82/1.99 ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.82/1.99 inference(skolemize,[status(sab)],[5691])).
% 1.82/1.99 tff(5693,plain,
% 1.82/1.99 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5692, 5685])).
% 1.82/1.99 tff(5694,plain,
% 1.82/1.99 (c2_1(a589)),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[171, 5674])).
% 1.82/1.99 tff(5695,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | c0_1(a589) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp47 | c0_1(a589) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5696,plain,
% 1.82/1.99 ((hskp47 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp47 | c0_1(a589) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5697,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | c0_1(a589) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589))))),
% 1.82/1.99 inference(monotonicity,[status(thm)],[5696])).
% 1.82/1.99 tff(5698,plain,
% 1.82/1.99 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp47 | c0_1(a589) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)))),
% 1.82/1.99 inference(transitivity,[status(thm)],[5697, 5695])).
% 1.82/1.99 tff(5699,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.82/1.99 inference(quant_inst,[status(thm)],[])).
% 1.82/1.99 tff(5700,plain,
% 1.82/1.99 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp47 | c0_1(a589) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589))),
% 1.82/1.99 inference(modus_ponens,[status(thm)],[5699, 5698])).
% 1.82/1.99 tff(5701,plain,
% 1.82/1.99 (hskp47 | (~c2_1(a586))),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5700, 156, 5694, 5676, 5046, 5675, 5679, 5693])).
% 1.82/1.99 tff(5702,plain,
% 1.82/1.99 (hskp47),
% 1.82/1.99 inference(unit_resolution,[status(thm)],[5701, 5683])).
% 1.82/1.99 tff(5703,plain,
% 1.82/1.99 (((~hskp47) | (~c2_1(a564))) <=> ((~hskp47) | (~c2_1(a564)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5704,plain,
% 1.82/1.99 (((~c2_1(a564)) | (~hskp47)) <=> ((~hskp47) | (~c2_1(a564)))),
% 1.82/1.99 inference(rewrite,[status(thm)],[])).
% 1.82/1.99 tff(5705,axiom,((~c2_1(a564)) | (~hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.82/2.00 tff(5706,plain,
% 1.82/2.00 ((~hskp47) | (~c2_1(a564))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5705, 5704])).
% 1.82/2.00 tff(5707,plain,
% 1.82/2.00 ((~hskp47) | (~c2_1(a564))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5706, 5703])).
% 1.82/2.00 tff(5708,plain,
% 1.82/2.00 (~c2_1(a564)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5707, 5702])).
% 1.82/2.00 tff(5709,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5710,plain,
% 1.82/2.00 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))) <=> (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5711,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[5710])).
% 1.82/2.00 tff(5712,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589))),
% 1.82/2.00 inference(transitivity,[status(thm)],[5711, 5709])).
% 1.82/2.00 tff(5713,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(5714,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a589) | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5713, 5712])).
% 1.82/2.00 tff(5715,plain,
% 1.82/2.00 ((~c1_1(a548)) | (~c2_1(a586))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5714, 156, 5676, 5675, 5680, 5679, 24, 5283, 609, 5677])).
% 1.82/2.00 tff(5716,plain,
% 1.82/2.00 (~c1_1(a548)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5715, 5683])).
% 1.82/2.00 tff(5717,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a548) | c2_1(a573) | c0_1(a573) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a548) | c2_1(a573) | c0_1(a573) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a573)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5718,plain,
% 1.82/2.00 ((hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a548) | c1_1(a548) | c3_1(a548)) <=> (hskp38 | c3_1(a548) | c2_1(a573) | c0_1(a573) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a573)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5719,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a548) | c2_1(a573) | c0_1(a573) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a573))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[5718])).
% 1.82/2.00 tff(5720,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a548) | c2_1(a573) | c0_1(a573) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a573)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[5719, 5717])).
% 1.82/2.00 tff(5721,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a548) | c1_1(a548) | c3_1(a548))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(5722,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a548) | c2_1(a573) | c0_1(a573) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a573))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5721, 5720])).
% 1.82/2.00 tff(5723,plain,
% 1.82/2.00 (hskp38 | c1_1(a548) | (~c3_1(a573))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5722, 156, 2895, 5672, 5671, 24, 663])).
% 1.82/2.00 tff(5724,plain,
% 1.82/2.00 (hskp38),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5723, 5682, 5716])).
% 1.82/2.00 tff(5725,plain,
% 1.82/2.00 (c0_1(a547)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[677, 5724])).
% 1.82/2.00 tff(5726,plain,
% 1.82/2.00 (c1_1(a547)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[685, 5724])).
% 1.82/2.00 tff(5727,plain,
% 1.82/2.00 (c2_1(a547)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[693, 5724])).
% 1.82/2.00 tff(5728,plain,
% 1.82/2.00 (((~hskp47) | c1_1(a564)) <=> ((~hskp47) | c1_1(a564))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5729,axiom,((~hskp47) | c1_1(a564)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.82/2.00 tff(5730,plain,
% 1.82/2.00 ((~hskp47) | c1_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.82/2.00 tff(5731,plain,
% 1.82/2.00 ((~hskp47) | c1_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5730, 5728])).
% 1.82/2.00 tff(5732,plain,
% 1.82/2.00 ((~hskp47) | c1_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5731, 5728])).
% 1.82/2.00 tff(5733,plain,
% 1.82/2.00 ((~hskp47) | c1_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5732, 5728])).
% 1.82/2.00 tff(5734,plain,
% 1.82/2.00 ((~hskp47) | c1_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5733, 5728])).
% 1.82/2.00 tff(5735,plain,
% 1.82/2.00 (c1_1(a564)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5734, 5702])).
% 1.82/2.00 tff(5736,plain,
% 1.82/2.00 (((~hskp47) | c0_1(a564)) <=> ((~hskp47) | c0_1(a564))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5737,axiom,((~hskp47) | c0_1(a564)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.82/2.00 tff(5738,plain,
% 1.82/2.00 ((~hskp47) | c0_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5737, 5736])).
% 1.82/2.00 tff(5739,plain,
% 1.82/2.00 ((~hskp47) | c0_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5738, 5736])).
% 1.82/2.00 tff(5740,plain,
% 1.82/2.00 ((~hskp47) | c0_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5739, 5736])).
% 1.82/2.00 tff(5741,plain,
% 1.82/2.00 ((~hskp47) | c0_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5740, 5736])).
% 1.82/2.00 tff(5742,plain,
% 1.82/2.00 ((~hskp47) | c0_1(a564)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5741, 5736])).
% 1.82/2.00 tff(5743,plain,
% 1.82/2.00 (c0_1(a564)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5742, 5702])).
% 1.82/2.00 tff(5744,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a564)) | (~c0_1(a564)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a564)) | (~c0_1(a564)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5745,plain,
% 1.82/2.00 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564))) <=> (c2_1(a564) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a564)) | (~c0_1(a564)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5746,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a564)) | (~c0_1(a564)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[5745])).
% 1.82/2.00 tff(5747,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a564)) | (~c0_1(a564)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[5746, 5744])).
% 1.82/2.00 tff(5748,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(5749,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c2_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c1_1(a564)) | (~c0_1(a564)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 1.82/2.00 tff(5750,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5749, 156, 5743, 5735, 5727, 5726, 5725, 5708, 5672, 5673, 707, 5682])).
% 1.82/2.00 tff(5751,plain,(c0_1(a545) | c3_1(a548) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(5752,plain,
% 1.82/2.00 (c0_1(a545)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5751, 2895, 24, 35])).
% 1.82/2.00 tff(5753,plain,
% 1.82/2.00 (~hskp4),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1666, 5752])).
% 1.82/2.00 tff(5754,plain,
% 1.82/2.00 (hskp27),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[205, 5753, 2896])).
% 1.82/2.00 tff(5755,plain,
% 1.82/2.00 (~c3_1(a586)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3996, 5754])).
% 1.82/2.00 tff(5756,plain,
% 1.82/2.00 (~c0_1(a586)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3924, 5754])).
% 1.82/2.00 tff(5757,plain,
% 1.82/2.00 (~hskp35),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5310, 5756, 5046, 5753, 5755])).
% 1.82/2.00 tff(5758,plain,
% 1.82/2.00 (~hskp39),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5127, 5756, 5046, 5753, 5755])).
% 1.82/2.00 tff(5759,plain,
% 1.82/2.00 (~hskp28),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5066, 5056, 5046, 5753, 5755, 5756])).
% 1.82/2.00 tff(5760,plain,
% 1.82/2.00 (~hskp15),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1276, 5759])).
% 1.82/2.00 tff(5761,plain,
% 1.82/2.00 (c1_1(a548)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3668, 5759, 56])).
% 1.82/2.00 tff(5762,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5262, 5761, 5760, 5753, 2895, 56, 5059, 5046, 5755, 5756, 5056])).
% 1.82/2.00 tff(5763,plain,(c0_1(a548) | c3_1(a548) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(5764,plain,
% 1.82/2.00 (c0_1(a548)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5763, 2895, 24, 35])).
% 1.82/2.00 tff(5765,plain,
% 1.82/2.00 (hskp24),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5389, 5764, 2895, 5758])).
% 1.82/2.00 tff(5766,plain,
% 1.82/2.00 (~c3_1(a581)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3513, 5765])).
% 1.82/2.00 tff(5767,plain,
% 1.82/2.00 (~c1_1(a581)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3519, 5765])).
% 1.82/2.00 tff(5768,plain,
% 1.82/2.00 (c2_1(a581)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3541, 5765])).
% 1.82/2.00 tff(5769,plain,
% 1.82/2.00 (~hskp17),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5411, 5768, 5046, 5756, 5755, 5758, 5767, 5766])).
% 1.82/2.00 tff(5770,plain,
% 1.82/2.00 (hskp19),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[4803, 57, 5004, 110])).
% 1.82/2.00 tff(5771,plain,
% 1.82/2.00 (hskp28),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5069, 5770])).
% 1.82/2.00 tff(5772,plain,
% 1.82/2.00 (~hskp35),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5310, 87, 3797, 23, 86])).
% 1.82/2.00 tff(5773,plain,
% 1.82/2.00 ((~c0_1(a548)) | c1_1(a548) | (~c2_1(a586))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5317, 156, 5772, 3797, 86, 24, 3950])).
% 1.82/2.00 tff(5774,plain,
% 1.82/2.00 (~c2_1(a586)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5773, 57, 5004])).
% 1.82/2.00 tff(5775,plain,
% 1.82/2.00 (~hskp26),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3104, 5774, 87, 86, 35])).
% 1.82/2.00 tff(5776,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5066, 5775, 5771, 3797, 23, 86, 87])).
% 1.82/2.00 tff(5777,plain,(c1_1(a548) | (~c1_1(a586)) | hskp4 | c3_1(a586) | c0_1(a586) | hskp33 | (~c0_1(a548)) | c2_1(a548) | hskp50), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(5778,plain,
% 1.82/2.00 (c1_1(a548)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5777, 110, 5753, 5755, 5756, 35, 5764, 24, 5046])).
% 1.82/2.00 tff(5779,plain,
% 1.82/2.00 (c2_1(a586)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5506, 5778, 2895, 35, 5755, 5764, 5756])).
% 1.82/2.00 tff(5780,plain,
% 1.82/2.00 (hskp32 | (~c0_1(a548)) | (~c1_1(a548)) | (~c2_1(a586))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5513, 156, 5046, 2895, 5755, 4894])).
% 1.82/2.00 tff(5781,plain,
% 1.82/2.00 (hskp32),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5780, 5779, 5764, 5778])).
% 1.82/2.00 tff(5782,plain,
% 1.82/2.00 (~c2_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5534, 5781])).
% 1.82/2.00 tff(5783,plain,
% 1.82/2.00 (c0_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5522, 5781])).
% 1.82/2.00 tff(5784,plain,
% 1.82/2.00 (c1_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5542, 156, 5757, 5783, 5046, 5782, 5755, 3950, 5779])).
% 1.82/2.00 tff(5785,plain,
% 1.82/2.00 (hskp26),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5066, 1967, 5046, 5753, 5755, 5756])).
% 1.82/2.00 tff(5786,plain,
% 1.82/2.00 (c2_1(a586)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3104, 5785, 5756, 5755, 35])).
% 1.82/2.00 tff(5787,plain,
% 1.82/2.00 ((~c0_1(a548)) | c1_1(a548) | (~c2_1(a586))),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5317, 156, 5757, 5046, 5755, 24, 3950])).
% 1.82/2.00 tff(5788,plain,
% 1.82/2.00 (c1_1(a548)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5787, 5786, 5764])).
% 1.82/2.00 tff(5789,plain,
% 1.82/2.00 (c3_1(a569)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5454, 156, 35, 2895, 1268, 1256, 5764, 85, 5788])).
% 1.82/2.00 tff(5790,plain,
% 1.82/2.00 (hskp32),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5780, 5786, 5764, 5788])).
% 1.82/2.00 tff(5791,plain,
% 1.82/2.00 (~c2_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5534, 5790])).
% 1.82/2.00 tff(5792,plain,
% 1.82/2.00 (c0_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5522, 5790])).
% 1.82/2.00 tff(5793,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5794,plain,
% 1.82/2.00 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596))) <=> (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5795,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[5794])).
% 1.82/2.00 tff(5796,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[5795, 5793])).
% 1.82/2.00 tff(5797,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(5798,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a569) | c1_1(a569) | (~ndr1_0) | (~c3_1(a569)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5797, 5796])).
% 1.82/2.00 tff(5799,plain,
% 1.82/2.00 (~c1_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5798, 156, 5792, 5791, 5756, 5755, 1268, 1262, 609, 5786, 5789])).
% 1.82/2.00 tff(5800,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5542, 156, 5757, 5792, 5046, 5791, 5755, 3950, 5786, 5799])).
% 1.82/2.00 tff(5801,plain,((~hskp15) | hskp33 | c3_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(5802,plain,
% 1.82/2.00 (~hskp15),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5801, 2895, 35, 24])).
% 1.82/2.00 tff(5803,plain,
% 1.82/2.00 (~hskp41),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5654, 5768, 5046, 5756, 5755, 5758, 5767, 5766])).
% 1.82/2.00 tff(5804,plain,
% 1.82/2.00 (~c3_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5528, 5781])).
% 1.82/2.00 tff(5805,plain,
% 1.82/2.00 (~hskp9),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5562, 5784, 5756, 5782, 5755, 5779, 5804, 35, 5783])).
% 1.82/2.00 tff(5806,plain,
% 1.82/2.00 (hskp19),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[567, 5805, 5769, 5803, 5802, 110])).
% 1.82/2.00 tff(5807,plain,
% 1.82/2.00 (~c0_1(a573)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1691, 5806])).
% 1.82/2.00 tff(5808,plain,
% 1.82/2.00 (~c2_1(a573)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1704, 5806])).
% 1.82/2.00 tff(5809,plain,
% 1.82/2.00 (hskp28),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5069, 5806])).
% 1.82/2.00 tff(5810,plain,
% 1.82/2.00 (hskp26),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5066, 5809, 5046, 5753, 5755, 5756])).
% 1.82/2.00 tff(5811,plain,
% 1.82/2.00 (c3_1(a573)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[3151, 5810, 5808, 5807, 35])).
% 1.82/2.00 tff(5812,plain,
% 1.82/2.00 (~c1_1(a573)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1675, 5806])).
% 1.82/2.00 tff(5813,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5814,plain,
% 1.82/2.00 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596))) <=> (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5815,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[5814])).
% 1.82/2.00 tff(5816,plain,
% 1.82/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[5815, 5813])).
% 1.82/2.00 tff(5817,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(5818,plain,
% 1.82/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c0_1(a586) | c3_1(a586) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | (~c2_1(a586)) | (~c1_1(a596)) | (~c0_1(a596))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5817, 5816])).
% 1.82/2.00 tff(5819,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5818, 156, 5783, 5782, 5756, 5755, 5807, 5812, 609, 5811, 5779, 5784])).
% 1.82/2.00 tff(5820,plain,(hskp50 | hskp33 | c3_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(5821,plain,
% 1.82/2.00 (hskp50),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5820, 2895, 35, 24])).
% 1.82/2.00 tff(5822,plain,
% 1.82/2.00 (c0_1(a574)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[815, 5821])).
% 1.82/2.00 tff(5823,plain,
% 1.82/2.00 (c1_1(a574)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[807, 5821])).
% 1.82/2.00 tff(5824,plain,
% 1.82/2.00 (c2_1(a586)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[2766, 5821, 5756, 5755, 35])).
% 1.82/2.00 tff(5825,plain,
% 1.82/2.00 (~c3_1(a574)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[799, 5821])).
% 1.82/2.00 tff(5826,plain,
% 1.82/2.00 (~hskp25),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5379, 5825, 5046, 5757, 5824, 5823, 5822, 5755, 35])).
% 1.82/2.00 tff(5827,plain,
% 1.82/2.00 (~hskp16),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5107, 5826, 5046, 5753, 5755, 5756])).
% 1.82/2.00 tff(5828,plain,
% 1.82/2.00 (hskp18),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[382, 5827, 5769])).
% 1.82/2.00 tff(5829,plain,
% 1.82/2.00 (~c1_1(a572)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[389, 5828])).
% 1.82/2.00 tff(5830,plain,
% 1.82/2.00 (c0_1(a572)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[397, 5828])).
% 1.82/2.00 tff(5831,plain,
% 1.82/2.00 (c2_1(a572)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5426, 5830, 5046, 5824, 5755, 5829, 5757])).
% 1.82/2.00 tff(5832,plain,
% 1.82/2.00 (~c3_1(a572)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[420, 5828])).
% 1.82/2.00 tff(5833,plain,
% 1.82/2.00 (hskp37),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[428, 156, 5830, 5832, 5829, 415, 5831])).
% 1.82/2.00 tff(5834,plain,
% 1.82/2.00 (~c3_1(a544)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[450, 5833])).
% 1.82/2.00 tff(5835,plain,
% 1.82/2.00 (~c2_1(a544)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[436, 5833])).
% 1.82/2.00 tff(5836,plain,
% 1.82/2.00 (c1_1(a544)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[444, 5833])).
% 1.82/2.00 tff(5837,plain,
% 1.82/2.00 (~hskp7),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5466, 5836, 5767, 5766, 5768, 5802, 5835, 5834])).
% 1.82/2.00 tff(5838,plain,
% 1.82/2.00 (hskp40 | hskp7),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[521, 156, 5830, 5829, 513, 5831])).
% 1.82/2.00 tff(5839,plain,
% 1.82/2.00 (hskp40),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5838, 5837])).
% 1.82/2.00 tff(5840,plain,
% 1.82/2.00 (c3_1(a551)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[540, 5839])).
% 1.82/2.00 tff(5841,plain,
% 1.82/2.00 (c2_1(a551)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[532, 5839])).
% 1.82/2.00 tff(5842,plain,
% 1.82/2.00 (c1_1(a551)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[552, 5841, 5834, 5802, 5836, 5835, 5840])).
% 1.82/2.00 tff(5843,plain,
% 1.82/2.00 (hskp46),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5478, 156, 5046, 5830, 5756, 5829, 2215, 5824, 5831])).
% 1.82/2.00 tff(5844,plain,
% 1.82/2.00 (~c0_1(a562)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[64, 5843])).
% 1.82/2.00 tff(5845,plain,
% 1.82/2.00 (~c3_1(a562)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[270, 5843])).
% 1.82/2.00 tff(5846,plain,
% 1.82/2.00 (c1_1(a562)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[288, 5843])).
% 1.82/2.00 tff(5847,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5488, 156, 5753, 5846, 5840, 5841, 5845, 5844, 22, 5842])).
% 1.82/2.00 tff(5848,plain,(c3_1(a548) | hskp33 | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(5849,plain,
% 1.82/2.00 (c3_1(a548)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5848, 35, 24])).
% 1.82/2.00 tff(5850,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5851,plain,
% 1.82/2.00 ((hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548))) <=> (hskp26 | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5852,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[5851])).
% 1.82/2.00 tff(5853,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[5852, 5850])).
% 1.82/2.00 tff(5854,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(5855,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a586) | c3_1(a586) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5854, 5853])).
% 1.82/2.00 tff(5856,plain,
% 1.82/2.00 ($false),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5855, 156, 1661, 3797, 249, 87, 86, 56, 1686, 57])).
% 1.82/2.00 tff(5857,plain,(c1_1(a548) | hskp26 | (~c1_1(a586)) | (~c3_1(a548)) | c0_1(a586) | c3_1(a586) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.00 tff(5858,plain,
% 1.82/2.00 (hskp26),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5857, 57, 4884, 5849, 87, 86, 56])).
% 1.82/2.00 tff(5859,plain,
% 1.82/2.00 (~c3_1(a584)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1620, 5858])).
% 1.82/2.00 tff(5860,plain,
% 1.82/2.00 (c1_1(a584)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1637, 5858])).
% 1.82/2.00 tff(5861,plain,
% 1.82/2.00 (c0_1(a584)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[1629, 5858])).
% 1.82/2.00 tff(5862,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5863,plain,
% 1.82/2.00 ((hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp32 | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(5864,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.82/2.00 inference(monotonicity,[status(thm)],[5863])).
% 1.82/2.00 tff(5865,plain,
% 1.82/2.00 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/2.00 inference(transitivity,[status(thm)],[5864, 5862])).
% 1.82/2.00 tff(5866,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/2.00 inference(quant_inst,[status(thm)],[])).
% 1.82/2.00 tff(5867,plain,
% 1.82/2.00 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a586) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[5866, 5865])).
% 1.82/2.00 tff(5868,plain,
% 1.82/2.00 (hskp32),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5867, 156, 4884, 5861, 5860, 86, 5859, 4894, 902])).
% 1.82/2.00 tff(5869,plain,
% 1.82/2.00 (~c2_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5534, 5868])).
% 1.82/2.00 tff(5870,plain,
% 1.82/2.00 (c0_1(a596)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[5522, 5868])).
% 1.82/2.00 tff(5871,plain,
% 1.82/2.00 (~c1_1(a548)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2559, 23, 5849, 24, 56])).
% 1.82/2.01 tff(5872,plain,
% 1.82/2.01 (hskp28),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[3668, 5871, 56])).
% 1.82/2.01 tff(5873,plain,
% 1.82/2.01 (hskp26),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5066, 5872, 4884, 23, 86, 87])).
% 1.82/2.01 tff(5874,plain,
% 1.82/2.01 (c2_1(a586)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[3104, 5873, 87, 86, 35])).
% 1.82/2.01 tff(5875,plain,
% 1.82/2.01 (c3_1(a589)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[185, 5872])).
% 1.82/2.01 tff(5876,plain,
% 1.82/2.01 (c2_1(a589)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[171, 5872])).
% 1.82/2.01 tff(5877,plain,
% 1.82/2.01 (~c1_1(a589)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[3914, 156, 23, 5876, 5875, 4884, 87, 86, 22])).
% 1.82/2.01 tff(5878,plain,
% 1.82/2.01 (~c0_1(a589)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[177, 5872])).
% 1.82/2.01 tff(5879,plain,
% 1.82/2.01 (hskp47),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5700, 156, 5876, 5875, 4884, 5878, 86, 5693, 5874])).
% 1.82/2.01 tff(5880,plain,
% 1.82/2.01 (~c2_1(a564)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5707, 5879])).
% 1.82/2.01 tff(5881,plain,
% 1.82/2.01 (c1_1(a564)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5734, 5879])).
% 1.82/2.01 tff(5882,plain,
% 1.82/2.01 (c0_1(a564)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5742, 5879])).
% 1.82/2.01 tff(5883,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a564)) | (~c0_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5884,plain,
% 1.82/2.01 (((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564))) <=> (c2_1(a564) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5885,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a564)) | (~c0_1(a564))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[5884])).
% 1.82/2.01 tff(5886,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[5885, 5883])).
% 1.82/2.01 tff(5887,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(5888,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c0_1(a589) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a589)) | c1_1(a589) | (~c1_1(a564)) | (~c0_1(a564))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5887, 5886])).
% 1.82/2.01 tff(5889,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5888, 156, 5882, 5881, 5875, 5880, 5878, 87, 86, 609, 5877, 5874])).
% 1.82/2.01 tff(5890,plain,(hskp4 | c0_1(a586) | c3_1(a586) | hskp33 | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(5891,plain,
% 1.82/2.01 (hskp4),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5890, 56, 86, 35, 87, 24])).
% 1.82/2.01 tff(5892,plain,
% 1.82/2.01 (~c0_1(a545)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1666, 5891])).
% 1.82/2.01 tff(5893,plain,
% 1.82/2.01 (hskp38),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1659, 5858, 35, 5891, 5892])).
% 1.82/2.01 tff(5894,plain,
% 1.82/2.01 (c0_1(a547)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[677, 5893])).
% 1.82/2.01 tff(5895,plain,
% 1.82/2.01 (c1_1(a547)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[685, 5893])).
% 1.82/2.01 tff(5896,plain,
% 1.82/2.01 (c2_1(a547)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[693, 5893])).
% 1.82/2.01 tff(5897,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a596)) | (~c0_1(a596)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a596)) | (~c0_1(a596)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5898,plain,
% 1.82/2.01 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596))) <=> (c2_1(a596) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a596)) | (~c0_1(a596)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5899,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a596) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a596)) | (~c0_1(a596)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[5898])).
% 1.82/2.01 tff(5900,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a596)) | (~c0_1(a596)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[5899, 5897])).
% 1.82/2.01 tff(5901,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(5902,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a596) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a596)) | (~c0_1(a596)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5901, 5900])).
% 1.82/2.01 tff(5903,plain,
% 1.82/2.01 (~c1_1(a596)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5902, 156, 5896, 5895, 5894, 5870, 5849, 5869, 24, 707, 57])).
% 1.82/2.01 tff(5904,plain,
% 1.82/2.01 (~c3_1(a596)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5528, 5868])).
% 1.82/2.01 tff(5905,plain,
% 1.82/2.01 (~hskp0),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2694, 5894, 5849, 57, 5895, 24, 5896])).
% 1.82/2.01 tff(5906,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5907,plain,
% 1.82/2.01 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a596) | c1_1(a596) | c3_1(a596)) <=> (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5908,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[5907])).
% 1.82/2.01 tff(5909,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[5908, 5906])).
% 1.82/2.01 tff(5910,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a596) | c1_1(a596) | c3_1(a596))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(5911,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5910, 5909])).
% 1.82/2.01 tff(5912,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5911, 156, 5905, 5896, 5895, 5894, 5904, 5869, 108, 5903])).
% 1.82/2.01 tff(5913,plain,(c1_1(a548) | c2_1(a548) | c3_1(a586) | (~c2_1(a586)) | hskp33 | c0_1(a586) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(5914,plain,
% 1.82/2.01 (c1_1(a548)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5913, 902, 86, 24, 35, 87, 56])).
% 1.82/2.01 tff(5915,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5916,plain,
% 1.82/2.01 ((hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5917,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[5916])).
% 1.82/2.01 tff(5918,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[5917, 5915])).
% 1.82/2.01 tff(5919,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(5920,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a586) | c3_1(a586) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 1.82/2.01 tff(5921,plain,
% 1.82/2.01 (hskp39 | c0_1(a586) | (~c1_1(a548))),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5920, 156, 4884, 5849, 86, 24, 281])).
% 1.82/2.01 tff(5922,plain,
% 1.82/2.01 (hskp39),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5921, 5914, 87])).
% 1.82/2.01 tff(5923,plain,
% 1.82/2.01 (c1_1(a549)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[303, 5922])).
% 1.82/2.01 tff(5924,plain,
% 1.82/2.01 (c2_1(a549)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[311, 5922])).
% 1.82/2.01 tff(5925,plain,
% 1.82/2.01 (c3_1(a549)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[319, 5922])).
% 1.82/2.01 tff(5926,plain,
% 1.82/2.01 (hskp25),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4507, 156, 5925, 5924, 5923, 5849, 24, 55, 5914])).
% 1.82/2.01 tff(5927,plain,
% 1.82/2.01 (~c1_1(a582)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1190, 5926])).
% 1.82/2.01 tff(5928,plain,
% 1.82/2.01 (~c2_1(a582)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1196, 5926])).
% 1.82/2.01 tff(5929,plain,
% 1.82/2.01 (~c3_1(a582)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1202, 5926])).
% 1.82/2.01 tff(5930,plain,
% 1.82/2.01 (hskp34),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[4519, 5914, 5849, 24, 56])).
% 1.82/2.01 tff(5931,plain,
% 1.82/2.01 (~c1_1(a537)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1124, 5930])).
% 1.82/2.01 tff(5932,plain,
% 1.82/2.01 (c3_1(a537)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1132, 5930])).
% 1.82/2.01 tff(5933,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5934,plain,
% 1.82/2.01 (((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5935,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[5934])).
% 1.82/2.01 tff(5936,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[5935, 5933])).
% 1.82/2.01 tff(5937,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(5938,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a537) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5937, 5936])).
% 1.82/2.01 tff(5939,plain,
% 1.82/2.01 (~c2_1(a537)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5938, 156, 5932, 5849, 5931, 5929, 5928, 5927, 24, 45, 5914])).
% 1.82/2.01 tff(5940,plain,
% 1.82/2.01 (c0_1(a537)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[1147, 5930])).
% 1.82/2.01 tff(5941,plain,
% 1.82/2.01 (hskp51),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2631, 156, 5940, 5932, 5931, 5929, 5928, 5927, 2608])).
% 1.82/2.01 tff(5942,plain,
% 1.82/2.01 (~c2_1(a583)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2637, 5941])).
% 1.82/2.01 tff(5943,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5944,plain,
% 1.82/2.01 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5945,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[5944])).
% 1.82/2.01 tff(5946,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[5945, 5943])).
% 1.82/2.01 tff(5947,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(5948,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5947, 5946])).
% 1.82/2.01 tff(5949,plain,
% 1.82/2.01 (hskp38),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5948, 156, 5849, 5929, 5928, 5927, 24, 56, 663])).
% 1.82/2.01 tff(5950,plain,
% 1.82/2.01 (c0_1(a547)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[677, 5949])).
% 1.82/2.01 tff(5951,plain,
% 1.82/2.01 (c1_1(a547)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[685, 5949])).
% 1.82/2.01 tff(5952,plain,
% 1.82/2.01 (c2_1(a547)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[693, 5949])).
% 1.82/2.01 tff(5953,plain,
% 1.82/2.01 (c0_1(a583)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2653, 5941])).
% 1.82/2.01 tff(5954,plain,
% 1.82/2.01 (~c1_1(a583)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2672, 156, 5953, 5952, 5951, 5950, 5932, 5942, 5931, 707, 5939])).
% 1.82/2.01 tff(5955,plain,
% 1.82/2.01 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(5956,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[5955])).
% 1.82/2.01 tff(5957,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5958,plain,
% 1.82/2.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(5959,plain,
% 1.82/2.01 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[5958])).
% 1.82/2.01 tff(5960,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause240')).
% 1.82/2.01 tff(5961,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5960, 5959])).
% 1.82/2.01 tff(5962,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5961, 5957])).
% 1.82/2.01 tff(5963,plain,(
% 1.82/2.01 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.82/2.01 inference(skolemize,[status(sab)],[5962])).
% 1.82/2.01 tff(5964,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5963, 5956])).
% 1.82/2.01 tff(5965,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp5 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5966,plain,
% 1.82/2.01 ((hskp5 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp5 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5967,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp5 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537)))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[5966])).
% 1.82/2.01 tff(5968,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537))),
% 1.82/2.01 inference(transitivity,[status(thm)],[5967, 5965])).
% 1.82/2.01 tff(5969,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(5970,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | c2_1(a537)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5969, 5968])).
% 1.82/2.01 tff(5971,plain,
% 1.82/2.01 (hskp5),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5970, 156, 5932, 4884, 5931, 86, 5964, 902, 5939])).
% 1.82/2.01 tff(5972,plain,
% 1.82/2.01 (((~hskp5) | (~c1_1(a546))) <=> ((~hskp5) | (~c1_1(a546)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5973,plain,
% 1.82/2.01 (((~c1_1(a546)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a546)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5974,axiom,((~c1_1(a546)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 1.82/2.01 tff(5975,plain,
% 1.82/2.01 ((~hskp5) | (~c1_1(a546))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5974, 5973])).
% 1.82/2.01 tff(5976,plain,
% 1.82/2.01 ((~hskp5) | (~c1_1(a546))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5975, 5972])).
% 1.82/2.01 tff(5977,plain,
% 1.82/2.01 (~c1_1(a546)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5976, 5971])).
% 1.82/2.01 tff(5978,plain,
% 1.82/2.01 (((~hskp5) | (~c3_1(a546))) <=> ((~hskp5) | (~c3_1(a546)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5979,plain,
% 1.82/2.01 (((~c3_1(a546)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a546)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5980,axiom,((~c3_1(a546)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 1.82/2.01 tff(5981,plain,
% 1.82/2.01 ((~hskp5) | (~c3_1(a546))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5980, 5979])).
% 1.82/2.01 tff(5982,plain,
% 1.82/2.01 ((~hskp5) | (~c3_1(a546))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5981, 5978])).
% 1.82/2.01 tff(5983,plain,
% 1.82/2.01 (~c3_1(a546)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5982, 5971])).
% 1.82/2.01 tff(5984,plain,
% 1.82/2.01 (((~hskp5) | c2_1(a546)) <=> ((~hskp5) | c2_1(a546))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5985,axiom,((~hskp5) | c2_1(a546)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.82/2.01 tff(5986,plain,
% 1.82/2.01 ((~hskp5) | c2_1(a546)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5985, 5984])).
% 1.82/2.01 tff(5987,plain,
% 1.82/2.01 ((~hskp5) | c2_1(a546)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5986, 5984])).
% 1.82/2.01 tff(5988,plain,
% 1.82/2.01 ((~hskp5) | c2_1(a546)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5987, 5984])).
% 1.82/2.01 tff(5989,plain,
% 1.82/2.01 ((~hskp5) | c2_1(a546)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5988, 5984])).
% 1.82/2.01 tff(5990,plain,
% 1.82/2.01 ((~hskp5) | c2_1(a546)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[5989, 5984])).
% 1.82/2.01 tff(5991,plain,
% 1.82/2.01 (c2_1(a546)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[5990, 5971])).
% 1.82/2.01 tff(5992,plain,
% 1.82/2.01 (c3_1(a583)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[2645, 5941])).
% 1.82/2.01 tff(5993,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c3_1(a546) | c1_1(a546) | (~ndr1_0) | (~c2_1(a546)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c3_1(a546) | c1_1(a546) | (~ndr1_0) | (~c2_1(a546)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5994,plain,
% 1.82/2.01 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a546) | c3_1(a546) | (~c2_1(a546)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583))) <=> (c2_1(a583) | c3_1(a546) | c1_1(a546) | (~ndr1_0) | (~c2_1(a546)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(5995,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a546) | c3_1(a546) | (~c2_1(a546)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c3_1(a546) | c1_1(a546) | (~ndr1_0) | (~c2_1(a546)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[5994])).
% 1.82/2.02 tff(5996,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a546) | c3_1(a546) | (~c2_1(a546)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c3_1(a546) | c1_1(a546) | (~ndr1_0) | (~c2_1(a546)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[5995, 5993])).
% 1.82/2.02 tff(5997,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a546) | c3_1(a546) | (~c2_1(a546)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(5998,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c3_1(a546) | c1_1(a546) | (~ndr1_0) | (~c2_1(a546)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[5997, 5996])).
% 1.82/2.02 tff(5999,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5998, 156, 5953, 5992, 5991, 5942, 5983, 5977, 921, 5954])).
% 1.82/2.02 tff(6000,plain,((~c2_1(a586)) | c3_1(a586) | c2_1(a548) | c0_1(a548) | c0_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(6001,plain,
% 1.82/2.02 (~c2_1(a586)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6000, 56, 24, 86, 87, 35])).
% 1.82/2.02 tff(6002,plain,
% 1.82/2.02 (c1_1(a548)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5857, 3105, 4884, 5849, 87, 86, 56])).
% 1.82/2.02 tff(6003,plain,
% 1.82/2.02 (hskp39),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5921, 6002, 87])).
% 1.82/2.02 tff(6004,plain,
% 1.82/2.02 (c1_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[303, 6003])).
% 1.82/2.02 tff(6005,plain,
% 1.82/2.02 (c2_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[311, 6003])).
% 1.82/2.02 tff(6006,plain,
% 1.82/2.02 (c3_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[319, 6003])).
% 1.82/2.02 tff(6007,plain,
% 1.82/2.02 (hskp25),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4507, 156, 6006, 6005, 6004, 5849, 24, 55, 6002])).
% 1.82/2.02 tff(6008,plain,
% 1.82/2.02 (~c1_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1190, 6007])).
% 1.82/2.02 tff(6009,plain,
% 1.82/2.02 (~c2_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1196, 6007])).
% 1.82/2.02 tff(6010,plain,
% 1.82/2.02 (~c3_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1202, 6007])).
% 1.82/2.02 tff(6011,plain,
% 1.82/2.02 (hskp34),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4519, 6002, 5849, 24, 56])).
% 1.82/2.02 tff(6012,plain,
% 1.82/2.02 (~c1_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1124, 6011])).
% 1.82/2.02 tff(6013,plain,
% 1.82/2.02 (c3_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1132, 6011])).
% 1.82/2.02 tff(6014,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6015,plain,
% 1.82/2.02 ((hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp15 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6016,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[6015])).
% 1.82/2.02 tff(6017,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[6016, 6014])).
% 1.82/2.02 tff(6018,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(6019,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6018, 6017])).
% 1.82/2.02 tff(6020,plain,
% 1.82/2.02 (~c2_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6019, 156, 109, 6013, 4884, 6012, 86, 483, 653])).
% 1.82/2.02 tff(6021,plain,
% 1.82/2.02 (c0_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1147, 6011])).
% 1.82/2.02 tff(6022,plain,
% 1.82/2.02 (hskp19),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1154, 156, 110, 6021, 6012, 34, 6020])).
% 1.82/2.02 tff(6023,plain,
% 1.82/2.02 (hskp28),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5069, 6022])).
% 1.82/2.02 tff(6024,plain,
% 1.82/2.02 (c3_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[185, 6023])).
% 1.82/2.02 tff(6025,plain,
% 1.82/2.02 (c2_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[171, 6023])).
% 1.82/2.02 tff(6026,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6027,plain,
% 1.82/2.02 ((hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp15 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6028,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[6027])).
% 1.82/2.02 tff(6029,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 1.82/2.02 inference(transitivity,[status(thm)],[6028, 6026])).
% 1.82/2.02 tff(6030,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(6031,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6030, 6029])).
% 1.82/2.02 tff(6032,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6031, 156, 109, 625, 591, 3797, 86, 483, 1716, 653])).
% 1.82/2.02 tff(6033,plain,(c2_1(a586) | hskp15 | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a586)) | c3_1(a586) | c1_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(6034,plain,
% 1.82/2.02 (c1_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6033, 6025, 4884, 109, 653, 86, 6024])).
% 1.82/2.02 tff(6035,plain,
% 1.82/2.02 (~c0_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[177, 6023])).
% 1.82/2.02 tff(6036,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp43 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | (~c0_1(a537)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6037,plain,
% 1.82/2.02 ((hskp43 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589))) <=> (hskp43 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | (~c0_1(a537)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6038,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | (~c0_1(a537))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[6037])).
% 1.82/2.02 tff(6039,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp43 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | (~c0_1(a537)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[6038, 6036])).
% 1.82/2.02 tff(6040,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp43 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(6041,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp43 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp43 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | (~c0_1(a537))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6040, 6039])).
% 1.82/2.02 tff(6042,plain,
% 1.82/2.02 (hskp43),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6041, 156, 6021, 6025, 6012, 6035, 3893, 6034, 6020])).
% 1.82/2.02 tff(6043,plain,
% 1.82/2.02 (~c1_1(a557)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3803, 6042])).
% 1.82/2.02 tff(6044,plain,
% 1.82/2.02 (c3_1(a557)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3829, 6042])).
% 1.82/2.02 tff(6045,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a557) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a557)) | (~c2_1(a557)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a557) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a557)) | (~c2_1(a557)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6046,plain,
% 1.82/2.02 (((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a557) | (~c3_1(a557)) | (~c2_1(a557)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (c1_1(a557) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a557)) | (~c2_1(a557)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6047,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a557) | (~c3_1(a557)) | (~c2_1(a557)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a557) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a557)) | (~c2_1(a557))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[6046])).
% 1.82/2.02 tff(6048,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a557) | (~c3_1(a557)) | (~c2_1(a557)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a557) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a557)) | (~c2_1(a557)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[6047, 6045])).
% 1.82/2.02 tff(6049,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c1_1(a557) | (~c3_1(a557)) | (~c2_1(a557)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(6050,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a557) | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c3_1(a557)) | (~c2_1(a557))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6049, 6048])).
% 1.82/2.02 tff(6051,plain,
% 1.82/2.02 (~c2_1(a557)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6050, 156, 6044, 5849, 6043, 6010, 6009, 6008, 24, 45, 6002])).
% 1.82/2.02 tff(6052,plain,
% 1.82/2.02 (~c0_1(a573)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1691, 6022])).
% 1.82/2.02 tff(6053,plain,
% 1.82/2.02 (hskp46),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2834, 6002, 5849, 56])).
% 1.82/2.02 tff(6054,plain,
% 1.82/2.02 (~c1_1(a573)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1675, 6022])).
% 1.82/2.02 tff(6055,plain,
% 1.82/2.02 (~c3_1(a573)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3247, 6054, 3105, 6053, 6052])).
% 1.82/2.02 tff(6056,plain,
% 1.82/2.02 (~c2_1(a573)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1704, 6022])).
% 1.82/2.02 tff(6057,plain,
% 1.82/2.02 (hskp38),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3088, 156, 5849, 6056, 6054, 24, 56, 663, 6055])).
% 1.82/2.02 tff(6058,plain,
% 1.82/2.02 (c0_1(a547)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[677, 6057])).
% 1.82/2.02 tff(6059,plain,
% 1.82/2.02 (c1_1(a547)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[685, 6057])).
% 1.82/2.02 tff(6060,plain,
% 1.82/2.02 (c2_1(a547)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[693, 6057])).
% 1.82/2.02 tff(6061,plain,
% 1.82/2.02 (hskp0),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4925, 156, 6060, 6059, 6058, 6010, 6009, 6008, 108])).
% 1.82/2.02 tff(6062,plain,
% 1.82/2.02 (~c2_1(a535)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[713, 6061])).
% 1.82/2.02 tff(6063,plain,
% 1.82/2.02 (c0_1(a535)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[721, 6061])).
% 1.82/2.02 tff(6064,plain,
% 1.82/2.02 (c1_1(a535)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[729, 6061])).
% 1.82/2.02 tff(6065,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a557) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a557)) | c2_1(a557) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a557) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a557)) | c2_1(a557) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6066,plain,
% 1.82/2.02 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a557) | c1_1(a557) | (~c3_1(a557)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c1_1(a557) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a557)) | c2_1(a557) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6067,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a557) | c1_1(a557) | (~c3_1(a557)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a557) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a557)) | c2_1(a557) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[6066])).
% 1.82/2.02 tff(6068,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a557) | c1_1(a557) | (~c3_1(a557)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a557) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a557)) | c2_1(a557) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[6067, 6065])).
% 1.82/2.02 tff(6069,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a557) | c1_1(a557) | (~c3_1(a557)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(6070,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a557) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | (~c3_1(a557)) | c2_1(a557) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6069, 6068])).
% 1.82/2.02 tff(6071,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6070, 156, 6044, 6060, 6059, 6058, 6064, 6063, 6043, 6062, 707, 6051])).
% 1.82/2.02 tff(6072,plain,(c2_1(a586) | c2_1(a548) | c0_1(a548) | hskp15 | c3_1(a586) | hskp50 | c0_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(6073,plain,
% 1.82/2.02 (hskp15),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6072, 6001, 56, 24, 86, 110, 87, 35])).
% 1.82/2.02 tff(6074,plain,
% 1.82/2.02 (~c1_1(a569)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1261, 6073])).
% 1.82/2.02 tff(6075,plain,
% 1.82/2.02 (~c0_1(a569)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1267, 6073])).
% 1.82/2.02 tff(6076,plain,
% 1.82/2.02 (~hskp26),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3104, 6001, 87, 86, 35])).
% 1.82/2.02 tff(6077,plain,
% 1.82/2.02 (c1_1(a548)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5857, 6076, 4884, 5849, 87, 86, 56])).
% 1.82/2.02 tff(6078,plain,
% 1.82/2.02 (hskp46),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2834, 6077, 5849, 56])).
% 1.82/2.02 tff(6079,plain,
% 1.82/2.02 (~c0_1(a562)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[64, 6078])).
% 1.82/2.02 tff(6080,plain,
% 1.82/2.02 (~c3_1(a562)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[270, 6078])).
% 1.82/2.02 tff(6081,plain,
% 1.82/2.02 (c1_1(a562)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[288, 6078])).
% 1.82/2.02 tff(6082,plain,
% 1.82/2.02 (~c3_1(a569)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2874, 156, 6076, 6081, 6080, 6079, 6075, 6074, 1686])).
% 1.82/2.02 tff(6083,plain,
% 1.82/2.02 (~c2_1(a569)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1255, 6073])).
% 1.82/2.02 tff(6084,plain,
% 1.82/2.02 (hskp34),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4519, 6077, 5849, 24, 56])).
% 1.82/2.02 tff(6085,plain,
% 1.82/2.02 (~c1_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1124, 6084])).
% 1.82/2.02 tff(6086,plain,
% 1.82/2.02 (c3_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1132, 6084])).
% 1.82/2.02 tff(6087,plain,
% 1.82/2.02 (c3_1(a569) | (~c2_1(a537))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4850, 156, 6086, 5849, 6085, 6074, 6083, 24, 45, 6077])).
% 1.82/2.02 tff(6088,plain,
% 1.82/2.02 (~c2_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6087, 6082])).
% 1.82/2.02 tff(6089,plain,
% 1.82/2.02 (c0_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1147, 6084])).
% 1.82/2.02 tff(6090,plain,
% 1.82/2.02 (hskp51 | c3_1(a569)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3462, 156, 6089, 6086, 6085, 6074, 6083, 2608])).
% 1.82/2.02 tff(6091,plain,
% 1.82/2.02 (hskp51),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6090, 6082])).
% 1.82/2.02 tff(6092,plain,
% 1.82/2.02 (~c2_1(a583)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2637, 6091])).
% 1.82/2.02 tff(6093,plain,
% 1.82/2.02 (hskp38 | c3_1(a569)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2821, 156, 5849, 6074, 6083, 24, 56, 663])).
% 1.82/2.02 tff(6094,plain,
% 1.82/2.02 (hskp38),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6093, 6082])).
% 1.82/2.02 tff(6095,plain,
% 1.82/2.02 (c0_1(a547)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[677, 6094])).
% 1.82/2.02 tff(6096,plain,
% 1.82/2.02 (c1_1(a547)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[685, 6094])).
% 1.82/2.02 tff(6097,plain,
% 1.82/2.02 (c2_1(a547)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[693, 6094])).
% 1.82/2.02 tff(6098,plain,
% 1.82/2.02 (c0_1(a583)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2653, 6091])).
% 1.82/2.02 tff(6099,plain,
% 1.82/2.02 (~c1_1(a583)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2672, 156, 6098, 6097, 6096, 6095, 6086, 6092, 6085, 707, 6088])).
% 1.82/2.02 tff(6100,plain,
% 1.82/2.02 (hskp39),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5921, 6077, 87])).
% 1.82/2.02 tff(6101,plain,
% 1.82/2.02 (c1_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[303, 6100])).
% 1.82/2.02 tff(6102,plain,
% 1.82/2.02 (c2_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[311, 6100])).
% 1.82/2.02 tff(6103,plain,
% 1.82/2.02 (c3_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[319, 6100])).
% 1.82/2.02 tff(6104,plain,
% 1.82/2.02 (hskp25),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4507, 156, 6103, 6102, 6101, 5849, 24, 55, 6077])).
% 1.82/2.02 tff(6105,plain,
% 1.82/2.02 (~c1_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1190, 6104])).
% 1.82/2.02 tff(6106,plain,
% 1.82/2.02 (~c2_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1196, 6104])).
% 1.82/2.02 tff(6107,plain,
% 1.82/2.02 (~c3_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1202, 6104])).
% 1.82/2.02 tff(6108,plain,
% 1.82/2.02 (hskp0),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4925, 156, 6097, 6096, 6095, 6107, 6106, 6105, 108])).
% 1.82/2.02 tff(6109,plain,
% 1.82/2.02 (~c2_1(a535)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[713, 6108])).
% 1.82/2.02 tff(6110,plain,
% 1.82/2.02 (c0_1(a535)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[721, 6108])).
% 1.82/2.02 tff(6111,plain,
% 1.82/2.02 (c1_1(a535)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[729, 6108])).
% 1.82/2.02 tff(6112,plain,
% 1.82/2.02 (c3_1(a583)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[2645, 6091])).
% 1.82/2.02 tff(6113,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3580, 156, 6112, 6097, 6096, 6095, 6111, 6110, 6092, 6109, 707, 6099])).
% 1.82/2.02 tff(6114,plain,(c0_1(a548) | c2_1(a548) | c0_1(a586) | c3_1(a586) | hskp50 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(6115,plain,
% 1.82/2.02 (c0_1(a548)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6114, 110, 87, 86, 24, 35])).
% 1.82/2.02 tff(6116,plain,
% 1.82/2.02 (hskp19),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4803, 57, 6115, 110])).
% 1.82/2.02 tff(6117,plain,
% 1.82/2.02 (hskp4),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5777, 57, 110, 86, 87, 35, 6115, 24, 4884])).
% 1.82/2.02 tff(6118,plain,
% 1.82/2.02 (~hskp6),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[211, 6115])).
% 1.82/2.02 tff(6119,plain,
% 1.82/2.02 (~c0_1(a545)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1666, 6117])).
% 1.82/2.02 tff(6120,plain,
% 1.82/2.02 (~c1_1(a573)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1675, 6116])).
% 1.82/2.02 tff(6121,plain,
% 1.82/2.02 (~c0_1(a573)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1691, 6116])).
% 1.82/2.02 tff(6122,plain,
% 1.82/2.02 (~c2_1(a573)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1704, 6116])).
% 1.82/2.02 tff(6123,plain,
% 1.82/2.02 (c1_1(a545)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[193, 6117])).
% 1.82/2.02 tff(6124,plain,
% 1.82/2.02 (~c3_1(a545)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3068, 156, 6118, 6123, 6122, 6121, 6120, 6119, 1745])).
% 1.82/2.02 tff(6125,plain,
% 1.82/2.02 (hskp26),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1753, 6124, 6118, 6117, 6116])).
% 1.82/2.02 tff(6126,plain,
% 1.82/2.02 (c2_1(a586)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[3104, 6125, 87, 86, 35])).
% 1.82/2.02 tff(6127,plain,
% 1.82/2.02 (hskp28),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5069, 6116])).
% 1.82/2.02 tff(6128,plain,
% 1.82/2.02 (~c0_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[177, 6127])).
% 1.82/2.02 tff(6129,plain,
% 1.82/2.02 (c3_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[185, 6127])).
% 1.82/2.02 tff(6130,plain,
% 1.82/2.02 (~c1_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1751, 156, 6118, 6129, 6128, 6122, 6121, 6120, 1745])).
% 1.82/2.02 tff(6131,plain,
% 1.82/2.02 (c2_1(a589)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[171, 6127])).
% 1.82/2.02 tff(6132,plain,
% 1.82/2.02 (hskp47 | (~c2_1(a586))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5700, 156, 6131, 6129, 4884, 6128, 86, 5693])).
% 1.82/2.02 tff(6133,plain,
% 1.82/2.02 (hskp47),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6132, 6126])).
% 1.82/2.02 tff(6134,plain,
% 1.82/2.02 (~c2_1(a564)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5707, 6133])).
% 1.82/2.02 tff(6135,plain,
% 1.82/2.02 (c1_1(a564)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5734, 6133])).
% 1.82/2.02 tff(6136,plain,
% 1.82/2.02 (c0_1(a564)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5742, 6133])).
% 1.82/2.02 tff(6137,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5888, 156, 6136, 6135, 6129, 6134, 6128, 87, 86, 609, 6130, 6126])).
% 1.82/2.02 tff(6138,plain,(c1_1(a548) | c0_1(a586) | c3_1(a586) | hskp33 | hskp50 | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(6139,plain,
% 1.82/2.02 (c1_1(a548)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6138, 110, 86, 35, 87, 24])).
% 1.82/2.02 tff(6140,plain,
% 1.82/2.02 (hskp39),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5921, 6139, 87])).
% 1.82/2.02 tff(6141,plain,
% 1.82/2.02 (c1_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[303, 6140])).
% 1.82/2.02 tff(6142,plain,
% 1.82/2.02 (c2_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[311, 6140])).
% 1.82/2.02 tff(6143,plain,
% 1.82/2.02 (c3_1(a549)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[319, 6140])).
% 1.82/2.02 tff(6144,plain,
% 1.82/2.02 (hskp25),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4507, 156, 6143, 6142, 6141, 5849, 24, 55, 6139])).
% 1.82/2.02 tff(6145,plain,
% 1.82/2.02 (~c1_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1190, 6144])).
% 1.82/2.02 tff(6146,plain,
% 1.82/2.02 (~c2_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1196, 6144])).
% 1.82/2.02 tff(6147,plain,
% 1.82/2.02 (~c3_1(a582)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1202, 6144])).
% 1.82/2.02 tff(6148,plain,
% 1.82/2.02 (hskp34),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[4517, 156, 6143, 6142, 6141, 6147, 6146, 6145, 1112])).
% 1.82/2.02 tff(6149,plain,
% 1.82/2.02 (~c1_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1124, 6148])).
% 1.82/2.02 tff(6150,plain,
% 1.82/2.02 (c3_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[1132, 6148])).
% 1.82/2.02 tff(6151,plain,
% 1.82/2.02 (~c2_1(a537)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[5938, 156, 6150, 5849, 6149, 6147, 6146, 6145, 24, 45, 6139])).
% 1.82/2.02 tff(6152,plain,
% 1.82/2.02 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(6153,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[6152])).
% 1.82/2.02 tff(6154,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6155,plain,
% 1.82/2.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(6156,plain,
% 1.82/2.02 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[6155])).
% 1.82/2.02 tff(6157,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause233')).
% 1.82/2.02 tff(6158,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6157, 6156])).
% 1.82/2.02 tff(6159,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6158, 6154])).
% 1.82/2.02 tff(6160,plain,(
% 1.82/2.02 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.82/2.02 inference(skolemize,[status(sab)],[6159])).
% 1.82/2.02 tff(6161,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6160, 6153])).
% 1.82/2.02 tff(6162,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6163,plain,
% 1.82/2.02 ((hskp12 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (hskp12 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6164,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[6163])).
% 1.82/2.02 tff(6165,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[6164, 6162])).
% 1.82/2.02 tff(6166,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(6167,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6166, 6165])).
% 1.82/2.02 tff(6168,plain,
% 1.82/2.02 (hskp12),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6167, 156, 5849, 6147, 6146, 6145, 24, 6161, 6139])).
% 1.82/2.02 tff(6169,plain,
% 1.82/2.02 (((~hskp12) | (~c2_1(a563))) <=> ((~hskp12) | (~c2_1(a563)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6170,plain,
% 1.82/2.02 (((~c2_1(a563)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a563)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6171,axiom,((~c2_1(a563)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.82/2.02 tff(6172,plain,
% 1.82/2.02 ((~hskp12) | (~c2_1(a563))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6171, 6170])).
% 1.82/2.02 tff(6173,plain,
% 1.82/2.02 ((~hskp12) | (~c2_1(a563))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6172, 6169])).
% 1.82/2.02 tff(6174,plain,
% 1.82/2.02 (~c2_1(a563)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6173, 6168])).
% 1.82/2.02 tff(6175,plain,
% 1.82/2.02 (((~hskp12) | (~c0_1(a563))) <=> ((~hskp12) | (~c0_1(a563)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6176,plain,
% 1.82/2.02 (((~c0_1(a563)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a563)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6177,axiom,((~c0_1(a563)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.82/2.02 tff(6178,plain,
% 1.82/2.02 ((~hskp12) | (~c0_1(a563))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6177, 6176])).
% 1.82/2.02 tff(6179,plain,
% 1.82/2.02 ((~hskp12) | (~c0_1(a563))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[6178, 6175])).
% 1.82/2.02 tff(6180,plain,
% 1.82/2.02 (~c0_1(a563)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[6179, 6168])).
% 1.82/2.02 tff(6181,plain,
% 1.82/2.02 (((~hskp12) | c3_1(a563)) <=> ((~hskp12) | c3_1(a563))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(6182,axiom,((~hskp12) | c3_1(a563)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.82/2.02 tff(6183,plain,
% 1.82/2.02 ((~hskp12) | c3_1(a563)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6182, 6181])).
% 1.82/2.03 tff(6184,plain,
% 1.82/2.03 ((~hskp12) | c3_1(a563)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6183, 6181])).
% 1.82/2.03 tff(6185,plain,
% 1.82/2.03 ((~hskp12) | c3_1(a563)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6184, 6181])).
% 1.82/2.03 tff(6186,plain,
% 1.82/2.03 ((~hskp12) | c3_1(a563)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6185, 6181])).
% 1.82/2.03 tff(6187,plain,
% 1.82/2.03 ((~hskp12) | c3_1(a563)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6186, 6181])).
% 1.82/2.03 tff(6188,plain,
% 1.82/2.03 (c3_1(a563)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6187, 6168])).
% 1.82/2.03 tff(6189,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c0_1(a563) | c2_1(a563) | (~ndr1_0) | (~c3_1(a563)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c0_1(a563) | c2_1(a563) | (~ndr1_0) | (~c3_1(a563)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6190,plain,
% 1.82/2.03 ((hskp38 | (~ndr1_0) | c2_1(a563) | c0_1(a563) | (~c3_1(a563)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c0_1(a563) | c2_1(a563) | (~ndr1_0) | (~c3_1(a563)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6191,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a563) | c0_1(a563) | (~c3_1(a563)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c0_1(a563) | c2_1(a563) | (~ndr1_0) | (~c3_1(a563))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6190])).
% 1.82/2.03 tff(6192,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a563) | c0_1(a563) | (~c3_1(a563)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c0_1(a563) | c2_1(a563) | (~ndr1_0) | (~c3_1(a563)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6191, 6189])).
% 1.82/2.03 tff(6193,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a563) | c0_1(a563) | (~c3_1(a563)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6194,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a582) | c2_1(a582) | c1_1(a582) | c0_1(a563) | c2_1(a563) | (~ndr1_0) | (~c3_1(a563))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6193, 6192])).
% 1.82/2.03 tff(6195,plain,
% 1.82/2.03 (hskp38),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6194, 156, 6188, 6147, 6146, 6145, 6180, 6174, 663])).
% 1.82/2.03 tff(6196,plain,
% 1.82/2.03 (c0_1(a547)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[677, 6195])).
% 1.82/2.03 tff(6197,plain,
% 1.82/2.03 (c1_1(a547)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[685, 6195])).
% 1.82/2.03 tff(6198,plain,
% 1.82/2.03 (c2_1(a547)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[693, 6195])).
% 1.82/2.03 tff(6199,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6200,plain,
% 1.82/2.03 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))) <=> (c1_1(a537) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6201,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6200])).
% 1.82/2.03 tff(6202,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6201, 6199])).
% 1.82/2.03 tff(6203,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6204,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6203, 6202])).
% 1.82/2.03 tff(6205,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6204, 156, 6198, 6197, 6196, 6150, 6149, 24, 6115, 707, 6139, 6151])).
% 1.82/2.03 tff(6206,plain,(hskp50 | c2_1(a548) | c0_1(a586) | c3_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(6207,plain,
% 1.82/2.03 (hskp50),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6206, 87, 24, 86, 35])).
% 1.82/2.03 tff(6208,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4931, 1667, 1622, 35, 794])).
% 1.82/2.03 tff(6209,plain,((~hskp4) | hskp33 | (~hskp50)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(6210,plain,
% 1.82/2.03 (~hskp4),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6209, 6207, 35])).
% 1.82/2.03 tff(6211,plain,
% 1.82/2.03 (~hskp39),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5127, 6210, 4884, 87, 86])).
% 1.82/2.03 tff(6212,plain,
% 1.82/2.03 (c2_1(a586)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2766, 6207, 87, 86, 35])).
% 1.82/2.03 tff(6213,plain,
% 1.82/2.03 (c0_1(a548)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6000, 6212, 24, 86, 87, 35])).
% 1.82/2.03 tff(6214,plain,
% 1.82/2.03 (~hskp35),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5310, 6210, 4884, 87, 86])).
% 1.82/2.03 tff(6215,plain,
% 1.82/2.03 (hskp35 | (~c0_1(a548)) | c1_1(a548) | (~c2_1(a586))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5317, 156, 4884, 86, 24, 3950])).
% 1.82/2.03 tff(6216,plain,
% 1.82/2.03 (c1_1(a548)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6215, 6214, 6213, 6212])).
% 1.82/2.03 tff(6217,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5921, 6216, 6211, 87])).
% 1.82/2.03 tff(6218,plain,(c0_1(a586) | c3_1(a586) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(6219,plain,
% 1.82/2.03 (c0_1(a586)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6218, 86, 24, 35])).
% 1.82/2.03 tff(6220,plain,
% 1.82/2.03 (~hskp27),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[3924, 6219])).
% 1.82/2.03 tff(6221,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a590)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6222,plain,
% 1.82/2.03 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586))) <=> (c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a590)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6223,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a590))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6222])).
% 1.82/2.03 tff(6224,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a590)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6223, 6221])).
% 1.82/2.03 tff(6225,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6226,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a590))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6225, 6224])).
% 1.82/2.03 tff(6227,plain,
% 1.82/2.03 (~c2_1(a590)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6226, 156, 3797, 249, 4587, 4581, 1996, 56, 609, 653, 57])).
% 1.82/2.03 tff(6228,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a590))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6229,plain,
% 1.82/2.03 ((hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a590) | c3_1(a590) | c0_1(a590)) <=> (hskp33 | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a590))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6230,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a590) | c3_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a590)))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6229])).
% 1.82/2.03 tff(6231,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a590) | c3_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a590))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6230, 6228])).
% 1.82/2.03 tff(6232,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a590) | c3_1(a590) | c0_1(a590))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6233,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a590) | c0_1(a590) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a590)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6232, 6231])).
% 1.82/2.03 tff(6234,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6233, 156, 35, 3797, 4587, 4581, 1996, 86, 85, 6227])).
% 1.82/2.03 tff(6235,plain,((~hskp29) | hskp33 | (~c1_1(a586)) | (~c0_1(a586)) | c3_1(a586) | (~c3_1(a548)) | c0_1(a548) | c2_1(a586) | c1_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(6236,plain,
% 1.82/2.03 (~hskp29),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6235, 653, 4884, 6219, 86, 5849, 56, 35, 57])).
% 1.82/2.03 tff(6237,plain,
% 1.82/2.03 (hskp30),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4620, 6236, 5849, 57])).
% 1.82/2.03 tff(6238,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a591) | c0_1(a591) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c3_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c3_1(a591))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6239,plain,
% 1.82/2.03 ((hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a591) | c3_1(a591) | c0_1(a591)) <=> (hskp33 | c2_1(a591) | c0_1(a591) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c3_1(a591))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6240,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a591) | c0_1(a591) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c3_1(a591)))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6239])).
% 1.82/2.03 tff(6241,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c3_1(a591))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6240, 6238])).
% 1.82/2.03 tff(6242,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a591) | c3_1(a591) | c0_1(a591))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6243,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | (~c0_1(a586)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c3_1(a591)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6242, 6241])).
% 1.82/2.03 tff(6244,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6243, 156, 35, 3797, 4715, 4714, 1996, 86, 85, 4717])).
% 1.82/2.03 tff(6245,plain,((~hskp30) | hskp33 | (~c1_1(a586)) | (~c0_1(a586)) | c3_1(a586) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(6246,plain,
% 1.82/2.03 (hskp46),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6245, 6237, 4884, 6219, 86, 35])).
% 1.82/2.03 tff(6247,plain,
% 1.82/2.03 (~c0_1(a562)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[64, 6246])).
% 1.82/2.03 tff(6248,plain,
% 1.82/2.03 (~c3_1(a562)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[270, 6246])).
% 1.82/2.03 tff(6249,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a562) | c0_1(a562) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a562) | c0_1(a562) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a562)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6250,plain,
% 1.82/2.03 (((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586))) <=> (c3_1(a562) | c0_1(a562) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a562)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6251,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a562) | c0_1(a562) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a562))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6250])).
% 1.82/2.03 tff(6252,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a562) | c0_1(a562) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a562)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6251, 6249])).
% 1.82/2.03 tff(6253,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6254,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a562) | c0_1(a562) | (~c0_1(a586)) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a562))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6253, 6252])).
% 1.82/2.03 tff(6255,plain,
% 1.82/2.03 (~c2_1(a562)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6254, 156, 4884, 5849, 6248, 6247, 6219, 56, 609, 653, 57])).
% 1.82/2.03 tff(6256,plain,
% 1.82/2.03 (c1_1(a562)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[288, 6246])).
% 1.82/2.03 tff(6257,plain,
% 1.82/2.03 (hskp26),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2071, 156, 6256, 5849, 6248, 6247, 56, 1686, 57])).
% 1.82/2.03 tff(6258,plain,
% 1.82/2.03 (~c3_1(a584)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1620, 6257])).
% 1.82/2.03 tff(6259,plain,
% 1.82/2.03 (c1_1(a584)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1637, 6257])).
% 1.82/2.03 tff(6260,plain,
% 1.82/2.03 (c0_1(a584)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1629, 6257])).
% 1.82/2.03 tff(6261,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6262,plain,
% 1.82/2.03 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562) | c3_1(a562) | c0_1(a562)) <=> (hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6263,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562) | c3_1(a562) | c0_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562)))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6262])).
% 1.82/2.03 tff(6264,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562) | c3_1(a562) | c0_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6263, 6261])).
% 1.82/2.03 tff(6265,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562) | c3_1(a562) | c0_1(a562))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6266,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a562) | c0_1(a562) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a562)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6265, 6264])).
% 1.82/2.03 tff(6267,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6266, 156, 35, 6260, 6259, 6248, 6247, 6258, 85, 6255])).
% 1.82/2.03 tff(6268,plain,(c2_1(a586) | hskp33 | c0_1(a548) | c1_1(a548) | c3_1(a586) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(6269,plain,
% 1.82/2.03 (c2_1(a586)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6268, 57, 56, 35, 86, 24])).
% 1.82/2.03 tff(6270,plain,
% 1.82/2.03 (hskp47 | (~c2_1(a586))),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5700, 156, 4533, 4534, 4884, 4535, 86, 5693])).
% 1.82/2.03 tff(6271,plain,
% 1.82/2.03 (hskp47),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6270, 6269])).
% 1.82/2.03 tff(6272,plain,
% 1.82/2.03 (~c2_1(a564)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5707, 6271])).
% 1.82/2.03 tff(6273,plain,
% 1.82/2.03 (c1_1(a564)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5734, 6271])).
% 1.82/2.03 tff(6274,plain,
% 1.82/2.03 (c0_1(a564)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[5742, 6271])).
% 1.82/2.03 tff(6275,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | (~c0_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a564)) | (~c0_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | (~c0_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6276,plain,
% 1.82/2.03 (((~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564))) <=> (c2_1(a564) | (~c0_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(6277,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | (~c0_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a564)) | (~c0_1(a564))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[6276])).
% 1.82/2.03 tff(6278,plain,
% 1.82/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | (~c0_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[6277, 6275])).
% 1.82/2.03 tff(6279,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(6280,plain,
% 1.82/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | (~c0_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a564)) | (~c0_1(a564))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[6279, 6278])).
% 1.82/2.03 tff(6281,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6280, 156, 6274, 6273, 4884, 5849, 6272, 6219, 24, 707, 6269, 57])).
% 1.82/2.03 tff(6282,plain,(c1_1(a548) | c2_1(a548) | c3_1(a586) | c0_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(6283,plain,
% 1.82/2.03 (c1_1(a548)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[6282, 56, 86, 24, 35])).
% 1.82/2.03 tff(6284,plain,
% 1.82/2.03 (hskp46),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2834, 6283, 5849, 56])).
% 1.82/2.03 tff(6285,plain,
% 1.82/2.03 (~c0_1(a562)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[64, 6284])).
% 1.82/2.03 tff(6286,plain,
% 1.82/2.03 (~c3_1(a562)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[270, 6284])).
% 1.82/2.03 tff(6287,plain,
% 1.82/2.03 (c1_1(a562)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[288, 6284])).
% 1.82/2.03 tff(6288,plain,
% 1.82/2.03 (hskp39),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[2063, 156, 6287, 5849, 6286, 6285, 24, 281, 6283])).
% 1.82/2.03 tff(6289,plain,
% 1.82/2.03 (c1_1(a549)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[303, 6288])).
% 1.82/2.03 tff(6290,plain,
% 1.82/2.03 (c2_1(a549)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[311, 6288])).
% 1.82/2.03 tff(6291,plain,
% 1.82/2.03 (c3_1(a549)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[319, 6288])).
% 1.82/2.03 tff(6292,plain,
% 1.82/2.03 (hskp25),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[4507, 156, 6291, 6290, 6289, 5849, 24, 55, 6283])).
% 1.82/2.03 tff(6293,plain,
% 1.82/2.03 (~c1_1(a582)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1190, 6292])).
% 1.82/2.03 tff(6294,plain,
% 1.82/2.03 (~c2_1(a582)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[1196, 6292])).
% 1.82/2.04 tff(6295,plain,
% 1.82/2.04 (~c3_1(a582)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1202, 6292])).
% 1.82/2.04 tff(6296,plain,
% 1.82/2.04 (hskp34),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4519, 6283, 5849, 24, 56])).
% 1.82/2.04 tff(6297,plain,
% 1.82/2.04 (~c1_1(a537)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1124, 6296])).
% 1.82/2.04 tff(6298,plain,
% 1.82/2.04 (hskp4),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[2559, 6283, 5849, 24, 56])).
% 1.82/2.04 tff(6299,plain,
% 1.82/2.04 (~c0_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1666, 6298])).
% 1.82/2.04 tff(6300,plain,
% 1.82/2.04 (c1_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[193, 6298])).
% 1.82/2.04 tff(6301,plain,
% 1.82/2.04 (~c2_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1643, 6298])).
% 1.82/2.04 tff(6302,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~c0_1(a586)) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | (~c0_1(a586)) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a586)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6303,plain,
% 1.82/2.04 ((hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | (~c0_1(a586)) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a586)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6304,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~c0_1(a586)) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a586))))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[6303])).
% 1.82/2.04 tff(6305,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | (~c0_1(a586)) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a586)))),
% 1.82/2.04 inference(transitivity,[status(thm)],[6304, 6302])).
% 1.82/2.04 tff(6306,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a586) | (~c0_1(a586)) | (~c1_1(a586)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(6307,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | (~c0_1(a586)) | c3_1(a586) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a586))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6306, 6305])).
% 1.82/2.04 tff(6308,plain,
% 1.82/2.04 (c3_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6307, 156, 35, 4884, 6219, 86, 6301, 6299, 85])).
% 1.82/2.04 tff(6309,plain,
% 1.82/2.04 (hskp38),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1211, 6308, 6301, 6300, 6299])).
% 1.82/2.04 tff(6310,plain,
% 1.82/2.04 (c0_1(a547)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[677, 6309])).
% 1.82/2.04 tff(6311,plain,
% 1.82/2.04 (c1_1(a547)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[685, 6309])).
% 1.82/2.04 tff(6312,plain,
% 1.82/2.04 (c2_1(a547)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[693, 6309])).
% 1.82/2.04 tff(6313,plain,
% 1.82/2.04 (hskp42),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[3196, 156, 6312, 6311, 6310, 5849, 24, 1364, 6283])).
% 1.82/2.04 tff(6314,plain,
% 1.82/2.04 (~c2_1(a556)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1385, 6313])).
% 1.82/2.04 tff(6315,plain,
% 1.82/2.04 (c3_1(a537)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1132, 6296])).
% 1.82/2.04 tff(6316,plain,
% 1.82/2.04 (c3_1(a556)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1403, 6313])).
% 1.82/2.04 tff(6317,plain,
% 1.82/2.04 (c1_1(a556)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1411, 6313])).
% 1.82/2.04 tff(6318,plain,
% 1.82/2.04 (~c2_1(a537)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[2192, 156, 6317, 6316, 6315, 6314, 6297, 6295, 6294, 6293, 45])).
% 1.82/2.04 tff(6319,plain,
% 1.82/2.04 (hskp0),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4925, 156, 6312, 6311, 6310, 6295, 6294, 6293, 108])).
% 1.82/2.04 tff(6320,plain,
% 1.82/2.04 (~c2_1(a535)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[713, 6319])).
% 1.82/2.04 tff(6321,plain,
% 1.82/2.04 (c0_1(a535)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[721, 6319])).
% 1.82/2.04 tff(6322,plain,
% 1.82/2.04 (c1_1(a535)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[729, 6319])).
% 1.82/2.04 tff(6323,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[2754, 156, 6312, 6311, 6310, 6315, 6322, 6321, 6297, 6320, 707, 6318])).
% 1.82/2.04 tff(6324,plain,(c0_1(a548) | c2_1(a548) | hskp33 | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.04 tff(6325,plain,
% 1.82/2.04 (c0_1(a548)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6324, 86, 35, 24])).
% 1.82/2.04 tff(6326,plain,
% 1.82/2.04 (~hskp6),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[211, 6325])).
% 1.82/2.04 tff(6327,plain,
% 1.82/2.04 (hskp4),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[205, 6326, 6220])).
% 1.82/2.04 tff(6328,plain,
% 1.82/2.04 (~c0_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1666, 6327])).
% 1.82/2.04 tff(6329,plain,
% 1.82/2.04 (~c2_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1643, 6327])).
% 1.82/2.04 tff(6330,plain,
% 1.82/2.04 (c3_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6307, 156, 35, 4884, 6219, 86, 6329, 6328, 85])).
% 1.82/2.04 tff(6331,plain,
% 1.82/2.04 (~hskp50),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6209, 6327, 35])).
% 1.82/2.04 tff(6332,plain,
% 1.82/2.04 (~hskp19),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[3077, 6328, 35, 6220, 6326])).
% 1.82/2.04 tff(6333,plain,
% 1.82/2.04 (c1_1(a548)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4803, 6332, 6325, 6331])).
% 1.82/2.04 tff(6334,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a548) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a548) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6335,plain,
% 1.82/2.04 ((hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545))) <=> (hskp46 | c2_1(a548) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6336,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a548) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c3_1(a548)) | (~c1_1(a548))))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[6335])).
% 1.82/2.04 tff(6337,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a548) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.82/2.04 inference(transitivity,[status(thm)],[6336, 6334])).
% 1.82/2.04 tff(6338,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c0_1(a545) | (~c3_1(a545)))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(6339,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a548) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c3_1(a548)) | (~c1_1(a548))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6338, 6337])).
% 1.82/2.04 tff(6340,plain,
% 1.82/2.04 (hskp46 | (~c3_1(a545))),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6339, 156, 5849, 24, 6329, 6328, 12, 6333])).
% 1.82/2.04 tff(6341,plain,
% 1.82/2.04 (hskp46),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6340, 6330])).
% 1.82/2.04 tff(6342,plain,
% 1.82/2.04 (~c0_1(a562)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[64, 6341])).
% 1.82/2.04 tff(6343,plain,
% 1.82/2.04 (~c3_1(a562)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[270, 6341])).
% 1.82/2.04 tff(6344,plain,
% 1.82/2.04 (c1_1(a545)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[193, 6327])).
% 1.82/2.04 tff(6345,plain,
% 1.82/2.04 (hskp38),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1211, 6330, 6329, 6344, 6328])).
% 1.82/2.04 tff(6346,plain,
% 1.82/2.04 (c0_1(a547)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[677, 6345])).
% 1.82/2.04 tff(6347,plain,
% 1.82/2.04 (c1_1(a547)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[685, 6345])).
% 1.82/2.04 tff(6348,plain,
% 1.82/2.04 (c2_1(a547)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[693, 6345])).
% 1.82/2.04 tff(6349,plain,
% 1.82/2.04 (c1_1(a562)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[288, 6341])).
% 1.82/2.04 tff(6350,plain,
% 1.82/2.04 (hskp34),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[2160, 156, 6349, 6348, 6347, 6346, 6343, 6342, 75])).
% 1.82/2.04 tff(6351,plain,
% 1.82/2.04 (~c1_1(a537)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1124, 6350])).
% 1.82/2.04 tff(6352,plain,
% 1.82/2.04 (c0_1(a537)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1147, 6350])).
% 1.82/2.04 tff(6353,plain,
% 1.82/2.04 (c2_1(a537)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1154, 156, 6331, 6332, 6352, 6351, 34])).
% 1.82/2.04 tff(6354,plain,
% 1.82/2.04 (hskp39),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1586, 6348, 6330, 6347, 6346, 6344, 6329, 6328])).
% 1.82/2.04 tff(6355,plain,
% 1.82/2.04 (c1_1(a549)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[303, 6354])).
% 1.82/2.04 tff(6356,plain,
% 1.82/2.04 (c2_1(a549)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[311, 6354])).
% 1.82/2.04 tff(6357,plain,
% 1.82/2.04 (c3_1(a549)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[319, 6354])).
% 1.82/2.04 tff(6358,plain,
% 1.82/2.04 (hskp25),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4507, 156, 6357, 6356, 6355, 5849, 24, 55, 6333])).
% 1.82/2.04 tff(6359,plain,
% 1.82/2.04 (~c1_1(a582)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1190, 6358])).
% 1.82/2.04 tff(6360,plain,
% 1.82/2.04 (~c2_1(a582)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1196, 6358])).
% 1.82/2.04 tff(6361,plain,
% 1.82/2.04 (~c3_1(a582)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1202, 6358])).
% 1.82/2.04 tff(6362,plain,
% 1.82/2.04 (hskp42),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[3196, 156, 6348, 6347, 6346, 5849, 24, 1364, 6333])).
% 1.82/2.04 tff(6363,plain,
% 1.82/2.04 (~c2_1(a556)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1385, 6362])).
% 1.82/2.04 tff(6364,plain,
% 1.82/2.04 (c3_1(a537)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1132, 6350])).
% 1.82/2.04 tff(6365,plain,
% 1.82/2.04 (c3_1(a556)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1403, 6362])).
% 1.82/2.04 tff(6366,plain,
% 1.82/2.04 (c1_1(a556)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1411, 6362])).
% 1.82/2.04 tff(6367,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[2192, 156, 6366, 6365, 6364, 6363, 6351, 6361, 6360, 6359, 45, 6353])).
% 1.82/2.04 tff(6368,plain,(c3_1(a586) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.82/2.04 tff(6369,plain,
% 1.82/2.04 (c3_1(a586)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6368, 35, 24])).
% 1.82/2.04 tff(6370,plain,
% 1.82/2.04 (~hskp27),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[3996, 6369])).
% 1.82/2.04 tff(6371,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a591) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | c3_1(a591) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a591) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | c3_1(a591) | (~c1_1(a591)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6372,plain,
% 1.82/2.04 ((hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548))) <=> (hskp26 | c0_1(a591) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | c3_1(a591) | (~c1_1(a591)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6373,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a591) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | c3_1(a591) | (~c1_1(a591))))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[6372])).
% 1.82/2.04 tff(6374,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a591) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | c3_1(a591) | (~c1_1(a591)))),
% 1.82/2.04 inference(transitivity,[status(thm)],[6373, 6371])).
% 1.82/2.04 tff(6375,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(6376,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a591) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | c3_1(a591) | (~c1_1(a591))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6375, 6374])).
% 1.82/2.04 tff(6377,plain,
% 1.82/2.04 (hskp26),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6376, 156, 4716, 249, 4714, 56, 1686, 57, 4717])).
% 1.82/2.04 tff(6378,plain,
% 1.82/2.04 (~c3_1(a584)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1620, 6377])).
% 1.82/2.04 tff(6379,plain,
% 1.82/2.04 (c1_1(a584)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1637, 6377])).
% 1.82/2.04 tff(6380,plain,
% 1.82/2.04 (c0_1(a584)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1629, 6377])).
% 1.82/2.04 tff(6381,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a591))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6382,plain,
% 1.82/2.04 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a591) | c3_1(a591) | c0_1(a591)) <=> (hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a591))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6383,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a591)))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[6382])).
% 1.82/2.04 tff(6384,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a591))),
% 1.82/2.04 inference(transitivity,[status(thm)],[6383, 6381])).
% 1.82/2.04 tff(6385,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a591) | c3_1(a591) | c0_1(a591))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(6386,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a591)),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6385, 6384])).
% 1.82/2.04 tff(6387,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6386, 156, 35, 6380, 6379, 4715, 4714, 6378, 85, 4717])).
% 1.82/2.04 tff(6388,plain,((~hskp30) | hskp33 | (~c3_1(a548)) | c0_1(a548) | c1_1(a548) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.82/2.04 tff(6389,plain,
% 1.82/2.04 (~hskp30),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6388, 946, 5849, 56, 57, 35])).
% 1.82/2.04 tff(6390,plain,
% 1.82/2.04 (hskp29),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4620, 6389, 5849, 57])).
% 1.82/2.04 tff(6391,plain,
% 1.82/2.04 (~c3_1(a590)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4586, 6390])).
% 1.82/2.04 tff(6392,plain,
% 1.82/2.04 (((~hskp29) | (~c1_1(a590))) <=> ((~hskp29) | (~c1_1(a590)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6393,plain,
% 1.82/2.04 (((~c1_1(a590)) | (~hskp29)) <=> ((~hskp29) | (~c1_1(a590)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6394,axiom,((~c1_1(a590)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.82/2.04 tff(6395,plain,
% 1.82/2.04 ((~hskp29) | (~c1_1(a590))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6394, 6393])).
% 1.82/2.04 tff(6396,plain,
% 1.82/2.04 ((~hskp29) | (~c1_1(a590))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6395, 6392])).
% 1.82/2.04 tff(6397,plain,
% 1.82/2.04 (~c1_1(a590)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6396, 6390])).
% 1.82/2.04 tff(6398,assumption,(~c2_1(a590)), introduced(assumption)).
% 1.82/2.04 tff(6399,assumption,(~c1_1(a590)), introduced(assumption)).
% 1.82/2.04 tff(6400,assumption,(~c3_1(a590)), introduced(assumption)).
% 1.82/2.04 tff(6401,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a590))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6402,plain,
% 1.82/2.04 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a590))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6403,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a590)))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[6402])).
% 1.82/2.04 tff(6404,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a590))),
% 1.82/2.04 inference(transitivity,[status(thm)],[6403, 6401])).
% 1.82/2.04 tff(6405,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(6406,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a590)),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6405, 6404])).
% 1.82/2.04 tff(6407,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6406, 156, 58, 249, 6400, 6399, 24, 56, 663, 6398])).
% 1.82/2.04 tff(6408,plain,(c2_1(a590) | hskp38 | (~c3_1(a548)) | c3_1(a590) | c1_1(a590) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.04 tff(6409,plain,
% 1.82/2.04 (c2_1(a590)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6408, 6397, 5849, 56, 6391, 24, 58])).
% 1.82/2.04 tff(6410,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a562)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6411,plain,
% 1.82/2.04 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586))) <=> (hskp26 | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a562)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6412,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a562))))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[6411])).
% 1.82/2.04 tff(6413,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a562)))),
% 1.82/2.04 inference(transitivity,[status(thm)],[6412, 6410])).
% 1.82/2.04 tff(6414,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(6415,plain,
% 1.82/2.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a562))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6414, 6413])).
% 1.82/2.04 tff(6416,plain,
% 1.82/2.04 (hskp26),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6415, 156, 3245, 88, 3244, 65, 87, 6369, 1686])).
% 1.82/2.04 tff(6417,plain,
% 1.82/2.04 (~c3_1(a584)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1620, 6416])).
% 1.82/2.04 tff(6418,plain,
% 1.82/2.04 (c1_1(a584)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1637, 6416])).
% 1.82/2.04 tff(6419,plain,
% 1.82/2.04 (c0_1(a584)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[1629, 6416])).
% 1.82/2.04 tff(6420,plain,
% 1.82/2.04 (c0_1(a544)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[2862, 156, 35, 1649, 1648, 2503, 2502, 1647, 85])).
% 1.82/2.04 tff(6421,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6422,plain,
% 1.82/2.04 (((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c1_1(a586) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6423,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562))))),
% 1.82/2.04 inference(monotonicity,[status(thm)],[6422])).
% 1.82/2.04 tff(6424,plain,
% 1.82/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562)))),
% 1.82/2.04 inference(transitivity,[status(thm)],[6423, 6421])).
% 1.82/2.04 tff(6425,plain,
% 1.82/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.82/2.04 inference(quant_inst,[status(thm)],[])).
% 1.82/2.04 tff(6426,plain,
% 1.82/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a562) | c0_1(a562) | c2_1(a544) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c0_1(a544)) | (~c1_1(a544)) | (~c2_1(a562))),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[6425, 6424])).
% 1.82/2.04 tff(6427,plain,
% 1.82/2.04 ((~c0_1(a544)) | (~c2_1(a562))),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6426, 156, 2504, 88, 972, 971, 2503, 87, 4948, 609])).
% 1.82/2.04 tff(6428,plain,
% 1.82/2.04 (~c2_1(a562)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6427, 6420])).
% 1.82/2.04 tff(6429,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[4690, 156, 35, 2504, 972, 971, 2502, 85, 6420, 6428])).
% 1.82/2.04 tff(6430,plain,((~hskp37) | hskp33 | c3_1(a562) | c0_1(a562) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.04 tff(6431,plain,
% 1.82/2.04 (~hskp37),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6430, 3244, 35, 65, 88, 87, 6369, 6419, 6418, 6417])).
% 1.82/2.04 tff(6432,plain,
% 1.82/2.04 (~hskp18),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[2583, 58, 5849, 24, 56, 6431])).
% 1.82/2.04 tff(6433,plain,
% 1.82/2.04 ($false),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[5948, 156, 58, 249, 5371, 1279, 1280, 24, 56, 663])).
% 1.82/2.04 tff(6434,plain,((~hskp25) | hskp38 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.04 tff(6435,plain,
% 1.82/2.04 (~hskp25),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6434, 58, 5849, 24, 56])).
% 1.82/2.04 tff(6436,plain,
% 1.82/2.04 (c3_1(a591)),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[6386, 156, 35, 1649, 1648, 4715, 4714, 1647, 85])).
% 1.82/2.04 tff(6437,plain,
% 1.82/2.04 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a591) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a591) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.82/2.04 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(6438,plain,
% 1.82/2.04 ((hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591))) <=> (hskp25 | c2_1(a591) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6439,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a591) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a591)) | (~c1_1(a591))))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[6438])).
% 1.82/2.05 tff(6440,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a591) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[6439, 6437])).
% 1.82/2.05 tff(6441,plain,
% 1.82/2.05 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(6442,plain,
% 1.82/2.05 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a591) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a591)) | (~c1_1(a591))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[6441, 6440])).
% 1.82/2.05 tff(6443,plain,
% 1.82/2.05 ((~c1_1(a589)) | (~c3_1(a591))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6442, 156, 1423, 4716, 625, 591, 4715, 55])).
% 1.82/2.05 tff(6444,plain,
% 1.82/2.05 (~c1_1(a589)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6443, 6436])).
% 1.82/2.05 tff(6445,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a562)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6446,plain,
% 1.82/2.05 ((hskp39 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a562)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6447,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a562))))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[6446])).
% 1.82/2.05 tff(6448,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a562)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[6447, 6445])).
% 1.82/2.05 tff(6449,plain,
% 1.82/2.05 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(6450,plain,
% 1.82/2.05 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a562))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[6449, 6448])).
% 1.82/2.05 tff(6451,plain,
% 1.82/2.05 (hskp39 | (~c3_1(a591))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6450, 156, 973, 4716, 972, 971, 4715, 281])).
% 1.82/2.05 tff(6452,plain,
% 1.82/2.05 (hskp39),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6451, 6436])).
% 1.82/2.05 tff(6453,plain,
% 1.82/2.05 ($false),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[2535, 6452, 6444, 58, 591, 625])).
% 1.82/2.05 tff(6454,plain,((~hskp30) | hskp38 | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a562)) | c3_1(a562) | c0_1(a562) | hskp25 | hskp33 | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.05 tff(6455,plain,
% 1.82/2.05 (~hskp30),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6454, 58, 4534, 4533, 3245, 3244, 65, 6435, 35, 6419, 6418, 6417])).
% 1.82/2.05 tff(6456,plain,
% 1.82/2.05 (hskp29),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[4620, 6455, 5849, 57])).
% 1.82/2.05 tff(6457,plain,
% 1.82/2.05 (~c0_1(a590)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[4580, 6456])).
% 1.82/2.05 tff(6458,plain,
% 1.82/2.05 (~c1_1(a590)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6396, 6456])).
% 1.82/2.05 tff(6459,plain,
% 1.82/2.05 (~c3_1(a590)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[4586, 6456])).
% 1.82/2.05 tff(6460,plain,
% 1.82/2.05 (~hskp39),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[2535, 1716, 58, 591, 625])).
% 1.82/2.05 tff(6461,plain,
% 1.82/2.05 (~hskp16),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[2301, 6460, 973, 625, 971, 591, 58, 972, 1716])).
% 1.82/2.05 tff(6462,plain,
% 1.82/2.05 (hskp17),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[382, 6461, 1795])).
% 1.82/2.05 tff(6463,plain,
% 1.82/2.05 (~c2_1(a571)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[573, 6462])).
% 1.82/2.05 tff(6464,plain,
% 1.82/2.05 (hskp26),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6415, 156, 973, 88, 972, 971, 87, 4948, 1686])).
% 1.82/2.05 tff(6465,plain,
% 1.82/2.05 (~c3_1(a584)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[1620, 6464])).
% 1.82/2.05 tff(6466,plain,
% 1.82/2.05 (c1_1(a584)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[1637, 6464])).
% 1.82/2.05 tff(6467,plain,
% 1.82/2.05 (c0_1(a584)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[1629, 6464])).
% 1.82/2.05 tff(6468,assumption,(~hskp24), introduced(assumption)).
% 1.82/2.05 tff(6469,plain,
% 1.82/2.05 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | c2_1(a584))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | c2_1(a584))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6470,plain,
% 1.82/2.05 ((hskp39 | hskp24 | (~ndr1_0) | c2_1(a584) | c3_1(a584) | (~c0_1(a584))) <=> (hskp39 | hskp24 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | c2_1(a584))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6471,plain,
% 1.82/2.05 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a584) | c3_1(a584) | (~c0_1(a584)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | c2_1(a584)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[6470])).
% 1.82/2.05 tff(6472,plain,
% 1.82/2.05 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a584) | c3_1(a584) | (~c0_1(a584)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | c2_1(a584))),
% 1.82/2.05 inference(transitivity,[status(thm)],[6471, 6469])).
% 1.82/2.05 tff(6473,plain,
% 1.82/2.05 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a584) | c3_1(a584) | (~c0_1(a584)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(6474,plain,
% 1.82/2.05 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | c2_1(a584)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[6473, 6472])).
% 1.82/2.05 tff(6475,plain,
% 1.82/2.05 (hskp24 | c2_1(a584)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6474, 156, 859, 1649, 1647, 3496])).
% 1.82/2.05 tff(6476,plain,
% 1.82/2.05 (c2_1(a584)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6475, 6468])).
% 1.82/2.05 tff(6477,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6478,plain,
% 1.82/2.05 ((hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584) | (~c1_1(a584)) | (~c2_1(a584))) <=> (hskp32 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6479,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584) | (~c1_1(a584)) | (~c2_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584))))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[6478])).
% 1.82/2.05 tff(6480,plain,
% 1.82/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584) | (~c1_1(a584)) | (~c2_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[6479, 6477])).
% 1.82/2.05 tff(6481,plain,
% 1.82/2.05 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584) | (~c1_1(a584)) | (~c2_1(a584)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(6482,plain,
% 1.82/2.05 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[6481, 6480])).
% 1.82/2.05 tff(6483,plain,
% 1.82/2.05 (hskp32 | (~c2_1(a584))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6482, 156, 1649, 1648, 1647, 4894])).
% 1.82/2.05 tff(6484,plain,
% 1.82/2.05 (hskp32),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6483, 6476])).
% 1.82/2.05 tff(6485,plain,
% 1.82/2.05 (~c2_1(a596)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[5534, 6484])).
% 1.82/2.05 tff(6486,plain,
% 1.82/2.05 (~c3_1(a596)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[5528, 6484])).
% 1.82/2.05 tff(6487,plain,
% 1.82/2.05 (c0_1(a596)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[5522, 6484])).
% 1.82/2.05 tff(6488,plain,
% 1.82/2.05 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a596)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a596)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6489,plain,
% 1.82/2.05 ((hskp39 | hskp24 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c0_1(a596))) <=> (hskp39 | hskp24 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a596)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6490,plain,
% 1.82/2.05 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c0_1(a596)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a596))))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[6489])).
% 1.82/2.05 tff(6491,plain,
% 1.82/2.05 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c0_1(a596)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a596)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[6490, 6488])).
% 1.82/2.05 tff(6492,plain,
% 1.82/2.05 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c0_1(a596)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(6493,plain,
% 1.82/2.05 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a596))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 1.82/2.05 tff(6494,plain,
% 1.82/2.05 ($false),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6493, 156, 859, 6468, 6487, 6486, 6485, 3496])).
% 1.82/2.05 tff(6495,plain,(hskp24 | hskp39 | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.05 tff(6496,plain,
% 1.82/2.05 (hskp24),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[6495, 6460, 6467, 6466, 6465])).
% 1.82/2.05 tff(6497,plain,
% 1.82/2.05 (~c3_1(a581)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[3513, 6496])).
% 1.82/2.05 tff(6498,plain,
% 1.82/2.05 (~c1_1(a581)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[3519, 6496])).
% 1.82/2.05 tff(6499,plain,
% 1.82/2.05 (c3_1(a571)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[623, 6462])).
% 1.82/2.05 tff(6500,plain,
% 1.82/2.05 (c0_1(a571)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[581, 6462])).
% 1.82/2.05 tff(6501,plain,
% 1.82/2.05 (c2_1(a581)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[3541, 6496])).
% 1.82/2.05 tff(6502,plain,
% 1.82/2.05 (c1_1(a571)),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[5402, 156, 6501, 6500, 6499, 6498, 6497, 6463, 921])).
% 1.82/2.05 tff(6503,assumption,(~c0_1(a590)), introduced(assumption)).
% 1.82/2.05 tff(6504,assumption,(c2_1(a590)), introduced(assumption)).
% 1.82/2.05 tff(6505,plain,
% 1.82/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a590)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6506,plain,
% 1.82/2.05 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571))) <=> (c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a590)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(6507,plain,
% 1.82/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a590))))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[6506])).
% 1.82/2.05 tff(6508,plain,
% 1.82/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a590)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[6507, 6505])).
% 1.90/2.05 tff(6509,plain,
% 1.90/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))),
% 1.90/2.05 inference(quant_inst,[status(thm)],[])).
% 1.90/2.05 tff(6510,plain,
% 1.90/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a590))),
% 1.90/2.05 inference(modus_ponens,[status(thm)],[6509, 6508])).
% 1.90/2.05 tff(6511,plain,
% 1.90/2.05 (c1_1(a571)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6510, 156, 925, 924, 6400, 6399, 923, 921, 6504])).
% 1.90/2.05 tff(6512,plain,
% 1.90/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a590)))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6513,plain,
% 1.90/2.05 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a590)))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6514,plain,
% 1.90/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a590))))),
% 1.90/2.05 inference(monotonicity,[status(thm)],[6513])).
% 1.90/2.05 tff(6515,plain,
% 1.90/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a590)))),
% 1.90/2.05 inference(transitivity,[status(thm)],[6514, 6512])).
% 1.90/2.05 tff(6516,plain,
% 1.90/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.90/2.05 inference(quant_inst,[status(thm)],[])).
% 1.90/2.05 tff(6517,plain,
% 1.90/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c2_1(a590))),
% 1.90/2.05 inference(modus_ponens,[status(thm)],[6516, 6515])).
% 1.90/2.05 tff(6518,plain,
% 1.90/2.05 ($false),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6517, 156, 88, 925, 6400, 6503, 87, 4948, 923, 609, 6504, 6511])).
% 1.90/2.05 tff(6519,plain,((~hskp17) | c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~c2_1(a590)) | c1_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.05 tff(6520,plain,
% 1.90/2.05 (~c2_1(a590)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6519, 6462, 6400, 6399, 87, 4948, 6503, 88])).
% 1.90/2.05 tff(6521,plain,
% 1.90/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a590))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6522,plain,
% 1.90/2.05 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a590))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6523,plain,
% 1.90/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a590)))),
% 1.90/2.05 inference(monotonicity,[status(thm)],[6522])).
% 1.90/2.05 tff(6524,plain,
% 1.90/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a590))),
% 1.90/2.05 inference(transitivity,[status(thm)],[6523, 6521])).
% 1.90/2.05 tff(6525,plain,
% 1.90/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 1.90/2.05 inference(quant_inst,[status(thm)],[])).
% 1.90/2.05 tff(6526,plain,
% 1.90/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a590) | c1_1(a590) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a590)),
% 1.90/2.05 inference(modus_ponens,[status(thm)],[6525, 6524])).
% 1.90/2.05 tff(6527,plain,
% 1.90/2.05 ($false),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6526, 156, 625, 591, 6499, 6400, 6399, 6463, 45, 1716, 6520, 6502])).
% 1.90/2.05 tff(6528,plain,(c1_1(a589) | (~c2_1(a589)) | (~c3_1(a589)) | c3_1(a590) | c1_1(a590) | c0_1(a586) | (~c3_1(a586)) | c0_1(a590) | c1_1(a586) | hskp18 | (~c1_1(a562)) | c0_1(a562) | hskp38 | c3_1(a562)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.05 tff(6529,plain,
% 1.90/2.05 (c1_1(a589)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6528, 6459, 4534, 4533, 6458, 87, 6369, 6457, 88, 6432, 3245, 65, 58, 3244])).
% 1.90/2.05 tff(6530,assumption,(c1_1(a589)), introduced(assumption)).
% 1.90/2.05 tff(6531,plain,
% 1.90/2.05 ($false),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[2291, 156, 23, 3245, 625, 591, 3244, 65, 22, 6530])).
% 1.90/2.05 tff(6532,plain,((~hskp46) | hskp4 | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))), inference(lemma,lemma(discharge,[]))).
% 1.90/2.05 tff(6533,plain,
% 1.90/2.05 (hskp4),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6532, 6529, 4533, 4534, 59])).
% 1.90/2.05 tff(6534,plain,
% 1.90/2.05 (~c0_1(a545)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1666, 6533])).
% 1.90/2.05 tff(6535,plain,
% 1.90/2.05 ($false),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1659, 6534, 6533, 35, 6416, 58])).
% 1.90/2.05 tff(6536,plain,(hskp38 | hskp33 | (~hskp46) | c0_1(a586) | c1_1(a586) | c1_1(a548) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.05 tff(6537,plain,
% 1.90/2.05 (hskp38),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6536, 59, 35, 87, 88, 57, 24, 56])).
% 1.90/2.05 tff(6538,plain,
% 1.90/2.05 (c2_1(a547)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[693, 6537])).
% 1.90/2.05 tff(6539,plain,
% 1.90/2.05 (c1_1(a547)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[685, 6537])).
% 1.90/2.05 tff(6540,plain,
% 1.90/2.05 (c0_1(a547)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[677, 6537])).
% 1.90/2.05 tff(6541,plain,
% 1.90/2.05 (~hskp0),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[2694, 6540, 5849, 57, 6539, 24, 6538])).
% 1.90/2.05 tff(6542,plain,
% 1.90/2.05 (hskp34),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[2160, 156, 3245, 6538, 6539, 6540, 3244, 65, 75])).
% 1.90/2.05 tff(6543,plain,
% 1.90/2.05 (~c1_1(a537)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1124, 6542])).
% 1.90/2.05 tff(6544,plain,
% 1.90/2.05 (c3_1(a537)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1132, 6542])).
% 1.90/2.05 tff(6545,plain,
% 1.90/2.05 (c0_1(a537)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1147, 6542])).
% 1.90/2.05 tff(6546,plain,
% 1.90/2.05 ($false),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[4925, 156, 837, 733, 732, 731, 5371, 1279, 1280, 108])).
% 1.90/2.05 tff(6547,plain,((~hskp25) | hskp0 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547))), inference(lemma,lemma(discharge,[]))).
% 1.90/2.05 tff(6548,plain,
% 1.90/2.05 (~hskp25),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6547, 6541, 6538, 6539, 6540])).
% 1.90/2.05 tff(6549,plain,
% 1.90/2.05 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6550,plain,
% 1.90/2.05 ((hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547))) <=> (hskp42 | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6551,plain,
% 1.90/2.05 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.90/2.05 inference(monotonicity,[status(thm)],[6550])).
% 1.90/2.05 tff(6552,plain,
% 1.90/2.05 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.05 inference(transitivity,[status(thm)],[6551, 6549])).
% 1.90/2.05 tff(6553,plain,
% 1.90/2.05 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))),
% 1.90/2.05 inference(quant_inst,[status(thm)],[])).
% 1.90/2.05 tff(6554,plain,
% 1.90/2.05 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a591) | (~ndr1_0) | (~c3_1(a591)) | (~c1_1(a591)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.90/2.05 inference(modus_ponens,[status(thm)],[6553, 6552])).
% 1.90/2.05 tff(6555,plain,
% 1.90/2.05 (hskp42 | (~c3_1(a591))),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6554, 156, 733, 732, 731, 4716, 4715, 1364])).
% 1.90/2.05 tff(6556,plain,
% 1.90/2.05 (hskp42),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6555, 6436])).
% 1.90/2.05 tff(6557,plain,
% 1.90/2.05 (~c2_1(a556)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1385, 6556])).
% 1.90/2.05 tff(6558,plain,
% 1.90/2.05 (c1_1(a549)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[303, 6452])).
% 1.90/2.05 tff(6559,plain,
% 1.90/2.05 (c2_1(a549)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[311, 6452])).
% 1.90/2.05 tff(6560,plain,
% 1.90/2.05 (c3_1(a549)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[319, 6452])).
% 1.90/2.05 tff(6561,plain,
% 1.90/2.05 (c3_1(a556)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1403, 6556])).
% 1.90/2.05 tff(6562,plain,
% 1.90/2.05 (c1_1(a556)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[1411, 6556])).
% 1.90/2.05 tff(6563,plain,
% 1.90/2.05 ($false),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[5026, 156, 1423, 6562, 6561, 6560, 6559, 6558, 6557, 55])).
% 1.90/2.05 tff(6564,plain,((~hskp30) | hskp25 | (~c1_1(a562)) | c3_1(a562) | c0_1(a562) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp33 | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.05 tff(6565,plain,
% 1.90/2.05 (~hskp30),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6564, 6548, 3245, 3244, 65, 6538, 6539, 6540, 35, 6419, 6418, 6417])).
% 1.90/2.05 tff(6566,plain,
% 1.90/2.05 (hskp29),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[4620, 6565, 5849, 57])).
% 1.90/2.05 tff(6567,plain,
% 1.90/2.05 (~c3_1(a590)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[4586, 6566])).
% 1.90/2.05 tff(6568,plain,
% 1.90/2.05 (~c1_1(a590)),
% 1.90/2.05 inference(unit_resolution,[status(thm)],[6396, 6566])).
% 1.90/2.05 tff(6569,plain,
% 1.90/2.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | c2_1(a590) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | c2_1(a590) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6570,plain,
% 1.90/2.05 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | c2_1(a590) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.05 inference(rewrite,[status(thm)],[])).
% 1.90/2.05 tff(6571,plain,
% 1.90/2.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | c2_1(a590) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.90/2.05 inference(monotonicity,[status(thm)],[6570])).
% 1.90/2.05 tff(6572,plain,
% 1.90/2.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | c2_1(a590) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.05 inference(transitivity,[status(thm)],[6571, 6569])).
% 1.90/2.05 tff(6573,plain,
% 1.90/2.05 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 1.90/2.05 inference(quant_inst,[status(thm)],[])).
% 1.90/2.05 tff(6574,plain,
% 1.90/2.05 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | c2_1(a590) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6573, 6572])).
% 1.90/2.06 tff(6575,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6574, 156, 837, 733, 732, 731, 6400, 6399, 108, 6398])).
% 1.90/2.06 tff(6576,plain,(c2_1(a590) | hskp0 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c3_1(a590) | c1_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6577,plain,
% 1.90/2.06 (c2_1(a590)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6576, 6399, 733, 732, 731, 6400, 837])).
% 1.90/2.06 tff(6578,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c3_1(a590) | (~c0_1(a590)) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a590) | (~c0_1(a590)) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6579,plain,
% 1.90/2.06 ((hskp37 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c1_1(a590) | c3_1(a590) | (~c0_1(a590))) <=> (hskp37 | c3_1(a590) | (~c0_1(a590)) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6580,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c1_1(a590) | c3_1(a590) | (~c0_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c3_1(a590) | (~c0_1(a590)) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6579])).
% 1.90/2.06 tff(6581,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c1_1(a590) | c3_1(a590) | (~c0_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a590) | (~c0_1(a590)) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6580, 6578])).
% 1.90/2.06 tff(6582,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c1_1(a590) | c3_1(a590) | (~c0_1(a590)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6583,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a590) | (~c0_1(a590)) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6582, 6581])).
% 1.90/2.06 tff(6584,plain,
% 1.90/2.06 (~c0_1(a590)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6583, 156, 422, 6400, 6399, 415, 6577])).
% 1.90/2.06 tff(6585,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a537) | c0_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a537) | c0_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6586,plain,
% 1.90/2.06 ((hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp8 | c1_1(a537) | c0_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6587,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a537) | c0_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6586])).
% 1.90/2.06 tff(6588,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a537) | c0_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6587, 6585])).
% 1.90/2.06 tff(6589,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6590,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a537) | c0_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6589, 6588])).
% 1.90/2.06 tff(6591,plain,
% 1.90/2.06 (hskp8 | c0_1(a590)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6590, 156, 4780, 4779, 4778, 6399, 2407, 6577])).
% 1.90/2.06 tff(6592,plain,
% 1.90/2.06 (hskp8),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6591, 6584])).
% 1.90/2.06 tff(6593,assumption,(hskp8), introduced(assumption)).
% 1.90/2.06 tff(6594,plain,
% 1.90/2.06 (~c2_1(a552)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2424, 6593])).
% 1.90/2.06 tff(6595,plain,
% 1.90/2.06 (~c1_1(a552)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2453, 6593])).
% 1.90/2.06 tff(6596,plain,
% 1.90/2.06 (~c3_1(a552)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2430, 6593])).
% 1.90/2.06 tff(6597,assumption,(~hskp51), introduced(assumption)).
% 1.90/2.06 tff(6598,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[3636, 156, 6597, 4780, 4779, 4778, 6596, 6595, 6594, 2608])).
% 1.90/2.06 tff(6599,plain,((~hskp8) | hskp51 | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6600,plain,
% 1.90/2.06 (hskp51),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6599, 6592, 4780, 4779, 4778])).
% 1.90/2.06 tff(6601,plain,
% 1.90/2.06 (~c2_1(a583)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2637, 6600])).
% 1.90/2.06 tff(6602,plain,
% 1.90/2.06 (c0_1(a583)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2653, 6600])).
% 1.90/2.06 tff(6603,plain,
% 1.90/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6604,plain,
% 1.90/2.06 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583))) <=> (c1_1(a586) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6605,plain,
% 1.90/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6604])).
% 1.90/2.06 tff(6606,plain,
% 1.90/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6605, 6603])).
% 1.90/2.06 tff(6607,plain,
% 1.90/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6608,plain,
% 1.90/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6607, 6606])).
% 1.90/2.06 tff(6609,plain,
% 1.90/2.06 (~c1_1(a583)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6608, 156, 6602, 88, 6601, 6400, 6584, 87, 4948, 609, 6577])).
% 1.90/2.06 tff(6610,plain,
% 1.90/2.06 (c3_1(a583)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2645, 6600])).
% 1.90/2.06 tff(6611,plain,
% 1.90/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6612,plain,
% 1.90/2.06 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583))) <=> (c2_1(a583) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6613,plain,
% 1.90/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c2_1(a583) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6612])).
% 1.90/2.06 tff(6614,plain,
% 1.90/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6613, 6611])).
% 1.90/2.06 tff(6615,plain,
% 1.90/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a583)) | c1_1(a583) | (~c3_1(a583)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6616,plain,
% 1.90/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c2_1(a583) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a583)) | c1_1(a583) | (~c0_1(a583))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6615, 6614])).
% 1.90/2.06 tff(6617,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6616, 156, 6602, 6610, 6601, 6400, 6399, 921, 6609, 6577])).
% 1.90/2.06 tff(6618,plain,(c1_1(a590) | c3_1(a590) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537) | hskp37 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6619,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6618, 6568, 6567, 88, 87, 6369, 6545, 6544, 6543, 6431, 6538, 6539, 6540, 6541])).
% 1.90/2.06 tff(6620,plain,((~hskp46) | c1_1(a586) | c0_1(a586) | c1_1(a548) | c2_1(a548) | hskp33 | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6621,plain,
% 1.90/2.06 (~hskp46),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6620, 57, 87, 88, 24, 35, 56])).
% 1.90/2.06 tff(6622,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a586) | c0_1(a591) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c0_1(a591) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6623,plain,
% 1.90/2.06 ((hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586))) <=> (hskp26 | c1_1(a586) | c0_1(a591) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6624,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a586) | c0_1(a591) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6623])).
% 1.90/2.06 tff(6625,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c0_1(a591) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6624, 6622])).
% 1.90/2.06 tff(6626,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6627,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a586) | c0_1(a591) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6626, 6625])).
% 1.90/2.06 tff(6628,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6627, 156, 1661, 4716, 88, 4714, 87, 4948, 1686, 4717])).
% 1.90/2.06 tff(6629,plain,((~hskp30) | hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6630,plain,
% 1.90/2.06 (hskp26),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6629, 4713, 88, 87, 4948, 946])).
% 1.90/2.06 tff(6631,plain,
% 1.90/2.06 (~c3_1(a584)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[1620, 6630])).
% 1.90/2.06 tff(6632,plain,
% 1.90/2.06 (c1_1(a584)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[1637, 6630])).
% 1.90/2.06 tff(6633,plain,
% 1.90/2.06 (c0_1(a584)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[1629, 6630])).
% 1.90/2.06 tff(6634,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6386, 156, 35, 6633, 6632, 4715, 4714, 6631, 85, 4717])).
% 1.90/2.06 tff(6635,plain,((~hskp30) | hskp33 | hskp46 | c1_1(a586) | c0_1(a586) | (~c3_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6636,plain,
% 1.90/2.06 (~hskp30),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6635, 6621, 35, 88, 87, 6369])).
% 1.90/2.06 tff(6637,plain,
% 1.90/2.06 (hskp29),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4620, 6636, 5849, 57])).
% 1.90/2.06 tff(6638,plain,
% 1.90/2.06 (~c0_1(a590)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4580, 6637])).
% 1.90/2.06 tff(6639,plain,
% 1.90/2.06 (~c3_1(a590)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4586, 6637])).
% 1.90/2.06 tff(6640,plain,
% 1.90/2.06 (hskp24),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6495, 1630, 859, 1638, 1621])).
% 1.90/2.06 tff(6641,assumption,(hskp24), introduced(assumption)).
% 1.90/2.06 tff(6642,plain,
% 1.90/2.06 (~c1_1(a581)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[3519, 6641])).
% 1.90/2.06 tff(6643,plain,
% 1.90/2.06 (c2_1(a581)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[3541, 6641])).
% 1.90/2.06 tff(6644,plain,
% 1.90/2.06 (~c3_1(a581)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[3513, 6641])).
% 1.90/2.06 tff(6645,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c0_1(a589) | c1_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)) | (~c2_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a589) | c1_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)) | (~c2_1(a589)) | (~c1_1(a589)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6646,plain,
% 1.90/2.06 ((hskp46 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589))) <=> (hskp46 | c0_1(a589) | c1_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)) | (~c2_1(a589)) | (~c1_1(a589)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6647,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c0_1(a589) | c1_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)) | (~c2_1(a589)) | (~c1_1(a589))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6646])).
% 1.90/2.06 tff(6648,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a589) | c1_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)) | (~c2_1(a589)) | (~c1_1(a589)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6647, 6645])).
% 1.90/2.06 tff(6649,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6650,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c0_1(a589) | c1_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)) | (~c2_1(a589)) | (~c1_1(a589))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6649, 6648])).
% 1.90/2.06 tff(6651,plain,
% 1.90/2.06 (hskp46 | (~c0_1(a581))),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6650, 156, 625, 5396, 590, 5395, 2215, 6530])).
% 1.90/2.06 tff(6652,plain,
% 1.90/2.06 (~c0_1(a581)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6651, 946])).
% 1.90/2.06 tff(6653,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a581) | (~ndr1_0) | c0_1(a581) | (~c2_1(a581)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a581) | (~ndr1_0) | c0_1(a581) | (~c2_1(a581)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6654,plain,
% 1.90/2.06 ((hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a581) | c0_1(a581) | (~c2_1(a581))) <=> (hskp46 | c3_1(a581) | (~ndr1_0) | c0_1(a581) | (~c2_1(a581)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6655,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a581) | c0_1(a581) | (~c2_1(a581)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a581) | (~ndr1_0) | c0_1(a581) | (~c2_1(a581)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6654])).
% 1.90/2.06 tff(6656,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a581) | c0_1(a581) | (~c2_1(a581)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a581) | (~ndr1_0) | c0_1(a581) | (~c2_1(a581)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6655, 6653])).
% 1.90/2.06 tff(6657,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a581) | c0_1(a581) | (~c2_1(a581)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6658,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a581) | (~ndr1_0) | c0_1(a581) | (~c2_1(a581)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6657, 6656])).
% 1.90/2.06 tff(6659,plain,
% 1.90/2.06 (hskp46 | c0_1(a581)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6658, 156, 625, 591, 5396, 5394, 858, 6530])).
% 1.90/2.06 tff(6660,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6659, 6652, 946])).
% 1.90/2.06 tff(6661,plain,(hskp46 | (~c2_1(a589)) | (~c3_1(a589)) | (~c2_1(a581)) | c3_1(a581) | (~c1_1(a589)) | c0_1(a589) | c1_1(a581)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6662,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6661, 6644, 6643, 591, 625, 946, 6530, 590, 6642])).
% 1.90/2.06 tff(6663,plain,((~hskp24) | (~c3_1(a589)) | (~c2_1(a589)) | hskp46 | (~c1_1(a589)) | c0_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6664,plain,
% 1.90/2.06 (~c1_1(a589)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6663, 6640, 4533, 4534, 946, 4535])).
% 1.90/2.06 tff(6665,plain,
% 1.90/2.06 (~c2_1(a570)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2299, 156, 58, 625, 591, 365, 357, 1537, 1716])).
% 1.90/2.06 tff(6666,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[963, 156, 946, 365, 357, 349, 12, 6665])).
% 1.90/2.06 tff(6667,plain,((~hskp16) | hskp46 | hskp38 | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6668,plain,
% 1.90/2.06 (~hskp16),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6667, 6664, 4533, 58, 4534, 946])).
% 1.90/2.06 tff(6669,assumption,(~hskp16), introduced(assumption)).
% 1.90/2.06 tff(6670,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6671,plain,
% 1.90/2.06 ((hskp46 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548))) <=> (hskp46 | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.90/2.06 inference(rewrite,[status(thm)],[])).
% 1.90/2.06 tff(6672,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a571)) | (~c1_1(a571))))),
% 1.90/2.06 inference(monotonicity,[status(thm)],[6671])).
% 1.90/2.06 tff(6673,plain,
% 1.90/2.06 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 1.90/2.06 inference(transitivity,[status(thm)],[6672, 6670])).
% 1.90/2.06 tff(6674,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)))),
% 1.90/2.06 inference(quant_inst,[status(thm)],[])).
% 1.90/2.06 tff(6675,plain,
% 1.90/2.06 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a571) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c3_1(a571)) | (~c1_1(a571))),
% 1.90/2.06 inference(modus_ponens,[status(thm)],[6674, 6673])).
% 1.90/2.06 tff(6676,plain,
% 1.90/2.06 ($false),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6675, 156, 946, 924, 249, 923, 24, 56, 12, 5250])).
% 1.90/2.06 tff(6677,plain,((~hskp17) | hskp46 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.90/2.06 tff(6678,plain,
% 1.90/2.06 (~hskp17),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[6677, 98, 5849, 24, 56, 110, 946])).
% 1.90/2.06 tff(6679,plain,
% 1.90/2.06 (hskp18),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[382, 6678, 6669])).
% 1.90/2.06 tff(6680,plain,
% 1.90/2.06 (hskp15),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2224, 6679, 110, 946, 98])).
% 1.90/2.06 tff(6681,plain,
% 1.90/2.06 (~c1_1(a569)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[1261, 6680])).
% 1.90/2.06 tff(6682,plain,
% 1.90/2.06 (~c0_1(a569)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[1267, 6680])).
% 1.90/2.06 tff(6683,plain,
% 1.90/2.06 (hskp37),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2583, 6679, 5849, 24, 56, 58])).
% 1.90/2.06 tff(6684,plain,
% 1.90/2.06 (c1_1(a544)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[444, 6683])).
% 1.90/2.06 tff(6685,plain,
% 1.90/2.06 (~c3_1(a544)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[450, 6683])).
% 1.90/2.06 tff(6686,plain,
% 1.90/2.06 (~c2_1(a544)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[436, 6683])).
% 1.90/2.06 tff(6687,plain,
% 1.90/2.06 (~c2_1(a569)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[1255, 6680])).
% 1.90/2.06 tff(6688,plain,
% 1.90/2.06 (c3_1(a569)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[2821, 156, 58, 5849, 6681, 6687, 24, 56, 663])).
% 1.90/2.06 tff(6689,plain,
% 1.90/2.06 (c0_1(a544)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4555, 6688, 6686, 6685, 6684, 6682, 6681, 35])).
% 1.90/2.06 tff(6690,plain,
% 1.90/2.06 (~hskp30),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4719, 6689, 946, 6684, 6685, 35])).
% 1.90/2.06 tff(6691,plain,
% 1.90/2.06 (hskp29),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4620, 6690, 5849, 57])).
% 1.90/2.06 tff(6692,plain,
% 1.90/2.06 (~c0_1(a590)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4580, 6691])).
% 1.90/2.06 tff(6693,plain,
% 1.90/2.06 (~c3_1(a590)),
% 1.90/2.06 inference(unit_resolution,[status(thm)],[4586, 6691])).
% 1.90/2.06 tff(6694,plain,
% 1.90/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6695,plain,
% 1.90/2.07 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c1_1(a586) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6696,plain,
% 1.90/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[6695])).
% 1.90/2.07 tff(6697,plain,
% 1.90/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6696, 6694])).
% 1.90/2.07 tff(6698,plain,
% 1.90/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 1.90/2.07 inference(quant_inst,[status(thm)],[])).
% 1.90/2.07 tff(6699,plain,
% 1.90/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c2_1(a544) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)) | (~c0_1(a544)) | (~c1_1(a544))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[6698, 6697])).
% 1.90/2.07 tff(6700,plain,
% 1.90/2.07 (~c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6699, 156, 6684, 88, 6686, 6693, 6692, 87, 6369, 609, 6689])).
% 1.90/2.07 tff(6701,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4600, 156, 35, 6684, 6685, 6693, 6692, 85, 6689, 6700])).
% 1.90/2.07 tff(6702,plain,(hskp19 | hskp33 | c1_1(a586) | c0_1(a586) | c1_1(a548) | c2_1(a548) | hskp46 | hskp38 | c0_1(a548) | hskp50 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6703,plain,
% 1.90/2.07 (hskp19),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6702, 6668, 88, 87, 57, 24, 946, 58, 56, 110, 35])).
% 1.90/2.07 tff(6704,plain,
% 1.90/2.07 (~c0_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1691, 6703])).
% 1.90/2.07 tff(6705,plain,
% 1.90/2.07 (~c2_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1704, 6703])).
% 1.90/2.07 tff(6706,plain,
% 1.90/2.07 (c3_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[3151, 6705, 1615, 6704, 35])).
% 1.90/2.07 tff(6707,plain,
% 1.90/2.07 (~c1_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6396, 4575])).
% 1.90/2.07 tff(6708,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a590))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6709,plain,
% 1.90/2.07 ((hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a590))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6710,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a590)))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[6709])).
% 1.90/2.07 tff(6711,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a590))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6710, 6708])).
% 1.90/2.07 tff(6712,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 1.90/2.07 inference(quant_inst,[status(thm)],[])).
% 1.90/2.07 tff(6713,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a590)),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[6712, 6711])).
% 1.90/2.07 tff(6714,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6713, 156, 58, 6400, 6399, 1719, 3143, 663, 3243, 6398])).
% 1.90/2.07 tff(6715,plain,(c2_1(a590) | hskp38 | c3_1(a590) | c1_1(a590) | c2_1(a573) | c0_1(a573) | (~c3_1(a573))), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6716,plain,
% 1.90/2.07 (c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6715, 4587, 3243, 6707, 1719, 3143, 58])).
% 1.90/2.07 tff(6717,plain,
% 1.90/2.07 (~hskp17),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6519, 6707, 4587, 4581, 87, 6369, 6716, 88])).
% 1.90/2.07 tff(6718,plain,
% 1.90/2.07 (hskp18),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[382, 6717, 6669])).
% 1.90/2.07 tff(6719,plain,
% 1.90/2.07 (hskp37),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2583, 6718, 5849, 24, 56, 58])).
% 1.90/2.07 tff(6720,plain,
% 1.90/2.07 (~c2_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[436, 6719])).
% 1.90/2.07 tff(6721,plain,
% 1.90/2.07 (c1_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[444, 6719])).
% 1.90/2.07 tff(6722,plain,
% 1.90/2.07 (~c0_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6699, 156, 6721, 88, 6720, 4587, 4581, 87, 6369, 609, 6716])).
% 1.90/2.07 tff(6723,plain,
% 1.90/2.07 (~c3_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[450, 6719])).
% 1.90/2.07 tff(6724,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2862, 156, 35, 1649, 1648, 6720, 6723, 1647, 85, 6722])).
% 1.90/2.07 tff(6725,plain,((~hskp29) | hskp33 | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a584) | c1_1(a586) | c0_1(a586) | c2_1(a548) | c0_1(a548) | hskp38 | hskp16 | (~c3_1(a573)) | c2_1(a573) | c0_1(a573)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6726,plain,
% 1.90/2.07 (~hskp29),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6725, 1630, 35, 1638, 1621, 88, 87, 24, 56, 58, 6668, 6706, 6705, 6704])).
% 1.90/2.07 tff(6727,plain,
% 1.90/2.07 (hskp30),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4620, 6726, 5849, 57])).
% 1.90/2.07 tff(6728,plain,
% 1.90/2.07 (~c0_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4626, 6727])).
% 1.90/2.07 tff(6729,plain,
% 1.90/2.07 (~c2_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4632, 6727])).
% 1.90/2.07 tff(6730,plain,
% 1.90/2.07 (c1_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4640, 6727])).
% 1.90/2.07 tff(6731,plain,
% 1.90/2.07 (~c3_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4647, 156, 946, 6730, 6729, 6728, 12])).
% 1.90/2.07 tff(6732,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6386, 156, 35, 1630, 1638, 6729, 6728, 1621, 85, 6731])).
% 1.90/2.07 tff(6733,plain,((~hskp26) | hskp33 | hskp46 | c1_1(a548) | c2_1(a548) | c1_1(a586) | c0_1(a586) | c0_1(a548) | hskp38 | hskp50 | hskp39), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6734,plain,
% 1.90/2.07 (~hskp26),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6733, 58, 946, 57, 24, 88, 87, 56, 35, 110, 859])).
% 1.90/2.07 tff(6735,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a590)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6736,plain,
% 1.90/2.07 ((hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a590)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6737,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a590))))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[6736])).
% 1.90/2.07 tff(6738,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a590)))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6737, 6735])).
% 1.90/2.07 tff(6739,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 1.90/2.07 inference(quant_inst,[status(thm)],[])).
% 1.90/2.07 tff(6740,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a590))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[6739, 6738])).
% 1.90/2.07 tff(6741,plain,
% 1.90/2.07 (~c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6740, 156, 946, 625, 591, 4587, 4581, 858, 6530])).
% 1.90/2.07 tff(6742,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a590))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6743,plain,
% 1.90/2.07 ((hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a590))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6744,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a590)))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[6743])).
% 1.90/2.07 tff(6745,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a590))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6744, 6742])).
% 1.90/2.07 tff(6746,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 1.90/2.07 inference(quant_inst,[status(thm)],[])).
% 1.90/2.07 tff(6747,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a590)),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 1.90/2.07 tff(6748,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6747, 156, 3650, 625, 591, 4587, 6707, 1112, 6530, 6741])).
% 1.90/2.07 tff(6749,plain,((~hskp29) | hskp34 | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6750,plain,
% 1.90/2.07 (~hskp29),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6749, 6530, 625, 591, 3650, 946])).
% 1.90/2.07 tff(6751,plain,
% 1.90/2.07 (hskp30),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4620, 6750, 249, 57])).
% 1.90/2.07 tff(6752,plain,
% 1.90/2.07 (~c2_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4632, 6751])).
% 1.90/2.07 tff(6753,plain,
% 1.90/2.07 (c1_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4640, 6751])).
% 1.90/2.07 tff(6754,plain,
% 1.90/2.07 (~c3_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6442, 156, 1423, 6753, 625, 591, 6752, 55, 6530])).
% 1.90/2.07 tff(6755,plain,
% 1.90/2.07 (~c0_1(a591)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4626, 6751])).
% 1.90/2.07 tff(6756,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6627, 156, 1661, 6753, 88, 6755, 87, 4948, 1686, 6754])).
% 1.90/2.07 tff(6757,plain,((~c1_1(a589)) | hskp26 | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | hskp25 | (~c2_1(a589)) | (~c3_1(a589)) | (~c3_1(a548)) | c1_1(a548) | c2_1(a548) | hskp34 | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6758,plain,
% 1.90/2.07 (~c1_1(a589)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6757, 1661, 88, 87, 6369, 1423, 4533, 4534, 5849, 57, 24, 3650, 946])).
% 1.90/2.07 tff(6759,plain,
% 1.90/2.07 (~hskp16),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6667, 6758, 4533, 58, 4534, 946])).
% 1.90/2.07 tff(6760,plain,
% 1.90/2.07 (~hskp30),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6629, 1661, 88, 87, 6369, 946])).
% 1.90/2.07 tff(6761,plain,
% 1.90/2.07 (hskp29),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4620, 6760, 5849, 57])).
% 1.90/2.07 tff(6762,plain,
% 1.90/2.07 (~c1_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6396, 6761])).
% 1.90/2.07 tff(6763,plain,
% 1.90/2.07 (hskp19),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6702, 6759, 88, 87, 57, 24, 946, 58, 56, 110, 35])).
% 1.90/2.07 tff(6764,plain,
% 1.90/2.07 (~c1_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1675, 6763])).
% 1.90/2.07 tff(6765,plain,
% 1.90/2.07 (~c2_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1704, 6763])).
% 1.90/2.07 tff(6766,plain,
% 1.90/2.07 (c3_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[3088, 156, 58, 5849, 6765, 6764, 24, 56, 663])).
% 1.90/2.07 tff(6767,plain,
% 1.90/2.07 (~c0_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1691, 6763])).
% 1.90/2.07 tff(6768,plain,
% 1.90/2.07 (~c3_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4586, 6761])).
% 1.90/2.07 tff(6769,plain,
% 1.90/2.07 (c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6715, 6768, 58, 6762, 6765, 6767, 6766])).
% 1.90/2.07 tff(6770,plain,
% 1.90/2.07 (~c0_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4580, 6761])).
% 1.90/2.07 tff(6771,plain,
% 1.90/2.07 (~hskp17),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6519, 6768, 88, 6770, 87, 6369, 6769, 6762])).
% 1.90/2.07 tff(6772,plain,
% 1.90/2.07 (hskp18),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[382, 6771, 6759])).
% 1.90/2.07 tff(6773,plain,
% 1.90/2.07 (hskp37),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2583, 6772, 5849, 24, 56, 58])).
% 1.90/2.07 tff(6774,plain,
% 1.90/2.07 (hskp15),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2512, 6773, 6758, 4534, 4533])).
% 1.90/2.07 tff(6775,plain,
% 1.90/2.07 (~c1_1(a569)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1261, 6774])).
% 1.90/2.07 tff(6776,plain,
% 1.90/2.07 (~c0_1(a569)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1267, 6774])).
% 1.90/2.07 tff(6777,plain,
% 1.90/2.07 (c1_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[444, 6773])).
% 1.90/2.07 tff(6778,plain,
% 1.90/2.07 (~c3_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[450, 6773])).
% 1.90/2.07 tff(6779,plain,
% 1.90/2.07 (~c2_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[436, 6773])).
% 1.90/2.07 tff(6780,plain,
% 1.90/2.07 (~c0_1(a544)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6699, 156, 6777, 88, 6779, 6768, 6770, 87, 6369, 609, 6769])).
% 1.90/2.07 tff(6781,plain,
% 1.90/2.07 (~c2_1(a569)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1255, 6774])).
% 1.90/2.07 tff(6782,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a573) | c0_1(a573) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c0_1(a573) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a573)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6783,plain,
% 1.90/2.07 ((hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (hskp38 | c2_1(a573) | c0_1(a573) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a573)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6784,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c2_1(a573) | c0_1(a573) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a573))))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[6783])).
% 1.90/2.07 tff(6785,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c0_1(a573) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a573)))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6784, 6782])).
% 1.90/2.07 tff(6786,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.90/2.07 inference(quant_inst,[status(thm)],[])).
% 1.90/2.07 tff(6787,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c2_1(a573) | c0_1(a573) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a573))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[6786, 6785])).
% 1.90/2.07 tff(6788,plain,
% 1.90/2.07 (c3_1(a569)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6787, 156, 58, 6765, 6767, 6775, 6781, 663, 6766])).
% 1.90/2.07 tff(6789,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4555, 6788, 6780, 6779, 6778, 6777, 6776, 6775, 35])).
% 1.90/2.07 tff(6790,plain,(hskp26 | hskp33 | hskp38 | c1_1(a586) | c0_1(a586) | c2_1(a548) | c0_1(a548) | c1_1(a548) | hskp46 | hskp50 | hskp25 | hskp34), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6791,plain,
% 1.90/2.07 (hskp34),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6790, 6734, 58, 88, 87, 24, 56, 57, 946, 110, 1423, 35])).
% 1.90/2.07 tff(6792,plain,
% 1.90/2.07 (c0_1(a537)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1147, 6791])).
% 1.90/2.07 tff(6793,plain,
% 1.90/2.07 (~c1_1(a537)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1124, 6791])).
% 1.90/2.07 tff(6794,plain,
% 1.90/2.07 (c3_1(a537)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1132, 6791])).
% 1.90/2.07 tff(6795,plain,
% 1.90/2.07 (hskp19 | c2_1(a537)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1154, 156, 110, 4780, 4778, 34])).
% 1.90/2.07 tff(6796,plain,
% 1.90/2.07 (c2_1(a537)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6795, 98])).
% 1.90/2.07 tff(6797,plain,
% 1.90/2.07 (hskp16),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6702, 98, 88, 87, 57, 24, 946, 58, 56, 110, 35])).
% 1.90/2.07 tff(6798,plain,
% 1.90/2.07 (c1_1(a589)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6667, 6797, 4533, 58, 4534, 946])).
% 1.90/2.07 tff(6799,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6800,plain,
% 1.90/2.07 ((hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6801,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[6800])).
% 1.90/2.07 tff(6802,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6801, 6799])).
% 1.90/2.07 tff(6803,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 1.90/2.07 inference(quant_inst,[status(thm)],[])).
% 1.90/2.07 tff(6804,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[6803, 6802])).
% 1.90/2.07 tff(6805,plain,
% 1.90/2.07 ((~c1_1(a589)) | (~c2_1(a537))),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6804, 156, 58, 4779, 4533, 4534, 4778, 1537])).
% 1.90/2.07 tff(6806,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6805, 6798, 6796])).
% 1.90/2.07 tff(6807,plain,(hskp19 | hskp38 | (~c3_1(a537)) | c1_1(a537) | hskp46 | hskp50 | (~c0_1(a537)) | c1_1(a586) | c0_1(a586) | c1_1(a548) | c2_1(a548) | c0_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6808,plain,
% 1.90/2.07 (hskp19),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6807, 58, 6794, 6793, 946, 110, 6792, 88, 87, 57, 24, 56, 35])).
% 1.90/2.07 tff(6809,plain,
% 1.90/2.07 (~c0_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1691, 6808])).
% 1.90/2.07 tff(6810,plain,
% 1.90/2.07 (~c2_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1704, 6808])).
% 1.90/2.07 tff(6811,plain,
% 1.90/2.07 (~hskp30),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6629, 6734, 88, 87, 6369, 946])).
% 1.90/2.07 tff(6812,plain,
% 1.90/2.07 (hskp29),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4620, 6811, 5849, 57])).
% 1.90/2.07 tff(6813,plain,
% 1.90/2.07 (~c1_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6396, 6812])).
% 1.90/2.07 tff(6814,plain,
% 1.90/2.07 (~c3_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4586, 6812])).
% 1.90/2.07 tff(6815,plain,
% 1.90/2.07 (~c1_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[1675, 6808])).
% 1.90/2.07 tff(6816,plain,
% 1.90/2.07 (c3_1(a573)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[3088, 156, 58, 5849, 6810, 6815, 24, 56, 663])).
% 1.90/2.07 tff(6817,plain,
% 1.90/2.07 (c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6715, 6816, 6814, 6813, 6810, 6809, 58])).
% 1.90/2.07 tff(6818,plain,
% 1.90/2.07 (~c0_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4580, 6812])).
% 1.90/2.07 tff(6819,plain,
% 1.90/2.07 (hskp8 | (~c2_1(a590))),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6590, 156, 6792, 6794, 6793, 6818, 6813, 2407])).
% 1.90/2.07 tff(6820,plain,
% 1.90/2.07 (hskp8),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6819, 6817])).
% 1.90/2.07 tff(6821,plain,
% 1.90/2.07 (hskp51),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6599, 6820, 6792, 6794, 6793])).
% 1.90/2.07 tff(6822,plain,
% 1.90/2.07 (~c2_1(a583)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2637, 6821])).
% 1.90/2.07 tff(6823,plain,
% 1.90/2.07 (c3_1(a583)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2645, 6821])).
% 1.90/2.07 tff(6824,plain,
% 1.90/2.07 (c0_1(a583)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2653, 6821])).
% 1.90/2.07 tff(6825,plain,
% 1.90/2.07 (c1_1(a583)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6616, 156, 6824, 6823, 6822, 6814, 6813, 921, 6817])).
% 1.90/2.07 tff(6826,plain,
% 1.90/2.07 ((~c1_1(a589)) | (~c2_1(a590))),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6740, 156, 946, 4533, 4534, 6814, 6818, 858])).
% 1.90/2.07 tff(6827,plain,
% 1.90/2.07 (~c1_1(a589)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6826, 6817])).
% 1.90/2.07 tff(6828,plain,
% 1.90/2.07 (~c2_1(a552)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2424, 6820])).
% 1.90/2.07 tff(6829,plain,
% 1.90/2.07 (~c1_1(a552)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2453, 6820])).
% 1.90/2.07 tff(6830,plain,
% 1.90/2.07 (~c3_1(a552)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2430, 6820])).
% 1.90/2.07 tff(6831,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[3471, 156, 6823, 4533, 4534, 6822, 6830, 6829, 6828, 45, 6827, 6825])).
% 1.90/2.07 tff(6832,plain,(hskp38 | hskp46 | c2_1(a548) | c0_1(a548) | hskp50 | c1_1(a586) | c0_1(a586) | c1_1(a548) | hskp33 | hskp25 | hskp39), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6833,plain,
% 1.90/2.07 (hskp39),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6832, 6435, 24, 56, 110, 88, 87, 57, 35, 946, 58])).
% 1.90/2.07 tff(6834,plain,
% 1.90/2.07 (c1_1(a589)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2535, 6833, 58, 4534, 4533])).
% 1.90/2.07 tff(6835,plain,
% 1.90/2.07 (~hskp30),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6635, 946, 35, 88, 87, 6369])).
% 1.90/2.07 tff(6836,plain,
% 1.90/2.07 (hskp29),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4620, 6835, 5849, 57])).
% 1.90/2.07 tff(6837,plain,
% 1.90/2.07 (~c0_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4580, 6836])).
% 1.90/2.07 tff(6838,plain,
% 1.90/2.07 (~c3_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4586, 6836])).
% 1.90/2.07 tff(6839,plain,
% 1.90/2.07 ((~c1_1(a589)) | (~c2_1(a590))),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6740, 156, 946, 4533, 4534, 6838, 6837, 858])).
% 1.90/2.07 tff(6840,plain,
% 1.90/2.07 (~c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6839, 6834])).
% 1.90/2.07 tff(6841,plain,
% 1.90/2.07 (~c1_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6396, 6836])).
% 1.90/2.07 tff(6842,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6406, 156, 58, 5849, 6838, 6841, 24, 56, 663, 6840])).
% 1.90/2.07 tff(6843,plain,(hskp38 | c2_1(a548) | c0_1(a548) | hskp46 | hskp50 | c1_1(a586) | c0_1(a586) | c1_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6844,plain,
% 1.90/2.07 (hskp38),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6843, 946, 56, 24, 110, 88, 87, 57, 35])).
% 1.90/2.07 tff(6845,plain,
% 1.90/2.07 (c0_1(a547)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[677, 6844])).
% 1.90/2.07 tff(6846,plain,
% 1.90/2.07 (c1_1(a547)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[685, 6844])).
% 1.90/2.07 tff(6847,plain,
% 1.90/2.07 (c2_1(a547)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[693, 6844])).
% 1.90/2.07 tff(6848,plain,
% 1.90/2.07 (~hskp0),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2694, 6845, 5849, 57, 6846, 24, 6847])).
% 1.90/2.07 tff(6849,plain,
% 1.90/2.07 (c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6576, 6848, 6847, 6846, 6845, 6838, 6841])).
% 1.90/2.07 tff(6850,plain,
% 1.90/2.07 (~hskp17),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6519, 6849, 6838, 6837, 87, 6369, 6841, 88])).
% 1.90/2.07 tff(6851,plain,
% 1.90/2.07 (~hskp0),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2694, 2769, 249, 57, 2770, 24, 2771])).
% 1.90/2.07 tff(6852,plain,
% 1.90/2.07 ($false),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[4530, 2502, 2504, 57, 2768, 249, 2503, 24, 3650])).
% 1.90/2.07 tff(6853,plain,((~hskp37) | c1_1(a548) | (~hskp38) | (~c3_1(a548)) | c2_1(a548) | hskp34), inference(lemma,lemma(discharge,[]))).
% 1.90/2.07 tff(6854,plain,
% 1.90/2.07 (~hskp37),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6853, 3650, 2768, 249, 24, 57])).
% 1.90/2.07 tff(6855,plain,
% 1.90/2.07 (~hskp18),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[2703, 6854, 2771, 2770, 2769, 6851])).
% 1.90/2.07 tff(6856,plain,
% 1.90/2.07 (hskp16),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[382, 6855, 332])).
% 1.90/2.07 tff(6857,plain,
% 1.90/2.07 (c1_1(a570)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[356, 6856])).
% 1.90/2.07 tff(6858,plain,
% 1.90/2.07 (c3_1(a570)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[364, 6856])).
% 1.90/2.07 tff(6859,assumption,(c2_1(a570)), introduced(assumption)).
% 1.90/2.07 tff(6860,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a590)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6861,plain,
% 1.90/2.07 ((hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a590)))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(6862,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a590))))),
% 1.90/2.07 inference(monotonicity,[status(thm)],[6861])).
% 1.90/2.07 tff(6863,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a590)))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6862, 6860])).
% 1.90/2.07 tff(6864,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 1.90/2.07 inference(quant_inst,[status(thm)],[])).
% 1.90/2.07 tff(6865,plain,
% 1.90/2.07 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a590))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 1.90/2.07 tff(6866,plain,
% 1.90/2.07 ((~c2_1(a570)) | (~c2_1(a590))),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6865, 156, 946, 948, 947, 6400, 6503, 858])).
% 1.90/2.07 tff(6867,plain,
% 1.90/2.07 (~c2_1(a590)),
% 1.90/2.07 inference(unit_resolution,[status(thm)],[6866, 6859])).
% 1.90/2.07 tff(6868,plain,
% 1.90/2.07 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a590))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(6869,plain,
% 1.90/2.08 ((hskp34 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a590))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(6870,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a590)))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[6869])).
% 1.90/2.08 tff(6871,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a590))),
% 1.90/2.08 inference(transitivity,[status(thm)],[6870, 6868])).
% 1.90/2.08 tff(6872,plain,
% 1.90/2.08 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 1.90/2.08 inference(quant_inst,[status(thm)],[])).
% 1.90/2.08 tff(6873,plain,
% 1.90/2.08 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | c2_1(a590)),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[6872, 6871])).
% 1.90/2.08 tff(6874,plain,
% 1.90/2.08 ($false),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[6873, 156, 3650, 948, 947, 6400, 6399, 1112, 6859, 6867])).
% 1.90/2.08 tff(6875,plain,((~c2_1(a570)) | hskp34 | (~c3_1(a570)) | (~c1_1(a570)) | c3_1(a590) | c1_1(a590) | hskp46 | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.90/2.08 tff(6876,plain,
% 1.90/2.08 (~c2_1(a570)),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[6875, 3650, 6858, 6857, 6400, 6399, 946, 6503])).
% 1.90/2.08 tff(6877,plain,
% 1.90/2.08 (~c0_1(a570)),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[348, 6856])).
% 1.90/2.08 tff(6878,assumption,(~hskp42), introduced(assumption)).
% 1.90/2.08 tff(6879,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(6880,plain,
% 1.90/2.08 ((hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547))) <=> (hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(6881,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[6880])).
% 1.90/2.08 tff(6882,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.90/2.08 inference(transitivity,[status(thm)],[6881, 6879])).
% 1.90/2.08 tff(6883,plain,
% 1.90/2.08 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c1_1(a547)) | (~c2_1(a547)) | (~c0_1(a547)))),
% 1.90/2.08 inference(quant_inst,[status(thm)],[])).
% 1.90/2.08 tff(6884,plain,
% 1.90/2.08 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[6883, 6882])).
% 1.90/2.08 tff(6885,plain,
% 1.90/2.08 ($false),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[6884, 156, 6878, 733, 732, 731, 948, 947, 1364, 970])).
% 1.90/2.08 tff(6886,plain,(c2_1(a570) | hskp42 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | (~c3_1(a570)) | (~c1_1(a570))), inference(lemma,lemma(discharge,[]))).
% 1.90/2.08 tff(6887,plain,
% 1.90/2.08 (hskp42),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[6886, 6876, 2771, 2770, 2769, 6858, 6857])).
% 1.90/2.08 tff(6888,plain,
% 1.90/2.08 (~c2_1(a556)),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[1385, 6887])).
% 1.90/2.08 tff(6889,plain,
% 1.90/2.08 (c3_1(a556)),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[1403, 6887])).
% 1.90/2.08 tff(6890,plain,
% 1.90/2.08 (c1_1(a556)),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[1411, 6887])).
% 1.90/2.08 tff(6891,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a556) | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a556) | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(6892,plain,
% 1.90/2.08 ((hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570))) <=> (hskp46 | c2_1(a556) | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(6893,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a556) | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[6892])).
% 1.90/2.08 tff(6894,plain,
% 1.90/2.08 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a556) | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.90/2.08 inference(transitivity,[status(thm)],[6893, 6891])).
% 1.90/2.08 tff(6895,plain,
% 1.90/2.08 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a570) | c0_1(a570) | (~c3_1(a570)))),
% 1.93/2.08 inference(quant_inst,[status(thm)],[])).
% 1.93/2.08 tff(6896,plain,
% 1.93/2.08 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a556) | c0_1(a570) | (~ndr1_0) | c2_1(a570) | (~c3_1(a570)) | (~c3_1(a556)) | (~c1_1(a556))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[6895, 6894])).
% 1.93/2.08 tff(6897,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6896, 156, 946, 6890, 6889, 6858, 6888, 6877, 12, 6876])).
% 1.93/2.08 tff(6898,plain,(hskp34 | hskp46 | c3_1(a590) | c1_1(a590) | c0_1(a590) | hskp17 | (~hskp38) | (~c3_1(a548)) | c2_1(a548) | c1_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6899,plain,
% 1.93/2.08 (hskp34),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6898, 6850, 946, 6841, 6837, 6838, 6844, 5849, 24, 57])).
% 1.93/2.08 tff(6900,plain,
% 1.93/2.08 (~c1_1(a537)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1124, 6899])).
% 1.93/2.08 tff(6901,plain,
% 1.93/2.08 (c3_1(a537)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1132, 6899])).
% 1.93/2.08 tff(6902,plain,
% 1.93/2.08 (c0_1(a537)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1147, 6899])).
% 1.93/2.08 tff(6903,assumption,(~hskp8), introduced(assumption)).
% 1.93/2.08 tff(6904,plain,
% 1.93/2.08 (~c2_1(a590)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6590, 156, 6903, 4780, 4779, 4778, 4581, 6707, 2407])).
% 1.93/2.08 tff(6905,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6574, 156, 837, 733, 732, 731, 4587, 6707, 108, 6904])).
% 1.93/2.08 tff(6906,plain,((~hskp29) | hskp0 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp8 | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6907,plain,
% 1.93/2.08 (hskp8),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6906, 6902, 6847, 6846, 6845, 6848, 6836, 6901, 6900])).
% 1.93/2.08 tff(6908,plain,
% 1.93/2.08 (~c2_1(a552)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2424, 6907])).
% 1.93/2.08 tff(6909,plain,
% 1.93/2.08 (~c1_1(a552)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2453, 6907])).
% 1.93/2.08 tff(6910,plain,
% 1.93/2.08 (~c3_1(a552)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2430, 6907])).
% 1.93/2.08 tff(6911,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2735, 156, 6848, 6847, 6846, 6845, 6910, 6909, 6908, 108])).
% 1.93/2.08 tff(6912,plain,(hskp46 | c2_1(a548) | c1_1(a548) | c0_1(a586) | c1_1(a586) | c0_1(a548) | hskp50 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6913,plain,
% 1.93/2.08 (hskp50),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6912, 6621, 57, 87, 88, 56, 24, 35])).
% 1.93/2.08 tff(6914,plain,
% 1.93/2.08 (~c3_1(a574)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[799, 6913])).
% 1.93/2.08 tff(6915,plain,
% 1.93/2.08 (c1_1(a574)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[807, 6913])).
% 1.93/2.08 tff(6916,plain,
% 1.93/2.08 (c0_1(a574)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[815, 6913])).
% 1.93/2.08 tff(6917,plain,
% 1.93/2.08 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(6918,plain,
% 1.93/2.08 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a590) | c3_1(a590) | c0_1(a590)) <=> (hskp33 | c3_1(a574) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(6919,plain,
% 1.93/2.08 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a590) | c3_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a574)) | (~c1_1(a574))))),
% 1.93/2.08 inference(monotonicity,[status(thm)],[6918])).
% 1.93/2.08 tff(6920,plain,
% 1.93/2.08 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a590) | c3_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.93/2.08 inference(transitivity,[status(thm)],[6919, 6917])).
% 1.93/2.08 tff(6921,plain,
% 1.93/2.08 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a590) | c3_1(a590) | c0_1(a590))),
% 1.93/2.08 inference(quant_inst,[status(thm)],[])).
% 1.93/2.08 tff(6922,plain,
% 1.93/2.08 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c2_1(a590) | (~c0_1(a574)) | (~c1_1(a574))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 1.93/2.08 tff(6923,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6922, 156, 35, 2476, 2475, 2474, 6400, 6503, 85, 6398])).
% 1.93/2.08 tff(6924,plain,(c2_1(a590) | hskp33 | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | c3_1(a590) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6925,plain,
% 1.93/2.08 (c2_1(a590)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6924, 6916, 35, 6915, 6914, 6639, 6638])).
% 1.93/2.08 tff(6926,plain,
% 1.93/2.08 ((~c1_1(a589)) | (~c2_1(a590))),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6740, 156, 6621, 4533, 4534, 6639, 6638, 858])).
% 1.93/2.08 tff(6927,plain,
% 1.93/2.08 (~c1_1(a589)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6926, 6925])).
% 1.93/2.08 tff(6928,plain,
% 1.93/2.08 (c2_1(a590)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6924, 2476, 35, 2475, 2474, 6400, 6503])).
% 1.93/2.08 tff(6929,plain,
% 1.93/2.08 (~c0_1(a544)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6699, 156, 2504, 88, 2503, 6400, 6503, 87, 4948, 609, 6928])).
% 1.93/2.08 tff(6930,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2994, 156, 35, 2476, 2475, 2474, 2503, 2502, 85, 6929])).
% 1.93/2.08 tff(6931,plain,((~hskp37) | hskp33 | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | c1_1(a586) | c3_1(a590) | c0_1(a590) | c0_1(a586) | (~c3_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6932,plain,
% 1.93/2.08 (~hskp37),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6931, 6916, 35, 6915, 6914, 88, 6639, 6638, 87, 6369])).
% 1.93/2.08 tff(6933,plain,
% 1.93/2.08 (~c1_1(a590)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6396, 6637])).
% 1.93/2.08 tff(6934,plain,
% 1.93/2.08 (~hskp17),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6519, 6925, 6639, 6638, 87, 6369, 6933, 88])).
% 1.93/2.08 tff(6935,plain,
% 1.93/2.08 (~hskp16),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6667, 58, 625, 946, 591, 1716])).
% 1.93/2.08 tff(6936,plain,
% 1.93/2.08 (~hskp18),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2583, 58, 249, 24, 56, 422])).
% 1.93/2.08 tff(6937,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[382, 6936, 6935, 332])).
% 1.93/2.08 tff(6938,plain,(hskp38 | hskp17 | (~c3_1(a548)) | c2_1(a548) | c0_1(a548) | hskp37 | (~c2_1(a589)) | hskp46 | (~c3_1(a589)) | c1_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6939,plain,
% 1.93/2.08 (hskp38),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6938, 6934, 5849, 24, 56, 6932, 4533, 6621, 4534, 6927])).
% 1.93/2.08 tff(6940,plain,
% 1.93/2.08 (c2_1(a547)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[693, 6939])).
% 1.93/2.08 tff(6941,plain,
% 1.93/2.08 (c1_1(a547)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[685, 6939])).
% 1.93/2.08 tff(6942,plain,
% 1.93/2.08 (c0_1(a547)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[677, 6939])).
% 1.93/2.08 tff(6943,plain,
% 1.93/2.08 (~hskp0),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2694, 6942, 5849, 57, 6941, 24, 6940])).
% 1.93/2.08 tff(6944,plain,
% 1.93/2.08 (hskp34),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6898, 6939, 6621, 6933, 6638, 6639, 6934, 5849, 24, 57])).
% 1.93/2.08 tff(6945,plain,
% 1.93/2.08 (~c1_1(a537)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1124, 6944])).
% 1.93/2.08 tff(6946,plain,
% 1.93/2.08 (c0_1(a537)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1147, 6944])).
% 1.93/2.08 tff(6947,plain,
% 1.93/2.08 (c3_1(a537)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1132, 6944])).
% 1.93/2.08 tff(6948,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6618, 6947, 6946, 88, 87, 6369, 6639, 6933, 6945, 6932, 6940, 6941, 6942, 6943])).
% 1.93/2.08 tff(6949,plain,(c1_1(a548) | c1_1(a586) | c0_1(a586) | c2_1(a548) | c0_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6950,plain,
% 1.93/2.08 (c1_1(a548)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6949, 56, 87, 24, 88, 35])).
% 1.93/2.08 tff(6951,plain,
% 1.93/2.08 (hskp46),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2834, 6950, 5849, 56])).
% 1.93/2.08 tff(6952,plain,
% 1.93/2.08 (~c0_1(a562)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[64, 6951])).
% 1.93/2.08 tff(6953,plain,
% 1.93/2.08 (~c3_1(a562)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[270, 6951])).
% 1.93/2.08 tff(6954,plain,
% 1.93/2.08 (c1_1(a562)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[288, 6951])).
% 1.93/2.08 tff(6955,plain,
% 1.93/2.08 (hskp39),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2063, 156, 6954, 5849, 6953, 6952, 24, 281, 6950])).
% 1.93/2.08 tff(6956,plain,
% 1.93/2.08 (c1_1(a549)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[303, 6955])).
% 1.93/2.08 tff(6957,plain,
% 1.93/2.08 (c2_1(a549)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[311, 6955])).
% 1.93/2.08 tff(6958,plain,
% 1.93/2.08 (c3_1(a549)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[319, 6955])).
% 1.93/2.08 tff(6959,plain,
% 1.93/2.08 (hskp25),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[4507, 156, 6958, 6957, 6956, 5849, 24, 55, 6950])).
% 1.93/2.08 tff(6960,plain,
% 1.93/2.08 (~c1_1(a582)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1190, 6959])).
% 1.93/2.08 tff(6961,plain,
% 1.93/2.08 (~c2_1(a582)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1196, 6959])).
% 1.93/2.08 tff(6962,plain,
% 1.93/2.08 (~c3_1(a582)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1202, 6959])).
% 1.93/2.08 tff(6963,plain,
% 1.93/2.08 (hskp4),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[2559, 6950, 5849, 24, 56])).
% 1.93/2.08 tff(6964,plain,
% 1.93/2.08 (~c0_1(a545)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1666, 6963])).
% 1.93/2.08 tff(6965,plain,
% 1.93/2.08 (hskp26),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6415, 156, 6954, 88, 6953, 6952, 87, 6369, 1686])).
% 1.93/2.08 tff(6966,plain,
% 1.93/2.08 (hskp38),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1659, 6965, 35, 6964, 6963])).
% 1.93/2.08 tff(6967,plain,
% 1.93/2.08 (c0_1(a547)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[677, 6966])).
% 1.93/2.08 tff(6968,plain,
% 1.93/2.08 (c1_1(a547)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[685, 6966])).
% 1.93/2.08 tff(6969,plain,
% 1.93/2.08 (c2_1(a547)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[693, 6966])).
% 1.93/2.08 tff(6970,plain,
% 1.93/2.08 (hskp42),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[3196, 156, 6969, 6968, 6967, 5849, 24, 1364, 6950])).
% 1.93/2.08 tff(6971,plain,
% 1.93/2.08 (~c2_1(a556)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1385, 6970])).
% 1.93/2.08 tff(6972,plain,
% 1.93/2.08 (c3_1(a556)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1403, 6970])).
% 1.93/2.08 tff(6973,plain,
% 1.93/2.08 (c1_1(a556)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1411, 6970])).
% 1.93/2.08 tff(6974,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c2_1(a556) | (~c3_1(a586)) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a556) | (~c3_1(a586)) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(6975,plain,
% 1.93/2.08 (((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)) | c2_1(a582) | c1_1(a582) | c3_1(a582)) <=> (c1_1(a586) | c2_1(a556) | (~c3_1(a586)) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(6976,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a586) | c2_1(a556) | (~c3_1(a586)) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 1.93/2.08 inference(monotonicity,[status(thm)],[6975])).
% 1.93/2.08 tff(6977,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)) | c2_1(a582) | c1_1(a582) | c3_1(a582))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a556) | (~c3_1(a586)) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 1.93/2.08 inference(transitivity,[status(thm)],[6976, 6974])).
% 1.93/2.08 tff(6978,plain,
% 1.93/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)) | c2_1(a582) | c1_1(a582) | c3_1(a582))),
% 1.93/2.08 inference(quant_inst,[status(thm)],[])).
% 1.93/2.08 tff(6979,plain,
% 1.93/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a586) | c2_1(a556) | (~c3_1(a586)) | c3_1(a582) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | (~c2_1(a586)) | (~c3_1(a556)) | (~c1_1(a556))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[6978, 6977])).
% 1.93/2.08 tff(6980,plain,
% 1.93/2.08 (~c2_1(a586)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6979, 156, 6973, 6972, 88, 6971, 6369, 6962, 6961, 6960, 45])).
% 1.93/2.08 tff(6981,plain,
% 1.93/2.08 (hskp0),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6547, 6959, 6969, 6968, 6967])).
% 1.93/2.08 tff(6982,plain,
% 1.93/2.08 (~c2_1(a535)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[713, 6981])).
% 1.93/2.08 tff(6983,plain,
% 1.93/2.08 (c0_1(a535)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[721, 6981])).
% 1.93/2.08 tff(6984,plain,
% 1.93/2.08 (c1_1(a535)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[729, 6981])).
% 1.93/2.08 tff(6985,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(6986,plain,
% 1.93/2.08 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535))) <=> (c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(6987,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.93/2.08 inference(monotonicity,[status(thm)],[6986])).
% 1.93/2.08 tff(6988,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.93/2.08 inference(transitivity,[status(thm)],[6987, 6985])).
% 1.93/2.08 tff(6989,plain,
% 1.93/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a586) | c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~c0_1(a535)) | (~c1_1(a535)))),
% 1.93/2.08 inference(quant_inst,[status(thm)],[])).
% 1.93/2.08 tff(6990,plain,
% 1.93/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | (~c3_1(a586)) | c2_1(a535) | (~ndr1_0) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a586) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[6989, 6988])).
% 1.93/2.08 tff(6991,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6990, 156, 6969, 6968, 6967, 88, 6984, 6983, 6369, 6982, 707, 6980])).
% 1.93/2.08 tff(6992,plain,(c0_1(a548) | c1_1(a586) | c2_1(a548) | hskp33 | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(6993,plain,
% 1.93/2.08 (c0_1(a548)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6992, 88, 24, 35, 87])).
% 1.93/2.08 tff(6994,plain,
% 1.93/2.08 (~hskp6),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[211, 6993])).
% 1.93/2.08 tff(6995,plain,
% 1.93/2.08 (hskp4),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[205, 6994, 6370])).
% 1.93/2.08 tff(6996,plain,
% 1.93/2.08 (~hskp50),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6209, 6995, 35])).
% 1.93/2.08 tff(6997,plain,
% 1.93/2.08 (~c0_1(a545)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1666, 6995])).
% 1.93/2.08 tff(6998,plain,
% 1.93/2.08 (~hskp19),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[3077, 6997, 35, 6370, 6994])).
% 1.93/2.08 tff(6999,plain,
% 1.93/2.08 (c1_1(a548)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[4803, 6998, 6993, 6996])).
% 1.93/2.08 tff(7000,plain,
% 1.93/2.08 (~hskp6),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[211, 5004])).
% 1.93/2.08 tff(7001,plain,
% 1.93/2.08 (hskp4),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[205, 7000, 6370])).
% 1.93/2.08 tff(7002,plain,
% 1.93/2.08 (~c2_1(a545)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1643, 7001])).
% 1.93/2.08 tff(7003,plain,
% 1.93/2.08 (~c0_1(a545)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1666, 7001])).
% 1.93/2.08 tff(7004,plain,
% 1.93/2.08 (~hskp19),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[3077, 7003, 35, 6370, 7000])).
% 1.93/2.08 tff(7005,plain,
% 1.93/2.08 (~hskp45),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[833, 765, 35, 7004, 7003, 7002])).
% 1.93/2.08 tff(7006,plain,
% 1.93/2.08 (~hskp50),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6209, 7001, 35])).
% 1.93/2.08 tff(7007,plain,
% 1.93/2.08 (c1_1(a548)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[4803, 7004, 5004, 7006])).
% 1.93/2.08 tff(7008,plain,
% 1.93/2.08 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(7009,plain,
% 1.93/2.08 ((hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp45 | c2_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(7010,plain,
% 1.93/2.08 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548))))),
% 1.93/2.08 inference(monotonicity,[status(thm)],[7009])).
% 1.93/2.08 tff(7011,plain,
% 1.93/2.08 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548)))),
% 1.93/2.08 inference(transitivity,[status(thm)],[7010, 7008])).
% 1.93/2.08 tff(7012,plain,
% 1.93/2.08 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 1.93/2.08 inference(quant_inst,[status(thm)],[])).
% 1.93/2.08 tff(7013,plain,
% 1.93/2.08 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a548) | (~c0_1(a548)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a548))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[7012, 7011])).
% 1.93/2.08 tff(7014,plain,
% 1.93/2.08 (hskp45 | c3_1(a545)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[7013, 156, 24, 5004, 7002, 7003, 757, 7007])).
% 1.93/2.08 tff(7015,plain,
% 1.93/2.08 ($false),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[7014, 7005, 765])).
% 1.93/2.08 tff(7016,plain,(c3_1(a545) | c2_1(a548) | (~c0_1(a548)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.08 tff(7017,plain,
% 1.93/2.08 (c3_1(a545)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[7016, 6993, 24, 35])).
% 1.93/2.08 tff(7018,plain,
% 1.93/2.08 (~c2_1(a545)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[1643, 6995])).
% 1.93/2.08 tff(7019,plain,
% 1.93/2.08 (hskp46 | (~c3_1(a545))),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[6339, 156, 5849, 24, 7018, 6997, 12, 6999])).
% 1.93/2.08 tff(7020,plain,
% 1.93/2.08 (hskp46),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[7019, 7017])).
% 1.93/2.08 tff(7021,plain,
% 1.93/2.08 (~c0_1(a562)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[64, 7020])).
% 1.93/2.08 tff(7022,plain,
% 1.93/2.08 (~c3_1(a562)),
% 1.93/2.08 inference(unit_resolution,[status(thm)],[270, 7020])).
% 1.93/2.08 tff(7023,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a562)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(7024,plain,
% 1.93/2.08 (((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))) <=> (c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a562)))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(7025,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a562))))),
% 1.93/2.08 inference(monotonicity,[status(thm)],[7024])).
% 1.93/2.08 tff(7026,plain,
% 1.93/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a562)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7025, 7023])).
% 1.93/2.09 tff(7027,plain,
% 1.93/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a586) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7028,plain,
% 1.93/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a586) | c3_1(a562) | c0_1(a562) | c0_1(a586) | (~c3_1(a586)) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c1_1(a548)) | (~c2_1(a562))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7027, 7026])).
% 1.93/2.09 tff(7029,plain,
% 1.93/2.09 (~c2_1(a562)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7028, 156, 88, 7022, 7021, 87, 6369, 24, 6993, 609, 6999])).
% 1.93/2.09 tff(7030,plain,
% 1.93/2.09 (c1_1(a562)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[288, 7020])).
% 1.93/2.09 tff(7031,plain,
% 1.93/2.09 (hskp26),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6415, 156, 7030, 88, 7022, 7021, 87, 6369, 1686])).
% 1.93/2.09 tff(7032,plain,
% 1.93/2.09 (~c3_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1620, 7031])).
% 1.93/2.09 tff(7033,plain,
% 1.93/2.09 (c1_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1637, 7031])).
% 1.93/2.09 tff(7034,plain,
% 1.93/2.09 (c0_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1629, 7031])).
% 1.93/2.09 tff(7035,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6266, 156, 35, 7034, 7033, 7022, 7021, 7032, 85, 7029])).
% 1.93/2.09 tff(7036,plain,(c1_1(a586) | hskp33 | c0_1(a586) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7037,plain,
% 1.93/2.09 (c1_1(a586)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7036, 87, 35, 24])).
% 1.93/2.09 tff(7038,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7039,plain,
% 1.93/2.09 ((hskp46 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a586) | c0_1(a586) | (~c3_1(a586))) <=> (hskp46 | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7040,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586)))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7039])).
% 1.93/2.09 tff(7041,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a586) | c0_1(a586) | (~c3_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7040, 7038])).
% 1.93/2.09 tff(7042,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a586) | c0_1(a586) | (~c3_1(a586)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7043,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c0_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586)),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7042, 7041])).
% 1.93/2.09 tff(7044,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7043, 156, 946, 3797, 87, 4948, 12, 653])).
% 1.93/2.09 tff(7045,plain,(c2_1(a586) | hskp46 | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7046,plain,
% 1.93/2.09 (c2_1(a586)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7045, 946, 7037, 87, 6369])).
% 1.93/2.09 tff(7047,plain,
% 1.93/2.09 (~c1_1(a548)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[2834, 946, 5849, 56])).
% 1.93/2.09 tff(7048,plain,
% 1.93/2.09 (c2_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6408, 6399, 249, 6400, 58, 24, 56])).
% 1.93/2.09 tff(7049,plain,
% 1.93/2.09 (c2_1(a586)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7045, 946, 3797, 87, 4948])).
% 1.93/2.09 tff(7050,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7051,plain,
% 1.93/2.09 ((hskp46 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp46 | c3_1(a590) | c0_1(a590) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7052,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590))))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7051])).
% 1.93/2.09 tff(7053,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7052, 7050])).
% 1.93/2.09 tff(7054,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7055,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7054, 7053])).
% 1.93/2.09 tff(7056,plain,
% 1.93/2.09 (c0_1(a590) | (~c2_1(a590))),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7055, 156, 946, 3797, 6400, 4948, 858, 7049])).
% 1.93/2.09 tff(7057,plain,
% 1.93/2.09 (c0_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7056, 7048])).
% 1.93/2.09 tff(7058,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~c0_1(a590)) | c1_1(a590) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | (~c0_1(a590)) | c1_1(a590) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7059,plain,
% 1.93/2.09 ((hskp46 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp46 | (~c0_1(a590)) | c1_1(a590) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7060,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~c0_1(a590)) | c1_1(a590) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590))))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7059])).
% 1.93/2.09 tff(7061,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | (~c0_1(a590)) | c1_1(a590) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7060, 7058])).
% 1.93/2.09 tff(7062,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c0_1(a590)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7063,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | (~c0_1(a590)) | c1_1(a590) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a590))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7062, 7061])).
% 1.93/2.09 tff(7064,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7063, 156, 946, 3797, 7057, 6399, 87, 2215, 7049, 7048])).
% 1.93/2.09 tff(7065,plain,(c1_1(a590) | hskp46 | (~c1_1(a586)) | c0_1(a586) | c3_1(a590) | (~c3_1(a586)) | (~c3_1(a548)) | hskp38 | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7066,plain,
% 1.93/2.09 (c1_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7065, 6400, 7037, 87, 946, 6369, 5849, 58, 24, 56])).
% 1.93/2.09 tff(7067,plain,
% 1.93/2.09 (~hskp29),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6396, 7066])).
% 1.93/2.09 tff(7068,plain,
% 1.93/2.09 (hskp30),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4620, 7067, 5849, 7047])).
% 1.93/2.09 tff(7069,plain,
% 1.93/2.09 (~c2_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4632, 7068])).
% 1.93/2.09 tff(7070,plain,
% 1.93/2.09 (c1_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4640, 7068])).
% 1.93/2.09 tff(7071,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a591) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a591) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7072,plain,
% 1.93/2.09 ((hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591))) <=> (hskp25 | c2_1(a591) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7073,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a591) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a591)) | (~c1_1(a591))))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7072])).
% 1.93/2.09 tff(7074,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a591) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7073, 7071])).
% 1.93/2.09 tff(7075,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7076,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a591) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a591)) | (~c1_1(a591))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7075, 7074])).
% 1.93/2.09 tff(7077,plain,
% 1.93/2.09 (~c3_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7076, 156, 6435, 7070, 7037, 7069, 6369, 55, 7046])).
% 1.93/2.09 tff(7078,plain,
% 1.93/2.09 (~c0_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4626, 7068])).
% 1.93/2.09 tff(7079,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | (~ndr1_0) | c3_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | (~ndr1_0) | c3_1(a591))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7080,plain,
% 1.93/2.09 ((hskp33 | (~ndr1_0) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | c2_1(a591) | c3_1(a591) | c0_1(a591)) <=> (hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | (~ndr1_0) | c3_1(a591))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7081,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | (~ndr1_0) | c3_1(a591)))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7080])).
% 1.93/2.09 tff(7082,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | c2_1(a591) | c3_1(a591) | c0_1(a591))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | (~ndr1_0) | c3_1(a591))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7081, 7079])).
% 1.93/2.09 tff(7083,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | c2_1(a591) | c3_1(a591) | c0_1(a591))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7084,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c2_1(a591) | c0_1(a591) | c3_1(a590) | (~c0_1(a590)) | (~c1_1(a590)) | (~ndr1_0) | c3_1(a591)),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7083, 7082])).
% 1.93/2.09 tff(7085,plain,
% 1.93/2.09 (~c0_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7084, 156, 35, 7069, 7078, 6400, 7066, 85, 7077])).
% 1.93/2.09 tff(7086,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a590) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a590) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7087,plain,
% 1.93/2.09 ((hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590))) <=> (hskp4 | c3_1(a590) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7088,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a590) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7087])).
% 1.93/2.09 tff(7089,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a590) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7088, 7086])).
% 1.93/2.09 tff(7090,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7091,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a590) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7090, 7089])).
% 1.93/2.09 tff(7092,plain,
% 1.93/2.09 (hskp4 | c0_1(a590) | (~c1_1(a590))),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7091, 156, 7037, 6400, 6369, 22, 7046])).
% 1.93/2.09 tff(7093,plain,
% 1.93/2.09 (hskp4),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7092, 7085, 7066])).
% 1.93/2.09 tff(7094,plain,
% 1.93/2.09 (hskp26),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6376, 156, 7070, 5849, 7078, 56, 1686, 7047, 7077])).
% 1.93/2.09 tff(7095,plain,
% 1.93/2.09 (c0_1(a545)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1659, 7094, 35, 58, 7093])).
% 1.93/2.09 tff(7096,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1666, 7095, 7093])).
% 1.93/2.09 tff(7097,plain,(c3_1(a590) | hskp33 | hskp38 | c0_1(a548) | c2_1(a548) | c0_1(a586) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7098,plain,
% 1.93/2.09 (c3_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7097, 58, 35, 56, 24, 87, 946])).
% 1.93/2.09 tff(7099,plain,
% 1.93/2.09 (~hskp29),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4586, 7098])).
% 1.93/2.09 tff(7100,plain,
% 1.93/2.09 (hskp30),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4620, 7099, 5849, 7047])).
% 1.93/2.09 tff(7101,plain,
% 1.93/2.09 (~c2_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4632, 7100])).
% 1.93/2.09 tff(7102,plain,
% 1.93/2.09 (c1_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4640, 7100])).
% 1.93/2.09 tff(7103,plain,
% 1.93/2.09 (~c3_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7076, 156, 6435, 7102, 7037, 7101, 6369, 55, 7046])).
% 1.93/2.09 tff(7104,plain,
% 1.93/2.09 (~c0_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4626, 7100])).
% 1.93/2.09 tff(7105,plain,
% 1.93/2.09 (hskp26),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6376, 156, 7102, 5849, 7104, 56, 1686, 7047, 7103])).
% 1.93/2.09 tff(7106,plain,
% 1.93/2.09 (~c3_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1620, 7105])).
% 1.93/2.09 tff(7107,plain,
% 1.93/2.09 (c1_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1637, 7105])).
% 1.93/2.09 tff(7108,plain,
% 1.93/2.09 (c0_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1629, 7105])).
% 1.93/2.09 tff(7109,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6386, 156, 35, 7108, 7107, 7101, 7104, 7106, 85, 7103])).
% 1.93/2.09 tff(7110,plain,(hskp38 | hskp33 | c0_1(a548) | c2_1(a548) | c0_1(a586) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7111,plain,
% 1.93/2.09 (hskp38),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7110, 946, 56, 24, 87, 35])).
% 1.93/2.09 tff(7112,plain,
% 1.93/2.09 (c2_1(a547)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[693, 7111])).
% 1.93/2.09 tff(7113,plain,
% 1.93/2.09 (c1_1(a547)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[685, 7111])).
% 1.93/2.09 tff(7114,plain,
% 1.93/2.09 (c0_1(a547)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[677, 7111])).
% 1.93/2.09 tff(7115,plain,
% 1.93/2.09 (~hskp0),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[2694, 7114, 5849, 7047, 7113, 24, 7112])).
% 1.93/2.09 tff(7116,plain,
% 1.93/2.09 (~hskp25),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6547, 7115, 7112, 7113, 7114])).
% 1.93/2.09 tff(7117,plain,
% 1.93/2.09 (~c3_1(a591)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7076, 156, 1423, 4716, 3797, 4715, 4948, 55, 902])).
% 1.93/2.09 tff(7118,plain,
% 1.93/2.09 (hskp26),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6376, 156, 4716, 249, 4714, 56, 1686, 57, 7117])).
% 1.93/2.09 tff(7119,plain,
% 1.93/2.09 (~c3_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1620, 7118])).
% 1.93/2.09 tff(7120,plain,
% 1.93/2.09 (c1_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1637, 7118])).
% 1.93/2.09 tff(7121,plain,
% 1.93/2.09 (c0_1(a584)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1629, 7118])).
% 1.93/2.09 tff(7122,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6386, 156, 35, 7121, 7120, 4715, 4714, 7119, 85, 7117])).
% 1.93/2.09 tff(7123,plain,((~hskp30) | hskp33 | (~c3_1(a548)) | c0_1(a548) | c1_1(a548) | hskp25 | (~c1_1(a586)) | (~c3_1(a586)) | (~c2_1(a586))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7124,plain,
% 1.93/2.09 (~hskp30),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7123, 7047, 5849, 56, 35, 7116, 7037, 6369, 7046])).
% 1.93/2.09 tff(7125,plain,
% 1.93/2.09 (hskp29),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4620, 7124, 5849, 7047])).
% 1.93/2.09 tff(7126,plain,
% 1.93/2.09 (~c3_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[4586, 7125])).
% 1.93/2.09 tff(7127,plain,
% 1.93/2.09 (~c1_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[6396, 7125])).
% 1.93/2.09 tff(7128,plain,
% 1.93/2.09 (c0_1(a590)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7056, 6577])).
% 1.93/2.09 tff(7129,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7063, 156, 946, 3797, 7128, 6399, 87, 2215, 7049, 6577])).
% 1.93/2.09 tff(7130,plain,(c1_1(a590) | hskp46 | (~c1_1(a586)) | c0_1(a586) | c3_1(a590) | (~c3_1(a586)) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7131,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7130, 7127, 7126, 7037, 87, 946, 6369, 7112, 7113, 7114, 7115])).
% 1.93/2.09 tff(7132,plain,(hskp46 | c0_1(a586) | c2_1(a548) | c0_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7133,plain,
% 1.93/2.09 (hskp46),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7132, 56, 24, 87, 35])).
% 1.93/2.09 tff(7134,plain,
% 1.93/2.09 (~c0_1(a562)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[64, 7133])).
% 1.93/2.09 tff(7135,plain,
% 1.93/2.09 (~c3_1(a562)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[270, 7133])).
% 1.93/2.09 tff(7136,plain,
% 1.93/2.09 (c1_1(a562)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[288, 7133])).
% 1.93/2.09 tff(7137,plain,
% 1.93/2.09 (hskp26),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[2071, 156, 973, 5849, 972, 971, 56, 1686, 57])).
% 1.93/2.09 tff(7138,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7139,plain,
% 1.93/2.09 ((hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586))) <=> (hskp25 | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7140,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7139])).
% 1.93/2.09 tff(7141,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7140, 7138])).
% 1.93/2.09 tff(7142,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7143,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7142, 7141])).
% 1.93/2.09 tff(7144,plain,
% 1.93/2.09 (~c1_1(a589)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7143, 156, 1423, 625, 591, 3797, 4948, 55, 653])).
% 1.93/2.09 tff(7145,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c1_1(a562)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7146,plain,
% 1.93/2.09 ((hskp39 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp39 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c1_1(a562)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7147,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c1_1(a562))))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7146])).
% 1.93/2.09 tff(7148,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c1_1(a562)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7147, 7145])).
% 1.93/2.09 tff(7149,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7150,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c1_1(a562))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7149, 7148])).
% 1.93/2.09 tff(7151,plain,
% 1.93/2.09 (hskp39),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7150, 156, 973, 3797, 972, 971, 4948, 281, 653])).
% 1.93/2.09 tff(7152,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[2535, 7151, 7144, 58, 591, 625])).
% 1.93/2.09 tff(7153,plain,(c2_1(a586) | hskp38 | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a562)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7154,plain,
% 1.93/2.09 (c2_1(a586)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7153, 4534, 58, 4533, 973, 3797, 972, 971, 6369, 6435])).
% 1.93/2.09 tff(7155,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a562)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7156,plain,
% 1.93/2.09 ((hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp4 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a562)))),
% 1.93/2.09 inference(rewrite,[status(thm)],[])).
% 1.93/2.09 tff(7157,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a562))))),
% 1.93/2.09 inference(monotonicity,[status(thm)],[7156])).
% 1.93/2.09 tff(7158,plain,
% 1.93/2.09 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a562)))),
% 1.93/2.09 inference(transitivity,[status(thm)],[7157, 7155])).
% 1.93/2.09 tff(7159,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 1.93/2.09 inference(quant_inst,[status(thm)],[])).
% 1.93/2.09 tff(7160,plain,
% 1.93/2.09 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c3_1(a562) | c0_1(a562) | (~c3_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c1_1(a562))),
% 1.93/2.09 inference(modus_ponens,[status(thm)],[7159, 7158])).
% 1.93/2.09 tff(7161,plain,
% 1.93/2.09 (hskp4 | (~c2_1(a586))),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7160, 156, 973, 3797, 972, 971, 6369, 22])).
% 1.93/2.09 tff(7162,plain,
% 1.93/2.09 (hskp4),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7161, 7154])).
% 1.93/2.09 tff(7163,plain,
% 1.93/2.09 (~c0_1(a545)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1666, 7162])).
% 1.93/2.09 tff(7164,plain,
% 1.93/2.09 ($false),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[1659, 7163, 7162, 35, 58, 7137])).
% 1.93/2.09 tff(7165,plain,(c1_1(a548) | hskp33 | hskp38 | (~c1_1(a562)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.09 tff(7166,plain,
% 1.93/2.09 (c1_1(a548)),
% 1.93/2.09 inference(unit_resolution,[status(thm)],[7165, 58, 35, 973, 3797, 972, 971, 56, 24])).
% 1.93/2.10 tff(7167,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~c3_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~c3_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7168,plain,
% 1.93/2.10 ((hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548))) <=> (hskp25 | (~c3_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7169,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~c3_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[7168])).
% 1.93/2.10 tff(7170,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~c3_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[7169, 7167])).
% 1.93/2.10 tff(7171,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a586)) | (~c2_1(a586)) | (~c1_1(a586)) | c2_1(a548) | (~c3_1(a548)) | (~c1_1(a548)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(7172,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | (~c3_1(a586)) | c2_1(a548) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[7171, 7170])).
% 1.93/2.10 tff(7173,plain,
% 1.93/2.10 (hskp25 | (~c1_1(a548)) | (~c1_1(a586)) | (~c2_1(a586))),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7172, 156, 5849, 6369, 24, 55])).
% 1.93/2.10 tff(7174,plain,
% 1.93/2.10 (~c2_1(a586)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7173, 7166, 3797, 6435])).
% 1.93/2.10 tff(7175,plain,
% 1.93/2.10 (hskp39 | (~c1_1(a548))),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2063, 156, 973, 5849, 972, 971, 24, 281])).
% 1.93/2.10 tff(7176,plain,
% 1.93/2.10 (hskp39),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7175, 7166])).
% 1.93/2.10 tff(7177,plain,
% 1.93/2.10 (c3_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[319, 7176])).
% 1.93/2.10 tff(7178,plain,
% 1.93/2.10 (hskp4),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2559, 7166, 5849, 24, 56])).
% 1.93/2.10 tff(7179,plain,
% 1.93/2.10 (~hskp50),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6209, 7178, 35])).
% 1.93/2.10 tff(7180,plain,
% 1.93/2.10 (c1_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[303, 7176])).
% 1.93/2.10 tff(7181,plain,
% 1.93/2.10 (hskp34),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4519, 7166, 5849, 24, 56])).
% 1.93/2.10 tff(7182,plain,
% 1.93/2.10 (c2_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[311, 7176])).
% 1.93/2.10 tff(7183,plain,
% 1.93/2.10 (c2_1(a537)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1154, 156, 110, 98, 3626, 3624, 34])).
% 1.93/2.10 tff(7184,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1544, 156, 58, 1498, 1497, 1496, 3625, 3624, 1537, 7183])).
% 1.93/2.10 tff(7185,plain,((~hskp34) | hskp38 | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7186,plain,
% 1.93/2.10 (hskp19),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7185, 7182, 58, 7181, 7180, 7179, 7177])).
% 1.93/2.10 tff(7187,plain,
% 1.93/2.10 (hskp28),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[5069, 7186])).
% 1.93/2.10 tff(7188,plain,
% 1.93/2.10 (c2_1(a589)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[171, 7187])).
% 1.93/2.10 tff(7189,plain,
% 1.93/2.10 (c3_1(a589)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[185, 7187])).
% 1.93/2.10 tff(7190,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7153, 7189, 7188, 58, 7174, 973, 3797, 972, 971, 6369, 6435])).
% 1.93/2.10 tff(7191,plain,(hskp38 | (~c1_1(a562)) | (~c1_1(a586)) | c3_1(a562) | c0_1(a562) | hskp33 | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7192,plain,
% 1.93/2.10 (hskp38),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7191, 7136, 7037, 7135, 7134, 35, 24, 56])).
% 1.93/2.10 tff(7193,plain,
% 1.93/2.10 (c0_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[677, 7192])).
% 1.93/2.10 tff(7194,plain,
% 1.93/2.10 (c1_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[685, 7192])).
% 1.93/2.10 tff(7195,plain,
% 1.93/2.10 (c2_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[693, 7192])).
% 1.93/2.10 tff(7196,plain,
% 1.93/2.10 (~hskp0),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2694, 57, 5849, 731, 732, 24, 733])).
% 1.93/2.10 tff(7197,plain,
% 1.93/2.10 (~c3_1(a584)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1620, 7137])).
% 1.93/2.10 tff(7198,plain,
% 1.93/2.10 (c1_1(a584)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1637, 7137])).
% 1.93/2.10 tff(7199,plain,
% 1.93/2.10 (~hskp25),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6547, 7196, 733, 732, 731])).
% 1.93/2.10 tff(7200,plain,
% 1.93/2.10 (c0_1(a584)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1629, 7137])).
% 1.93/2.10 tff(7201,plain,
% 1.93/2.10 (~hskp30),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6564, 7200, 973, 972, 971, 733, 732, 731, 35, 7199, 7198, 7197])).
% 1.93/2.10 tff(7202,plain,
% 1.93/2.10 (hskp29),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4620, 7201, 5849, 57])).
% 1.93/2.10 tff(7203,plain,
% 1.93/2.10 (~c3_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4586, 7202])).
% 1.93/2.10 tff(7204,plain,
% 1.93/2.10 (~c1_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6396, 7202])).
% 1.93/2.10 tff(7205,plain,
% 1.93/2.10 (c2_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6576, 7204, 733, 732, 731, 7203, 7196])).
% 1.93/2.10 tff(7206,plain,
% 1.93/2.10 (hskp34),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2160, 156, 973, 733, 732, 731, 972, 971, 75])).
% 1.93/2.10 tff(7207,plain,
% 1.93/2.10 (~c1_1(a537)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1124, 7206])).
% 1.93/2.10 tff(7208,plain,
% 1.93/2.10 (c3_1(a537)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1132, 7206])).
% 1.93/2.10 tff(7209,plain,
% 1.93/2.10 (c0_1(a537)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1147, 7206])).
% 1.93/2.10 tff(7210,plain,
% 1.93/2.10 (hskp8),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6906, 7202, 732, 7209, 731, 733, 7196, 7208, 7207])).
% 1.93/2.10 tff(7211,plain,
% 1.93/2.10 (hskp51),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6599, 7210, 7209, 7208, 7207])).
% 1.93/2.10 tff(7212,plain,
% 1.93/2.10 (~c2_1(a583)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2637, 7211])).
% 1.93/2.10 tff(7213,plain,
% 1.93/2.10 (c3_1(a583)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2645, 7211])).
% 1.93/2.10 tff(7214,plain,
% 1.93/2.10 (c0_1(a583)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2653, 7211])).
% 1.93/2.10 tff(7215,plain,
% 1.93/2.10 (c1_1(a583)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6616, 156, 7214, 7213, 7212, 7203, 7204, 921, 7205])).
% 1.93/2.10 tff(7216,plain,
% 1.93/2.10 (~c0_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4580, 7202])).
% 1.93/2.10 tff(7217,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7218,plain,
% 1.93/2.10 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583))) <=> (c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7219,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[7218])).
% 1.93/2.10 tff(7220,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[7219, 7217])).
% 1.93/2.10 tff(7221,plain,
% 1.93/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(7222,plain,
% 1.93/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c3_1(a590) | c0_1(a590) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c1_1(a548) | (~c2_1(a590)) | (~c1_1(a583)) | (~c0_1(a583))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[7221, 7220])).
% 1.93/2.10 tff(7223,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7222, 156, 7214, 5849, 7212, 7203, 7216, 56, 609, 57, 7215, 7205])).
% 1.93/2.10 tff(7224,plain,(c1_1(a548) | c0_1(a548) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | c2_1(a548) | (~c1_1(a562)) | c3_1(a562) | c0_1(a562) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7225,plain,
% 1.93/2.10 (c1_1(a548)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7224, 56, 7195, 7194, 7193, 24, 7136, 7135, 7134, 35])).
% 1.93/2.10 tff(7226,plain,
% 1.93/2.10 (hskp42 | (~c1_1(a548))),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[3196, 156, 7195, 7194, 7193, 5849, 24, 1364])).
% 1.93/2.10 tff(7227,plain,
% 1.93/2.10 (hskp42),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7226, 7225])).
% 1.93/2.10 tff(7228,plain,
% 1.93/2.10 (~c2_1(a556)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1385, 7227])).
% 1.93/2.10 tff(7229,plain,
% 1.93/2.10 (hskp39 | (~c1_1(a548))),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2063, 156, 7136, 5849, 7135, 7134, 24, 281])).
% 1.93/2.10 tff(7230,plain,
% 1.93/2.10 (hskp39),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7229, 7225])).
% 1.93/2.10 tff(7231,plain,
% 1.93/2.10 (c1_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[303, 7230])).
% 1.93/2.10 tff(7232,plain,
% 1.93/2.10 (c2_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[311, 7230])).
% 1.93/2.10 tff(7233,plain,
% 1.93/2.10 (c3_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[319, 7230])).
% 1.93/2.10 tff(7234,plain,
% 1.93/2.10 (c3_1(a556)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1403, 7227])).
% 1.93/2.10 tff(7235,plain,
% 1.93/2.10 (c1_1(a556)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1411, 7227])).
% 1.93/2.10 tff(7236,plain,
% 1.93/2.10 (hskp25),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[5026, 156, 7235, 7234, 7233, 7232, 7231, 7228, 55])).
% 1.93/2.10 tff(7237,plain,
% 1.93/2.10 (~c1_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1190, 7236])).
% 1.93/2.10 tff(7238,plain,
% 1.93/2.10 (~c2_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1196, 7236])).
% 1.93/2.10 tff(7239,plain,
% 1.93/2.10 (~c3_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1202, 7236])).
% 1.93/2.10 tff(7240,plain,
% 1.93/2.10 (hskp34),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2160, 156, 7136, 7195, 7194, 7193, 7135, 7134, 75])).
% 1.93/2.10 tff(7241,plain,
% 1.93/2.10 (~c1_1(a537)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1124, 7240])).
% 1.93/2.10 tff(7242,plain,
% 1.93/2.10 (c3_1(a537)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1132, 7240])).
% 1.93/2.10 tff(7243,plain,
% 1.93/2.10 (~c2_1(a537)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2192, 156, 7235, 7234, 7242, 7228, 7241, 7239, 7238, 7237, 45])).
% 1.93/2.10 tff(7244,plain,
% 1.93/2.10 (hskp0),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6547, 7236, 7195, 7194, 7193])).
% 1.93/2.10 tff(7245,plain,
% 1.93/2.10 (~c2_1(a535)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[713, 7244])).
% 1.93/2.10 tff(7246,plain,
% 1.93/2.10 (c0_1(a535)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[721, 7244])).
% 1.93/2.10 tff(7247,plain,
% 1.93/2.10 (c1_1(a535)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[729, 7244])).
% 1.93/2.10 tff(7248,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2754, 156, 7195, 7194, 7193, 7242, 7247, 7246, 7241, 7245, 707, 7243])).
% 1.93/2.10 tff(7249,plain,(c0_1(a548) | c2_1(a548) | hskp33 | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7250,plain,
% 1.93/2.10 (c0_1(a548)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7249, 87, 35, 24])).
% 1.93/2.10 tff(7251,plain,
% 1.93/2.10 (c3_1(a545)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7016, 7250, 24, 35])).
% 1.93/2.10 tff(7252,plain,
% 1.93/2.10 (~hskp6),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[211, 7250])).
% 1.93/2.10 tff(7253,plain,
% 1.93/2.10 (hskp4),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[205, 7252, 6370])).
% 1.93/2.10 tff(7254,plain,
% 1.93/2.10 (~c2_1(a545)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1643, 7253])).
% 1.93/2.10 tff(7255,plain,
% 1.93/2.10 (c1_1(a545)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[193, 7253])).
% 1.93/2.10 tff(7256,plain,
% 1.93/2.10 (~c0_1(a545)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1666, 7253])).
% 1.93/2.10 tff(7257,plain,
% 1.93/2.10 (hskp38),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1211, 7255, 7251, 7254, 7256])).
% 1.93/2.10 tff(7258,plain,
% 1.93/2.10 (c1_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[685, 7257])).
% 1.93/2.10 tff(7259,plain,
% 1.93/2.10 (c0_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[677, 7257])).
% 1.93/2.10 tff(7260,plain,
% 1.93/2.10 (c2_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[693, 7257])).
% 1.93/2.10 tff(7261,plain,
% 1.93/2.10 (hskp39),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1586, 7260, 7251, 7255, 7259, 7258, 7254, 7256])).
% 1.93/2.10 tff(7262,plain,
% 1.93/2.10 (c1_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[303, 7261])).
% 1.93/2.10 tff(7263,plain,
% 1.93/2.10 (c2_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[311, 7261])).
% 1.93/2.10 tff(7264,plain,
% 1.93/2.10 (c3_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[319, 7261])).
% 1.93/2.10 tff(7265,plain,
% 1.93/2.10 (hskp25),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1184, 156, 7264, 7263, 7262, 7255, 7254, 55, 7251])).
% 1.93/2.10 tff(7266,plain,
% 1.93/2.10 (~c1_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1190, 7265])).
% 1.93/2.10 tff(7267,plain,
% 1.93/2.10 (~c2_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1196, 7265])).
% 1.93/2.10 tff(7268,plain,
% 1.93/2.10 (~hskp19),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[3077, 7256, 35, 6370, 7252])).
% 1.93/2.10 tff(7269,plain,
% 1.93/2.10 (~hskp50),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6209, 7253, 35])).
% 1.93/2.10 tff(7270,plain,
% 1.93/2.10 (~c0_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1288, 156, 7269, 7268, 7267, 7266, 34])).
% 1.93/2.10 tff(7271,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a586) | (~c3_1(a586)) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a586) | (~c3_1(a586)) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a586)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7272,plain,
% 1.93/2.10 ((hskp6 | (~ndr1_0) | c0_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a582) | c1_1(a582) | c0_1(a582)) <=> (hskp6 | c0_1(a586) | (~c3_1(a586)) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a586)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7273,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a586) | (~c3_1(a586)) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a586))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[7272])).
% 1.93/2.10 tff(7274,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a582) | c1_1(a582) | c0_1(a582))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a586) | (~c3_1(a586)) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a586)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[7273, 7271])).
% 1.93/2.10 tff(7275,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a586) | (~c3_1(a586)) | (~c1_1(a586)) | c2_1(a582) | c1_1(a582) | c0_1(a582))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(7276,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a586) | (~c3_1(a586)) | c2_1(a582) | c1_1(a582) | (~ndr1_0) | c0_1(a582) | (~c1_1(a586))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[7275, 7274])).
% 1.93/2.10 tff(7277,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7276, 156, 7252, 7037, 87, 6369, 7267, 7266, 1745, 7270])).
% 1.93/2.10 tff(7278,plain,(c0_1(a586) | hskp33 | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7279,plain,
% 1.93/2.10 (c0_1(a586)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7278, 35, 24])).
% 1.93/2.10 tff(7280,plain,
% 1.93/2.10 (c2_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6408, 6399, 249, 56, 6400, 24, 58])).
% 1.93/2.10 tff(7281,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c3_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | c2_1(a586) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c3_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | c2_1(a586) | (~c2_1(a590)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7282,plain,
% 1.93/2.10 (((~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a586)) | c1_1(a586) | (~c3_1(a586))) <=> (c1_1(a586) | c3_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | c2_1(a586) | (~c2_1(a590)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7283,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a586)) | c1_1(a586) | (~c3_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a586) | c3_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | c2_1(a586) | (~c2_1(a590))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[7282])).
% 1.93/2.10 tff(7284,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a586)) | c1_1(a586) | (~c3_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c3_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | c2_1(a586) | (~c2_1(a590)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[7283, 7281])).
% 1.93/2.10 tff(7285,plain,
% 1.93/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a586)) | c1_1(a586) | (~c3_1(a586)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(7286,plain,
% 1.93/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a586) | c3_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | c2_1(a586) | (~c2_1(a590))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[7285, 7284])).
% 1.93/2.10 tff(7287,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7286, 156, 88, 6400, 6399, 1996, 4948, 921, 653, 7280])).
% 1.93/2.10 tff(7288,plain,(c1_1(a590) | c1_1(a586) | c3_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | c2_1(a586) | (~c3_1(a548)) | c0_1(a548) | c2_1(a548) | hskp38), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7289,plain,
% 1.93/2.10 (c2_1(a586)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7288, 6397, 6391, 7279, 6369, 88, 5849, 56, 24, 58])).
% 1.93/2.10 tff(7290,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | c1_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7291,plain,
% 1.93/2.10 ((hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586))) <=> (hskp38 | c1_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7292,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | c1_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[7291])).
% 1.93/2.10 tff(7293,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[7292, 7290])).
% 1.93/2.10 tff(7294,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp38 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c1_1(a586) | (~c3_1(a586)) | (~c2_1(a586)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(7295,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp38 | c1_1(a586) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a586)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[7294, 7293])).
% 1.93/2.10 tff(7296,plain,
% 1.93/2.10 ((~c2_1(a586)) | (~c1_1(a589))),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7295, 156, 58, 4533, 4534, 88, 6369, 1537])).
% 1.93/2.10 tff(7297,plain,
% 1.93/2.10 (~c1_1(a589)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7296, 7289])).
% 1.93/2.10 tff(7298,plain,
% 1.93/2.10 (~hskp37),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4732, 7289, 5849, 7279, 24, 57, 56, 58, 88, 946, 35])).
% 1.93/2.10 tff(7299,plain,
% 1.93/2.10 (hskp17),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6938, 7298, 5849, 24, 56, 58, 4533, 946, 4534, 7297])).
% 1.93/2.10 tff(7300,plain,
% 1.93/2.10 (~c2_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[573, 7299])).
% 1.93/2.10 tff(7301,plain,
% 1.93/2.10 (c3_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[623, 7299])).
% 1.93/2.10 tff(7302,plain,
% 1.93/2.10 (c0_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[581, 7299])).
% 1.93/2.10 tff(7303,plain,
% 1.93/2.10 (c1_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6510, 156, 7302, 7301, 6391, 6397, 7300, 921, 6409])).
% 1.93/2.10 tff(7304,plain,
% 1.93/2.10 (~c0_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4580, 6390])).
% 1.93/2.10 tff(7305,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a590) | c0_1(a590) | c0_1(a589) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | c0_1(a589) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7306,plain,
% 1.93/2.10 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c3_1(a590) | c0_1(a590) | c0_1(a589) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7307,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a590) | c0_1(a590) | c0_1(a589) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[7306])).
% 1.93/2.10 tff(7308,plain,
% 1.93/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | c0_1(a589) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[7307, 7305])).
% 1.93/2.10 tff(7309,plain,
% 1.93/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(7310,plain,
% 1.93/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | c0_1(a589) | c2_1(a571) | (~ndr1_0) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[7309, 7308])).
% 1.93/2.10 tff(7311,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7310, 156, 4534, 7302, 6391, 7304, 4535, 7300, 609, 7297, 6409, 7303])).
% 1.93/2.10 tff(7312,plain,(hskp46 | c2_1(a548) | c0_1(a548) | hskp38 | c1_1(a586) | c1_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7313,plain,
% 1.93/2.10 (hskp46),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7312, 57, 56, 58, 88, 24, 35])).
% 1.93/2.10 tff(7314,plain,
% 1.93/2.10 (~c0_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[64, 7313])).
% 1.93/2.10 tff(7315,plain,
% 1.93/2.10 (~c3_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[270, 7313])).
% 1.93/2.10 tff(7316,plain,
% 1.93/2.10 (c1_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[288, 7313])).
% 1.93/2.10 tff(7317,plain,
% 1.93/2.10 (hskp26),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2071, 156, 7316, 5849, 7315, 7314, 56, 1686, 57])).
% 1.93/2.10 tff(7318,plain,
% 1.93/2.10 (~c3_1(a584)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1620, 7317])).
% 1.93/2.10 tff(7319,plain,
% 1.93/2.10 (c1_1(a584)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1637, 7317])).
% 1.93/2.10 tff(7320,plain,
% 1.93/2.10 (c0_1(a584)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1629, 7317])).
% 1.93/2.10 tff(7321,plain,
% 1.93/2.10 (~hskp30),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6454, 7320, 58, 7316, 7315, 4533, 7314, 6435, 35, 4534, 7319, 7318])).
% 1.93/2.10 tff(7322,plain,
% 1.93/2.10 (hskp29),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4620, 7321, 5849, 57])).
% 1.93/2.10 tff(7323,plain,
% 1.93/2.10 (~c3_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4586, 7322])).
% 1.93/2.10 tff(7324,plain,
% 1.93/2.10 (~c1_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6396, 7322])).
% 1.93/2.10 tff(7325,plain,
% 1.93/2.10 (c2_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6408, 7324, 5849, 56, 7323, 24, 58])).
% 1.93/2.10 tff(7326,plain,
% 1.93/2.10 (c2_1(a586)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7288, 7324, 7323, 7279, 6369, 88, 5849, 56, 24, 58])).
% 1.93/2.10 tff(7327,plain,
% 1.93/2.10 (~hskp37),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4745, 7326, 35, 7279, 24, 56, 58, 88, 57, 5849])).
% 1.93/2.10 tff(7328,plain,
% 1.93/2.10 (~hskp18),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2583, 7327, 5849, 24, 56, 58])).
% 1.93/2.10 tff(7329,plain,
% 1.93/2.10 (~c1_1(a589)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7296, 7326])).
% 1.93/2.10 tff(7330,plain,
% 1.93/2.10 (~hskp39),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2535, 7329, 58, 4534, 4533])).
% 1.93/2.10 tff(7331,plain,
% 1.93/2.10 (~hskp16),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2301, 7330, 7316, 7314, 58, 4534, 4533, 7315, 7329])).
% 1.93/2.10 tff(7332,plain,
% 1.93/2.10 (hskp17),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[382, 7331, 7328])).
% 1.93/2.10 tff(7333,plain,
% 1.93/2.10 (~c2_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[573, 7332])).
% 1.93/2.10 tff(7334,plain,
% 1.93/2.10 (c3_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[623, 7332])).
% 1.93/2.10 tff(7335,plain,
% 1.93/2.10 (c0_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[581, 7332])).
% 1.93/2.10 tff(7336,plain,
% 1.93/2.10 (c1_1(a571)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6510, 156, 7335, 7334, 7323, 7324, 7333, 921, 7325])).
% 1.93/2.10 tff(7337,plain,
% 1.93/2.10 (~c0_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4580, 7322])).
% 1.93/2.10 tff(7338,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7310, 156, 4534, 7335, 7323, 7337, 4535, 7333, 609, 7329, 7325, 7336])).
% 1.93/2.10 tff(7339,plain,(c1_1(a548) | hskp38 | c2_1(a548) | c0_1(a548) | c1_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7340,plain,
% 1.93/2.10 (c1_1(a548)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7339, 58, 24, 56, 88, 35])).
% 1.93/2.10 tff(7341,plain,
% 1.93/2.10 (hskp46),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2834, 7340, 5849, 56])).
% 1.93/2.10 tff(7342,plain,
% 1.93/2.10 (~c0_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[64, 7341])).
% 1.93/2.10 tff(7343,plain,
% 1.93/2.10 (~c3_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[270, 7341])).
% 1.93/2.10 tff(7344,plain,
% 1.93/2.10 (c1_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[288, 7341])).
% 1.93/2.10 tff(7345,plain,
% 1.93/2.10 (hskp39),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2063, 156, 7344, 5849, 7343, 7342, 24, 281, 7340])).
% 1.93/2.10 tff(7346,plain,
% 1.93/2.10 (c1_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[303, 7345])).
% 1.93/2.10 tff(7347,plain,
% 1.93/2.10 (c2_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[311, 7345])).
% 1.93/2.10 tff(7348,plain,
% 1.93/2.10 (c3_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[319, 7345])).
% 1.93/2.10 tff(7349,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4507, 156, 6435, 7348, 7347, 7346, 5849, 24, 55, 7340])).
% 1.93/2.10 tff(7350,plain,(hskp38 | c2_1(a548) | c0_1(a548) | c1_1(a586) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7351,plain,
% 1.93/2.10 (hskp38),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7350, 56, 24, 88, 35])).
% 1.93/2.10 tff(7352,plain,
% 1.93/2.10 (c0_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[677, 7351])).
% 1.93/2.10 tff(7353,plain,
% 1.93/2.10 (c1_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[685, 7351])).
% 1.93/2.10 tff(7354,plain,
% 1.93/2.10 (c2_1(a547)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[693, 7351])).
% 1.93/2.10 tff(7355,plain,
% 1.93/2.10 (~hskp0),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2694, 57, 5849, 7352, 7353, 24, 7354])).
% 1.93/2.10 tff(7356,plain,
% 1.93/2.10 (c2_1(a590)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6576, 6707, 733, 732, 731, 4587, 837])).
% 1.93/2.10 tff(7357,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2735, 156, 837, 733, 732, 731, 6596, 6595, 6594, 108])).
% 1.93/2.10 tff(7358,plain,((~hskp8) | hskp0 | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7359,plain,
% 1.93/2.10 (~hskp8),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7358, 837, 733, 732, 731])).
% 1.93/2.10 tff(7360,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a586) | c0_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a586) | c0_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7361,plain,
% 1.93/2.10 ((hskp8 | (~ndr1_0) | c1_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp8 | c1_1(a586) | c0_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)))),
% 1.93/2.10 inference(rewrite,[status(thm)],[])).
% 1.93/2.10 tff(7362,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a586) | c0_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590))))),
% 1.93/2.10 inference(monotonicity,[status(thm)],[7361])).
% 1.93/2.10 tff(7363,plain,
% 1.93/2.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a586) | c0_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590)))),
% 1.93/2.10 inference(transitivity,[status(thm)],[7362, 7360])).
% 1.93/2.10 tff(7364,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a586) | (~c3_1(a586)) | (~c0_1(a586)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 1.93/2.10 inference(quant_inst,[status(thm)],[])).
% 1.93/2.10 tff(7365,plain,
% 1.93/2.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a586) | c0_1(a590) | c1_1(a590) | (~c0_1(a586)) | (~c3_1(a586)) | (~ndr1_0) | (~c2_1(a590))),
% 1.93/2.10 inference(modus_ponens,[status(thm)],[7364, 7363])).
% 1.93/2.10 tff(7366,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7365, 156, 7359, 88, 4581, 6707, 1996, 4948, 2407, 7356])).
% 1.93/2.10 tff(7367,plain,((~hskp29) | c1_1(a586) | (~c0_1(a586)) | (~c3_1(a586)) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7368,plain,
% 1.93/2.10 (~hskp29),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7367, 7355, 7279, 6369, 7354, 7353, 7352, 88])).
% 1.93/2.10 tff(7369,plain,
% 1.93/2.10 (hskp30),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[4620, 7368, 5849, 57])).
% 1.93/2.10 tff(7370,plain,
% 1.93/2.10 (hskp46),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[6388, 7369, 5849, 56, 57, 35])).
% 1.93/2.10 tff(7371,plain,
% 1.93/2.10 (~c0_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[64, 7370])).
% 1.93/2.10 tff(7372,plain,
% 1.93/2.10 (c1_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[288, 7370])).
% 1.93/2.10 tff(7373,plain,
% 1.93/2.10 (~c3_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[270, 7370])).
% 1.93/2.10 tff(7374,plain,
% 1.93/2.10 ($false),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7224, 7373, 7372, 56, 7354, 7352, 24, 7353, 57, 7371, 35])).
% 1.93/2.10 tff(7375,plain,(c1_1(a548) | c0_1(a548) | c2_1(a548) | hskp33 | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.10 tff(7376,plain,
% 1.93/2.10 (c1_1(a548)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7375, 56, 24, 35, 88])).
% 1.93/2.10 tff(7377,plain,
% 1.93/2.10 (hskp42 | (~c1_1(a548))),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[3196, 156, 7354, 7353, 7352, 5849, 24, 1364])).
% 1.93/2.10 tff(7378,plain,
% 1.93/2.10 (hskp42),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[7377, 7376])).
% 1.93/2.10 tff(7379,plain,
% 1.93/2.10 (~c2_1(a556)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1385, 7378])).
% 1.93/2.10 tff(7380,plain,
% 1.93/2.10 (hskp46),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[2834, 7376, 5849, 56])).
% 1.93/2.10 tff(7381,plain,
% 1.93/2.10 (~c0_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[64, 7380])).
% 1.93/2.10 tff(7382,plain,
% 1.93/2.10 (~c3_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[270, 7380])).
% 1.93/2.10 tff(7383,plain,
% 1.93/2.10 (c3_1(a556)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1403, 7378])).
% 1.93/2.10 tff(7384,plain,
% 1.93/2.10 (c1_1(a556)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1411, 7378])).
% 1.93/2.10 tff(7385,plain,
% 1.93/2.10 (c1_1(a562)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[288, 7380])).
% 1.93/2.10 tff(7386,plain,
% 1.93/2.10 (hskp39),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1419, 156, 7385, 7384, 7383, 7382, 7381, 7379, 281])).
% 1.93/2.10 tff(7387,plain,
% 1.93/2.10 (c1_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[303, 7386])).
% 1.93/2.10 tff(7388,plain,
% 1.93/2.10 (c2_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[311, 7386])).
% 1.93/2.10 tff(7389,plain,
% 1.93/2.10 (c3_1(a549)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[319, 7386])).
% 1.93/2.10 tff(7390,plain,
% 1.93/2.10 (hskp25),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[5026, 156, 7384, 7383, 7389, 7388, 7387, 7379, 55])).
% 1.93/2.10 tff(7391,plain,
% 1.93/2.10 (~c1_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1190, 7390])).
% 1.93/2.10 tff(7392,plain,
% 1.93/2.10 (~c2_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1196, 7390])).
% 1.93/2.10 tff(7393,plain,
% 1.93/2.10 (~c3_1(a582)),
% 1.93/2.10 inference(unit_resolution,[status(thm)],[1202, 7390])).
% 1.93/2.10 tff(7394,plain,
% 1.93/2.10 (~c2_1(a586)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6979, 156, 7384, 7383, 88, 7379, 6369, 7393, 7392, 7391, 45])).
% 1.93/2.11 tff(7395,plain,
% 1.93/2.11 (hskp0),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6547, 7390, 7354, 7353, 7352])).
% 1.93/2.11 tff(7396,plain,
% 1.93/2.11 (~c2_1(a535)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[713, 7395])).
% 1.93/2.11 tff(7397,plain,
% 1.93/2.11 (c0_1(a535)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[721, 7395])).
% 1.93/2.11 tff(7398,plain,
% 1.93/2.11 (c1_1(a535)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[729, 7395])).
% 1.93/2.11 tff(7399,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6990, 156, 7354, 7353, 7352, 88, 7398, 7397, 6369, 7396, 707, 7394])).
% 1.93/2.11 tff(7400,plain,(c0_1(a548) | c1_1(a586) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7401,plain,
% 1.93/2.11 (c0_1(a548)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7400, 88, 24, 35])).
% 1.93/2.11 tff(7402,plain,
% 1.93/2.11 (~hskp6),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[211, 7401])).
% 1.93/2.11 tff(7403,plain,
% 1.93/2.11 (hskp4),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[205, 7402, 6370])).
% 1.93/2.11 tff(7404,plain,
% 1.93/2.11 (~hskp50),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6209, 7403, 35])).
% 1.93/2.11 tff(7405,plain,
% 1.93/2.11 (~c0_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1666, 7403])).
% 1.93/2.11 tff(7406,plain,
% 1.93/2.11 (~hskp19),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[3077, 7405, 35, 6370, 7402])).
% 1.93/2.11 tff(7407,plain,
% 1.93/2.11 (hskp50 | hskp19 | c1_1(a586) | c2_1(a586)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1944, 156, 7279, 34])).
% 1.93/2.11 tff(7408,plain,
% 1.93/2.11 (c2_1(a586)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7407, 7406, 88, 7404])).
% 1.93/2.11 tff(7409,plain,
% 1.93/2.11 (c3_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7016, 7401, 24, 35])).
% 1.93/2.11 tff(7410,plain,
% 1.93/2.11 (~c2_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1643, 7403])).
% 1.93/2.11 tff(7411,plain,
% 1.93/2.11 (c1_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[193, 7403])).
% 1.93/2.11 tff(7412,plain,
% 1.93/2.11 (hskp38),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[4967, 7402, 88, 6369, 35])).
% 1.93/2.11 tff(7413,plain,
% 1.93/2.11 (c1_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[685, 7412])).
% 1.93/2.11 tff(7414,plain,
% 1.93/2.11 (c0_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[677, 7412])).
% 1.93/2.11 tff(7415,plain,
% 1.93/2.11 (c2_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[693, 7412])).
% 1.93/2.11 tff(7416,plain,
% 1.93/2.11 (hskp39),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1586, 7415, 7409, 7411, 7414, 7413, 7410, 7405])).
% 1.93/2.11 tff(7417,plain,
% 1.93/2.11 (c1_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[303, 7416])).
% 1.93/2.11 tff(7418,plain,
% 1.93/2.11 (c2_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[311, 7416])).
% 1.93/2.11 tff(7419,plain,
% 1.93/2.11 (c3_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[319, 7416])).
% 1.93/2.11 tff(7420,plain,
% 1.93/2.11 (hskp25),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1184, 156, 7419, 7418, 7417, 7411, 7410, 55, 7409])).
% 1.93/2.11 tff(7421,plain,
% 1.93/2.11 (~c1_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1190, 7420])).
% 1.93/2.11 tff(7422,plain,
% 1.93/2.11 (~c2_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1196, 7420])).
% 1.93/2.11 tff(7423,plain,
% 1.93/2.11 (~c3_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1202, 7420])).
% 1.93/2.11 tff(7424,plain,
% 1.93/2.11 (c1_1(a548)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[4803, 7406, 7401, 7404])).
% 1.93/2.11 tff(7425,plain,
% 1.93/2.11 (hskp42),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[3196, 156, 7415, 7413, 7414, 5849, 24, 1364, 7424])).
% 1.93/2.11 tff(7426,plain,
% 1.93/2.11 (~c2_1(a556)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1385, 7425])).
% 1.93/2.11 tff(7427,plain,
% 1.93/2.11 (c3_1(a556)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1403, 7425])).
% 1.93/2.11 tff(7428,plain,
% 1.93/2.11 (c1_1(a556)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1411, 7425])).
% 1.93/2.11 tff(7429,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6979, 156, 7428, 7427, 88, 7426, 6369, 7423, 7422, 7421, 45, 7408])).
% 1.93/2.11 tff(7430,plain,(c1_1(a586) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7431,plain,
% 1.93/2.11 (c1_1(a586)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7430, 35, 24])).
% 1.93/2.11 tff(7432,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7191, 3244, 3245, 7431, 58, 65, 35, 24, 56])).
% 1.93/2.11 tff(7433,plain,((~hskp46) | hskp38 | hskp33 | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7434,plain,
% 1.93/2.11 (~hskp46),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7433, 58, 35, 24, 56])).
% 1.93/2.11 tff(7435,plain,
% 1.93/2.11 (~c1_1(a548)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2834, 7434, 5849, 56])).
% 1.93/2.11 tff(7436,plain,
% 1.93/2.11 (c2_1(a590)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6408, 6391, 5849, 56, 58, 24, 6397])).
% 1.93/2.11 tff(7437,plain,
% 1.93/2.11 (~c2_1(a586)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7055, 156, 946, 7431, 6391, 7304, 6369, 858, 7436])).
% 1.93/2.11 tff(7438,plain,
% 1.93/2.11 (~c1_1(a589)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6740, 156, 946, 4533, 4534, 6391, 7304, 858, 7436])).
% 1.93/2.11 tff(7439,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a590) | c0_1(a590) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7440,plain,
% 1.93/2.11 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586))) <=> (c3_1(a590) | c0_1(a590) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7441,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a590) | c0_1(a590) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590))))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[7440])).
% 1.93/2.11 tff(7442,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590)))),
% 1.93/2.11 inference(transitivity,[status(thm)],[7441, 7439])).
% 1.93/2.11 tff(7443,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a586) | (~c0_1(a586)) | (~c1_1(a586)))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(7444,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a590) | c0_1(a590) | c0_1(a589) | (~c0_1(a586)) | (~ndr1_0) | (~c1_1(a586)) | c2_1(a586) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a590))),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[7443, 7442])).
% 1.93/2.11 tff(7445,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7444, 156, 4534, 7431, 6391, 7304, 4535, 7279, 609, 7438, 7437, 7436])).
% 1.93/2.11 tff(7446,plain,(hskp46 | c0_1(a548) | hskp38 | c2_1(a548) | c1_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7447,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7446, 7435, 7434, 58, 24, 56, 35])).
% 1.93/2.11 tff(7448,plain,(hskp38 | c2_1(a548) | c0_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7449,plain,
% 1.93/2.11 (hskp38),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7448, 56, 24, 35])).
% 1.93/2.11 tff(7450,plain,
% 1.93/2.11 (c2_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[693, 7449])).
% 1.93/2.11 tff(7451,plain,
% 1.93/2.11 (c1_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[685, 7449])).
% 1.93/2.11 tff(7452,plain,
% 1.93/2.11 (c0_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[677, 7449])).
% 1.93/2.11 tff(7453,plain,
% 1.93/2.11 (~hskp0),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2694, 57, 5849, 7452, 7451, 24, 7450])).
% 1.93/2.11 tff(7454,plain,
% 1.93/2.11 (c2_1(a590)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6576, 6397, 7450, 7451, 7452, 6391, 7453])).
% 1.93/2.11 tff(7455,plain,
% 1.93/2.11 (~c2_1(a586)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7055, 156, 946, 7431, 6391, 7304, 6369, 858, 7454])).
% 1.93/2.11 tff(7456,plain,
% 1.93/2.11 (~c1_1(a589)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6740, 156, 946, 4533, 4534, 6391, 7304, 858, 7454])).
% 1.93/2.11 tff(7457,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7444, 156, 4534, 7431, 6391, 7304, 4535, 7279, 609, 7456, 7455, 7454])).
% 1.93/2.11 tff(7458,plain,(hskp46 | c1_1(a548) | c2_1(a548) | c0_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7459,plain,
% 1.93/2.11 (hskp46),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7458, 57, 24, 56, 35])).
% 1.93/2.11 tff(7460,plain,
% 1.93/2.11 (~c0_1(a562)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[64, 7459])).
% 1.93/2.11 tff(7461,plain,
% 1.93/2.11 (c1_1(a562)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[288, 7459])).
% 1.93/2.11 tff(7462,plain,
% 1.93/2.11 (~c3_1(a562)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[270, 7459])).
% 1.93/2.11 tff(7463,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7224, 7462, 7461, 56, 7450, 7452, 24, 7451, 57, 7460, 35])).
% 1.93/2.11 tff(7464,plain,(c1_1(a548) | c0_1(a548) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7465,plain,
% 1.93/2.11 (c1_1(a548)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7464, 56, 24, 35])).
% 1.93/2.11 tff(7466,plain,
% 1.93/2.11 (hskp42 | (~c1_1(a548))),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[3196, 156, 7450, 7451, 7452, 5849, 24, 1364])).
% 1.93/2.11 tff(7467,plain,
% 1.93/2.11 (hskp42),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7466, 7465])).
% 1.93/2.11 tff(7468,plain,
% 1.93/2.11 (~c2_1(a556)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1385, 7467])).
% 1.93/2.11 tff(7469,plain,
% 1.93/2.11 (hskp46),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2834, 7465, 5849, 56])).
% 1.93/2.11 tff(7470,plain,
% 1.93/2.11 (~c0_1(a562)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[64, 7469])).
% 1.93/2.11 tff(7471,plain,
% 1.93/2.11 (~c3_1(a562)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[270, 7469])).
% 1.93/2.11 tff(7472,plain,
% 1.93/2.11 (c3_1(a556)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1403, 7467])).
% 1.93/2.11 tff(7473,plain,
% 1.93/2.11 (c1_1(a556)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1411, 7467])).
% 1.93/2.11 tff(7474,plain,
% 1.93/2.11 (c1_1(a562)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[288, 7469])).
% 1.93/2.11 tff(7475,plain,
% 1.93/2.11 (hskp39),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1419, 156, 7474, 7473, 7472, 7471, 7470, 7468, 281])).
% 1.93/2.11 tff(7476,plain,
% 1.93/2.11 (c1_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[303, 7475])).
% 1.93/2.11 tff(7477,plain,
% 1.93/2.11 (c2_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[311, 7475])).
% 1.93/2.11 tff(7478,plain,
% 1.93/2.11 (c3_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[319, 7475])).
% 1.93/2.11 tff(7479,plain,
% 1.93/2.11 (hskp25),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[5026, 156, 7473, 7472, 7478, 7477, 7476, 7468, 55])).
% 1.93/2.11 tff(7480,plain,
% 1.93/2.11 (~c1_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1190, 7479])).
% 1.93/2.11 tff(7481,plain,
% 1.93/2.11 (~c2_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1196, 7479])).
% 1.93/2.11 tff(7482,plain,
% 1.93/2.11 (~c3_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1202, 7479])).
% 1.93/2.11 tff(7483,plain,
% 1.93/2.11 (hskp34),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[4519, 7465, 5849, 24, 56])).
% 1.93/2.11 tff(7484,plain,
% 1.93/2.11 (~c1_1(a537)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1124, 7483])).
% 1.93/2.11 tff(7485,plain,
% 1.93/2.11 (c3_1(a537)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1132, 7483])).
% 1.93/2.11 tff(7486,plain,
% 1.93/2.11 (~c2_1(a537)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2192, 156, 7473, 7472, 7485, 7468, 7484, 7482, 7481, 7480, 45])).
% 1.93/2.11 tff(7487,plain,
% 1.93/2.11 (hskp0),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6547, 7479, 7450, 7451, 7452])).
% 1.93/2.11 tff(7488,plain,
% 1.93/2.11 (~c2_1(a535)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[713, 7487])).
% 1.93/2.11 tff(7489,plain,
% 1.93/2.11 (c0_1(a535)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[721, 7487])).
% 1.93/2.11 tff(7490,plain,
% 1.93/2.11 (c1_1(a535)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[729, 7487])).
% 1.93/2.11 tff(7491,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2754, 156, 7450, 7451, 7452, 7485, 7490, 7489, 7484, 7488, 707, 7486])).
% 1.93/2.11 tff(7492,plain,(c0_1(a548) | c2_1(a548) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7493,plain,
% 1.93/2.11 (c0_1(a548)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7492, 35, 24])).
% 1.93/2.11 tff(7494,plain,
% 1.93/2.11 (c3_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7016, 7493, 24, 35])).
% 1.93/2.11 tff(7495,plain,
% 1.93/2.11 (~hskp6),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[211, 7493])).
% 1.93/2.11 tff(7496,plain,
% 1.93/2.11 (hskp4),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[205, 7495, 6370])).
% 1.93/2.11 tff(7497,plain,
% 1.93/2.11 (~c2_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1643, 7496])).
% 1.93/2.11 tff(7498,plain,
% 1.93/2.11 (c1_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[193, 7496])).
% 1.93/2.11 tff(7499,plain,
% 1.93/2.11 (~c0_1(a545)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1666, 7496])).
% 1.93/2.11 tff(7500,plain,
% 1.93/2.11 (hskp38),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1211, 7498, 7494, 7497, 7499])).
% 1.93/2.11 tff(7501,plain,
% 1.93/2.11 (c1_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[685, 7500])).
% 1.93/2.11 tff(7502,plain,
% 1.93/2.11 (c0_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[677, 7500])).
% 1.93/2.11 tff(7503,plain,
% 1.93/2.11 (c2_1(a547)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[693, 7500])).
% 1.93/2.11 tff(7504,plain,
% 1.93/2.11 (hskp39),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1586, 7503, 7494, 7498, 7502, 7501, 7497, 7499])).
% 1.93/2.11 tff(7505,plain,
% 1.93/2.11 (c1_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[303, 7504])).
% 1.93/2.11 tff(7506,plain,
% 1.93/2.11 (c2_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[311, 7504])).
% 1.93/2.11 tff(7507,plain,
% 1.93/2.11 (c3_1(a549)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[319, 7504])).
% 1.93/2.11 tff(7508,plain,
% 1.93/2.11 (hskp25),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1184, 156, 7507, 7506, 7505, 7498, 7497, 55, 7494])).
% 1.93/2.11 tff(7509,plain,
% 1.93/2.11 (~c1_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1190, 7508])).
% 1.93/2.11 tff(7510,plain,
% 1.93/2.11 (~c2_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1196, 7508])).
% 1.93/2.11 tff(7511,plain,
% 1.93/2.11 (~hskp19),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[3077, 7499, 35, 6370, 7495])).
% 1.93/2.11 tff(7512,plain,
% 1.93/2.11 (~hskp50),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6209, 7496, 35])).
% 1.93/2.11 tff(7513,plain,
% 1.93/2.11 (~c0_1(a582)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1288, 156, 7512, 7511, 7510, 7509, 34])).
% 1.93/2.11 tff(7514,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[5619, 156, 7495, 7498, 7510, 7509, 7499, 1745, 7494, 7513])).
% 1.93/2.11 tff(7515,plain,(hskp33 | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7516,plain,
% 1.93/2.11 (hskp33),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7515, 24])).
% 1.93/2.11 tff(7517,plain,
% 1.93/2.11 (hskp34),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[4294, 4940, 3667])).
% 1.93/2.11 tff(7518,plain,
% 1.93/2.11 (~c1_1(a537)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1124, 7517])).
% 1.93/2.11 tff(7519,plain,
% 1.93/2.11 (c3_1(a537)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1132, 7517])).
% 1.93/2.11 tff(7520,plain,
% 1.93/2.11 (c0_1(a537)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1147, 7517])).
% 1.93/2.11 tff(7521,plain,
% 1.93/2.11 (c2_1(a537)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[4788, 86, 88, 4779, 4778, 4780])).
% 1.93/2.11 tff(7522,plain,
% 1.93/2.11 (hskp15 | c3_1(a545) | (~c2_1(a537))),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2094, 156, 4779, 4941, 4778, 4944, 483])).
% 1.93/2.11 tff(7523,plain,
% 1.93/2.11 (hskp15),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7522, 7521, 765])).
% 1.93/2.11 tff(7524,plain,
% 1.93/2.11 (hskp28),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1276, 7523])).
% 1.93/2.11 tff(7525,plain,
% 1.93/2.11 (~c0_1(a589)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[177, 7524])).
% 1.93/2.11 tff(7526,assumption,(hskp51), introduced(assumption)).
% 1.93/2.11 tff(7527,plain,
% 1.93/2.11 (~c2_1(a583)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2637, 7526])).
% 1.93/2.11 tff(7528,plain,
% 1.93/2.11 (c3_1(a583)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2645, 7526])).
% 1.93/2.11 tff(7529,plain,
% 1.93/2.11 (c0_1(a583)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2653, 7526])).
% 1.93/2.11 tff(7530,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[3646, 156, 7529, 7528, 4780, 4779, 88, 7527, 4778, 86, 921, 4474])).
% 1.93/2.11 tff(7531,plain,((~hskp51) | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a586) | c1_1(a537) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7532,plain,
% 1.93/2.11 (~hskp51),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7531, 86, 88, 4779, 4778, 4780])).
% 1.93/2.11 tff(7533,plain,
% 1.93/2.11 (~hskp8),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6599, 7532, 4780, 4779, 4778])).
% 1.93/2.11 tff(7534,plain,
% 1.93/2.11 (c2_1(a589)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[171, 7524])).
% 1.93/2.11 tff(7535,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[2418, 156, 6903, 4780, 4779, 625, 4778, 590, 2407, 1716])).
% 1.93/2.11 tff(7536,plain,(c1_1(a589) | hskp8 | (~c0_1(a537)) | (~c3_1(a537)) | (~c2_1(a589)) | c1_1(a537) | c0_1(a589)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7537,plain,
% 1.93/2.11 (c1_1(a589)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7536, 7534, 4780, 4779, 7533, 4778, 7525])).
% 1.93/2.11 tff(7538,plain,
% 1.93/2.11 (~c2_1(a569)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1255, 7523])).
% 1.93/2.11 tff(7539,plain,
% 1.93/2.11 (~c1_1(a569)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1261, 7523])).
% 1.93/2.11 tff(7540,plain,
% 1.93/2.11 (~c0_1(a569)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1267, 7523])).
% 1.93/2.11 tff(7541,plain,
% 1.93/2.11 (c3_1(a589)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[185, 7524])).
% 1.93/2.11 tff(7542,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1789, 156, 1669, 7541, 7525, 7540, 7539, 7538, 1745, 7537])).
% 1.93/2.11 tff(7543,plain,(c3_1(a586) | hskp6 | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537) | c3_1(a545) | c1_1(a586)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7544,plain,
% 1.93/2.11 (c3_1(a586)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7543, 765, 7520, 7519, 7518, 1669, 88])).
% 1.93/2.11 tff(7545,assumption,(~c2_1(a584)), introduced(assumption)).
% 1.93/2.11 tff(7546,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7547,plain,
% 1.93/2.11 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584))) <=> (c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7548,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537)))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[7547])).
% 1.93/2.11 tff(7549,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537))),
% 1.93/2.11 inference(transitivity,[status(thm)],[7548, 7546])).
% 1.93/2.11 tff(7550,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(7551,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[7550, 7549])).
% 1.93/2.11 tff(7552,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7551, 156, 4779, 3428, 3427, 3426, 1649, 1648, 4778, 707, 4777, 7545])).
% 1.93/2.11 tff(7553,plain,(c2_1(a584) | (~c3_1(a537)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | (~c0_1(a584)) | (~c1_1(a584)) | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7554,plain,
% 1.93/2.11 (c2_1(a584)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7553, 1630, 3428, 3427, 3426, 4779, 1638, 4778, 4777])).
% 1.93/2.11 tff(7555,plain,
% 1.93/2.11 (hskp32 | (~c2_1(a584))),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[6482, 156, 1630, 1638, 1621, 4894])).
% 1.93/2.11 tff(7556,plain,
% 1.93/2.11 (hskp32),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7555, 7554])).
% 1.93/2.11 tff(7557,plain,
% 1.93/2.11 (~c2_1(a596)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[5534, 7556])).
% 1.93/2.11 tff(7558,plain,
% 1.93/2.11 (c0_1(a596)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[5522, 7556])).
% 1.93/2.11 tff(7559,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7560,plain,
% 1.93/2.11 (((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596))) <=> (c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7561,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537)))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[7560])).
% 1.93/2.11 tff(7562,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537))),
% 1.93/2.11 inference(transitivity,[status(thm)],[7561, 7559])).
% 1.93/2.11 tff(7563,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(7564,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[7563, 7562])).
% 1.93/2.11 tff(7565,plain,
% 1.93/2.11 (~c1_1(a596)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7564, 156, 4779, 7558, 1630, 1638, 4778, 7557, 707, 4777, 7554])).
% 1.93/2.11 tff(7566,plain,
% 1.93/2.11 (~c3_1(a596)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[5528, 7556])).
% 1.93/2.11 tff(7567,plain,
% 1.93/2.11 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | c1_1(a596))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | c1_1(a596))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7568,plain,
% 1.93/2.11 ((hskp0 | (~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a596) | c1_1(a596) | c3_1(a596)) <=> (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | c1_1(a596))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7569,plain,
% 1.93/2.11 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | c1_1(a596)))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[7568])).
% 1.93/2.11 tff(7570,plain,
% 1.93/2.11 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | c1_1(a596))),
% 1.93/2.11 inference(transitivity,[status(thm)],[7569, 7567])).
% 1.93/2.11 tff(7571,plain,
% 1.93/2.11 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a596) | c1_1(a596) | c3_1(a596))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(7572,plain,
% 1.93/2.11 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | c1_1(a596)),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[7571, 7570])).
% 1.93/2.11 tff(7573,plain,
% 1.93/2.11 ($false),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7572, 156, 837, 1630, 1638, 7566, 7557, 108, 7565, 7554])).
% 1.93/2.11 tff(7574,plain,((~hskp26) | hskp0 | (~c3_1(a537)) | c1_1(a537) | c2_1(a537) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.11 tff(7575,plain,
% 1.93/2.11 (~hskp26),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7574, 4777, 4779, 4778, 837, 3428, 3427, 3426])).
% 1.93/2.11 tff(7576,plain,
% 1.93/2.11 (~hskp15),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1971, 7575, 1669, 4942, 4941])).
% 1.93/2.11 tff(7577,plain,
% 1.93/2.11 (~hskp19),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[1753, 7575, 1669, 4940, 765])).
% 1.93/2.11 tff(7578,plain,
% 1.93/2.11 (hskp50),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[4964, 7575, 88, 4948, 4941, 4944, 4942, 7577, 765, 7576])).
% 1.93/2.11 tff(7579,plain,
% 1.93/2.11 (~c3_1(a574)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[799, 7578])).
% 1.93/2.11 tff(7580,plain,
% 1.93/2.11 (c1_1(a574)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[807, 7578])).
% 1.93/2.11 tff(7581,plain,
% 1.93/2.11 (c0_1(a574)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[815, 7578])).
% 1.93/2.11 tff(7582,assumption,(c2_1(a574)), introduced(assumption)).
% 1.93/2.11 tff(7583,plain,
% 1.93/2.11 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7584,plain,
% 1.93/2.11 ((hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574))) <=> (hskp32 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7585,plain,
% 1.93/2.11 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574))))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[7584])).
% 1.93/2.11 tff(7586,plain,
% 1.93/2.11 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.11 inference(transitivity,[status(thm)],[7585, 7583])).
% 1.93/2.11 tff(7587,plain,
% 1.93/2.11 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(7588,plain,
% 1.93/2.11 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574))),
% 1.93/2.11 inference(modus_ponens,[status(thm)],[7587, 7586])).
% 1.93/2.11 tff(7589,plain,
% 1.93/2.11 (hskp32 | (~c2_1(a574))),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7588, 156, 2476, 2475, 2474, 4894])).
% 1.93/2.11 tff(7590,plain,
% 1.93/2.11 (hskp32),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[7589, 7582])).
% 1.93/2.11 tff(7591,plain,
% 1.93/2.11 (~c2_1(a596)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[5534, 7590])).
% 1.93/2.11 tff(7592,plain,
% 1.93/2.11 (c0_1(a596)),
% 1.93/2.11 inference(unit_resolution,[status(thm)],[5522, 7590])).
% 1.93/2.11 tff(7593,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7594,plain,
% 1.93/2.11 (((~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596))) <=> (c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.11 inference(rewrite,[status(thm)],[])).
% 1.93/2.11 tff(7595,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574))))),
% 1.93/2.11 inference(monotonicity,[status(thm)],[7594])).
% 1.93/2.11 tff(7596,plain,
% 1.93/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.11 inference(transitivity,[status(thm)],[7595, 7593])).
% 1.93/2.11 tff(7597,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a596) | (~c0_1(a596)) | (~c1_1(a596)))),
% 1.93/2.11 inference(quant_inst,[status(thm)],[])).
% 1.93/2.11 tff(7598,plain,
% 1.93/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c0_1(a596)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574))),
% 1.93/2.12 inference(modus_ponens,[status(thm)],[7597, 7596])).
% 1.93/2.12 tff(7599,plain,
% 1.93/2.12 (~c1_1(a596)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7598, 156, 2476, 2475, 4779, 7592, 4778, 7591, 707, 4777, 7582])).
% 1.93/2.12 tff(7600,plain,
% 1.93/2.12 (~c3_1(a596)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[5528, 7590])).
% 1.93/2.12 tff(7601,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7602,plain,
% 1.93/2.12 ((hskp0 | (~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a596) | c1_1(a596) | c3_1(a596)) <=> (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7603,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574))))),
% 1.93/2.12 inference(monotonicity,[status(thm)],[7602])).
% 1.93/2.12 tff(7604,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 1.93/2.12 inference(transitivity,[status(thm)],[7603, 7601])).
% 1.93/2.12 tff(7605,plain,
% 1.93/2.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a574)) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a596) | c1_1(a596) | c3_1(a596))),
% 1.93/2.12 inference(quant_inst,[status(thm)],[])).
% 1.93/2.12 tff(7606,plain,
% 1.93/2.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c0_1(a574)) | (~c1_1(a574)) | (~c2_1(a574))),
% 1.93/2.12 inference(modus_ponens,[status(thm)],[7605, 7604])).
% 1.93/2.12 tff(7607,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7606, 156, 837, 2476, 2475, 7600, 7591, 108, 7599, 7582])).
% 1.93/2.12 tff(7608,plain,((~c2_1(a574)) | hskp0 | (~c0_1(a574)) | (~c1_1(a574)) | (~c3_1(a537)) | c1_1(a537) | c2_1(a537) | c3_1(a574)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7609,plain,
% 1.93/2.12 (~c2_1(a574)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7608, 7581, 837, 7580, 4779, 4778, 4777, 7579])).
% 1.93/2.12 tff(7610,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a574))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a574))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7611,plain,
% 1.93/2.12 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a574) | (~c0_1(a574)) | (~c1_1(a574))) <=> (c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a574))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7612,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a574) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a574)))),
% 1.93/2.12 inference(monotonicity,[status(thm)],[7611])).
% 1.93/2.12 tff(7613,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a574) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a574))),
% 1.93/2.12 inference(transitivity,[status(thm)],[7612, 7610])).
% 1.93/2.12 tff(7614,plain,
% 1.93/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a574) | (~c0_1(a574)) | (~c1_1(a574)))),
% 1.93/2.12 inference(quant_inst,[status(thm)],[])).
% 1.93/2.12 tff(7615,plain,
% 1.93/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a574)),
% 1.93/2.12 inference(modus_ponens,[status(thm)],[7614, 7613])).
% 1.93/2.12 tff(7616,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7615, 156, 7581, 7580, 4779, 3428, 3427, 3426, 4778, 707, 4777, 7609])).
% 1.93/2.12 tff(7617,plain,(c2_1(a537) | (~c3_1(a537)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | c1_1(a537) | hskp0 | c1_1(a586) | (~c3_1(a586)) | c3_1(a545) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7618,plain,
% 1.93/2.12 (c2_1(a537)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7617, 837, 3672, 3671, 3670, 7518, 7519, 88, 7544, 765, 1669])).
% 1.93/2.12 tff(7619,plain,
% 1.93/2.12 (hskp15 | c3_1(a545) | (~c2_1(a537))),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2094, 156, 7519, 4941, 7518, 4944, 483])).
% 1.93/2.12 tff(7620,plain,
% 1.93/2.12 (hskp15),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7619, 7618, 765])).
% 1.93/2.12 tff(7621,plain,
% 1.93/2.12 (hskp28),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1276, 7620])).
% 1.93/2.12 tff(7622,plain,
% 1.93/2.12 (~c0_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[177, 7621])).
% 1.93/2.12 tff(7623,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3725, 6594, 6596, 3667, 837, 6595])).
% 1.93/2.12 tff(7624,plain,((~hskp8) | (~hskp33) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7625,plain,
% 1.93/2.12 (~hskp8),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7624, 837, 3667])).
% 1.93/2.12 tff(7626,plain,
% 1.93/2.12 (c2_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[171, 7621])).
% 1.93/2.12 tff(7627,plain,
% 1.93/2.12 (c1_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7536, 7626, 7520, 7519, 7625, 7518, 7622])).
% 1.93/2.12 tff(7628,plain,
% 1.93/2.12 (~c2_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1255, 7620])).
% 1.93/2.12 tff(7629,plain,
% 1.93/2.12 (~c1_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1261, 7620])).
% 1.93/2.12 tff(7630,plain,
% 1.93/2.12 (~c0_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1267, 7620])).
% 1.93/2.12 tff(7631,plain,
% 1.93/2.12 (c3_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[185, 7621])).
% 1.93/2.12 tff(7632,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1789, 156, 1669, 7631, 7622, 7630, 7629, 7628, 1745, 7627])).
% 1.93/2.12 tff(7633,plain,(hskp0 | hskp6 | c3_1(a545) | c1_1(a586) | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7634,plain,
% 1.93/2.12 (c3_1(a545)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7633, 837, 2896, 88, 7516])).
% 1.93/2.12 tff(7635,plain,
% 1.93/2.12 (c0_1(a536)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3393, 7516])).
% 1.93/2.12 tff(7636,plain,
% 1.93/2.12 (c2_1(a536)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3401, 7516])).
% 1.93/2.12 tff(7637,plain,
% 1.93/2.12 (c1_1(a536)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3409, 7516])).
% 1.93/2.12 tff(7638,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7639,plain,
% 1.93/2.12 ((hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536))) <=> (hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7640,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536))))),
% 1.93/2.12 inference(monotonicity,[status(thm)],[7639])).
% 1.93/2.12 tff(7641,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)))),
% 1.93/2.12 inference(transitivity,[status(thm)],[7640, 7638])).
% 1.93/2.12 tff(7642,plain,
% 1.93/2.12 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))),
% 1.93/2.12 inference(quant_inst,[status(thm)],[])).
% 1.93/2.12 tff(7643,plain,
% 1.93/2.12 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536))),
% 1.93/2.12 inference(modus_ponens,[status(thm)],[7642, 7641])).
% 1.93/2.12 tff(7644,plain,
% 1.93/2.12 (hskp42 | (~c3_1(a545))),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7643, 156, 7637, 7636, 7635, 5011, 4938, 1364])).
% 1.93/2.12 tff(7645,plain,
% 1.93/2.12 (hskp42),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7644, 7634])).
% 1.93/2.12 tff(7646,plain,
% 1.93/2.12 (~c2_1(a556)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1385, 7645])).
% 1.93/2.12 tff(7647,plain,
% 1.93/2.12 (hskp0 | c3_1(a548) | c1_1(a548)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[4142, 156, 7637, 7636, 7635, 24, 108])).
% 1.93/2.12 tff(7648,plain,
% 1.93/2.12 (c1_1(a548)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7647, 837, 2895])).
% 1.93/2.12 tff(7649,plain,
% 1.93/2.12 (hskp39 | (~c3_1(a545)) | (~c1_1(a548))),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[5221, 156, 2895, 5011, 56, 4938, 281])).
% 1.93/2.12 tff(7650,plain,
% 1.93/2.12 (hskp39),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7649, 7634, 7648])).
% 1.93/2.12 tff(7651,plain,
% 1.93/2.12 (c1_1(a549)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[303, 7650])).
% 1.93/2.12 tff(7652,plain,
% 1.93/2.12 (c2_1(a549)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[311, 7650])).
% 1.93/2.12 tff(7653,plain,
% 1.93/2.12 (c3_1(a549)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[319, 7650])).
% 1.93/2.12 tff(7654,plain,
% 1.93/2.12 (c3_1(a556)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1403, 7645])).
% 1.93/2.12 tff(7655,plain,
% 1.93/2.12 (c1_1(a556)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1411, 7645])).
% 1.93/2.12 tff(7656,plain,
% 1.93/2.12 (~c3_1(a545)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1211, 58, 4941, 4944, 4942])).
% 1.93/2.12 tff(7657,plain,
% 1.93/2.12 (hskp0),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7633, 7656, 1669, 88, 3667])).
% 1.93/2.12 tff(7658,plain,
% 1.93/2.12 (~c2_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[713, 7657])).
% 1.93/2.12 tff(7659,plain,
% 1.93/2.12 (c0_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[721, 7657])).
% 1.93/2.12 tff(7660,plain,
% 1.93/2.12 (c1_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[729, 7657])).
% 1.93/2.12 tff(7661,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[4095, 156, 4779, 3428, 3427, 3426, 3449, 3448, 4778, 3443, 707, 4777])).
% 1.93/2.12 tff(7662,plain,(c2_1(a537) | (~c3_1(a537)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a535)) | (~c0_1(a535)) | c1_1(a537) | c2_1(a535)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7663,plain,
% 1.93/2.12 (c2_1(a537)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7662, 7660, 3672, 3671, 3670, 7519, 7659, 7518, 7658])).
% 1.93/2.12 tff(7664,plain,
% 1.93/2.12 (hskp15),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7619, 7663, 7656])).
% 1.93/2.12 tff(7665,plain,
% 1.93/2.12 (~c2_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1255, 7664])).
% 1.93/2.12 tff(7666,plain,
% 1.93/2.12 (~c1_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1261, 7664])).
% 1.93/2.12 tff(7667,plain,
% 1.93/2.12 (~c3_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3455, 156, 3672, 3671, 3670, 7660, 7659, 7666, 7665, 7658, 707])).
% 1.93/2.12 tff(7668,plain,
% 1.93/2.12 (~c0_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1267, 7664])).
% 1.93/2.12 tff(7669,plain,
% 1.93/2.12 (hskp28),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1276, 7664])).
% 1.93/2.12 tff(7670,plain,
% 1.93/2.12 (~c0_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[177, 7669])).
% 1.93/2.12 tff(7671,plain,
% 1.93/2.12 (c3_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[185, 7669])).
% 1.93/2.12 tff(7672,plain,
% 1.93/2.12 (~c1_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1789, 156, 1669, 7671, 7670, 7668, 7666, 7665, 1745])).
% 1.93/2.12 tff(7673,plain,
% 1.93/2.12 (hskp51),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3462, 156, 7520, 7519, 7518, 7666, 7665, 2608, 7667])).
% 1.93/2.12 tff(7674,plain,
% 1.93/2.12 (~c2_1(a583)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2637, 7673])).
% 1.93/2.12 tff(7675,plain,
% 1.93/2.12 (c2_1(a589)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[171, 7669])).
% 1.93/2.12 tff(7676,plain,
% 1.93/2.12 (c3_1(a583)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2645, 7673])).
% 1.93/2.12 tff(7677,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7678,plain,
% 1.93/2.12 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (c2_1(a583) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7679,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583))))),
% 1.93/2.12 inference(monotonicity,[status(thm)],[7678])).
% 1.93/2.12 tff(7680,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.93/2.12 inference(transitivity,[status(thm)],[7679, 7677])).
% 1.93/2.12 tff(7681,plain,
% 1.93/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.93/2.12 inference(quant_inst,[status(thm)],[])).
% 1.93/2.12 tff(7682,plain,
% 1.93/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | (~c3_1(a583)) | (~c1_1(a583))),
% 1.93/2.12 inference(modus_ponens,[status(thm)],[7681, 7680])).
% 1.93/2.12 tff(7683,plain,
% 1.93/2.12 (~c1_1(a583)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7682, 156, 7676, 7675, 7671, 7674, 7666, 7665, 45, 7672, 7667])).
% 1.93/2.12 tff(7684,plain,
% 1.93/2.12 (hskp26),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1971, 7664, 1669, 4942, 4941])).
% 1.93/2.12 tff(7685,plain,
% 1.93/2.12 (~hskp39),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2535, 7672, 58, 7671, 7675])).
% 1.93/2.12 tff(7686,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[6495, 1638, 1630, 859, 6468, 1621])).
% 1.93/2.12 tff(7687,plain,((~hskp26) | hskp39 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7688,plain,
% 1.93/2.12 (hskp24),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7687, 7685, 7684])).
% 1.93/2.12 tff(7689,plain,
% 1.93/2.12 (~c3_1(a581)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3513, 7688])).
% 1.93/2.12 tff(7690,plain,
% 1.93/2.12 (~c1_1(a581)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3519, 7688])).
% 1.93/2.12 tff(7691,plain,
% 1.93/2.12 (c2_1(a581)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3541, 7688])).
% 1.93/2.12 tff(7692,plain,
% 1.93/2.12 (c0_1(a583)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2653, 7673])).
% 1.93/2.12 tff(7693,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[3550, 156, 7692, 7676, 7691, 7674, 7690, 7689, 921, 7683])).
% 1.93/2.12 tff(7694,plain,(hskp38 | hskp6 | c1_1(a586) | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7695,plain,
% 1.93/2.12 (hskp38),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7694, 88, 2896, 7516])).
% 1.93/2.12 tff(7696,plain,
% 1.93/2.12 (c0_1(a547)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[677, 7695])).
% 1.93/2.12 tff(7697,plain,
% 1.93/2.12 (c1_1(a547)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[685, 7695])).
% 1.93/2.12 tff(7698,plain,
% 1.93/2.12 (c2_1(a547)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[693, 7695])).
% 1.93/2.12 tff(7699,plain,
% 1.93/2.12 (~hskp25),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[6547, 837, 7698, 7697, 7696])).
% 1.93/2.12 tff(7700,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[5026, 156, 7699, 7655, 7654, 7653, 7652, 7651, 7646, 55])).
% 1.93/2.12 tff(7701,plain,(hskp0 | c3_1(a548) | c0_1(a548) | c1_1(a586) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7702,plain,
% 1.93/2.12 (hskp0),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7701, 88, 56, 2895, 24])).
% 1.93/2.12 tff(7703,plain,
% 1.93/2.12 (~c2_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[713, 7702])).
% 1.93/2.12 tff(7704,plain,
% 1.93/2.12 (hskp34),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[4294, 4936, 7516])).
% 1.93/2.12 tff(7705,plain,
% 1.93/2.12 (c0_1(a537)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1147, 7704])).
% 1.93/2.12 tff(7706,plain,
% 1.93/2.12 (~c1_1(a537)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1124, 7704])).
% 1.93/2.12 tff(7707,plain,
% 1.93/2.12 (c3_1(a537)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1132, 7704])).
% 1.93/2.12 tff(7708,plain,
% 1.93/2.12 (c3_1(a586)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[4788, 4777, 88, 7707, 7706, 7705])).
% 1.93/2.12 tff(7709,plain,
% 1.93/2.12 (c3_1(a545)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7617, 837, 7637, 7636, 7635, 7706, 7707, 88, 7708, 4777, 2896])).
% 1.93/2.12 tff(7710,plain,
% 1.93/2.12 (hskp42),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7644, 7709])).
% 1.93/2.12 tff(7711,plain,
% 1.93/2.12 (~c2_1(a556)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1385, 7710])).
% 1.93/2.12 tff(7712,plain,
% 1.93/2.12 (hskp39),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7649, 7709, 7648])).
% 1.93/2.12 tff(7713,plain,
% 1.93/2.12 (c1_1(a549)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[303, 7712])).
% 1.93/2.12 tff(7714,plain,
% 1.93/2.12 (c2_1(a549)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[311, 7712])).
% 1.93/2.12 tff(7715,plain,
% 1.93/2.12 (c3_1(a549)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[319, 7712])).
% 1.93/2.12 tff(7716,plain,
% 1.93/2.12 (c3_1(a556)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1403, 7710])).
% 1.93/2.12 tff(7717,plain,
% 1.93/2.12 (c1_1(a556)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1411, 7710])).
% 1.93/2.12 tff(7718,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[5026, 156, 7699, 7717, 7716, 7715, 7714, 7713, 7711, 55])).
% 1.93/2.12 tff(7719,plain,(hskp0 | c3_1(a548) | c0_1(a548) | c1_1(a586) | c2_1(a537) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7720,plain,
% 1.93/2.12 (hskp0),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7719, 4777, 56, 88, 2895, 24])).
% 1.93/2.12 tff(7721,plain,
% 1.93/2.12 (~c2_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[713, 7720])).
% 1.93/2.12 tff(7722,plain,
% 1.93/2.12 (c1_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[729, 7720])).
% 1.93/2.12 tff(7723,plain,
% 1.93/2.12 (c0_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[721, 7720])).
% 1.93/2.12 tff(7724,plain,
% 1.93/2.12 ($false),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7662, 7723, 7722, 7637, 7636, 7635, 7707, 4777, 7706, 7721])).
% 1.93/2.12 tff(7725,plain,(c2_1(a537) | c0_1(a548) | c1_1(a586) | c3_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.12 tff(7726,plain,
% 1.93/2.12 (c2_1(a537)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7725, 88, 56, 2895, 24])).
% 1.93/2.12 tff(7727,plain,
% 1.93/2.12 (c0_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[721, 7702])).
% 1.93/2.12 tff(7728,plain,
% 1.93/2.12 (c1_1(a535)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[729, 7702])).
% 1.93/2.12 tff(7729,plain,
% 1.93/2.12 (hskp15),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[4987, 57, 24, 56, 2896, 1046, 111, 97])).
% 1.93/2.12 tff(7730,plain,
% 1.93/2.12 (~c2_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1255, 7729])).
% 1.93/2.12 tff(7731,plain,
% 1.93/2.12 (~c1_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[1261, 7729])).
% 1.93/2.12 tff(7732,plain,
% 1.93/2.12 (~c3_1(a569)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2783, 156, 733, 732, 731, 3449, 3448, 7731, 7730, 3443, 707])).
% 1.93/2.12 tff(7733,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7734,plain,
% 1.93/2.12 ((hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548)) <=> (hskp51 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7735,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c0_1(a537))))),
% 1.93/2.12 inference(monotonicity,[status(thm)],[7734])).
% 1.93/2.12 tff(7736,plain,
% 1.93/2.12 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c0_1(a537)))),
% 1.93/2.12 inference(transitivity,[status(thm)],[7735, 7733])).
% 1.93/2.12 tff(7737,plain,
% 1.93/2.12 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp51 | (~ndr1_0) | c1_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548))),
% 1.93/2.12 inference(quant_inst,[status(thm)],[])).
% 1.93/2.12 tff(7738,plain,
% 1.93/2.12 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp51 | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c0_1(a537))),
% 1.93/2.12 inference(modus_ponens,[status(thm)],[7737, 7736])).
% 1.93/2.12 tff(7739,plain,
% 1.93/2.12 (hskp51 | c1_1(a548)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7738, 156, 4780, 4779, 2895, 4778, 24, 2608])).
% 1.93/2.12 tff(7740,plain,
% 1.93/2.12 (hskp51),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[7739, 57])).
% 1.93/2.12 tff(7741,plain,
% 1.93/2.12 (~c2_1(a583)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2637, 7740])).
% 1.93/2.12 tff(7742,plain,
% 1.93/2.12 (c3_1(a583)),
% 1.93/2.12 inference(unit_resolution,[status(thm)],[2645, 7740])).
% 1.93/2.12 tff(7743,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7744,plain,
% 1.93/2.12 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (c2_1(a583) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.93/2.12 inference(rewrite,[status(thm)],[])).
% 1.93/2.12 tff(7745,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583))))),
% 1.93/2.12 inference(monotonicity,[status(thm)],[7744])).
% 1.93/2.12 tff(7746,plain,
% 1.93/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.93/2.12 inference(transitivity,[status(thm)],[7745, 7743])).
% 1.93/2.12 tff(7747,plain,
% 1.93/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(7748,plain,
% 1.97/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[7747, 7746])).
% 1.97/2.12 tff(7749,plain,
% 1.97/2.12 (~c1_1(a583)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7748, 156, 7742, 4779, 7741, 4778, 7731, 7730, 45, 7732, 1])).
% 1.97/2.12 tff(7750,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[3580, 156, 7742, 733, 732, 731, 3449, 3448, 7741, 3443, 707, 7749])).
% 1.97/2.12 tff(7751,plain,(c1_1(a548) | (~c2_1(a547)) | (~c1_1(a547)) | (~c0_1(a547)) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a535) | (~c3_1(a537)) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c3_1(a548) | c2_1(a548) | c0_1(a548) | (~c1_1(a545)) | c2_1(a545) | c0_1(a545)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(7752,plain,
% 1.97/2.12 (c1_1(a548)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7751, 7698, 7697, 7696, 7728, 7727, 7703, 7707, 7706, 7726, 7705, 2895, 24, 56, 5011, 4938, 4937])).
% 1.97/2.12 tff(7753,plain,
% 1.97/2.12 (hskp15 | (~c1_1(a548)) | (~c2_1(a537))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[3708, 156, 7707, 2895, 7706, 24, 483])).
% 1.97/2.12 tff(7754,plain,
% 1.97/2.12 (hskp15),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7753, 7752, 7726])).
% 1.97/2.12 tff(7755,plain,
% 1.97/2.12 (~c2_1(a569)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1255, 7754])).
% 1.97/2.12 tff(7756,plain,
% 1.97/2.12 (~c1_1(a569)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1261, 7754])).
% 1.97/2.12 tff(7757,plain,
% 1.97/2.12 (~c3_1(a569)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[2783, 156, 7698, 7697, 7696, 7728, 7727, 7756, 7755, 7703, 707])).
% 1.97/2.12 tff(7758,plain,
% 1.97/2.12 (~c0_1(a569)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1267, 7754])).
% 1.97/2.12 tff(7759,plain,
% 1.97/2.12 (hskp28),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1276, 7754])).
% 1.97/2.12 tff(7760,plain,
% 1.97/2.12 (~c0_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[177, 7759])).
% 1.97/2.12 tff(7761,plain,
% 1.97/2.12 (c3_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[185, 7759])).
% 1.97/2.12 tff(7762,plain,
% 1.97/2.12 (~c1_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1789, 156, 2896, 7761, 7760, 7758, 7756, 7755, 1745])).
% 1.97/2.12 tff(7763,plain,
% 1.97/2.12 (hskp51),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[3462, 156, 7705, 7707, 7706, 7756, 7755, 2608, 7757])).
% 1.97/2.12 tff(7764,plain,
% 1.97/2.12 (~c2_1(a583)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[2637, 7763])).
% 1.97/2.12 tff(7765,plain,
% 1.97/2.12 (c2_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[171, 7759])).
% 1.97/2.12 tff(7766,plain,
% 1.97/2.12 (c3_1(a583)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[2645, 7763])).
% 1.97/2.12 tff(7767,plain,
% 1.97/2.12 (~c1_1(a583)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7682, 156, 7766, 7765, 7761, 7764, 7756, 7755, 45, 7762, 7757])).
% 1.97/2.12 tff(7768,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[3580, 156, 7766, 7698, 7697, 7696, 7728, 7727, 7764, 7703, 707, 7767])).
% 1.97/2.12 tff(7769,plain,(c1_1(a586) | c3_1(a548) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(7770,plain,
% 1.97/2.12 (c1_1(a586)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7769, 2895, 24, 56])).
% 1.97/2.12 tff(7771,plain,
% 1.97/2.12 (~hskp4),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[4294, 3650, 3667])).
% 1.97/2.12 tff(7772,plain,
% 1.97/2.12 (hskp27),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[205, 7771, 1669])).
% 1.97/2.12 tff(7773,plain,
% 1.97/2.12 (~c3_1(a586)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[3996, 7772])).
% 1.97/2.12 tff(7774,plain,
% 1.97/2.12 (~c0_1(a586)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[3924, 7772])).
% 1.97/2.12 tff(7775,plain,
% 1.97/2.12 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a586)))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(7776,plain,
% 1.97/2.12 ((hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp34 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a586)))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(7777,plain,
% 1.97/2.12 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a586))))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[7776])).
% 1.97/2.12 tff(7778,plain,
% 1.97/2.12 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a586)))),
% 1.97/2.12 inference(transitivity,[status(thm)],[7777, 7775])).
% 1.97/2.12 tff(7779,plain,
% 1.97/2.12 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(7780,plain,
% 1.97/2.12 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a586))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[7779, 7778])).
% 1.97/2.12 tff(7781,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7780, 156, 3650, 3672, 3671, 3670, 3797, 7774, 7773, 75])).
% 1.97/2.12 tff(7782,plain,(hskp34 | (~c1_1(a586)) | hskp6 | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(7783,plain,
% 1.97/2.12 (hskp34),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7782, 7770, 2896, 7516])).
% 1.97/2.12 tff(7784,plain,
% 1.97/2.12 (~c1_1(a537)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1124, 7783])).
% 1.97/2.12 tff(7785,plain,
% 1.97/2.12 (c3_1(a537)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1132, 7783])).
% 1.97/2.12 tff(7786,plain,
% 1.97/2.12 (c0_1(a537)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1147, 7783])).
% 1.97/2.12 tff(7787,plain,
% 1.97/2.12 (~c2_1(a574)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7608, 800, 816, 808, 4779, 4778, 4777, 837])).
% 1.97/2.12 tff(7788,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7615, 156, 816, 808, 4779, 3428, 3427, 3426, 4778, 707, 4777, 7787])).
% 1.97/2.12 tff(7789,plain,((~hskp50) | (~c3_1(a537)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | c1_1(a537) | c2_1(a537) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(7790,plain,
% 1.97/2.12 (~hskp50),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7789, 837, 3672, 3671, 3670, 4778, 4777, 4779])).
% 1.97/2.12 tff(7791,plain,
% 1.97/2.12 (hskp50 | hskp19 | c2_1(a537)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1154, 156, 4780, 4778, 34])).
% 1.97/2.12 tff(7792,plain,
% 1.97/2.12 (hskp19),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7791, 7790, 4777])).
% 1.97/2.12 tff(7793,plain,
% 1.97/2.12 (hskp28),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[5069, 7792])).
% 1.97/2.12 tff(7794,plain,
% 1.97/2.12 (~c0_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[177, 7793])).
% 1.97/2.12 tff(7795,plain,
% 1.97/2.12 (c2_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[171, 7793])).
% 1.97/2.12 tff(7796,plain,
% 1.97/2.12 (c1_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7536, 7795, 4780, 4779, 7625, 4778, 7794])).
% 1.97/2.12 tff(7797,plain,
% 1.97/2.12 (~c1_1(a573)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1675, 7792])).
% 1.97/2.12 tff(7798,plain,
% 1.97/2.12 (~c0_1(a573)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1691, 7792])).
% 1.97/2.12 tff(7799,plain,
% 1.97/2.12 (~c2_1(a573)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1704, 7792])).
% 1.97/2.12 tff(7800,plain,
% 1.97/2.12 (c3_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[185, 7793])).
% 1.97/2.12 tff(7801,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1751, 156, 1669, 7800, 7794, 7799, 7798, 7797, 1745, 7796])).
% 1.97/2.12 tff(7802,plain,(hskp0 | hskp6 | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537) | c2_1(a537) | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(7803,plain,
% 1.97/2.12 (hskp0),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7802, 4777, 4780, 4779, 4778, 1669, 3667])).
% 1.97/2.12 tff(7804,plain,
% 1.97/2.12 (~c2_1(a535)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[713, 7803])).
% 1.97/2.12 tff(7805,plain,
% 1.97/2.12 (c1_1(a535)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[729, 7803])).
% 1.97/2.12 tff(7806,plain,
% 1.97/2.12 (c0_1(a535)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[721, 7803])).
% 1.97/2.12 tff(7807,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7662, 7806, 7805, 3672, 3671, 3670, 4779, 4777, 4778, 7804])).
% 1.97/2.12 tff(7808,plain,(c2_1(a537) | (~c3_1(a537)) | c1_1(a537) | (~c0_1(a537)) | hskp6 | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(7809,plain,
% 1.97/2.12 (c2_1(a537)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7808, 4779, 4778, 4780, 2896, 7516])).
% 1.97/2.12 tff(7810,plain,
% 1.97/2.12 (hskp15 | (~c1_1(a548)) | (~c2_1(a537))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[3708, 156, 4779, 2895, 4778, 24, 483])).
% 1.97/2.12 tff(7811,plain,
% 1.97/2.12 (hskp15),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7810, 7648, 7809])).
% 1.97/2.12 tff(7812,plain,
% 1.97/2.12 (hskp28),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1276, 7811])).
% 1.97/2.12 tff(7813,plain,
% 1.97/2.12 (~c0_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[177, 7812])).
% 1.97/2.12 tff(7814,plain,
% 1.97/2.12 (~hskp8),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7624, 837, 7516])).
% 1.97/2.12 tff(7815,plain,
% 1.97/2.12 (c2_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[171, 7812])).
% 1.97/2.12 tff(7816,plain,
% 1.97/2.12 (c1_1(a589)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7536, 7815, 4780, 4779, 7814, 4778, 7813])).
% 1.97/2.12 tff(7817,plain,
% 1.97/2.12 (~c2_1(a569)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[1255, 7811])).
% 1.97/2.13 tff(7818,plain,
% 1.97/2.13 (~c1_1(a569)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1261, 7811])).
% 1.97/2.13 tff(7819,plain,
% 1.97/2.13 (~c0_1(a569)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1267, 7811])).
% 1.97/2.13 tff(7820,plain,
% 1.97/2.13 (c3_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[185, 7812])).
% 1.97/2.13 tff(7821,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1789, 156, 2896, 7820, 7813, 7819, 7818, 7817, 1745, 7816])).
% 1.97/2.13 tff(7822,plain,(hskp0 | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537) | c3_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7823,plain,
% 1.97/2.13 (hskp0),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7822, 7786, 7785, 7784, 2895, 24])).
% 1.97/2.13 tff(7824,plain,
% 1.97/2.13 (~c2_1(a535)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[713, 7823])).
% 1.97/2.13 tff(7825,plain,
% 1.97/2.13 (c2_1(a537)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7808, 7785, 7784, 7786, 2896, 7516])).
% 1.97/2.13 tff(7826,plain,
% 1.97/2.13 (hskp0),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7822, 4780, 4779, 4778, 2895, 24])).
% 1.97/2.13 tff(7827,plain,
% 1.97/2.13 (~c2_1(a535)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[713, 7826])).
% 1.97/2.13 tff(7828,plain,
% 1.97/2.13 (c0_1(a535)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[721, 7826])).
% 1.97/2.13 tff(7829,plain,
% 1.97/2.13 (c1_1(a535)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[729, 7826])).
% 1.97/2.13 tff(7830,plain,
% 1.97/2.13 (c1_1(a583)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3478, 156, 7742, 7637, 7636, 7635, 7829, 7828, 7741, 7827, 707])).
% 1.97/2.13 tff(7831,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a548) | c2_1(a583) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a548) | c2_1(a583) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7832,plain,
% 1.97/2.13 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548)) <=> (c3_1(a548) | c2_1(a583) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7833,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a548) | c2_1(a583) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7832])).
% 1.97/2.13 tff(7834,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a548) | c2_1(a583) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7833, 7831])).
% 1.97/2.13 tff(7835,plain,
% 1.97/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a548) | c1_1(a548) | c3_1(a548))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7836,plain,
% 1.97/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a548) | c2_1(a583) | c1_1(a537) | c2_1(a548) | (~ndr1_0) | c1_1(a548) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7835, 7834])).
% 1.97/2.13 tff(7837,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7836, 156, 7742, 4779, 2895, 7741, 4778, 24, 45, 57, 7830, 7809])).
% 1.97/2.13 tff(7838,plain,(c1_1(a548) | (~c3_1(a537)) | c3_1(a548) | c1_1(a537) | c2_1(a548) | (~c0_1(a537))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7839,plain,
% 1.97/2.13 (c1_1(a548)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7838, 7785, 2895, 7784, 24, 7786])).
% 1.97/2.13 tff(7840,plain,
% 1.97/2.13 (hskp15 | (~c1_1(a548)) | (~c2_1(a537))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3708, 156, 7785, 2895, 7784, 24, 483])).
% 1.97/2.13 tff(7841,plain,
% 1.97/2.13 (hskp15),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7840, 7839, 7825])).
% 1.97/2.13 tff(7842,plain,
% 1.97/2.13 (~c2_1(a569)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1255, 7841])).
% 1.97/2.13 tff(7843,plain,
% 1.97/2.13 (~c1_1(a569)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1261, 7841])).
% 1.97/2.13 tff(7844,plain,
% 1.97/2.13 (c0_1(a535)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[721, 7823])).
% 1.97/2.13 tff(7845,plain,
% 1.97/2.13 (c1_1(a535)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[729, 7823])).
% 1.97/2.13 tff(7846,plain,
% 1.97/2.13 (~c3_1(a569)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3455, 156, 7637, 7636, 7635, 7845, 7844, 7843, 7842, 7824, 707])).
% 1.97/2.13 tff(7847,plain,
% 1.97/2.13 (~c0_1(a569)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1267, 7841])).
% 1.97/2.13 tff(7848,plain,
% 1.97/2.13 (hskp28),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1276, 7841])).
% 1.97/2.13 tff(7849,plain,
% 1.97/2.13 (~c0_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[177, 7848])).
% 1.97/2.13 tff(7850,plain,
% 1.97/2.13 (c3_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[185, 7848])).
% 1.97/2.13 tff(7851,plain,
% 1.97/2.13 (~c1_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1789, 156, 2896, 7850, 7849, 7847, 7843, 7842, 1745])).
% 1.97/2.13 tff(7852,plain,
% 1.97/2.13 (hskp51),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3462, 156, 7786, 7785, 7784, 7843, 7842, 2608, 7846])).
% 1.97/2.13 tff(7853,plain,
% 1.97/2.13 (~c2_1(a583)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2637, 7852])).
% 1.97/2.13 tff(7854,plain,
% 1.97/2.13 (c2_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[171, 7848])).
% 1.97/2.13 tff(7855,plain,
% 1.97/2.13 (c3_1(a583)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2645, 7852])).
% 1.97/2.13 tff(7856,plain,
% 1.97/2.13 (~c1_1(a583)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7682, 156, 7855, 7854, 7850, 7853, 7843, 7842, 45, 7851, 7846])).
% 1.97/2.13 tff(7857,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3478, 156, 7855, 7637, 7636, 7635, 7845, 7844, 7853, 7824, 707, 7856])).
% 1.97/2.13 tff(7858,plain,(c3_1(a548) | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7859,plain,
% 1.97/2.13 (c3_1(a548)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7858, 56, 24])).
% 1.97/2.13 tff(7860,assumption,(~c3_1(a537)), introduced(assumption)).
% 1.97/2.13 tff(7861,plain,
% 1.97/2.13 (~hskp34),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1132, 7860])).
% 1.97/2.13 tff(7862,plain,
% 1.97/2.13 (~c1_1(a548)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4519, 7861, 56, 24, 7859])).
% 1.97/2.13 tff(7863,plain,
% 1.97/2.13 (~c0_1(a544)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4702, 156, 2504, 7637, 7636, 7635, 249, 2503, 24, 707, 57])).
% 1.97/2.13 tff(7864,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4174, 156, 3650, 2504, 7637, 7636, 7635, 2502, 75, 7863])).
% 1.97/2.13 tff(7865,plain,((~hskp37) | hskp34 | (~c3_1(a548)) | c2_1(a548) | c1_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7866,plain,
% 1.97/2.13 (~hskp37),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7865, 7861, 7859, 24, 7862])).
% 1.97/2.13 tff(7867,plain,
% 1.97/2.13 (hskp28),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3668, 7862, 56])).
% 1.97/2.13 tff(7868,plain,
% 1.97/2.13 (c3_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[185, 7867])).
% 1.97/2.13 tff(7869,plain,
% 1.97/2.13 (~hskp46),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3658, 7861, 7637, 7636, 7635])).
% 1.97/2.13 tff(7870,plain,
% 1.97/2.13 (c2_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[171, 7867])).
% 1.97/2.13 tff(7871,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a537))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7872,plain,
% 1.97/2.13 ((hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a537) | c1_1(a537) | c3_1(a537)) <=> (hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a537))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7873,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a537)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7872])).
% 1.97/2.13 tff(7874,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a537))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7873, 7871])).
% 1.97/2.13 tff(7875,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a548) | c0_1(a548) | (~c3_1(a548)) | c2_1(a537) | c1_1(a537) | c3_1(a537))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7876,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a548) | c0_1(a548) | (~ndr1_0) | (~c3_1(a548)) | c2_1(a537)),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7875, 7874])).
% 1.97/2.13 tff(7877,plain,
% 1.97/2.13 (hskp38),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7876, 156, 7860, 7859, 4778, 24, 56, 663, 4777])).
% 1.97/2.13 tff(7878,plain,
% 1.97/2.13 (c2_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[693, 7877])).
% 1.97/2.13 tff(7879,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a537))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7880,plain,
% 1.97/2.13 ((hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | c3_1(a537)) <=> (hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a537))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7881,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a537)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7880])).
% 1.97/2.13 tff(7882,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a537))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7881, 7879])).
% 1.97/2.13 tff(7883,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a537) | c1_1(a537) | c3_1(a537))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7884,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a537)),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7883, 7882])).
% 1.97/2.13 tff(7885,plain,
% 1.97/2.13 (hskp0),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7884, 156, 7860, 7637, 7636, 7635, 4778, 108, 4777])).
% 1.97/2.13 tff(7886,plain,
% 1.97/2.13 (c1_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[685, 7877])).
% 1.97/2.13 tff(7887,plain,
% 1.97/2.13 (c0_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[677, 7877])).
% 1.97/2.13 tff(7888,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2694, 7887, 7886, 7859, 7862, 7885, 24, 7878])).
% 1.97/2.13 tff(7889,plain,(c2_1(a537) | c2_1(a548) | c3_1(a537) | c1_1(a537) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7890,plain,
% 1.97/2.13 (c2_1(a537)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7889, 7860, 24, 4778, 56])).
% 1.97/2.13 tff(7891,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c3_1(a537) | c1_1(a537) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a537) | c1_1(a537) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7892,plain,
% 1.97/2.13 (((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571))) <=> (c3_1(a537) | c1_1(a537) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7893,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c3_1(a537) | c1_1(a537) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a537))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7892])).
% 1.97/2.13 tff(7894,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a537) | c1_1(a537) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a537)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7893, 7891])).
% 1.97/2.13 tff(7895,plain,
% 1.97/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a571)) | c1_1(a571) | (~c3_1(a571)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7896,plain,
% 1.97/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a537) | c1_1(a537) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a537))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7895, 7894])).
% 1.97/2.13 tff(7897,plain,
% 1.97/2.13 (c1_1(a571)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7896, 156, 7860, 925, 924, 4778, 923, 921, 1])).
% 1.97/2.13 tff(7898,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7899,plain,
% 1.97/2.13 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7900,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7899])).
% 1.97/2.13 tff(7901,plain,
% 1.97/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7900, 7898])).
% 1.97/2.13 tff(7902,plain,
% 1.97/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a548) | c1_1(a548) | (~c3_1(a548)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7903,plain,
% 1.97/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a571) | c2_1(a548) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a548)) | c1_1(a548) | (~c1_1(a571)) | (~c0_1(a571))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7902, 7901])).
% 1.97/2.13 tff(7904,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7903, 156, 7637, 7636, 7635, 925, 249, 923, 24, 707, 57, 7897])).
% 1.97/2.13 tff(7905,plain,((~hskp17) | (~c3_1(a548)) | c2_1(a548) | c1_1(a548) | c3_1(a537) | c1_1(a537) | (~c2_1(a537))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7906,plain,
% 1.97/2.13 (~hskp17),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7905, 7862, 24, 7859, 7860, 4778, 7890])).
% 1.97/2.13 tff(7907,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7908,plain,
% 1.97/2.13 ((hskp37 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c1_1(a537) | c3_1(a537) | (~c0_1(a537))) <=> (hskp37 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7909,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c1_1(a537) | c3_1(a537) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7908])).
% 1.97/2.13 tff(7910,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c1_1(a537) | c3_1(a537) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7909, 7907])).
% 1.97/2.13 tff(7911,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c1_1(a537) | c3_1(a537) | (~c0_1(a537)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7912,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7911, 7910])).
% 1.97/2.13 tff(7913,plain,
% 1.97/2.13 (hskp37 | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a537))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7912, 156, 4778, 415])).
% 1.97/2.13 tff(7914,plain,
% 1.97/2.13 (~c0_1(a537)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7913, 7866, 7860, 7890])).
% 1.97/2.13 tff(7915,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7916,plain,
% 1.97/2.13 ((hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537))) <=> (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7917,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a537))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7916])).
% 1.97/2.13 tff(7918,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7917, 7915])).
% 1.97/2.13 tff(7919,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7920,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | (~c2_1(a537))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7919, 7918])).
% 1.97/2.13 tff(7921,plain,
% 1.97/2.13 (c0_1(a537) | (~c1_1(a589)) | (~c2_1(a537))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7920, 156, 7869, 7860, 7870, 7868, 858])).
% 1.97/2.13 tff(7922,plain,
% 1.97/2.13 (~c1_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7921, 7914, 7890])).
% 1.97/2.13 tff(7923,plain,
% 1.97/2.13 (hskp38),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6938, 7922, 7859, 24, 56, 7906, 7870, 7869, 7868, 7866])).
% 1.97/2.13 tff(7924,plain,
% 1.97/2.13 (c2_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[693, 7923])).
% 1.97/2.13 tff(7925,assumption,(~c0_1(a537)), introduced(assumption)).
% 1.97/2.13 tff(7926,plain,
% 1.97/2.13 (~c1_1(a589)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7921, 7925, 1])).
% 1.97/2.13 tff(7927,plain,
% 1.97/2.13 (hskp38),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6938, 422, 7859, 24, 56, 332, 7870, 7869, 7868, 7926])).
% 1.97/2.13 tff(7928,plain,
% 1.97/2.13 (c2_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[693, 7927])).
% 1.97/2.13 tff(7929,plain,
% 1.97/2.13 (c0_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[677, 7927])).
% 1.97/2.13 tff(7930,plain,
% 1.97/2.13 (c1_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[685, 7927])).
% 1.97/2.13 tff(7931,plain,
% 1.97/2.13 (~hskp18),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2703, 7930, 422, 837, 7929, 7928])).
% 1.97/2.13 tff(7932,plain,
% 1.97/2.13 (hskp16),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[382, 7931, 332])).
% 1.97/2.13 tff(7933,plain,
% 1.97/2.13 (c1_1(a570)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[356, 7932])).
% 1.97/2.13 tff(7934,plain,
% 1.97/2.13 (c3_1(a570)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[364, 7932])).
% 1.97/2.13 tff(7935,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7936,plain,
% 1.97/2.13 ((hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537))) <=> (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a537)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7937,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a537))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7936])).
% 1.97/2.13 tff(7938,plain,
% 1.97/2.13 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a537)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7937, 7935])).
% 1.97/2.13 tff(7939,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a570)) | (~c2_1(a570)) | (~c1_1(a570)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7940,plain,
% 1.97/2.13 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a570)) | (~c3_1(a570)) | (~c1_1(a570)) | (~c2_1(a537))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7939, 7938])).
% 1.97/2.13 tff(7941,plain,
% 1.97/2.13 (~c2_1(a570)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7940, 156, 7869, 7925, 7860, 7934, 7933, 858, 1])).
% 1.97/2.13 tff(7942,plain,
% 1.97/2.13 (~c0_1(a570)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[348, 7932])).
% 1.97/2.13 tff(7943,plain,
% 1.97/2.13 (hskp42),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6886, 7941, 7928, 7930, 7929, 7934, 7933])).
% 1.97/2.13 tff(7944,plain,
% 1.97/2.13 (~c2_1(a556)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1385, 7943])).
% 1.97/2.13 tff(7945,plain,
% 1.97/2.13 (c3_1(a556)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1403, 7943])).
% 1.97/2.13 tff(7946,plain,
% 1.97/2.13 (c1_1(a556)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1411, 7943])).
% 1.97/2.13 tff(7947,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6896, 156, 7869, 7946, 7945, 7934, 7944, 7942, 12, 7941])).
% 1.97/2.13 tff(7948,plain,(hskp37 | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | hskp17 | hskp0 | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7949,plain,
% 1.97/2.13 (hskp0),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7948, 7914, 7860, 7890, 7906, 7866, 24, 56])).
% 1.97/2.13 tff(7950,plain,
% 1.97/2.13 (c1_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[685, 7923])).
% 1.97/2.13 tff(7951,plain,
% 1.97/2.13 (c0_1(a547)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[677, 7923])).
% 1.97/2.13 tff(7952,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2694, 7951, 7950, 7859, 7862, 7949, 24, 7924])).
% 1.97/2.13 tff(7953,plain,(c3_1(a537) | c2_1(a548) | c0_1(a548) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7954,plain,
% 1.97/2.14 (c3_1(a537)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7953, 4778, 56, 24])).
% 1.97/2.14 tff(7955,plain,
% 1.97/2.14 (~hskp50),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7789, 837, 7637, 7636, 7635, 4778, 4777, 7954])).
% 1.97/2.14 tff(7956,plain,
% 1.97/2.14 (~hskp26),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7574, 837, 7954, 4778, 4777, 7637, 7636, 7635])).
% 1.97/2.14 tff(7957,plain,
% 1.97/2.14 (~hskp34),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1147, 7925])).
% 1.97/2.14 tff(7958,plain,
% 1.97/2.14 (~hskp46),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3658, 7957, 7637, 7636, 7635])).
% 1.97/2.14 tff(7959,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7960,plain,
% 1.97/2.14 ((hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537))) <=> (hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7961,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7960])).
% 1.97/2.14 tff(7962,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7961, 7959])).
% 1.97/2.14 tff(7963,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7964,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7963, 7962])).
% 1.97/2.14 tff(7965,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7964, 156, 1661, 7925, 4779, 4716, 4778, 4714, 1686, 4717])).
% 1.97/2.14 tff(7966,plain,((~hskp30) | hskp26 | c0_1(a537) | (~c3_1(a537)) | c1_1(a537) | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7967,plain,
% 1.97/2.14 (~hskp30),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7966, 7925, 1661, 7954, 4778, 7958])).
% 1.97/2.14 tff(7968,plain,
% 1.97/2.14 (hskp29),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4620, 7967, 7859, 57])).
% 1.97/2.14 tff(7969,plain,
% 1.97/2.14 (~c1_1(a589)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6749, 7968, 7957, 4534, 7958, 4533])).
% 1.97/2.14 tff(7970,plain,
% 1.97/2.14 (hskp19),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6677, 922, 56, 24, 7859, 110, 946])).
% 1.97/2.14 tff(7971,plain,
% 1.97/2.14 (~c2_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1704, 7970])).
% 1.97/2.14 tff(7972,plain,
% 1.97/2.14 (~c1_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1675, 7970])).
% 1.97/2.14 tff(7973,plain,
% 1.97/2.14 (c3_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4078, 7972, 7516, 7971, 837])).
% 1.97/2.14 tff(7974,plain,
% 1.97/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a573) | c1_1(a573) | c2_1(a571) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a573)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a573) | c1_1(a573) | c2_1(a571) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a573)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7975,plain,
% 1.97/2.14 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571))) <=> (c2_1(a573) | c1_1(a573) | c2_1(a571) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a573)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7976,plain,
% 1.97/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a573) | c1_1(a573) | c2_1(a571) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a573))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7975])).
% 1.97/2.14 tff(7977,plain,
% 1.97/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a573) | c1_1(a573) | c2_1(a571) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a573)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7976, 7974])).
% 1.97/2.14 tff(7978,plain,
% 1.97/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a573) | c1_1(a573) | (~c3_1(a573)) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7979,plain,
% 1.97/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a573) | c1_1(a573) | c2_1(a571) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a571)) | (~c0_1(a571)) | (~c3_1(a573))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7978, 7977])).
% 1.97/2.14 tff(7980,plain,
% 1.97/2.14 (~c1_1(a571)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7979, 156, 7637, 7636, 7635, 925, 7971, 7972, 923, 707, 7973])).
% 1.97/2.14 tff(7981,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a589) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a589) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a589)) | c1_1(a589))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7982,plain,
% 1.97/2.14 ((hskp8 | (~ndr1_0) | c1_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589))) <=> (hskp8 | c0_1(a589) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a589)) | c1_1(a589))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7983,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a589) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a589)) | c1_1(a589)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7982])).
% 1.97/2.14 tff(7984,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a589) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a589)) | c1_1(a589))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7983, 7981])).
% 1.97/2.14 tff(7985,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a571) | (~c3_1(a571)) | (~c0_1(a571)) | c1_1(a589) | c0_1(a589) | (~c2_1(a589)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7986,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a589) | (~ndr1_0) | (~c3_1(a571)) | c1_1(a571) | (~c0_1(a571)) | (~c2_1(a589)) | c1_1(a589)),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7985, 7984])).
% 1.97/2.14 tff(7987,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7986, 156, 7814, 625, 925, 924, 590, 2407, 1716, 7980])).
% 1.97/2.14 tff(7988,plain,((~hskp17) | (~c2_1(a589)) | c0_1(a589) | c1_1(a589) | hskp0 | c0_1(a548) | c2_1(a548) | hskp50 | hskp46), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7989,plain,
% 1.97/2.14 (~hskp17),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7988, 7969, 4535, 4533, 837, 56, 24, 110, 7958])).
% 1.97/2.14 tff(7990,plain,
% 1.97/2.14 (~hskp37),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7865, 7957, 7859, 24, 57])).
% 1.97/2.14 tff(7991,plain,
% 1.97/2.14 (hskp38),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6938, 7989, 7859, 24, 56, 7969, 4533, 7958, 4534, 7990])).
% 1.97/2.14 tff(7992,plain,
% 1.97/2.14 (~hskp46),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3658, 3650, 7637, 7636, 7635])).
% 1.97/2.14 tff(7993,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6898, 6707, 4587, 3650, 7992, 332, 2768, 4581, 249, 24, 57])).
% 1.97/2.14 tff(7994,plain,((~hskp29) | hskp34 | hskp17 | (~hskp38) | (~c3_1(a548)) | c2_1(a548) | c1_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7995,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7994, 7991, 7989, 7957, 7968, 7859, 24, 57])).
% 1.97/2.14 tff(7996,plain,(c0_1(a537) | c2_1(a548) | c1_1(a548) | c0_1(a548) | hskp0 | hskp50 | hskp26 | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7997,plain,
% 1.97/2.14 (c0_1(a537)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7996, 57, 24, 56, 837, 7955, 7956, 4778])).
% 1.97/2.14 tff(7998,plain,
% 1.97/2.14 (hskp50 | hskp19 | c2_1(a537) | (~c0_1(a537))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1154, 156, 4778, 34])).
% 1.97/2.14 tff(7999,plain,
% 1.97/2.14 (hskp19),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7998, 7997, 7955, 4777])).
% 1.97/2.14 tff(8000,plain,
% 1.97/2.14 (~c2_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1704, 7999])).
% 1.97/2.14 tff(8001,plain,
% 1.97/2.14 (~c1_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1675, 7999])).
% 1.97/2.14 tff(8002,plain,
% 1.97/2.14 (c3_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4078, 8001, 7516, 8000, 837])).
% 1.97/2.14 tff(8003,plain,
% 1.97/2.14 (~c0_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1691, 7999])).
% 1.97/2.14 tff(8004,plain,
% 1.97/2.14 (~hskp46),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3247, 3243, 1661, 1718, 3143])).
% 1.97/2.14 tff(8005,plain,
% 1.97/2.14 (~c3_1(a591)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4647, 156, 8004, 4716, 4715, 4714, 12])).
% 1.97/2.14 tff(8006,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a591) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c3_1(a591) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a591) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c3_1(a591) | (~c1_1(a591)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8007,plain,
% 1.97/2.14 ((hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573))) <=> (hskp26 | c0_1(a591) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c3_1(a591) | (~c1_1(a591)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8008,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a591) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c3_1(a591) | (~c1_1(a591))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8007])).
% 1.97/2.14 tff(8009,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a591) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c3_1(a591) | (~c1_1(a591)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8008, 8006])).
% 1.97/2.14 tff(8010,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a573) | c0_1(a573) | (~c3_1(a573)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8011,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a591) | c0_1(a573) | c1_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c3_1(a591) | (~c1_1(a591))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8010, 8009])).
% 1.97/2.14 tff(8012,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8011, 156, 1661, 4716, 4714, 3143, 1718, 1686, 3243, 8005])).
% 1.97/2.14 tff(8013,plain,((~hskp30) | hskp26 | c0_1(a573) | c1_1(a573) | (~c3_1(a573))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8014,plain,
% 1.97/2.14 (~hskp30),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8013, 8003, 7956, 8001, 8002])).
% 1.97/2.14 tff(8015,plain,
% 1.97/2.14 (hskp29),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4620, 8014, 7859, 57])).
% 1.97/2.14 tff(8016,plain,
% 1.97/2.14 (~c3_1(a590)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4586, 8015])).
% 1.97/2.14 tff(8017,plain,
% 1.97/2.14 (~c1_1(a590)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6396, 8015])).
% 1.97/2.14 tff(8018,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a590))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8019,plain,
% 1.97/2.14 ((hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a590))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8020,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a590)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8019])).
% 1.97/2.14 tff(8021,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a590))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8020, 8018])).
% 1.97/2.14 tff(8022,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8023,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c2_1(a590)),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 1.97/2.14 tff(8024,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8023, 156, 837, 3428, 3427, 3426, 6400, 6399, 108, 6398])).
% 1.97/2.14 tff(8025,plain,(c2_1(a590) | hskp0 | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | c3_1(a590) | c1_1(a590)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8026,plain,
% 1.97/2.14 (c2_1(a590)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8025, 6399, 3428, 3427, 3426, 6400, 837])).
% 1.97/2.14 tff(8027,plain,
% 1.97/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a537) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8028,plain,
% 1.97/2.14 (((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c1_1(a537) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8029,plain,
% 1.97/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a537) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8028])).
% 1.97/2.14 tff(8030,plain,
% 1.97/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8029, 8027])).
% 1.97/2.14 tff(8031,plain,
% 1.97/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8032,plain,
% 1.97/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8031, 8030])).
% 1.97/2.14 tff(8033,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8032, 156, 4780, 4779, 4778, 6400, 6399, 921, 4777, 6504])).
% 1.97/2.14 tff(8034,plain,(c2_1(a537) | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537) | c3_1(a590) | c1_1(a590) | (~c2_1(a590))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8035,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8034, 8026, 6399, 4779, 4778, 4777, 4780, 6400])).
% 1.97/2.14 tff(8036,plain,(c1_1(a590) | (~c3_1(a537)) | c1_1(a537) | c2_1(a537) | (~c0_1(a537)) | c3_1(a590) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8037,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8036, 8017, 8016, 4778, 4777, 7997, 7954, 7637, 7636, 7635, 837])).
% 1.97/2.14 tff(8038,plain,(c1_1(a548) | c1_1(a537) | c2_1(a537) | hskp0 | c2_1(a548) | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8039,plain,
% 1.97/2.14 (c1_1(a548)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8038, 837, 4777, 4778, 24, 56])).
% 1.97/2.14 tff(8040,plain,
% 1.97/2.14 (hskp34),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4519, 8039, 56, 24, 7859])).
% 1.97/2.14 tff(8041,plain,
% 1.97/2.14 (c0_1(a537)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1147, 8040])).
% 1.97/2.14 tff(8042,plain,
% 1.97/2.14 (hskp19),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7998, 8041, 7955, 4777])).
% 1.97/2.14 tff(8043,plain,
% 1.97/2.14 (~c0_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1691, 8042])).
% 1.97/2.14 tff(8044,plain,
% 1.97/2.14 (hskp46),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2834, 8039, 56, 7859])).
% 1.97/2.14 tff(8045,plain,
% 1.97/2.14 (~c1_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1675, 8042])).
% 1.97/2.14 tff(8046,plain,
% 1.97/2.14 (~c2_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1704, 8042])).
% 1.97/2.14 tff(8047,plain,
% 1.97/2.14 (c3_1(a573)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4078, 8045, 7516, 8046, 837])).
% 1.97/2.14 tff(8048,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3247, 8047, 8045, 7956, 8044, 8043])).
% 1.97/2.14 tff(8049,plain,(hskp0 | c2_1(a537) | c1_1(a537) | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8050,plain,
% 1.97/2.14 (hskp0),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8049, 4777, 4778, 56, 24])).
% 1.97/2.14 tff(8051,plain,
% 1.97/2.14 (~c2_1(a535)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[713, 8050])).
% 1.97/2.14 tff(8052,plain,
% 1.97/2.14 (c1_1(a535)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[729, 8050])).
% 1.97/2.14 tff(8053,plain,
% 1.97/2.14 (c0_1(a535)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[721, 8050])).
% 1.97/2.14 tff(8054,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7662, 8053, 8052, 7637, 7636, 7635, 7954, 4777, 4778, 8051])).
% 1.97/2.14 tff(8055,plain,(c2_1(a537) | c1_1(a537) | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8056,plain,
% 1.97/2.14 (c2_1(a537)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8055, 4778, 56, 24])).
% 1.97/2.14 tff(8057,plain,
% 1.97/2.14 (c2_1(a590)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8025, 6707, 7637, 7636, 7635, 4587, 837])).
% 1.97/2.14 tff(8058,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7903, 156, 7637, 7636, 7635, 925, 249, 923, 24, 707, 57, 6511])).
% 1.97/2.14 tff(8059,plain,((~hskp17) | (~c3_1(a548)) | c2_1(a548) | c1_1(a548) | c3_1(a590) | c1_1(a590) | (~c2_1(a590))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8060,plain,
% 1.97/2.14 (~hskp17),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8059, 4587, 24, 57, 7859, 6707, 8057])).
% 1.97/2.14 tff(8061,plain,
% 1.97/2.14 (~hskp37),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7865, 3650, 7859, 24, 57])).
% 1.97/2.14 tff(8062,plain,
% 1.97/2.14 (~c1_1(a589)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6749, 4575, 3650, 4534, 7992, 4533])).
% 1.97/2.14 tff(8063,plain,
% 1.97/2.14 (hskp38),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6938, 8060, 7859, 24, 56, 8062, 4533, 7992, 4534, 8061])).
% 1.97/2.14 tff(8064,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7994, 8063, 8060, 3650, 4575, 7859, 24, 57])).
% 1.97/2.14 tff(8065,plain,((~hskp29) | hskp34 | c2_1(a548) | c1_1(a548) | c0_1(a548) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8066,plain,
% 1.97/2.14 (~hskp29),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8065, 3650, 24, 57, 56, 837])).
% 1.97/2.14 tff(8067,plain,
% 1.97/2.14 (hskp30),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4620, 8066, 7859, 57])).
% 1.97/2.14 tff(8068,plain,
% 1.97/2.14 (~c0_1(a591)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4626, 8067])).
% 1.97/2.14 tff(8069,plain,
% 1.97/2.14 (~c2_1(a591)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4632, 8067])).
% 1.97/2.14 tff(8070,plain,
% 1.97/2.14 (c1_1(a591)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4640, 8067])).
% 1.97/2.14 tff(8071,plain,
% 1.97/2.14 (~c3_1(a591)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4647, 156, 7992, 8070, 8069, 8068, 12])).
% 1.97/2.14 tff(8072,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a591) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a591) | (~c1_1(a591)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8073,plain,
% 1.97/2.14 ((hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a591) | c0_1(a591) | (~c1_1(a591))) <=> (hskp34 | c0_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a591) | (~c1_1(a591)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8074,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a591) | c0_1(a591) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a591) | (~c1_1(a591))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8073])).
% 1.97/2.14 tff(8075,plain,
% 1.97/2.14 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a591) | c0_1(a591) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a591) | (~c1_1(a591)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8074, 8072])).
% 1.97/2.14 tff(8076,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c3_1(a591) | c0_1(a591) | (~c1_1(a591)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8077,plain,
% 1.97/2.14 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | c3_1(a591) | (~c1_1(a591))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8076, 8075])).
% 1.97/2.14 tff(8078,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8077, 156, 3650, 7637, 7636, 7635, 8070, 8068, 75, 8071])).
% 1.97/2.14 tff(8079,plain,(hskp34 | c1_1(a548) | c2_1(a548) | c0_1(a548) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8080,plain,
% 1.97/2.14 (hskp34),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8079, 57, 24, 56, 837])).
% 1.97/2.14 tff(8081,plain,
% 1.97/2.14 (c0_1(a537)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1147, 8080])).
% 1.97/2.14 tff(8082,plain,
% 1.97/2.14 (c1_1(a589)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7536, 8081, 7814, 7954, 4533, 4778, 4535])).
% 1.97/2.14 tff(8083,plain,
% 1.97/2.14 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.97/2.14 inference(bind,[status(th)],[])).
% 1.97/2.14 tff(8084,plain,
% 1.97/2.14 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.97/2.14 inference(quant_intro,[status(thm)],[8083])).
% 1.97/2.14 tff(8085,plain,
% 1.97/2.14 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8086,plain,
% 1.97/2.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.97/2.14 inference(bind,[status(th)],[])).
% 1.97/2.14 tff(8087,plain,
% 1.97/2.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.97/2.14 inference(quant_intro,[status(thm)],[8086])).
% 1.97/2.14 tff(8088,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause255')).
% 1.97/2.14 tff(8089,plain,
% 1.97/2.14 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8088, 8087])).
% 1.97/2.14 tff(8090,plain,
% 1.97/2.14 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8089, 8085])).
% 1.97/2.15 tff(8091,plain,(
% 1.97/2.15 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.97/2.15 inference(skolemize,[status(sab)],[8090])).
% 1.97/2.15 tff(8092,plain,
% 1.97/2.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8091, 8084])).
% 1.97/2.15 tff(8093,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8094,plain,
% 1.97/2.15 ((hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589))) <=> (hskp10 | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8095,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8094])).
% 1.97/2.15 tff(8096,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8095, 8093])).
% 1.97/2.15 tff(8097,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8098,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8097, 8096])).
% 1.97/2.15 tff(8099,plain,
% 1.97/2.15 (hskp10 | (~c1_1(a589)) | (~c0_1(a537))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8098, 156, 7954, 4533, 4535, 8092, 8056])).
% 1.97/2.15 tff(8100,plain,
% 1.97/2.15 (hskp10),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8099, 8081, 8082])).
% 1.97/2.15 tff(8101,plain,
% 1.97/2.15 (((~hskp10) | (~c0_1(a558))) <=> ((~hskp10) | (~c0_1(a558)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8102,plain,
% 1.97/2.15 (((~c0_1(a558)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a558)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8103,axiom,((~c0_1(a558)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.97/2.15 tff(8104,plain,
% 1.97/2.15 ((~hskp10) | (~c0_1(a558))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8103, 8102])).
% 1.97/2.15 tff(8105,plain,
% 1.97/2.15 ((~hskp10) | (~c0_1(a558))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8104, 8101])).
% 1.97/2.15 tff(8106,plain,
% 1.97/2.15 (~c0_1(a558)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8105, 8100])).
% 1.97/2.15 tff(8107,plain,
% 1.97/2.15 (((~hskp10) | (~c1_1(a558))) <=> ((~hskp10) | (~c1_1(a558)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8108,plain,
% 1.97/2.15 (((~c1_1(a558)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a558)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8109,axiom,((~c1_1(a558)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.97/2.15 tff(8110,plain,
% 1.97/2.15 ((~hskp10) | (~c1_1(a558))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8109, 8108])).
% 1.97/2.15 tff(8111,plain,
% 1.97/2.15 ((~hskp10) | (~c1_1(a558))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8110, 8107])).
% 1.97/2.15 tff(8112,plain,
% 1.97/2.15 (~c1_1(a558)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8111, 8100])).
% 1.97/2.15 tff(8113,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8114,plain,
% 1.97/2.15 ((hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589))) <=> (hskp46 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8115,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)) | (~c0_1(a537))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8114])).
% 1.97/2.15 tff(8116,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8115, 8113])).
% 1.97/2.15 tff(8117,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a589) | (~c1_1(a589)) | (~c2_1(a589)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8118,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c2_1(a589)) | (~c1_1(a589)) | (~c2_1(a537)) | (~c0_1(a537))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8117, 8116])).
% 1.97/2.15 tff(8119,plain,
% 1.97/2.15 (hskp46 | (~c1_1(a589)) | (~c0_1(a537))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8118, 156, 4533, 4778, 4535, 2215, 8056])).
% 1.97/2.15 tff(8120,plain,
% 1.97/2.15 (hskp46),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8119, 8081, 8082])).
% 1.97/2.15 tff(8121,plain,
% 1.97/2.15 (~c0_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[64, 8120])).
% 1.97/2.15 tff(8122,plain,
% 1.97/2.15 (~c3_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[270, 8120])).
% 1.97/2.15 tff(8123,plain,
% 1.97/2.15 (((~hskp10) | c3_1(a558)) <=> ((~hskp10) | c3_1(a558))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8124,axiom,((~hskp10) | c3_1(a558)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.97/2.15 tff(8125,plain,
% 1.97/2.15 ((~hskp10) | c3_1(a558)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8124, 8123])).
% 1.97/2.15 tff(8126,plain,
% 1.97/2.15 ((~hskp10) | c3_1(a558)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8125, 8123])).
% 1.97/2.15 tff(8127,plain,
% 1.97/2.15 ((~hskp10) | c3_1(a558)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8126, 8123])).
% 1.97/2.15 tff(8128,plain,
% 1.97/2.15 ((~hskp10) | c3_1(a558)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8127, 8123])).
% 1.97/2.15 tff(8129,plain,
% 1.97/2.15 ((~hskp10) | c3_1(a558)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8128, 8123])).
% 1.97/2.15 tff(8130,plain,
% 1.97/2.15 (c3_1(a558)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8129, 8100])).
% 1.97/2.15 tff(8131,plain,
% 1.97/2.15 (c1_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[288, 8120])).
% 1.97/2.15 tff(8132,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c1_1(a558) | c0_1(a558) | (~ndr1_0) | (~c3_1(a558)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c1_1(a558) | c0_1(a558) | (~ndr1_0) | (~c3_1(a558)) | (~c1_1(a562)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8133,plain,
% 1.97/2.15 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a558) | c0_1(a558) | (~c3_1(a558))) <=> (hskp26 | c3_1(a562) | c0_1(a562) | c1_1(a558) | c0_1(a558) | (~ndr1_0) | (~c3_1(a558)) | (~c1_1(a562)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8134,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a558) | c0_1(a558) | (~c3_1(a558)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a562) | c0_1(a562) | c1_1(a558) | c0_1(a558) | (~ndr1_0) | (~c3_1(a558)) | (~c1_1(a562))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8133])).
% 1.97/2.15 tff(8135,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a558) | c0_1(a558) | (~c3_1(a558)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c1_1(a558) | c0_1(a558) | (~ndr1_0) | (~c3_1(a558)) | (~c1_1(a562)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8134, 8132])).
% 1.97/2.15 tff(8136,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a558) | c0_1(a558) | (~c3_1(a558)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8137,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a562) | c0_1(a562) | c1_1(a558) | c0_1(a558) | (~ndr1_0) | (~c3_1(a558)) | (~c1_1(a562))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8136, 8135])).
% 1.97/2.15 tff(8138,plain,
% 1.97/2.15 (hskp26),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8137, 156, 8131, 8130, 8122, 8121, 8112, 8106, 1686])).
% 1.97/2.15 tff(8139,plain,
% 1.97/2.15 (c0_1(a584)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1629, 8138])).
% 1.97/2.15 tff(8140,plain,
% 1.97/2.15 (c1_1(a584)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1637, 8138])).
% 1.97/2.15 tff(8141,plain,
% 1.97/2.15 (hskp4),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6532, 8120, 8082, 4534, 4533])).
% 1.97/2.15 tff(8142,plain,
% 1.97/2.15 (~c2_1(a545)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1643, 8141])).
% 1.97/2.15 tff(8143,plain,
% 1.97/2.15 (c1_1(a545)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[193, 8141])).
% 1.97/2.15 tff(8144,plain,
% 1.97/2.15 (hskp38 | (~c1_1(a589))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6804, 156, 7954, 4533, 4534, 4778, 1537, 8056])).
% 1.97/2.15 tff(8145,plain,
% 1.97/2.15 (hskp38),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8144, 8082])).
% 1.97/2.15 tff(8146,plain,
% 1.97/2.15 (c0_1(a547)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[677, 8145])).
% 1.97/2.15 tff(8147,plain,
% 1.97/2.15 (c1_1(a547)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[685, 8145])).
% 1.97/2.15 tff(8148,plain,
% 1.97/2.15 (c2_1(a547)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[693, 8145])).
% 1.97/2.15 tff(8149,plain,
% 1.97/2.15 (~hskp25),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6547, 8148, 837, 8147, 8146])).
% 1.97/2.15 tff(8150,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8151,plain,
% 1.97/2.15 ((hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545))) <=> (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8152,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8151])).
% 1.97/2.15 tff(8153,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8152, 8150])).
% 1.97/2.15 tff(8154,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a545) | (~c3_1(a545)) | (~c1_1(a545)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8155,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a545) | (~ndr1_0) | (~c3_1(a545)) | (~c1_1(a545)) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8154, 8153])).
% 1.97/2.15 tff(8156,plain,
% 1.97/2.15 (~c3_1(a545)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8155, 156, 8149, 4533, 4534, 8143, 8142, 55, 8082])).
% 1.97/2.15 tff(8157,plain,
% 1.97/2.15 (hskp15),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2094, 156, 7954, 8143, 4778, 8142, 483, 8156, 8056])).
% 1.97/2.15 tff(8158,plain,
% 1.97/2.15 (~c2_1(a569)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1255, 8157])).
% 1.97/2.15 tff(8159,plain,
% 1.97/2.15 (~c1_1(a569)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1261, 8157])).
% 1.97/2.15 tff(8160,plain,
% 1.97/2.15 (~c3_1(a584)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1620, 8138])).
% 1.97/2.15 tff(8161,plain,
% 1.97/2.15 (c3_1(a569)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4855, 8158, 7859, 8056, 24, 8148, 8147, 8146, 7954, 4778, 8159])).
% 1.97/2.15 tff(8162,assumption,(c2_1(a584)), introduced(assumption)).
% 1.97/2.15 tff(8163,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | c0_1(a589) | c3_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a584)) | (~c2_1(a589)) | (~c3_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp47 | c0_1(a589) | c3_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a584)) | (~c2_1(a589)) | (~c3_1(a589)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8164,plain,
% 1.97/2.15 ((hskp47 | (~ndr1_0) | c3_1(a584) | (~c2_1(a584)) | (~c1_1(a584)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp47 | c0_1(a589) | c3_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a584)) | (~c2_1(a589)) | (~c3_1(a589)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8165,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a584) | (~c2_1(a584)) | (~c1_1(a584)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | c0_1(a589) | c3_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a584)) | (~c2_1(a589)) | (~c3_1(a589))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8164])).
% 1.97/2.15 tff(8166,plain,
% 1.97/2.15 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a584) | (~c2_1(a584)) | (~c1_1(a584)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp47 | c0_1(a589) | c3_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a584)) | (~c2_1(a589)) | (~c3_1(a589)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8165, 8163])).
% 1.97/2.15 tff(8167,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a584) | (~c2_1(a584)) | (~c1_1(a584)) | c0_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8168,plain,
% 1.97/2.15 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp47 | c0_1(a589) | c3_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a584)) | (~c2_1(a589)) | (~c3_1(a589))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8167, 8166])).
% 1.97/2.15 tff(8169,plain,
% 1.97/2.15 (hskp47 | (~c2_1(a584))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8168, 156, 625, 591, 1648, 590, 1647, 5693])).
% 1.97/2.15 tff(8170,plain,
% 1.97/2.15 (hskp47),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8169, 8162])).
% 1.97/2.15 tff(8171,plain,
% 1.97/2.15 (~c2_1(a564)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5707, 8170])).
% 1.97/2.15 tff(8172,plain,
% 1.97/2.15 (c1_1(a564)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5734, 8170])).
% 1.97/2.15 tff(8173,plain,
% 1.97/2.15 (c0_1(a564)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5742, 8170])).
% 1.97/2.15 tff(8174,plain,
% 1.97/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a569)) | (~c1_1(a564)) | (~c0_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a569)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8175,plain,
% 1.97/2.15 (((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564))) <=> (c2_1(a564) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a569)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8176,plain,
% 1.97/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a569)) | (~c1_1(a564)) | (~c0_1(a564))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8175])).
% 1.97/2.15 tff(8177,plain,
% 1.97/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a569)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8176, 8174])).
% 1.97/2.15 tff(8178,plain,
% 1.97/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8179,plain,
% 1.97/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a569)) | (~c1_1(a564)) | (~c0_1(a564))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8178, 8177])).
% 1.97/2.15 tff(8180,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8179, 156, 8173, 8172, 1649, 1648, 8171, 2775, 2774, 707, 2824, 8162])).
% 1.97/2.15 tff(8181,plain,((~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c1_1(a569) | c2_1(a569) | (~c3_1(a569)) | (~c2_1(a589)) | (~c3_1(a589)) | c0_1(a589) | c3_1(a584)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8182,plain,
% 1.97/2.15 (~c2_1(a584)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8181, 8161, 8160, 8159, 8158, 8140, 4533, 4534, 4535, 8139])).
% 1.97/2.15 tff(8183,plain,
% 1.97/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8184,plain,
% 1.97/2.15 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584))) <=> (c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8185,plain,
% 1.97/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8184])).
% 1.97/2.15 tff(8186,plain,
% 1.97/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8185, 8183])).
% 1.97/2.15 tff(8187,plain,
% 1.97/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8188,plain,
% 1.97/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a569)) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8187, 8186])).
% 1.97/2.15 tff(8189,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8188, 156, 8148, 8147, 8146, 8139, 8140, 8159, 8158, 707, 8161, 8182])).
% 1.97/2.15 tff(8190,plain,(c1_1(a548) | c2_1(a548) | c1_1(a537) | hskp0 | c0_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8191,plain,
% 1.97/2.15 (c1_1(a548)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8190, 837, 4778, 24, 56])).
% 1.97/2.15 tff(8192,plain,
% 1.97/2.15 (hskp42 | (~c3_1(a548)) | (~c1_1(a548))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3604, 156, 7637, 7636, 7635, 24, 1364])).
% 1.97/2.15 tff(8193,plain,
% 1.97/2.15 (hskp42),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8192, 8191, 7859])).
% 1.97/2.15 tff(8194,plain,
% 1.97/2.15 (~c2_1(a556)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1385, 8193])).
% 1.97/2.15 tff(8195,plain,
% 1.97/2.15 (hskp46),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2834, 8191, 56, 7859])).
% 1.97/2.15 tff(8196,plain,
% 1.97/2.15 (~c0_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[64, 8195])).
% 1.97/2.15 tff(8197,plain,
% 1.97/2.15 (~c3_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[270, 8195])).
% 1.97/2.15 tff(8198,plain,
% 1.97/2.15 (c3_1(a556)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1403, 8193])).
% 1.97/2.15 tff(8199,plain,
% 1.97/2.15 (c1_1(a556)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1411, 8193])).
% 1.97/2.15 tff(8200,plain,
% 1.97/2.15 (c1_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[288, 8195])).
% 1.97/2.15 tff(8201,plain,
% 1.97/2.15 (hskp39),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1419, 156, 8200, 8199, 8198, 8197, 8196, 8194, 281])).
% 1.97/2.15 tff(8202,plain,
% 1.97/2.15 (c1_1(a549)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[303, 8201])).
% 1.97/2.15 tff(8203,plain,
% 1.97/2.15 (c2_1(a549)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[311, 8201])).
% 1.97/2.15 tff(8204,plain,
% 1.97/2.15 (c3_1(a549)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[319, 8201])).
% 1.97/2.15 tff(8205,plain,
% 1.97/2.15 (hskp38),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1544, 156, 8204, 8203, 8202, 7954, 4778, 1537, 8056])).
% 1.97/2.15 tff(8206,plain,
% 1.97/2.15 (c0_1(a547)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[677, 8205])).
% 1.97/2.15 tff(8207,plain,
% 1.97/2.15 (hskp25),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5026, 156, 8199, 8198, 8204, 8203, 8202, 8194, 55])).
% 1.97/2.15 tff(8208,plain,
% 1.97/2.15 (c2_1(a547)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[693, 8205])).
% 1.97/2.15 tff(8209,plain,
% 1.97/2.15 (c1_1(a547)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[685, 8205])).
% 1.97/2.15 tff(8210,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6547, 8209, 8208, 837, 8207, 8206])).
% 1.97/2.15 tff(8211,plain,(hskp0 | c1_1(a537) | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8212,plain,
% 1.97/2.15 (hskp0),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8211, 4778, 56, 24])).
% 1.97/2.15 tff(8213,plain,
% 1.97/2.15 (~c2_1(a535)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[713, 8212])).
% 1.97/2.15 tff(8214,plain,
% 1.97/2.15 (c0_1(a535)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[721, 8212])).
% 1.97/2.15 tff(8215,plain,
% 1.97/2.15 (c1_1(a535)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[729, 8212])).
% 1.97/2.15 tff(8216,plain,
% 1.97/2.15 (c1_1(a548)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3590, 156, 7637, 7636, 7635, 7859, 8215, 8214, 24, 8213, 707])).
% 1.97/2.15 tff(8217,plain,
% 1.97/2.15 (hskp42),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8192, 8216, 7859])).
% 1.97/2.15 tff(8218,plain,
% 1.97/2.15 (~c2_1(a556)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1385, 8217])).
% 1.97/2.15 tff(8219,plain,
% 1.97/2.15 (hskp46),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2834, 8216, 56, 7859])).
% 1.97/2.15 tff(8220,plain,
% 1.97/2.15 (~c0_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[64, 8219])).
% 1.97/2.15 tff(8221,plain,
% 1.97/2.15 (~c3_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[270, 8219])).
% 1.97/2.15 tff(8222,plain,
% 1.97/2.15 (c3_1(a556)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1403, 8217])).
% 1.97/2.15 tff(8223,plain,
% 1.97/2.15 (c1_1(a556)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1411, 8217])).
% 1.97/2.15 tff(8224,plain,
% 1.97/2.15 (c1_1(a562)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[288, 8219])).
% 1.97/2.15 tff(8225,plain,
% 1.97/2.15 (hskp39),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1419, 156, 8224, 8223, 8222, 8221, 8220, 8218, 281])).
% 1.97/2.15 tff(8226,plain,
% 1.97/2.15 (c1_1(a549)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[303, 8225])).
% 1.97/2.15 tff(8227,plain,
% 1.97/2.15 (c2_1(a549)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[311, 8225])).
% 1.97/2.15 tff(8228,plain,
% 1.97/2.15 (c3_1(a549)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[319, 8225])).
% 1.97/2.15 tff(8229,plain,
% 1.97/2.15 (hskp25),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5026, 156, 8223, 8222, 8228, 8227, 8226, 8218, 55])).
% 1.97/2.15 tff(8230,plain,
% 1.97/2.15 (~c1_1(a582)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1190, 8229])).
% 1.97/2.15 tff(8231,plain,
% 1.97/2.15 (~c2_1(a582)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1196, 8229])).
% 1.97/2.15 tff(8232,plain,
% 1.97/2.15 (~c3_1(a582)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1202, 8229])).
% 1.97/2.15 tff(8233,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2192, 156, 8223, 8222, 7954, 8218, 4778, 8232, 8231, 8230, 45, 8056])).
% 1.97/2.15 tff(8234,plain,(c1_1(a537) | c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8235,plain,
% 1.97/2.15 (c1_1(a537)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8234, 56, 24])).
% 1.97/2.15 tff(8236,plain,
% 1.97/2.15 (~hskp34),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1124, 8235])).
% 1.97/2.15 tff(8237,plain,
% 1.97/2.15 (~c1_1(a548)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4519, 8236, 56, 24, 7859])).
% 1.97/2.15 tff(8238,plain,
% 1.97/2.15 (hskp0),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8079, 8237, 24, 56, 8236])).
% 1.97/2.15 tff(8239,plain,
% 1.97/2.15 (~c2_1(a535)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[713, 8238])).
% 1.97/2.15 tff(8240,plain,
% 1.97/2.15 (c0_1(a535)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[721, 8238])).
% 1.97/2.15 tff(8241,plain,
% 1.97/2.15 (c1_1(a535)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[729, 8238])).
% 1.97/2.15 tff(8242,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3590, 156, 7637, 7636, 7635, 7859, 8241, 8240, 24, 8239, 707, 8237])).
% 1.97/2.15 tff(8243,plain,(c0_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8244,plain,
% 1.97/2.15 (c0_1(a548)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8243, 24])).
% 1.97/2.15 tff(8245,plain,
% 1.97/2.15 (~hskp6),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[211, 8244])).
% 1.97/2.15 tff(8246,plain,
% 1.97/2.15 (~c1_1(a586)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7782, 1669, 3650, 3667])).
% 1.97/2.15 tff(8247,plain,
% 1.97/2.15 (hskp27),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[205, 1669, 7771])).
% 1.97/2.15 tff(8248,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[95, 8247, 8246])).
% 1.97/2.15 tff(8249,plain,(hskp6 | hskp34 | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8250,plain,
% 1.97/2.15 (hskp34),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8249, 8245, 7516])).
% 1.97/2.15 tff(8251,plain,
% 1.97/2.15 (~c1_1(a537)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1124, 8250])).
% 1.97/2.15 tff(8252,plain,
% 1.97/2.15 (c3_1(a537)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1132, 8250])).
% 1.97/2.15 tff(8253,plain,
% 1.97/2.15 (hskp34),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8249, 1669, 3667])).
% 1.97/2.15 tff(8254,plain,
% 1.97/2.15 (~c0_1(a537)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7808, 1669, 4778, 4779, 4777, 3667])).
% 1.97/2.15 tff(8255,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1147, 8254, 8253])).
% 1.97/2.15 tff(8256,plain,(hskp6 | c1_1(a537) | (~c3_1(a537)) | c2_1(a537) | (~hskp33)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8257,plain,
% 1.97/2.15 (c2_1(a537)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8256, 8252, 8245, 8251, 7516])).
% 1.97/2.15 tff(8258,plain,
% 1.97/2.15 (c0_1(a537)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1147, 8250])).
% 1.97/2.15 tff(8259,plain,
% 1.97/2.15 (hskp0),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7822, 2895, 8252, 8251, 8258, 24])).
% 1.97/2.15 tff(8260,plain,
% 1.97/2.15 (~c2_1(a535)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[713, 8259])).
% 1.97/2.15 tff(8261,plain,
% 1.97/2.15 (c1_1(a548)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7838, 2895, 8252, 8251, 24, 8258])).
% 1.97/2.15 tff(8262,plain,
% 1.97/2.15 (hskp15 | c3_1(a548) | (~c1_1(a548))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3708, 156, 8252, 8251, 24, 483, 8257])).
% 1.97/2.15 tff(8263,plain,
% 1.97/2.16 (hskp15),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8262, 2895, 8261])).
% 1.97/2.16 tff(8264,plain,
% 1.97/2.16 (~c2_1(a569)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1255, 8263])).
% 1.97/2.16 tff(8265,plain,
% 1.97/2.16 (~c1_1(a569)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1261, 8263])).
% 1.97/2.16 tff(8266,plain,
% 1.97/2.16 (c0_1(a535)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[721, 8259])).
% 1.97/2.16 tff(8267,plain,
% 1.97/2.16 (c1_1(a535)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[729, 8259])).
% 1.97/2.16 tff(8268,plain,
% 1.97/2.16 (~c3_1(a569)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3455, 156, 7637, 7636, 7635, 8267, 8266, 8265, 8264, 8260, 707])).
% 1.97/2.16 tff(8269,plain,
% 1.97/2.16 (~c0_1(a569)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1267, 8263])).
% 1.97/2.16 tff(8270,plain,
% 1.97/2.16 (hskp28),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1276, 8263])).
% 1.97/2.16 tff(8271,plain,
% 1.97/2.16 (~c0_1(a589)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[177, 8270])).
% 1.97/2.16 tff(8272,plain,
% 1.97/2.16 (c3_1(a589)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[185, 8270])).
% 1.97/2.16 tff(8273,plain,
% 1.97/2.16 (~c1_1(a589)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1789, 156, 8245, 8272, 8271, 8269, 8265, 8264, 1745])).
% 2.00/2.16 tff(8274,plain,
% 2.00/2.16 (hskp51),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[3462, 156, 8258, 8252, 8251, 8265, 8264, 2608, 8268])).
% 2.00/2.16 tff(8275,plain,
% 2.00/2.16 (~c2_1(a583)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[2637, 8274])).
% 2.00/2.16 tff(8276,plain,
% 2.00/2.16 (c2_1(a589)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[171, 8270])).
% 2.00/2.16 tff(8277,plain,
% 2.00/2.16 (c3_1(a583)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[2645, 8274])).
% 2.00/2.16 tff(8278,plain,
% 2.00/2.16 (~c1_1(a583)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[7682, 156, 8277, 8276, 8272, 8275, 8265, 8264, 45, 8273, 8268])).
% 2.00/2.16 tff(8279,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)) | (~c3_1(a583)) | c1_1(a583))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)) | (~c3_1(a583)) | c1_1(a583))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8280,plain,
% 2.00/2.16 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548))) <=> (c2_1(a583) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)) | (~c3_1(a583)) | c1_1(a583))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8281,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a583) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)) | (~c3_1(a583)) | c1_1(a583)))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8280])).
% 2.00/2.16 tff(8282,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)) | (~c3_1(a583)) | c1_1(a583))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8281, 8279])).
% 2.00/2.16 tff(8283,plain,
% 2.00/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a583) | c1_1(a583) | (~c3_1(a583)) | c2_1(a548) | (~c0_1(a548)) | (~c1_1(a548)))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8284,plain,
% 2.00/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a583) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a548)) | (~c3_1(a583)) | c1_1(a583)),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[8283, 8282])).
% 2.00/2.16 tff(8285,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8284, 156, 8277, 7637, 7636, 7635, 8275, 24, 8244, 707, 8261, 8278])).
% 2.00/2.16 tff(8286,plain,(c3_1(a548) | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(8287,plain,
% 2.00/2.16 (c3_1(a548)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8286, 24])).
% 2.00/2.16 tff(8288,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a537) | c3_1(a590) | c1_1(a590) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c3_1(a590) | c1_1(a590) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8289,plain,
% 2.00/2.16 (((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c1_1(a537) | c3_1(a590) | c1_1(a590) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8290,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a537) | c3_1(a590) | c1_1(a590) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8289])).
% 2.00/2.16 tff(8291,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c3_1(a590) | c1_1(a590) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8290, 8288])).
% 2.00/2.16 tff(8292,plain,
% 2.00/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a548) | (~c3_1(a548)) | (~c0_1(a548)) | c1_1(a590) | c3_1(a590) | (~c2_1(a590)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8293,plain,
% 2.00/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c3_1(a590) | c1_1(a590) | c2_1(a548) | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a537))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[8292, 8291])).
% 2.00/2.16 tff(8294,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8293, 156, 8258, 8252, 8287, 8251, 4587, 6707, 24, 8244, 921, 8057])).
% 2.00/2.16 tff(8295,plain,((~hskp29) | c2_1(a548) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(8296,plain,
% 2.00/2.16 (~hskp29),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8295, 837, 24])).
% 2.00/2.16 tff(8297,plain,
% 2.00/2.16 (c2_1(a589)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[171, 1967])).
% 2.00/2.16 tff(8298,plain,
% 2.00/2.16 (c1_1(a589)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[7536, 8297, 6903, 4779, 4780, 4778, 1969])).
% 2.00/2.16 tff(8299,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1789, 156, 1669, 1968, 1969, 1268, 1262, 1256, 1745, 8298])).
% 2.00/2.16 tff(8300,plain,((~hskp15) | hskp6 | hskp8 | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(8301,plain,
% 2.00/2.16 (~hskp15),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8300, 7814, 8245, 8252, 8258, 8251])).
% 2.00/2.16 tff(8302,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c2_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c2_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8303,plain,
% 2.00/2.16 ((hskp15 | (~ndr1_0) | c2_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp15 | c1_1(a537) | c2_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8304,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c2_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8303])).
% 2.00/2.16 tff(8305,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c2_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8304, 8302])).
% 2.00/2.16 tff(8306,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a591) | c3_1(a591) | (~c1_1(a591)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8307,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c2_1(a591) | (~ndr1_0) | c3_1(a591) | (~c1_1(a591)) | (~c3_1(a537)) | (~c2_1(a537))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[8306, 8305])).
% 2.00/2.16 tff(8308,plain,
% 2.00/2.16 (c3_1(a591)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8307, 156, 109, 4779, 4716, 4778, 4715, 483, 1])).
% 2.00/2.16 tff(8309,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8307, 156, 109, 4779, 4716, 4778, 4715, 483, 1, 4717])).
% 2.00/2.16 tff(8310,plain,((~hskp30) | hskp15 | (~c3_1(a537)) | c1_1(a537) | (~c2_1(a537)) | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(8311,plain,
% 2.00/2.16 (hskp46),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8310, 4713, 4779, 4778, 1, 109])).
% 2.00/2.16 tff(8312,plain,
% 2.00/2.16 (~c0_1(a562)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[64, 8311])).
% 2.00/2.16 tff(8313,plain,
% 2.00/2.16 (~c3_1(a562)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[270, 8311])).
% 2.00/2.16 tff(8314,plain,
% 2.00/2.16 (c1_1(a562)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[288, 8311])).
% 2.00/2.16 tff(8315,plain,
% 2.00/2.16 (hskp39),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[6450, 156, 8314, 4716, 8313, 8312, 4715, 281, 8308])).
% 2.00/2.16 tff(8316,plain,
% 2.00/2.16 (c1_1(a549)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[303, 8315])).
% 2.00/2.16 tff(8317,plain,
% 2.00/2.16 (c2_1(a549)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[311, 8315])).
% 2.00/2.16 tff(8318,plain,
% 2.00/2.16 (c3_1(a549)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[319, 8315])).
% 2.00/2.16 tff(8319,plain,
% 2.00/2.16 (hskp38),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1544, 156, 8318, 8317, 8316, 4779, 4778, 1537, 1])).
% 2.00/2.16 tff(8320,plain,
% 2.00/2.16 (c0_1(a547)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[677, 8319])).
% 2.00/2.16 tff(8321,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a591)) | (~c1_1(a591)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8322,plain,
% 2.00/2.16 ((hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536))) <=> (hskp42 | c2_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8323,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | c2_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a591)) | (~c1_1(a591))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8322])).
% 2.00/2.16 tff(8324,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a591)) | (~c1_1(a591)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8323, 8321])).
% 2.00/2.16 tff(8325,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a591) | (~c3_1(a591)) | (~c1_1(a591)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8326,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp42 | c2_1(a591) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a591)) | (~c1_1(a591))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[8325, 8324])).
% 2.00/2.16 tff(8327,plain,
% 2.00/2.16 (hskp42 | (~c3_1(a591))),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8326, 156, 3428, 3427, 3426, 4716, 4715, 1364])).
% 2.00/2.16 tff(8328,plain,
% 2.00/2.16 (hskp42),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8327, 8308])).
% 2.00/2.16 tff(8329,plain,
% 2.00/2.16 (~c2_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1385, 8328])).
% 2.00/2.16 tff(8330,plain,
% 2.00/2.16 (c3_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1403, 8328])).
% 2.00/2.16 tff(8331,plain,
% 2.00/2.16 (c1_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1411, 8328])).
% 2.00/2.16 tff(8332,plain,
% 2.00/2.16 (hskp25),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[5026, 156, 8331, 8330, 8318, 8317, 8316, 8329, 55])).
% 2.00/2.16 tff(8333,plain,
% 2.00/2.16 (c2_1(a547)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[693, 8319])).
% 2.00/2.16 tff(8334,plain,
% 2.00/2.16 (c1_1(a547)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[685, 8319])).
% 2.00/2.16 tff(8335,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[6547, 8334, 8333, 837, 8332, 8320])).
% 2.00/2.16 tff(8336,plain,((~hskp30) | hskp0 | (~c3_1(a537)) | c1_1(a537) | (~c2_1(a537)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(8337,plain,
% 2.00/2.16 (~hskp30),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8336, 837, 8252, 8251, 8257, 7637, 7636, 7635, 8301])).
% 2.00/2.16 tff(8338,plain,
% 2.00/2.16 (c1_1(a548)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[4620, 8337, 8287, 8296])).
% 2.00/2.16 tff(8339,plain,
% 2.00/2.16 (hskp42),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8192, 8338, 8287])).
% 2.00/2.16 tff(8340,plain,
% 2.00/2.16 (~c2_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1385, 8339])).
% 2.00/2.16 tff(8341,plain,
% 2.00/2.16 (c3_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1403, 8339])).
% 2.00/2.16 tff(8342,plain,
% 2.00/2.16 (c1_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1411, 8339])).
% 2.00/2.16 tff(8343,assumption,(hskp32), introduced(assumption)).
% 2.00/2.16 tff(8344,plain,
% 2.00/2.16 (~c2_1(a596)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[5534, 8343])).
% 2.00/2.16 tff(8345,plain,
% 2.00/2.16 (~c3_1(a596)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[5528, 8343])).
% 2.00/2.16 tff(8346,assumption,(~c2_1(a556)), introduced(assumption)).
% 2.00/2.16 tff(8347,assumption,(c3_1(a556)), introduced(assumption)).
% 2.00/2.16 tff(8348,assumption,(c1_1(a556)), introduced(assumption)).
% 2.00/2.16 tff(8349,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8350,plain,
% 2.00/2.16 (((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a596) | c1_1(a596) | c3_1(a596)) <=> (c2_1(a556) | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8351,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8350])).
% 2.00/2.16 tff(8352,plain,
% 2.00/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a596) | c1_1(a596) | c3_1(a596))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8351, 8349])).
% 2.00/2.16 tff(8353,plain,
% 2.00/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a596) | c1_1(a596) | c3_1(a596))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8354,plain,
% 2.00/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | c1_1(a596) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[8353, 8352])).
% 2.00/2.16 tff(8355,plain,
% 2.00/2.16 (c1_1(a596)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8354, 156, 8348, 8347, 4779, 8346, 4778, 8345, 8344, 45, 1])).
% 2.00/2.16 tff(8356,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8357,plain,
% 2.00/2.16 ((hskp15 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c1_1(a596)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537))) <=> (hskp15 | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8358,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c1_1(a596)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8357])).
% 2.00/2.16 tff(8359,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c1_1(a596)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8358, 8356])).
% 2.00/2.16 tff(8360,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a596) | c3_1(a596) | (~c1_1(a596)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8361,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a537) | c3_1(a596) | c2_1(a596) | (~ndr1_0) | (~c1_1(a596)) | (~c3_1(a537)) | (~c2_1(a537))),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[8360, 8359])).
% 2.00/2.16 tff(8362,plain,
% 2.00/2.16 ($false),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8361, 156, 109, 4779, 4778, 8345, 8344, 483, 8355, 1])).
% 2.00/2.16 tff(8363,plain,((~hskp32) | hskp15 | (~c3_1(a537)) | c1_1(a537) | (~c2_1(a537)) | (~c1_1(a556)) | (~c3_1(a556)) | c2_1(a556)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.16 tff(8364,plain,
% 2.00/2.16 (~hskp32),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8363, 8301, 8252, 8251, 8257, 8342, 8341, 8340])).
% 2.00/2.16 tff(8365,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | c0_1(a556))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | c0_1(a556))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8366,plain,
% 2.00/2.16 ((hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a556) | c0_1(a556) | (~c3_1(a556))) <=> (hskp46 | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | c0_1(a556))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8367,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a556) | c0_1(a556) | (~c3_1(a556)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | c0_1(a556)))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8366])).
% 2.00/2.16 tff(8368,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a556) | c0_1(a556) | (~c3_1(a556)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | c0_1(a556))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8367, 8365])).
% 2.00/2.16 tff(8369,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp46 | (~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c2_1(a556) | c0_1(a556) | (~c3_1(a556)))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8370,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp46 | c2_1(a556) | (~ndr1_0) | (~c3_1(a556)) | (~c1_1(a556)) | c0_1(a556)),
% 2.00/2.16 inference(modus_ponens,[status(thm)],[8369, 8368])).
% 2.00/2.16 tff(8371,plain,
% 2.00/2.16 (hskp46 | c0_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8370, 156, 8348, 8347, 8346, 12])).
% 2.00/2.16 tff(8372,plain,
% 2.00/2.16 (c0_1(a556)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[8371, 946])).
% 2.00/2.16 tff(8373,assumption,(~hskp32), introduced(assumption)).
% 2.00/2.16 tff(8374,assumption,(hskp2), introduced(assumption)).
% 2.00/2.16 tff(8375,plain,
% 2.00/2.16 (~c3_1(a540)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1338, 8374])).
% 2.00/2.16 tff(8376,plain,
% 2.00/2.16 (c1_1(a540)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1346, 8374])).
% 2.00/2.16 tff(8377,plain,
% 2.00/2.16 (c2_1(a540)),
% 2.00/2.16 inference(unit_resolution,[status(thm)],[1371, 8374])).
% 2.00/2.16 tff(8378,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8379,plain,
% 2.00/2.16 ((hskp32 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a540) | (~c1_1(a540)) | (~c2_1(a540))) <=> (hskp32 | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.00/2.16 inference(rewrite,[status(thm)],[])).
% 2.00/2.16 tff(8380,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a540) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.00/2.16 inference(monotonicity,[status(thm)],[8379])).
% 2.00/2.16 tff(8381,plain,
% 2.00/2.16 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a540) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.00/2.16 inference(transitivity,[status(thm)],[8380, 8378])).
% 2.00/2.16 tff(8382,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a540) | (~c0_1(a540)) | (~c1_1(a540)) | c3_1(a540) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.00/2.16 inference(quant_inst,[status(thm)],[])).
% 2.00/2.16 tff(8383,plain,
% 2.00/2.16 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a540) | (~ndr1_0) | (~c0_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8382, 8381])).
% 2.00/2.17 tff(8384,plain,
% 2.00/2.17 (~c0_1(a540)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8383, 156, 8373, 8377, 8376, 8375, 4894])).
% 2.00/2.17 tff(8385,plain,
% 2.00/2.17 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a537) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8386,plain,
% 2.00/2.17 ((hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540))) <=> (hskp46 | c1_1(a537) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8387,plain,
% 2.00/2.17 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a537) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | (~c2_1(a537)) | (~c0_1(a537))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8386])).
% 2.00/2.17 tff(8388,plain,
% 2.00/2.17 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8387, 8385])).
% 2.00/2.17 tff(8389,plain,
% 2.00/2.17 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8390,plain,
% 2.00/2.17 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | (~ndr1_0) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | (~c2_1(a537)) | (~c0_1(a537))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8389, 8388])).
% 2.00/2.17 tff(8391,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8390, 156, 946, 4780, 8377, 8376, 4778, 2215, 1, 8384])).
% 2.00/2.17 tff(8392,plain,((~hskp2) | hskp46 | (~c0_1(a537)) | c1_1(a537) | (~c2_1(a537)) | hskp32), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(8393,plain,
% 2.00/2.17 (~hskp2),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8392, 946, 4780, 4778, 1, 8373])).
% 2.00/2.17 tff(8394,plain,
% 2.00/2.17 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp2 | hskp1 | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8395,plain,
% 2.00/2.17 ((hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a548)) | (~c0_1(a548)) | (~c1_1(a548))) <=> (hskp2 | hskp1 | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8396,plain,
% 2.00/2.17 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a548)) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8395])).
% 2.00/2.17 tff(8397,plain,
% 2.00/2.17 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a548)) | (~c0_1(a548)) | (~c1_1(a548)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp2 | hskp1 | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8396, 8394])).
% 2.00/2.17 tff(8398,plain,
% 2.00/2.17 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a548)) | (~c0_1(a548)) | (~c1_1(a548)))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8399,plain,
% 2.00/2.17 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp2 | hskp1 | (~c0_1(a548)) | (~ndr1_0) | (~c3_1(a548)) | (~c1_1(a548))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8398, 8397])).
% 2.00/2.17 tff(8400,plain,
% 2.00/2.17 (hskp2 | hskp1 | (~c3_1(a548)) | (~c1_1(a548))),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8399, 156, 5004, 1326])).
% 2.00/2.17 tff(8401,plain,
% 2.00/2.17 (hskp1),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8400, 8393, 249, 2548])).
% 2.00/2.17 tff(8402,plain,
% 2.00/2.17 (~c1_1(a539)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1233, 8401])).
% 2.00/2.17 tff(8403,plain,
% 2.00/2.17 (~c2_1(a539)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1239, 8401])).
% 2.00/2.17 tff(8404,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a556) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a556)) | (~c0_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a556) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a556)) | (~c0_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8405,plain,
% 2.00/2.17 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a539) | c1_1(a539) | (~c3_1(a539)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556))) <=> (c2_1(a556) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a556)) | (~c0_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8406,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a539) | c1_1(a539) | (~c3_1(a539)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a556) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a556)) | (~c0_1(a556))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8405])).
% 2.00/2.17 tff(8407,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a539) | c1_1(a539) | (~c3_1(a539)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a556) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a556)) | (~c0_1(a556)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8406, 8404])).
% 2.00/2.17 tff(8408,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a539) | c1_1(a539) | (~c3_1(a539)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8409,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a556) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | (~c3_1(a539)) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c1_1(a556)) | (~c0_1(a556))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8408, 8407])).
% 2.00/2.17 tff(8410,plain,
% 2.00/2.17 (~c3_1(a539)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8409, 156, 8348, 3428, 3427, 3426, 8346, 8403, 8402, 707, 8372])).
% 2.00/2.17 tff(8411,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8412,plain,
% 2.00/2.17 (((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a539) | c1_1(a539) | c3_1(a539)) <=> (c2_1(a556) | c1_1(a537) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8413,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a539) | c1_1(a539) | c3_1(a539))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8412])).
% 2.00/2.17 tff(8414,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a539) | c1_1(a539) | c3_1(a539))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8413, 8411])).
% 2.00/2.17 tff(8415,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a539) | c1_1(a539) | c3_1(a539))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8416,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c2_1(a539) | c1_1(a539) | (~ndr1_0) | c3_1(a539) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8415, 8414])).
% 2.00/2.17 tff(8417,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8416, 156, 8348, 8347, 4779, 8346, 4778, 8403, 8402, 45, 1, 8410])).
% 2.00/2.17 tff(8418,plain,(hskp46 | (~c1_1(a556)) | (~c3_1(a556)) | (~c3_1(a537)) | c2_1(a556) | c1_1(a537) | (~c2_1(a537)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a548)) | (~c1_1(a548)) | (~c0_1(a548)) | (~c0_1(a537)) | hskp32), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(8419,plain,
% 2.00/2.17 (hskp46),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8418, 8342, 8341, 8252, 8340, 8251, 8257, 7637, 7636, 7635, 8287, 8338, 8244, 8258, 8364])).
% 2.00/2.17 tff(8420,plain,
% 2.00/2.17 (~c0_1(a562)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[64, 8419])).
% 2.00/2.17 tff(8421,plain,
% 2.00/2.17 (~c3_1(a562)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[270, 8419])).
% 2.00/2.17 tff(8422,plain,
% 2.00/2.17 (c1_1(a562)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[288, 8419])).
% 2.00/2.17 tff(8423,plain,
% 2.00/2.17 (hskp39),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1419, 156, 8422, 8342, 8341, 8421, 8420, 8340, 281])).
% 2.00/2.17 tff(8424,plain,
% 2.00/2.17 (c1_1(a549)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[303, 8423])).
% 2.00/2.17 tff(8425,plain,
% 2.00/2.17 (c2_1(a549)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[311, 8423])).
% 2.00/2.17 tff(8426,plain,
% 2.00/2.17 (c3_1(a549)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[319, 8423])).
% 2.00/2.17 tff(8427,plain,
% 2.00/2.17 (hskp38),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1544, 156, 8426, 8425, 8424, 8252, 8251, 1537, 8257])).
% 2.00/2.17 tff(8428,plain,
% 2.00/2.17 (c0_1(a547)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[677, 8427])).
% 2.00/2.17 tff(8429,plain,
% 2.00/2.17 (hskp25),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[5026, 156, 8342, 8341, 8426, 8425, 8424, 8340, 55])).
% 2.00/2.17 tff(8430,plain,
% 2.00/2.17 (c2_1(a547)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[693, 8427])).
% 2.00/2.17 tff(8431,plain,
% 2.00/2.17 (c1_1(a547)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[685, 8427])).
% 2.00/2.17 tff(8432,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[6547, 8431, 8430, 837, 8429, 8428])).
% 2.00/2.17 tff(8433,plain,(hskp0 | c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(8434,plain,
% 2.00/2.17 (hskp0),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8433, 24])).
% 2.00/2.17 tff(8435,plain,
% 2.00/2.17 (~c2_1(a535)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[713, 8434])).
% 2.00/2.17 tff(8436,plain,
% 2.00/2.17 (c0_1(a535)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[721, 8434])).
% 2.00/2.17 tff(8437,plain,
% 2.00/2.17 (c1_1(a535)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[729, 8434])).
% 2.00/2.17 tff(8438,plain,
% 2.00/2.17 (c1_1(a548)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3590, 156, 7637, 7636, 7635, 8287, 8437, 8436, 24, 8435, 707])).
% 2.00/2.17 tff(8439,plain,
% 2.00/2.17 (hskp42),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8192, 8438, 8287])).
% 2.00/2.17 tff(8440,plain,
% 2.00/2.17 (~c2_1(a556)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1385, 8439])).
% 2.00/2.17 tff(8441,plain,
% 2.00/2.17 (c3_1(a556)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1403, 8439])).
% 2.00/2.17 tff(8442,plain,
% 2.00/2.17 (c1_1(a556)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1411, 8439])).
% 2.00/2.17 tff(8443,plain,
% 2.00/2.17 (hskp32),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8418, 946, 8347, 4779, 8346, 4778, 1, 3428, 3427, 3426, 249, 2548, 5004, 4780, 8348])).
% 2.00/2.17 tff(8444,plain,
% 2.00/2.17 (hskp15),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8363, 8443, 4779, 4778, 1, 8348, 8347, 8346])).
% 2.00/2.17 tff(8445,plain,
% 2.00/2.17 (~c2_1(a569)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1255, 8444])).
% 2.00/2.17 tff(8446,plain,
% 2.00/2.17 (~c1_1(a569)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1261, 8444])).
% 2.00/2.17 tff(8447,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a556) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c1_1(a556)) | (~c0_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a556) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c1_1(a556)) | (~c0_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8448,plain,
% 2.00/2.17 (((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556))) <=> (c2_1(a556) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c1_1(a556)) | (~c0_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8449,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a556) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c1_1(a556)) | (~c0_1(a556))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8448])).
% 2.00/2.17 tff(8450,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a556) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c1_1(a556)) | (~c0_1(a556)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8449, 8447])).
% 2.00/2.17 tff(8451,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c1_1(a536)) | c2_1(a569) | c1_1(a569) | (~c3_1(a569)) | c2_1(a556) | (~c0_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8452,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a556) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a536)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c3_1(a569)) | (~c1_1(a556)) | (~c0_1(a556))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8451, 8450])).
% 2.00/2.17 tff(8453,plain,
% 2.00/2.17 (~c3_1(a569)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8452, 156, 8348, 3428, 3427, 3426, 8346, 8446, 8445, 707, 8372])).
% 2.00/2.17 tff(8454,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8455,plain,
% 2.00/2.17 (((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569)) <=> (c2_1(a556) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8456,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a556) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8455])).
% 2.00/2.17 tff(8457,plain,
% 2.00/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8456, 8454])).
% 2.00/2.17 tff(8458,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a556) | (~c3_1(a556)) | (~c1_1(a556)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a569) | c1_1(a569) | c3_1(a569))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8459,plain,
% 2.00/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a556) | c1_1(a537) | c1_1(a569) | c2_1(a569) | (~ndr1_0) | c3_1(a569) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a556)) | (~c1_1(a556))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8458, 8457])).
% 2.00/2.17 tff(8460,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8459, 156, 8348, 8347, 4779, 8346, 4778, 8446, 8445, 45, 8453, 1])).
% 2.00/2.17 tff(8461,plain,(hskp46 | (~c1_1(a556)) | (~c3_1(a556)) | (~c3_1(a537)) | c2_1(a556) | c1_1(a537) | (~c2_1(a537)) | (~c1_1(a536)) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a548)) | (~c1_1(a548)) | (~c0_1(a548)) | (~c0_1(a537))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(8462,plain,
% 2.00/2.17 (hskp46),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8461, 8442, 8441, 8252, 8440, 8251, 8257, 7637, 7636, 7635, 8287, 8438, 8244, 8258])).
% 2.00/2.17 tff(8463,plain,
% 2.00/2.17 (~c0_1(a562)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[64, 8462])).
% 2.00/2.17 tff(8464,plain,
% 2.00/2.17 (~c3_1(a562)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[270, 8462])).
% 2.00/2.17 tff(8465,plain,
% 2.00/2.17 (c1_1(a562)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[288, 8462])).
% 2.00/2.17 tff(8466,plain,
% 2.00/2.17 (hskp39),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1419, 156, 8465, 8442, 8441, 8464, 8463, 8440, 281])).
% 2.00/2.17 tff(8467,plain,
% 2.00/2.17 (c1_1(a549)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[303, 8466])).
% 2.00/2.17 tff(8468,plain,
% 2.00/2.17 (c2_1(a549)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[311, 8466])).
% 2.00/2.17 tff(8469,plain,
% 2.00/2.17 (c3_1(a549)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[319, 8466])).
% 2.00/2.17 tff(8470,plain,
% 2.00/2.17 (hskp25),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[5026, 156, 8442, 8441, 8469, 8468, 8467, 8440, 55])).
% 2.00/2.17 tff(8471,plain,
% 2.00/2.17 (~c1_1(a582)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1190, 8470])).
% 2.00/2.17 tff(8472,plain,
% 2.00/2.17 (~c2_1(a582)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1196, 8470])).
% 2.00/2.17 tff(8473,plain,
% 2.00/2.17 (~c3_1(a582)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1202, 8470])).
% 2.00/2.17 tff(8474,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[2192, 156, 8442, 8441, 8252, 8440, 8251, 8473, 8472, 8471, 45, 8257])).
% 2.00/2.17 tff(8475,plain,(c2_1(a548)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(8476,plain,
% 2.00/2.17 (~hskp6),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[217, 8475])).
% 2.00/2.17 tff(8477,plain,
% 2.00/2.17 (hskp27 | hskp4),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[205, 8476])).
% 2.00/2.17 tff(8478,plain,
% 2.00/2.17 (hskp27),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8477, 23])).
% 2.00/2.17 tff(8479,plain,
% 2.00/2.17 (~c3_1(a586)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3996, 8478])).
% 2.00/2.17 tff(8480,plain,
% 2.00/2.17 (~c0_1(a586)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3924, 8478])).
% 2.00/2.17 tff(8481,plain,
% 2.00/2.17 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c0_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8482,plain,
% 2.00/2.17 ((hskp28 | (~ndr1_0) | c2_1(a537) | c0_1(a537) | c1_1(a537)) <=> (hskp28 | c0_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8483,plain,
% 2.00/2.17 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a537) | c0_1(a537) | c1_1(a537))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | c0_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537)))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8482])).
% 2.00/2.17 tff(8484,plain,
% 2.00/2.17 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a537) | c0_1(a537) | c1_1(a537))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8483, 8481])).
% 2.00/2.17 tff(8485,plain,
% 2.00/2.17 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | (hskp28 | (~ndr1_0) | c2_1(a537) | c0_1(a537) | c1_1(a537))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8486,plain,
% 2.00/2.17 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(U))) | hskp28 | c0_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537)),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8485, 8484])).
% 2.00/2.17 tff(8487,plain,
% 2.00/2.17 (hskp28 | c0_1(a537) | c2_1(a537)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8486, 156, 4778, 122])).
% 2.00/2.17 tff(8488,plain,
% 2.00/2.17 (hskp28),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8487, 7925, 4777])).
% 2.00/2.17 tff(8489,plain,
% 2.00/2.17 (c1_1(a586)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[95, 8478])).
% 2.00/2.17 tff(8490,plain,
% 2.00/2.17 ($false),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[5066, 8479, 8480, 1661, 8489, 5060, 23])).
% 2.00/2.17 tff(8491,plain,(hskp4 | hskp26 | (~hskp28)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.17 tff(8492,plain,
% 2.00/2.17 (hskp4),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8491, 1661, 8488])).
% 2.00/2.17 tff(8493,plain,
% 2.00/2.17 (~c0_1(a545)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1666, 8492])).
% 2.00/2.17 tff(8494,plain,
% 2.00/2.17 (~c2_1(a545)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[1643, 8492])).
% 2.00/2.17 tff(8495,plain,
% 2.00/2.17 (~c0_1(a589)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[177, 8488])).
% 2.00/2.17 tff(8496,plain,
% 2.00/2.17 (c3_1(a589)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[185, 8488])).
% 2.00/2.17 tff(8497,plain,
% 2.00/2.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a537) | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a537) | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8498,plain,
% 2.00/2.17 ((hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c0_1(a537)) <=> (hskp6 | c0_1(a537) | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8499,plain,
% 2.00/2.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | c0_1(a537) | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537)))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8498])).
% 2.00/2.17 tff(8500,plain,
% 2.00/2.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a537) | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8499, 8497])).
% 2.00/2.17 tff(8501,plain,
% 2.00/2.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a589) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c0_1(a537))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8502,plain,
% 2.00/2.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp6 | c0_1(a537) | c1_1(a537) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537)),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8501, 8500])).
% 2.00/2.17 tff(8503,plain,
% 2.00/2.17 (~c1_1(a589)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8502, 156, 8476, 7925, 8496, 4778, 8495, 1745, 4777])).
% 2.00/2.17 tff(8504,plain,
% 2.00/2.17 (hskp34 | (~hskp33)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8249, 8476])).
% 2.00/2.17 tff(8505,plain,
% 2.00/2.17 (~hskp33),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8504, 7861])).
% 2.00/2.17 tff(8506,plain,
% 2.00/2.17 (~hskp4),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[6209, 794, 8505])).
% 2.00/2.17 tff(8507,plain,
% 2.00/2.17 (hskp27),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8477, 8506])).
% 2.00/2.17 tff(8508,plain,
% 2.00/2.17 (c1_1(a586)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[95, 8507])).
% 2.00/2.17 tff(8509,plain,
% 2.00/2.17 (~c0_1(a586)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3924, 8507])).
% 2.00/2.17 tff(8510,plain,
% 2.00/2.17 (~c3_1(a586)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3996, 8507])).
% 2.00/2.17 tff(8511,plain,
% 2.00/2.17 (c2_1(a586)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[2766, 8509, 8505, 794, 8510])).
% 2.00/2.17 tff(8512,plain,
% 2.00/2.17 (~hskp16),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[2365, 8510, 946, 8511, 8509])).
% 2.00/2.17 tff(8513,plain,
% 2.00/2.17 (~hskp39),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[5127, 8509, 8506, 8508, 8510])).
% 2.00/2.17 tff(8514,plain,
% 2.00/2.17 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8515,plain,
% 2.00/2.17 ((hskp39 | hskp24 | (~ndr1_0) | c2_1(a537) | c3_1(a537) | (~c0_1(a537))) <=> (hskp39 | hskp24 | c3_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))),
% 2.00/2.17 inference(rewrite,[status(thm)],[])).
% 2.00/2.17 tff(8516,plain,
% 2.00/2.17 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a537) | c3_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537))))),
% 2.00/2.17 inference(monotonicity,[status(thm)],[8515])).
% 2.00/2.17 tff(8517,plain,
% 2.00/2.17 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a537) | c3_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)))),
% 2.00/2.17 inference(transitivity,[status(thm)],[8516, 8514])).
% 2.00/2.17 tff(8518,plain,
% 2.00/2.17 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a537) | c3_1(a537) | (~c0_1(a537)))),
% 2.00/2.17 inference(quant_inst,[status(thm)],[])).
% 2.00/2.17 tff(8519,plain,
% 2.00/2.17 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537))),
% 2.00/2.17 inference(modus_ponens,[status(thm)],[8518, 8517])).
% 2.00/2.17 tff(8520,plain,
% 2.00/2.17 (hskp39 | hskp24 | c3_1(a537) | (~c0_1(a537))),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8519, 156, 3496, 4777])).
% 2.00/2.17 tff(8521,plain,
% 2.00/2.17 (hskp24),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[8520, 8513, 4780, 7860])).
% 2.00/2.17 tff(8522,plain,
% 2.00/2.17 (~c3_1(a581)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3513, 8521])).
% 2.00/2.17 tff(8523,plain,
% 2.00/2.17 (~c1_1(a581)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3519, 8521])).
% 2.00/2.17 tff(8524,plain,
% 2.00/2.17 (c2_1(a581)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[3541, 8521])).
% 2.00/2.17 tff(8525,plain,
% 2.00/2.17 (~hskp17),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[5411, 8524, 8510, 8508, 8509, 8513, 8523, 8522])).
% 2.00/2.17 tff(8526,plain,
% 2.00/2.17 (hskp18),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[382, 8525, 8512])).
% 2.00/2.17 tff(8527,plain,
% 2.00/2.17 (~c1_1(a572)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[389, 8526])).
% 2.00/2.17 tff(8528,plain,
% 2.00/2.17 (~hskp35),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[5310, 8508, 8506, 8509, 8510])).
% 2.00/2.17 tff(8529,plain,
% 2.00/2.17 (c0_1(a572)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[397, 8526])).
% 2.00/2.17 tff(8530,plain,
% 2.00/2.17 (c2_1(a572)),
% 2.00/2.17 inference(unit_resolution,[status(thm)],[5426, 8529, 8528, 8511, 8510, 8527, 8508])).
% 2.00/2.18 tff(8531,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5478, 156, 946, 8508, 8529, 8509, 8527, 2215, 8511, 8530])).
% 2.00/2.18 tff(8532,plain,((~hskp50) | hskp46 | (~c0_1(a537)) | c3_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8533,plain,
% 2.00/2.18 (~hskp50),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8532, 946, 4780, 7860, 4777])).
% 2.00/2.18 tff(8534,plain,
% 2.00/2.18 (hskp19),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[7998, 8533, 4780, 4777])).
% 2.00/2.18 tff(8535,plain,
% 2.00/2.18 (hskp28),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5069, 8534])).
% 2.00/2.18 tff(8536,plain,
% 2.00/2.18 (~c1_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1675, 8534])).
% 2.00/2.18 tff(8537,plain,
% 2.00/2.18 (~c0_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1691, 8534])).
% 2.00/2.18 tff(8538,plain,
% 2.00/2.18 (~c2_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1704, 8534])).
% 2.00/2.18 tff(8539,plain,
% 2.00/2.18 (~c0_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[177, 8535])).
% 2.00/2.18 tff(8540,plain,
% 2.00/2.18 (c3_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[185, 8535])).
% 2.00/2.18 tff(8541,plain,
% 2.00/2.18 (~c1_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1751, 156, 8476, 8540, 8539, 8538, 8537, 8536, 1745])).
% 2.00/2.18 tff(8542,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a537))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8543,plain,
% 2.00/2.18 ((hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a537) | c1_1(a537) | c3_1(a537)) <=> (hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a537))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8544,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a537)))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8543])).
% 2.00/2.18 tff(8545,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a537))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8544, 8542])).
% 2.00/2.18 tff(8546,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a573) | c0_1(a573) | (~c3_1(a573)) | c2_1(a537) | c1_1(a537) | c3_1(a537))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8547,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a573) | c0_1(a573) | (~ndr1_0) | (~c3_1(a573)) | c2_1(a537)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8546, 8545])).
% 2.00/2.18 tff(8548,plain,
% 2.00/2.18 (hskp38 | (~c3_1(a573))),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8547, 156, 7860, 4778, 1719, 3143, 663, 4777])).
% 2.00/2.18 tff(8549,plain,
% 2.00/2.18 (~c3_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8548, 58])).
% 2.00/2.18 tff(8550,plain,
% 2.00/2.18 (c3_1(a545)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[2044, 1645, 591, 1716, 109, 1644, 625])).
% 2.00/2.18 tff(8551,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1211, 8550, 1645, 58, 1644, 1667])).
% 2.00/2.18 tff(8552,plain,((~hskp4) | hskp38 | (~c3_1(a589)) | c1_1(a589) | hskp15 | (~c2_1(a589))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8553,plain,
% 2.00/2.18 (~hskp4),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8552, 58, 5061, 1716, 109, 5062])).
% 2.00/2.18 tff(8554,plain,
% 2.00/2.18 (hskp27),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8477, 8553])).
% 2.00/2.18 tff(8555,plain,
% 2.00/2.18 (c1_1(a586)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[95, 8554])).
% 2.00/2.18 tff(8556,plain,
% 2.00/2.18 (~hskp16),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[6667, 58, 946, 5062, 5061, 1716])).
% 2.00/2.18 tff(8557,plain,
% 2.00/2.18 (~hskp39),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[2535, 58, 5061, 1716, 5062])).
% 2.00/2.18 tff(8558,plain,
% 2.00/2.18 (hskp26),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8491, 8553, 5060])).
% 2.00/2.18 tff(8559,plain,
% 2.00/2.18 (hskp24),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[7687, 8558, 8557])).
% 2.00/2.18 tff(8560,plain,
% 2.00/2.18 (~c3_1(a581)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3513, 8559])).
% 2.00/2.18 tff(8561,plain,
% 2.00/2.18 (~c1_1(a581)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3519, 8559])).
% 2.00/2.18 tff(8562,plain,
% 2.00/2.18 (~c0_1(a586)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3924, 8554])).
% 2.00/2.18 tff(8563,plain,
% 2.00/2.18 (~c3_1(a586)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3996, 8554])).
% 2.00/2.18 tff(8564,plain,
% 2.00/2.18 (c2_1(a581)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3541, 8559])).
% 2.00/2.18 tff(8565,plain,
% 2.00/2.18 (~hskp17),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5411, 8564, 8563, 8555, 8562, 8557, 8561, 8560])).
% 2.00/2.18 tff(8566,plain,
% 2.00/2.18 (hskp18),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[382, 8565, 8556])).
% 2.00/2.18 tff(8567,plain,
% 2.00/2.18 (~c1_1(a572)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[389, 8566])).
% 2.00/2.18 tff(8568,plain,
% 2.00/2.18 (c2_1(a586)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3104, 8562, 35, 8563, 8558])).
% 2.00/2.18 tff(8569,plain,
% 2.00/2.18 (~hskp35),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5310, 8555, 8553, 8562, 8563])).
% 2.00/2.18 tff(8570,plain,
% 2.00/2.18 (c0_1(a572)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[397, 8566])).
% 2.00/2.18 tff(8571,plain,
% 2.00/2.18 (c2_1(a572)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5426, 8570, 8569, 8568, 8563, 8567, 8555])).
% 2.00/2.18 tff(8572,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5478, 156, 946, 8555, 8570, 8562, 8567, 2215, 8568, 8571])).
% 2.00/2.18 tff(8573,plain,(hskp38 | hskp46 | hskp33 | (~hskp28) | c1_1(a589) | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8574,plain,
% 2.00/2.18 (hskp15),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8573, 58, 8505, 946, 5060, 1716])).
% 2.00/2.18 tff(8575,plain,
% 2.00/2.18 (hskp4),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8491, 1661, 5060])).
% 2.00/2.18 tff(8576,plain,
% 2.00/2.18 (c1_1(a545)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[193, 8575])).
% 2.00/2.18 tff(8577,plain,
% 2.00/2.18 (~c0_1(a545)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1666, 8575])).
% 2.00/2.18 tff(8578,plain,
% 2.00/2.18 ((~hskp15) | hskp26 | (~c1_1(a545)) | c0_1(a545)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1971, 8476])).
% 2.00/2.18 tff(8579,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8578, 8577, 8576, 1250, 1661])).
% 2.00/2.18 tff(8580,plain,(hskp26 | (~hskp15) | (~hskp28)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8581,plain,
% 2.00/2.18 (hskp26),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8580, 8574, 5060])).
% 2.00/2.18 tff(8582,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3151, 8581, 8549, 8505, 1719, 3143])).
% 2.00/2.18 tff(8583,plain,(hskp38 | c2_1(a573) | c0_1(a573) | (~hskp28) | c3_1(a537) | c1_1(a537) | c2_1(a537) | hskp46 | c1_1(a589)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8584,plain,
% 2.00/2.18 (hskp38),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8583, 8538, 8537, 8535, 7860, 4778, 4777, 946, 8541])).
% 2.00/2.18 tff(8585,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8586,plain,
% 2.00/2.18 ((hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | c3_1(a537)) <=> (hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8587,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8586])).
% 2.00/2.18 tff(8588,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8587, 8585])).
% 2.00/2.18 tff(8589,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | c3_1(a537))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8590,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp0 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8589, 8588])).
% 2.00/2.18 tff(8591,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8590, 156, 837, 2771, 2770, 2769, 7860, 4778, 108, 4777])).
% 2.00/2.18 tff(8592,plain,((~hskp38) | hskp0 | c3_1(a537) | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8593,plain,
% 2.00/2.18 (hskp0),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8592, 8584, 7860, 4778, 4777])).
% 2.00/2.18 tff(8594,plain,
% 2.00/2.18 (~c2_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[713, 8593])).
% 2.00/2.18 tff(8595,plain,
% 2.00/2.18 (c0_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[721, 8593])).
% 2.00/2.18 tff(8596,plain,
% 2.00/2.18 (c1_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[729, 8593])).
% 2.00/2.18 tff(8597,plain,
% 2.00/2.18 (c0_1(a547)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[677, 8584])).
% 2.00/2.18 tff(8598,plain,
% 2.00/2.18 (c1_1(a547)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[685, 8584])).
% 2.00/2.18 tff(8599,plain,
% 2.00/2.18 (c2_1(a547)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[693, 8584])).
% 2.00/2.18 tff(8600,plain,
% 2.00/2.18 (~c3_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3125, 156, 8599, 8598, 8597, 8596, 8595, 8538, 8536, 8594, 707])).
% 2.00/2.18 tff(8601,plain,
% 2.00/2.18 (c2_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[171, 8535])).
% 2.00/2.18 tff(8602,plain,
% 2.00/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8603,plain,
% 2.00/2.18 (((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573)) <=> (c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8604,plain,
% 2.00/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8603])).
% 2.00/2.18 tff(8605,plain,
% 2.00/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8604, 8602])).
% 2.00/2.18 tff(8606,plain,
% 2.00/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a573) | c1_1(a573) | c3_1(a573))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8607,plain,
% 2.00/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a573) | c1_1(a573) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | c3_1(a573) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8606, 8605])).
% 2.00/2.18 tff(8608,plain,
% 2.00/2.18 (~c3_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8607, 156, 8601, 8540, 8596, 8538, 8536, 8594, 45, 8600, 8541])).
% 2.00/2.18 tff(8609,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a535) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a535) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8610,plain,
% 2.00/2.18 ((hskp15 | (~ndr1_0) | c2_1(a535) | c3_1(a535) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589))) <=> (hskp15 | c2_1(a535) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8611,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a535) | c3_1(a535) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a535) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8610])).
% 2.00/2.18 tff(8612,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a535) | c3_1(a535) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a535) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8611, 8609])).
% 2.00/2.18 tff(8613,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a535) | c3_1(a535) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8614,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a535) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8613, 8612])).
% 2.00/2.18 tff(8615,plain,
% 2.00/2.18 (hskp15),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8614, 156, 8601, 8540, 8596, 8594, 483, 8541, 8608])).
% 2.00/2.18 tff(8616,plain,
% 2.00/2.18 (~hskp26),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3151, 8600, 8505, 8538, 8537])).
% 2.00/2.18 tff(8617,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8580, 8616, 8615, 8535])).
% 2.00/2.18 tff(8618,plain,(hskp46 | c3_1(a537) | c1_1(a537) | c2_1(a537) | (~c0_1(a537))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8619,plain,
% 2.00/2.18 (hskp46),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8618, 4780, 4778, 4777, 7860])).
% 2.00/2.18 tff(8620,plain,
% 2.00/2.18 (c1_1(a562)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[288, 8619])).
% 2.00/2.18 tff(8621,plain,
% 2.00/2.18 (~c3_1(a562)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[270, 8619])).
% 2.00/2.18 tff(8622,plain,
% 2.00/2.18 (~c0_1(a562)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[64, 8619])).
% 2.00/2.18 tff(8623,plain,
% 2.00/2.18 (~hskp4),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[6209, 794, 35])).
% 2.00/2.18 tff(8624,plain,
% 2.00/2.18 (hskp27),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8477, 8623])).
% 2.00/2.18 tff(8625,plain,
% 2.00/2.18 (~c3_1(a586)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3996, 8624])).
% 2.00/2.18 tff(8626,plain,
% 2.00/2.18 (~c0_1(a586)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3924, 8624])).
% 2.00/2.18 tff(8627,plain,
% 2.00/2.18 (c1_1(a586)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[95, 8624])).
% 2.00/2.18 tff(8628,plain,
% 2.00/2.18 (~hskp35),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5310, 8627, 8623, 8626, 8625])).
% 2.00/2.18 tff(8629,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a562) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c2_1(a562)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a562) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c2_1(a562)) | (~c1_1(a562)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8630,plain,
% 2.00/2.18 ((hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a562) | (~c1_1(a562)) | (~c2_1(a562))) <=> (hskp35 | c3_1(a562) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c2_1(a562)) | (~c1_1(a562)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8631,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a562) | (~c1_1(a562)) | (~c2_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a562) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c2_1(a562)) | (~c1_1(a562))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8630])).
% 2.00/2.18 tff(8632,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a562) | (~c1_1(a562)) | (~c2_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a562) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c2_1(a562)) | (~c1_1(a562)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8631, 8629])).
% 2.00/2.18 tff(8633,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a562) | (~c1_1(a562)) | (~c2_1(a562)))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8634,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a562) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c2_1(a562)) | (~c1_1(a562))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8633, 8632])).
% 2.00/2.18 tff(8635,plain,
% 2.00/2.18 (hskp35 | (~c0_1(a537)) | (~c2_1(a562))),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8634, 156, 973, 972, 4778, 3950, 4777])).
% 2.00/2.18 tff(8636,plain,
% 2.00/2.18 (~c2_1(a562)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8635, 8628, 4780])).
% 2.00/2.18 tff(8637,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a562) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a562) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8638,plain,
% 2.00/2.18 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a562) | c3_1(a562) | c0_1(a562)) <=> (hskp33 | c3_1(a574) | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a562) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8639,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a562) | c3_1(a562) | c0_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a574) | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a562) | (~c0_1(a574)) | (~c1_1(a574))))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8638])).
% 2.00/2.18 tff(8640,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a562) | c3_1(a562) | c0_1(a562))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a562) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8639, 8637])).
% 2.00/2.18 tff(8641,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a562) | c3_1(a562) | c0_1(a562))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8642,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a574) | c3_1(a562) | c0_1(a562) | (~ndr1_0) | c2_1(a562) | (~c0_1(a574)) | (~c1_1(a574))),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8641, 8640])).
% 2.00/2.18 tff(8643,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8642, 156, 35, 816, 808, 800, 972, 971, 85, 8636])).
% 2.00/2.18 tff(8644,plain,((~hskp50) | hskp33 | c3_1(a562) | c0_1(a562) | (~c0_1(a537)) | (~c1_1(a562)) | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8645,plain,
% 2.00/2.18 (~hskp50),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8644, 8622, 8505, 8621, 4780, 8620, 4778, 4777])).
% 2.00/2.18 tff(8646,plain,
% 2.00/2.18 (hskp19),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[7998, 8645, 4780, 4777])).
% 2.00/2.18 tff(8647,plain,
% 2.00/2.18 (~c0_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1691, 8646])).
% 2.00/2.18 tff(8648,plain,
% 2.00/2.18 (~c2_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1704, 8646])).
% 2.00/2.18 tff(8649,plain,
% 2.00/2.18 (~c1_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1675, 8646])).
% 2.00/2.18 tff(8650,plain,
% 2.00/2.18 (hskp28),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[5069, 8646])).
% 2.00/2.18 tff(8651,plain,
% 2.00/2.18 (~c0_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[177, 8650])).
% 2.00/2.18 tff(8652,plain,
% 2.00/2.18 (c3_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[185, 8650])).
% 2.00/2.18 tff(8653,plain,
% 2.00/2.18 (~c1_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1751, 156, 8476, 8652, 8651, 8648, 8647, 8649, 1745])).
% 2.00/2.18 tff(8654,plain,
% 2.00/2.18 (hskp26),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[2437, 156, 8620, 8652, 8621, 8622, 8651, 1686, 8653])).
% 2.00/2.18 tff(8655,plain,
% 2.00/2.18 (c3_1(a573)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3151, 8654, 8505, 8648, 8647])).
% 2.00/2.18 tff(8656,plain,
% 2.00/2.18 (hskp38 | (~c3_1(a573))),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8547, 156, 7860, 4778, 8648, 8647, 663, 4777])).
% 2.00/2.18 tff(8657,plain,
% 2.00/2.18 (hskp38),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8656, 8655])).
% 2.00/2.18 tff(8658,plain,
% 2.00/2.18 (hskp0),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8592, 8657, 7860, 4778, 4777])).
% 2.00/2.18 tff(8659,plain,
% 2.00/2.18 (~c2_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[713, 8658])).
% 2.00/2.18 tff(8660,plain,
% 2.00/2.18 (c0_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[721, 8658])).
% 2.00/2.18 tff(8661,plain,
% 2.00/2.18 (c1_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[729, 8658])).
% 2.00/2.18 tff(8662,plain,
% 2.00/2.18 (c0_1(a547)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[677, 8657])).
% 2.00/2.18 tff(8663,plain,
% 2.00/2.18 (c1_1(a547)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[685, 8657])).
% 2.00/2.18 tff(8664,plain,
% 2.00/2.18 (c2_1(a547)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[693, 8657])).
% 2.00/2.18 tff(8665,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[3125, 156, 8664, 8663, 8662, 8661, 8660, 8648, 8649, 8659, 707, 8655])).
% 2.00/2.18 tff(8666,plain,((~c0_1(a537)) | c3_1(a537) | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8667,plain,
% 2.00/2.18 (~c0_1(a537)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8666, 7860, 4778, 4777])).
% 2.00/2.18 tff(8668,plain,
% 2.00/2.18 (hskp28),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8487, 8667, 4777])).
% 2.00/2.18 tff(8669,plain,
% 2.00/2.18 (~c0_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[177, 8668])).
% 2.00/2.18 tff(8670,plain,
% 2.00/2.18 (c3_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[185, 8668])).
% 2.00/2.18 tff(8671,plain,
% 2.00/2.18 (~c1_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8502, 156, 8476, 8667, 8670, 4778, 8669, 1745, 4777])).
% 2.00/2.18 tff(8672,plain,
% 2.00/2.18 (c2_1(a589)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[171, 8668])).
% 2.00/2.18 tff(8673,plain,
% 2.00/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a537) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a537))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a537) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a537))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8674,plain,
% 2.00/2.18 (((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537)) <=> (c3_1(a537) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a537))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8675,plain,
% 2.00/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a537) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a537)))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8674])).
% 2.00/2.18 tff(8676,plain,
% 2.00/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a537) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a537))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8675, 8673])).
% 2.00/2.18 tff(8677,plain,
% 2.00/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a535) | (~c3_1(a535)) | (~c1_1(a535)) | c1_1(a589) | (~c3_1(a589)) | (~c2_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8678,plain,
% 2.00/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a537) | c1_1(a537) | c2_1(a535) | (~ndr1_0) | (~c3_1(a535)) | (~c1_1(a535)) | (~c2_1(a589)) | (~c3_1(a589)) | c1_1(a589) | c2_1(a537)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8677, 8676])).
% 2.00/2.18 tff(8679,plain,
% 2.00/2.18 (~c3_1(a535)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8678, 156, 7860, 8672, 8670, 730, 4778, 714, 45, 8671, 4777])).
% 2.00/2.18 tff(8680,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a537))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8681,plain,
% 2.00/2.18 ((hskp33 | (~ndr1_0) | c3_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a537) | c3_1(a537) | c0_1(a537)) <=> (hskp33 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a537))),
% 2.00/2.18 inference(rewrite,[status(thm)],[])).
% 2.00/2.18 tff(8682,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a537) | c3_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a537)))),
% 2.00/2.18 inference(monotonicity,[status(thm)],[8681])).
% 2.00/2.18 tff(8683,plain,
% 2.00/2.18 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a537) | c3_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a537))),
% 2.00/2.18 inference(transitivity,[status(thm)],[8682, 8680])).
% 2.00/2.18 tff(8684,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a535) | (~c0_1(a535)) | (~c1_1(a535)) | c2_1(a537) | c3_1(a537) | c0_1(a537))),
% 2.00/2.18 inference(quant_inst,[status(thm)],[])).
% 2.00/2.18 tff(8685,plain,
% 2.00/2.18 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | c3_1(a535) | (~c1_1(a535)) | (~c0_1(a535)) | c2_1(a537)),
% 2.00/2.18 inference(modus_ponens,[status(thm)],[8684, 8683])).
% 2.00/2.18 tff(8686,plain,
% 2.00/2.18 ($false),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8685, 156, 8505, 8667, 7860, 730, 722, 85, 4777, 8679])).
% 2.00/2.18 tff(8687,plain,((~hskp0) | c3_1(a537) | c2_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.18 tff(8688,plain,
% 2.00/2.18 (~hskp0),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8687, 7860, 4777, 4778])).
% 2.00/2.18 tff(8689,plain,
% 2.00/2.18 (~hskp38),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8592, 8688, 7860, 4778, 4777])).
% 2.00/2.18 tff(8690,plain,
% 2.00/2.18 (hskp15),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[8573, 58, 8505, 946, 8668, 8671])).
% 2.00/2.18 tff(8691,plain,
% 2.00/2.18 (~c2_1(a569)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1255, 8690])).
% 2.00/2.18 tff(8692,plain,
% 2.00/2.18 (~c0_1(a569)),
% 2.00/2.18 inference(unit_resolution,[status(thm)],[1267, 8690])).
% 2.00/2.18 tff(8693,plain,
% 2.00/2.19 (hskp26),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8580, 8690, 8668])).
% 2.00/2.19 tff(8694,plain,
% 2.00/2.19 (~c3_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1620, 8693])).
% 2.00/2.19 tff(8695,plain,
% 2.00/2.19 (c1_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1637, 8693])).
% 2.00/2.19 tff(8696,plain,
% 2.00/2.19 (c0_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1629, 8693])).
% 2.00/2.19 tff(8697,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a569))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8698,plain,
% 2.00/2.19 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c3_1(a569) | c0_1(a569)) <=> (hskp33 | c3_1(a584) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a569))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8699,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a584) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a569)))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8698])).
% 2.00/2.19 tff(8700,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c3_1(a569) | c0_1(a569))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a569))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8699, 8697])).
% 2.00/2.19 tff(8701,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a569) | c3_1(a569) | c0_1(a569))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8702,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a584) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c3_1(a569)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8701, 8700])).
% 2.00/2.19 tff(8703,plain,
% 2.00/2.19 (c3_1(a569)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8702, 156, 8505, 8696, 8695, 8694, 8692, 8691, 85])).
% 2.00/2.19 tff(8704,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a537) | c1_1(a537) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8705,plain,
% 2.00/2.19 ((hskp38 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a537) | c1_1(a537) | c3_1(a537)) <=> (hskp38 | c3_1(a537) | c1_1(a537) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8706,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | c3_1(a537) | c1_1(a537) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c2_1(a537)))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8705])).
% 2.00/2.19 tff(8707,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c2_1(a537))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8706, 8704])).
% 2.00/2.19 tff(8708,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp38 | (~ndr1_0) | c2_1(a569) | c0_1(a569) | (~c3_1(a569)) | c2_1(a537) | c1_1(a537) | c3_1(a537))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8709,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp38 | c3_1(a537) | c1_1(a537) | c0_1(a569) | c2_1(a569) | (~ndr1_0) | (~c3_1(a569)) | c2_1(a537)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8708, 8707])).
% 2.00/2.19 tff(8710,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8709, 156, 58, 7860, 4778, 8692, 8691, 663, 8703, 4777])).
% 2.00/2.19 tff(8711,plain,(hskp38 | c3_1(a537) | c1_1(a537) | c2_1(a537) | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(8712,plain,
% 2.00/2.19 (hskp46),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8711, 8689, 4778, 4777, 7860])).
% 2.00/2.19 tff(8713,plain,
% 2.00/2.19 (~c0_1(a562)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[64, 8712])).
% 2.00/2.19 tff(8714,plain,
% 2.00/2.19 (c1_1(a562)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[288, 8712])).
% 2.00/2.19 tff(8715,plain,
% 2.00/2.19 (~c3_1(a562)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[270, 8712])).
% 2.00/2.19 tff(8716,plain,
% 2.00/2.19 (c2_1(a589)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[171, 8488])).
% 2.00/2.19 tff(8717,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8718,plain,
% 2.00/2.19 ((hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537)) <=> (hskp34 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8719,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537)))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8718])).
% 2.00/2.19 tff(8720,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8719, 8717])).
% 2.00/2.19 tff(8721,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a589)) | (~c2_1(a589)) | (~c1_1(a589)) | c2_1(a537) | c1_1(a537) | c3_1(a537))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8722,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a537) | c1_1(a537) | (~ndr1_0) | (~c2_1(a589)) | (~c3_1(a589)) | (~c1_1(a589)) | c2_1(a537)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8721, 8720])).
% 2.00/2.19 tff(8723,plain,
% 2.00/2.19 (~c1_1(a589)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8722, 156, 7861, 7860, 8716, 8496, 4778, 1112, 4777])).
% 2.00/2.19 tff(8724,plain,
% 2.00/2.19 (hskp26),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[2437, 156, 973, 8496, 972, 971, 8495, 1686, 8723])).
% 2.00/2.19 tff(8725,plain,
% 2.00/2.19 (~c3_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1620, 8724])).
% 2.00/2.19 tff(8726,plain,
% 2.00/2.19 (c1_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1637, 8724])).
% 2.00/2.19 tff(8727,plain,
% 2.00/2.19 (c0_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1629, 8724])).
% 2.00/2.19 tff(8728,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8729,plain,
% 2.00/2.19 ((hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c3_1(a537) | c0_1(a537)) <=> (hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8730,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c3_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537)))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8729])).
% 2.00/2.19 tff(8731,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c3_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8730, 8728])).
% 2.00/2.19 tff(8732,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a584) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c3_1(a537) | c0_1(a537))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8733,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a584) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8732, 8731])).
% 2.00/2.19 tff(8734,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8733, 156, 8505, 7925, 7860, 8727, 8726, 8725, 85, 4777])).
% 2.00/2.19 tff(8735,plain,(c0_1(a537) | c3_1(a537) | c2_1(a537) | (~c1_1(a562)) | c3_1(a562) | c0_1(a562) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(8736,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8735, 8715, 8714, 4777, 7860, 8667, 8713, 4778])).
% 2.00/2.19 tff(8737,plain,(c3_1(a537) | c2_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(8738,plain,
% 2.00/2.19 (c3_1(a537)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8737, 4777, 4778])).
% 2.00/2.19 tff(8739,plain,
% 2.00/2.19 (c1_1(a537) | (~c3_1(a537)) | c2_1(a537) | (~hskp33)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8256, 8476])).
% 2.00/2.19 tff(8740,plain,
% 2.00/2.19 (~hskp33),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8739, 8738, 4778, 4777])).
% 2.00/2.19 tff(8741,plain,
% 2.00/2.19 (hskp15),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8573, 58, 8740, 946, 8488, 8503])).
% 2.00/2.19 tff(8742,plain,
% 2.00/2.19 (~c1_1(a569)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1261, 8741])).
% 2.00/2.19 tff(8743,plain,
% 2.00/2.19 (~c0_1(a569)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1267, 8741])).
% 2.00/2.19 tff(8744,plain,
% 2.00/2.19 (~c2_1(a569)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1255, 8741])).
% 2.00/2.19 tff(8745,plain,
% 2.00/2.19 (hskp26),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8580, 8741, 8488])).
% 2.00/2.19 tff(8746,plain,
% 2.00/2.19 (~c3_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1620, 8745])).
% 2.00/2.19 tff(8747,plain,
% 2.00/2.19 (c1_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1637, 8745])).
% 2.00/2.19 tff(8748,plain,
% 2.00/2.19 (c0_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1629, 8745])).
% 2.00/2.19 tff(8749,plain,
% 2.00/2.19 (c3_1(a569)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8702, 156, 8740, 8748, 8747, 8746, 8743, 8744, 85])).
% 2.00/2.19 tff(8750,plain,
% 2.00/2.19 (c0_1(a544)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[4555, 2503, 2824, 2502, 2504, 2785, 2775, 8740])).
% 2.00/2.19 tff(8751,plain,
% 2.00/2.19 (~hskp30),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[4719, 8750, 946, 2504, 2502, 8740])).
% 2.00/2.19 tff(8752,plain,
% 2.00/2.19 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp30 | hskp29 | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8753,plain,
% 2.00/2.19 ((hskp30 | hskp29 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537))) <=> (hskp30 | hskp29 | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8754,plain,
% 2.00/2.19 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537)))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8753])).
% 2.00/2.19 tff(8755,plain,
% 2.00/2.19 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp30 | hskp29 | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8754, 8752])).
% 2.00/2.19 tff(8756,plain,
% 2.00/2.19 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8757,plain,
% 2.00/2.19 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp30 | hskp29 | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | c2_1(a537)),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8756, 8755])).
% 2.00/2.19 tff(8758,plain,
% 2.00/2.19 (hskp30 | hskp29 | (~c3_1(a537)) | c2_1(a537)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8757, 156, 4778, 4613])).
% 2.00/2.19 tff(8759,plain,
% 2.00/2.19 (hskp29),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8758, 8751, 8738, 4777])).
% 2.00/2.19 tff(8760,plain,
% 2.00/2.19 (~c0_1(a590)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[4580, 8759])).
% 2.00/2.19 tff(8761,plain,
% 2.00/2.19 (~c3_1(a590)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[4586, 8759])).
% 2.00/2.19 tff(8762,plain,
% 2.00/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c2_1(a544) | c1_1(a537) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c2_1(a544) | c1_1(a537) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8763,plain,
% 2.00/2.19 (((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544))) <=> (c0_1(a537) | c2_1(a544) | c1_1(a537) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8764,plain,
% 2.00/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c2_1(a544) | c1_1(a537) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a544)) | (~c1_1(a544))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8763])).
% 2.00/2.19 tff(8765,plain,
% 2.00/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c2_1(a544) | c1_1(a537) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a544)) | (~c1_1(a544)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8764, 8762])).
% 2.00/2.19 tff(8766,plain,
% 2.00/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a544) | (~c0_1(a544)) | (~c1_1(a544)))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8767,plain,
% 2.00/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c2_1(a544) | c1_1(a537) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a537)) | (~c0_1(a544)) | (~c1_1(a544))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8766, 8765])).
% 2.00/2.19 tff(8768,plain,
% 2.00/2.19 (~c2_1(a590)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8767, 156, 2504, 7925, 8738, 2503, 4778, 8761, 8760, 609, 8750])).
% 2.00/2.19 tff(8769,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[4600, 156, 8740, 2504, 2502, 8761, 8760, 85, 8750, 8768])).
% 2.00/2.19 tff(8770,plain,((~hskp37) | c0_1(a537) | c1_1(a537) | c2_1(a537) | hskp46 | (~c3_1(a569)) | c0_1(a569) | c1_1(a569)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(8771,plain,
% 2.00/2.19 (~hskp37),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8770, 8749, 4778, 4777, 946, 7925, 8743, 8742])).
% 2.00/2.19 tff(8772,plain,
% 2.00/2.19 (~hskp39),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[2535, 58, 8503, 8496, 8716])).
% 2.00/2.19 tff(8773,plain,
% 2.00/2.19 (hskp24),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[7687, 8745, 8772])).
% 2.00/2.19 tff(8774,plain,
% 2.00/2.19 (~c3_1(a581)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[3513, 8773])).
% 2.00/2.19 tff(8775,plain,
% 2.00/2.19 (~c1_1(a581)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[3519, 8773])).
% 2.00/2.19 tff(8776,plain,
% 2.00/2.19 (c2_1(a581)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[3541, 8773])).
% 2.00/2.19 tff(8777,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8778,plain,
% 2.00/2.19 ((hskp37 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c1_1(a581) | c3_1(a581) | (~c0_1(a581))) <=> (hskp37 | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8779,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c1_1(a581) | c3_1(a581) | (~c0_1(a581)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8778])).
% 2.00/2.19 tff(8780,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c1_1(a581) | c3_1(a581) | (~c0_1(a581)))) <=> ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8779, 8777])).
% 2.00/2.19 tff(8781,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp37 | (~ndr1_0) | c1_1(a581) | (~c2_1(a581)) | (~c0_1(a581)) | c1_1(a581) | c3_1(a581) | (~c0_1(a581)))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8782,plain,
% 2.00/2.19 ((~![V: $i, U: $i] : (hskp37 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp37 | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c0_1(a581)) | (~c2_1(a581))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8781, 8780])).
% 2.00/2.19 tff(8783,plain,
% 2.00/2.19 (hskp37 | (~c0_1(a581))),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8782, 156, 8776, 8775, 8774, 415])).
% 2.00/2.19 tff(8784,plain,
% 2.00/2.19 (~c0_1(a581)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8783, 8771])).
% 2.00/2.19 tff(8785,plain,
% 2.00/2.19 (~c2_1(a584)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8181, 8749, 8746, 8742, 8744, 8747, 8716, 8496, 8495, 8748])).
% 2.00/2.19 tff(8786,plain,
% 2.00/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c1_1(a537) | c3_1(a581) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | c0_1(a581) | (~c2_1(a581)) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c1_1(a537) | c3_1(a581) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | c0_1(a581) | (~c2_1(a581)) | (~c3_1(a537)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8787,plain,
% 2.00/2.19 (((~ndr1_0) | c0_1(a581) | c3_1(a581) | (~c2_1(a581)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584))) <=> (c0_1(a537) | c1_1(a537) | c3_1(a581) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | c0_1(a581) | (~c2_1(a581)) | (~c3_1(a537)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8788,plain,
% 2.00/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a581) | c3_1(a581) | (~c2_1(a581)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c1_1(a537) | c3_1(a581) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | c0_1(a581) | (~c2_1(a581)) | (~c3_1(a537))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8787])).
% 2.00/2.19 tff(8789,plain,
% 2.00/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a581) | c3_1(a581) | (~c2_1(a581)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c1_1(a537) | c3_1(a581) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | c0_1(a581) | (~c2_1(a581)) | (~c3_1(a537)))),
% 2.00/2.19 inference(transitivity,[status(thm)],[8788, 8786])).
% 2.00/2.19 tff(8790,plain,
% 2.00/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a581) | c3_1(a581) | (~c2_1(a581)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))),
% 2.00/2.19 inference(quant_inst,[status(thm)],[])).
% 2.00/2.19 tff(8791,plain,
% 2.00/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c1_1(a537) | c3_1(a581) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | c0_1(a581) | (~c2_1(a581)) | (~c3_1(a537))),
% 2.00/2.19 inference(modus_ponens,[status(thm)],[8790, 8789])).
% 2.00/2.19 tff(8792,plain,
% 2.00/2.19 ($false),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8791, 156, 7925, 8738, 8748, 8747, 8776, 4778, 8774, 609, 8785, 8784])).
% 2.00/2.19 tff(8793,plain,(hskp38 | c0_1(a537) | c1_1(a537) | c2_1(a537) | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.19 tff(8794,plain,
% 2.00/2.19 (hskp38),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8793, 7925, 4778, 4777, 946])).
% 2.00/2.19 tff(8795,plain,
% 2.00/2.19 (c1_1(a547)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[685, 8794])).
% 2.00/2.19 tff(8796,plain,
% 2.00/2.19 (c0_1(a547)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[677, 8794])).
% 2.00/2.19 tff(8797,plain,
% 2.00/2.19 (c2_1(a547)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[693, 8794])).
% 2.00/2.19 tff(8798,plain,
% 2.00/2.19 (c1_1(a545)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[193, 8492])).
% 2.00/2.19 tff(8799,plain,
% 2.00/2.19 (~hskp15),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8580, 1661, 8488])).
% 2.00/2.19 tff(8800,plain,
% 2.00/2.19 (c3_1(a545)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[2044, 8799, 8496, 8503, 8798, 8494, 8716])).
% 2.00/2.19 tff(8801,plain,
% 2.00/2.19 (hskp39),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[1586, 8800, 8798, 8797, 8796, 8795, 8494, 8493])).
% 2.00/2.19 tff(8802,plain,
% 2.00/2.19 (c1_1(a549)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[303, 8801])).
% 2.00/2.19 tff(8803,plain,
% 2.00/2.19 (~hskp30),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[7966, 1661, 8738, 7925, 4778, 946])).
% 2.00/2.19 tff(8804,plain,
% 2.00/2.19 (hskp29),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[8758, 8803, 8738, 4777])).
% 2.00/2.19 tff(8805,plain,
% 2.00/2.19 (c3_1(a549)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[319, 8801])).
% 2.00/2.19 tff(8806,plain,
% 2.00/2.19 (c2_1(a549)),
% 2.00/2.19 inference(unit_resolution,[status(thm)],[311, 8801])).
% 2.00/2.19 tff(8807,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a590)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8808,plain,
% 2.00/2.19 ((hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a590)))),
% 2.00/2.19 inference(rewrite,[status(thm)],[])).
% 2.00/2.19 tff(8809,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a590))))),
% 2.00/2.19 inference(monotonicity,[status(thm)],[8808])).
% 2.00/2.19 tff(8810,plain,
% 2.00/2.19 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a590)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8809, 8807])).
% 2.00/2.20 tff(8811,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8812,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a590))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8811, 8810])).
% 2.00/2.20 tff(8813,plain,
% 2.00/2.20 (~c2_1(a590)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8812, 156, 946, 1498, 1497, 1496, 4587, 4581, 858])).
% 2.00/2.20 tff(8814,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a590))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8815,plain,
% 2.00/2.20 ((hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a590) | c1_1(a590) | c3_1(a590)) <=> (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a590))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8816,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a590)))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8815])).
% 2.00/2.20 tff(8817,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a590) | c1_1(a590) | c3_1(a590))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a590))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8816, 8814])).
% 2.00/2.20 tff(8818,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp34 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c2_1(a590) | c1_1(a590) | c3_1(a590))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8819,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp34 | c3_1(a590) | c1_1(a590) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | c2_1(a590)),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8818, 8817])).
% 2.00/2.20 tff(8820,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8819, 156, 3650, 1498, 1497, 1496, 4587, 6707, 1112, 8813])).
% 2.00/2.20 tff(8821,plain,((~hskp29) | hskp34 | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8822,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8821, 8806, 8805, 7957, 8804, 8802, 946])).
% 2.00/2.20 tff(8823,plain,(hskp26 | hskp46 | c2_1(a537) | c1_1(a537) | c0_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8824,plain,
% 2.00/2.20 (hskp26),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8823, 7925, 4777, 4778, 946])).
% 2.00/2.20 tff(8825,plain,
% 2.00/2.20 (~c3_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1620, 8824])).
% 2.00/2.20 tff(8826,plain,
% 2.00/2.20 (c1_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1637, 8824])).
% 2.00/2.20 tff(8827,plain,
% 2.00/2.20 (c0_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1629, 8824])).
% 2.00/2.20 tff(8828,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a564)) | (~c0_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a564)) | (~c0_1(a564)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8829,plain,
% 2.00/2.20 (((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564))) <=> (c2_1(a564) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a564)) | (~c0_1(a564)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8830,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a564) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a564)) | (~c0_1(a564))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8829])).
% 2.00/2.20 tff(8831,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a564)) | (~c0_1(a564)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8830, 8828])).
% 2.00/2.20 tff(8832,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8833,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a564) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | (~c2_1(a584)) | (~c3_1(a537)) | c2_1(a537) | (~c1_1(a564)) | (~c0_1(a564))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8832, 8831])).
% 2.00/2.20 tff(8834,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8833, 156, 8173, 8172, 8738, 1649, 1648, 8171, 4778, 707, 4777, 8162])).
% 2.00/2.20 tff(8835,plain,((~c2_1(a584)) | (~c0_1(a584)) | (~c1_1(a584)) | c1_1(a537) | c2_1(a537) | (~c2_1(a589)) | (~c3_1(a589)) | c0_1(a589) | c3_1(a584)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8836,plain,
% 2.00/2.20 (~c2_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8835, 8827, 8826, 4778, 4777, 8716, 8496, 8495, 8825])).
% 2.00/2.20 tff(8837,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8838,plain,
% 2.00/2.20 (((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584))) <=> (c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8839,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8838])).
% 2.00/2.20 tff(8840,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8839, 8837])).
% 2.00/2.20 tff(8841,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c2_1(a537) | c1_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8842,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | c2_1(a537) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8841, 8840])).
% 2.00/2.20 tff(8843,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8842, 156, 8797, 8795, 8796, 8738, 8827, 8826, 4778, 707, 4777, 8836])).
% 2.00/2.20 tff(8844,plain,(c0_1(a537) | c1_1(a537) | c2_1(a537) | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8845,plain,
% 2.00/2.20 (c0_1(a537)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8844, 946, 4777, 4778])).
% 2.00/2.20 tff(8846,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a537) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8847,plain,
% 2.00/2.20 (((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537))) <=> (c1_1(a537) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8848,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c1_1(a537) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8847])).
% 2.00/2.20 tff(8849,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8848, 8846])).
% 2.00/2.20 tff(8850,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a581) | c3_1(a581) | (~c2_1(a581)) | (~c0_1(a537)) | c1_1(a537) | (~c3_1(a537)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8851,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c1_1(a537) | c1_1(a581) | c3_1(a581) | (~ndr1_0) | (~c2_1(a581)) | (~c3_1(a537)) | c2_1(a537) | (~c0_1(a537))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8850, 8849])).
% 2.00/2.20 tff(8852,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8851, 156, 4780, 4779, 6643, 4778, 6642, 6644, 921, 4777])).
% 2.00/2.20 tff(8853,plain,((~hskp24) | (~c0_1(a537)) | (~c3_1(a537)) | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8854,plain,
% 2.00/2.20 (~hskp24),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8853, 4780, 4777, 4778, 8738])).
% 2.00/2.20 tff(8855,plain,
% 2.00/2.20 (~hskp4),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[6209, 794, 8740])).
% 2.00/2.20 tff(8856,plain,
% 2.00/2.20 (hskp27),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8477, 8855])).
% 2.00/2.20 tff(8857,plain,
% 2.00/2.20 (~c3_1(a586)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[3996, 8856])).
% 2.00/2.20 tff(8858,plain,
% 2.00/2.20 (c1_1(a586)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[95, 8856])).
% 2.00/2.20 tff(8859,plain,
% 2.00/2.20 (~c0_1(a586)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[3924, 8856])).
% 2.00/2.20 tff(8860,plain,
% 2.00/2.20 (~hskp39),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[5127, 8859, 8855, 8858, 8857])).
% 2.00/2.20 tff(8861,plain,
% 2.00/2.20 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | c2_1(a574))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | c2_1(a574))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8862,plain,
% 2.00/2.20 ((hskp39 | hskp24 | (~ndr1_0) | c2_1(a574) | c3_1(a574) | (~c0_1(a574))) <=> (hskp39 | hskp24 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | c2_1(a574))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8863,plain,
% 2.00/2.20 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a574) | c3_1(a574) | (~c0_1(a574)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | c2_1(a574)))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8862])).
% 2.00/2.20 tff(8864,plain,
% 2.00/2.20 (((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a574) | c3_1(a574) | (~c0_1(a574)))) <=> ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | c2_1(a574))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8863, 8861])).
% 2.00/2.20 tff(8865,plain,
% 2.00/2.20 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp39 | hskp24 | (~ndr1_0) | c2_1(a574) | c3_1(a574) | (~c0_1(a574)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8866,plain,
% 2.00/2.20 ((~![U: $i] : (hskp39 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp39 | hskp24 | c3_1(a574) | (~ndr1_0) | (~c0_1(a574)) | c2_1(a574)),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8865, 8864])).
% 2.00/2.20 tff(8867,plain,
% 2.00/2.20 (c2_1(a574)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8866, 156, 8860, 8854, 816, 800, 3496])).
% 2.00/2.20 tff(8868,plain,
% 2.00/2.20 (~hskp35),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[5310, 8858, 8855, 8859, 8857])).
% 2.00/2.20 tff(8869,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a574) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a574) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8870,plain,
% 2.00/2.20 ((hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574))) <=> (hskp35 | c3_1(a574) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8871,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a574) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a574)) | (~c2_1(a574))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8870])).
% 2.00/2.20 tff(8872,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a574) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a574)) | (~c2_1(a574)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8871, 8869])).
% 2.00/2.20 tff(8873,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a537) | c1_1(a537) | (~c0_1(a537)) | c3_1(a574) | (~c1_1(a574)) | (~c2_1(a574)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8874,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a574) | c1_1(a537) | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a574)) | (~c2_1(a574))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8873, 8872])).
% 2.00/2.20 tff(8875,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8874, 156, 8868, 808, 4780, 800, 4778, 3950, 4777, 8867])).
% 2.00/2.20 tff(8876,plain,((~hskp50) | (~c0_1(a537)) | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8877,plain,
% 2.00/2.20 (~hskp50),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8876, 8845, 4778, 4777])).
% 2.00/2.20 tff(8878,plain,
% 2.00/2.20 (hskp19),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7998, 8877, 8845, 4777])).
% 2.00/2.20 tff(8879,plain,
% 2.00/2.20 (~c1_1(a573)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1675, 8878])).
% 2.00/2.20 tff(8880,plain,
% 2.00/2.20 (~c0_1(a573)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1691, 8878])).
% 2.00/2.20 tff(8881,plain,
% 2.00/2.20 (~c2_1(a573)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1704, 8878])).
% 2.00/2.20 tff(8882,plain,
% 2.00/2.20 (hskp28),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[5069, 8878])).
% 2.00/2.20 tff(8883,plain,
% 2.00/2.20 (~c0_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[177, 8882])).
% 2.00/2.20 tff(8884,plain,
% 2.00/2.20 (c3_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[185, 8882])).
% 2.00/2.20 tff(8885,plain,
% 2.00/2.20 (~c1_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1751, 156, 8476, 8884, 8883, 8881, 8880, 8879, 1745])).
% 2.00/2.20 tff(8886,plain,
% 2.00/2.20 (c2_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[171, 8882])).
% 2.00/2.20 tff(8887,plain,
% 2.00/2.20 (hskp8),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7536, 8885, 8738, 8845, 8886, 4778, 8883])).
% 2.00/2.20 tff(8888,plain,
% 2.00/2.20 (~c2_1(a552)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2424, 8887])).
% 2.00/2.20 tff(8889,plain,
% 2.00/2.20 (~c1_1(a552)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2453, 8887])).
% 2.00/2.20 tff(8890,plain,
% 2.00/2.20 (~c3_1(a552)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2430, 8887])).
% 2.00/2.20 tff(8891,plain,
% 2.00/2.20 (hskp51),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[6599, 8887, 8845, 8738, 4778])).
% 2.00/2.20 tff(8892,plain,
% 2.00/2.20 (~c2_1(a583)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2637, 8891])).
% 2.00/2.20 tff(8893,plain,
% 2.00/2.20 (c3_1(a583)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2645, 8891])).
% 2.00/2.20 tff(8894,plain,
% 2.00/2.20 (~c1_1(a583)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[3471, 156, 8893, 8886, 8884, 8892, 8890, 8889, 8888, 45, 8885])).
% 2.00/2.20 tff(8895,plain,
% 2.00/2.20 (~hskp24),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8853, 8845, 4777, 4778, 8738])).
% 2.00/2.20 tff(8896,plain,
% 2.00/2.20 (hskp15),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8573, 58, 35, 946, 5060, 1716])).
% 2.00/2.20 tff(8897,plain,
% 2.00/2.20 (~hskp39),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2535, 58, 1716, 5061, 5062])).
% 2.00/2.20 tff(8898,plain,
% 2.00/2.20 (~hskp26),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7687, 8897, 6468])).
% 2.00/2.20 tff(8899,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8580, 8898, 8896, 5060])).
% 2.00/2.20 tff(8900,plain,(hskp38 | (~hskp28) | hskp24 | hskp33 | hskp46 | c1_1(a589)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8901,plain,
% 2.00/2.20 (hskp38),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8900, 8882, 8895, 8740, 946, 8885])).
% 2.00/2.20 tff(8902,plain,
% 2.00/2.20 (c0_1(a547)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[677, 8901])).
% 2.00/2.20 tff(8903,plain,
% 2.00/2.20 (c1_1(a547)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[685, 8901])).
% 2.00/2.20 tff(8904,plain,
% 2.00/2.20 (c2_1(a547)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[693, 8901])).
% 2.00/2.20 tff(8905,plain,
% 2.00/2.20 (hskp0),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7358, 8904, 8887, 8903, 8902])).
% 2.00/2.20 tff(8906,plain,
% 2.00/2.20 (~c2_1(a535)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[713, 8905])).
% 2.00/2.20 tff(8907,plain,
% 2.00/2.20 (c0_1(a535)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[721, 8905])).
% 2.00/2.20 tff(8908,plain,
% 2.00/2.20 (c1_1(a535)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[729, 8905])).
% 2.00/2.20 tff(8909,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[3580, 156, 8893, 8904, 8903, 8902, 8908, 8907, 8892, 8906, 707, 8894])).
% 2.00/2.20 tff(8910,plain,(hskp46 | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8911,plain,
% 2.00/2.20 (hskp46),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8910, 4777, 4778])).
% 2.00/2.20 tff(8912,plain,
% 2.00/2.20 (~c0_1(a562)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[64, 8911])).
% 2.00/2.20 tff(8913,plain,
% 2.00/2.20 (~c3_1(a562)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[270, 8911])).
% 2.00/2.20 tff(8914,plain,
% 2.00/2.20 (c1_1(a562)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[288, 8911])).
% 2.00/2.20 tff(8915,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c1_1(a562)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8916,plain,
% 2.00/2.20 ((hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537))) <=> (hskp26 | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c1_1(a562)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8917,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c1_1(a562))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8916])).
% 2.00/2.20 tff(8918,plain,
% 2.00/2.20 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c1_1(a562)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8917, 8915])).
% 2.00/2.20 tff(8919,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c1_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8920,plain,
% 2.00/2.20 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c3_1(a537)) | (~c1_1(a562))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8919, 8918])).
% 2.00/2.20 tff(8921,plain,
% 2.00/2.20 (hskp26 | c0_1(a537)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8920, 156, 8914, 8738, 8913, 8912, 4778, 1686])).
% 2.00/2.20 tff(8922,plain,
% 2.00/2.20 (hskp26),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8921, 7925])).
% 2.00/2.20 tff(8923,plain,
% 2.00/2.20 (~c3_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1620, 8922])).
% 2.00/2.20 tff(8924,plain,
% 2.00/2.20 (c1_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1637, 8922])).
% 2.00/2.20 tff(8925,plain,
% 2.00/2.20 (c0_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1629, 8922])).
% 2.00/2.20 tff(8926,plain,
% 2.00/2.20 (~c2_1(a584)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8835, 8925, 8924, 4778, 4777, 8716, 8496, 8495, 8923])).
% 2.00/2.20 tff(8927,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | (~c2_1(a562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | (~c2_1(a562)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8928,plain,
% 2.00/2.20 (((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584))) <=> (c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | (~c2_1(a562)))),
% 2.00/2.20 inference(rewrite,[status(thm)],[])).
% 2.00/2.20 tff(8929,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | (~c2_1(a562))))),
% 2.00/2.20 inference(monotonicity,[status(thm)],[8928])).
% 2.00/2.20 tff(8930,plain,
% 2.00/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | (~c2_1(a562)))),
% 2.00/2.20 inference(transitivity,[status(thm)],[8929, 8927])).
% 2.00/2.20 tff(8931,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a562) | c3_1(a562) | (~c2_1(a562)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))),
% 2.00/2.20 inference(quant_inst,[status(thm)],[])).
% 2.00/2.20 tff(8932,plain,
% 2.00/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a562) | c0_1(a562) | c1_1(a537) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a537)) | (~c2_1(a562))),
% 2.00/2.20 inference(modus_ponens,[status(thm)],[8931, 8930])).
% 2.00/2.20 tff(8933,plain,
% 2.00/2.20 (~c2_1(a562)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8932, 156, 7925, 8738, 8925, 8924, 8913, 8912, 4778, 609, 8926])).
% 2.00/2.20 tff(8934,plain,
% 2.00/2.20 ($false),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[6266, 156, 8740, 8925, 8924, 8913, 8912, 8923, 85, 8933])).
% 2.00/2.20 tff(8935,plain,(c0_1(a537) | c1_1(a537) | c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.20 tff(8936,plain,
% 2.00/2.20 (c0_1(a537)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8935, 4777, 4778])).
% 2.00/2.20 tff(8937,plain,
% 2.00/2.20 (~hskp50),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8876, 8936, 4778, 4777])).
% 2.00/2.20 tff(8938,plain,
% 2.00/2.20 (hskp19),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7998, 8937, 8936, 4777])).
% 2.00/2.20 tff(8939,plain,
% 2.00/2.20 (~c1_1(a573)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1675, 8938])).
% 2.00/2.20 tff(8940,plain,
% 2.00/2.20 (~c0_1(a573)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1691, 8938])).
% 2.00/2.20 tff(8941,plain,
% 2.00/2.20 (~c2_1(a573)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1704, 8938])).
% 2.00/2.20 tff(8942,plain,
% 2.00/2.20 (hskp28),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[5069, 8938])).
% 2.00/2.20 tff(8943,plain,
% 2.00/2.20 (~c0_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[177, 8942])).
% 2.00/2.20 tff(8944,plain,
% 2.00/2.20 (c3_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[185, 8942])).
% 2.00/2.20 tff(8945,plain,
% 2.00/2.20 (~c1_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[1751, 156, 8476, 8944, 8943, 8941, 8940, 8939, 1745])).
% 2.00/2.20 tff(8946,plain,
% 2.00/2.20 (c2_1(a589)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[171, 8942])).
% 2.00/2.20 tff(8947,plain,
% 2.00/2.20 (hskp8),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7536, 8945, 8738, 8936, 8946, 4778, 8943])).
% 2.00/2.20 tff(8948,plain,
% 2.00/2.20 (~c2_1(a552)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2424, 8947])).
% 2.00/2.20 tff(8949,plain,
% 2.00/2.20 (~c1_1(a552)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2453, 8947])).
% 2.00/2.20 tff(8950,plain,
% 2.00/2.20 (~c3_1(a552)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2430, 8947])).
% 2.00/2.20 tff(8951,plain,
% 2.00/2.20 (hskp51),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[6599, 8947, 8936, 8738, 4778])).
% 2.00/2.20 tff(8952,plain,
% 2.00/2.20 (~c2_1(a583)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2637, 8951])).
% 2.00/2.20 tff(8953,plain,
% 2.00/2.20 (c3_1(a583)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2645, 8951])).
% 2.00/2.20 tff(8954,plain,
% 2.00/2.20 (~c1_1(a583)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[3471, 156, 8953, 8946, 8944, 8952, 8950, 8949, 8948, 45, 8945])).
% 2.00/2.20 tff(8955,plain,
% 2.00/2.20 (~hskp24),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[8853, 8936, 4777, 4778, 8738])).
% 2.00/2.20 tff(8956,plain,
% 2.00/2.20 (hskp26),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2437, 156, 8914, 8944, 8913, 8912, 8943, 1686, 8945])).
% 2.00/2.20 tff(8957,plain,
% 2.00/2.20 (hskp39),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7687, 8956, 8955])).
% 2.00/2.20 tff(8958,plain,
% 2.00/2.20 (hskp38),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[2535, 8957, 8945, 8944, 8946])).
% 2.00/2.20 tff(8959,plain,
% 2.00/2.20 (c0_1(a547)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[677, 8958])).
% 2.00/2.20 tff(8960,plain,
% 2.00/2.20 (c1_1(a547)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[685, 8958])).
% 2.00/2.20 tff(8961,plain,
% 2.00/2.20 (c2_1(a547)),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[693, 8958])).
% 2.00/2.20 tff(8962,plain,
% 2.00/2.20 (hskp0),
% 2.00/2.20 inference(unit_resolution,[status(thm)],[7358, 8961, 8947, 8960, 8959])).
% 2.00/2.21 tff(8963,plain,
% 2.00/2.21 (~c2_1(a535)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[713, 8962])).
% 2.00/2.21 tff(8964,plain,
% 2.00/2.21 (c0_1(a535)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[721, 8962])).
% 2.00/2.21 tff(8965,plain,
% 2.00/2.21 (c1_1(a535)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[729, 8962])).
% 2.00/2.21 tff(8966,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3580, 156, 8953, 8961, 8960, 8959, 8965, 8964, 8952, 8963, 707, 8954])).
% 2.00/2.21 tff(8967,plain,(c2_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(8968,plain,
% 2.00/2.21 (c2_1(a537)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8967, 4778])).
% 2.00/2.21 tff(8969,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a537)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(8970,plain,
% 2.00/2.21 ((hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537))) <=> (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a537)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(8971,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a537))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[8970])).
% 2.00/2.21 tff(8972,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a537)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[8971, 8969])).
% 2.00/2.21 tff(8973,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | (~c3_1(a549)) | (~c2_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c2_1(a537)))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(8974,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp46 | c0_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a549)) | (~c1_1(a549)) | (~c3_1(a549)) | (~c2_1(a537))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[8973, 8972])).
% 2.00/2.21 tff(8975,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8974, 156, 946, 1876, 1875, 1874, 7925, 7860, 858, 1])).
% 2.00/2.21 tff(8976,plain,((~hskp39) | hskp46 | c0_1(a537) | c3_1(a537) | (~c2_1(a537))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(8977,plain,
% 2.00/2.21 (~hskp39),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8976, 946, 7925, 7860, 8968])).
% 2.00/2.21 tff(8978,plain,
% 2.00/2.21 (hskp26),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8580, 1250, 1967])).
% 2.00/2.21 tff(8979,plain,
% 2.00/2.21 (c0_1(a584)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1629, 8978])).
% 2.00/2.21 tff(8980,plain,
% 2.00/2.21 (c1_1(a584)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1637, 8978])).
% 2.00/2.21 tff(8981,plain,
% 2.00/2.21 (~c3_1(a584)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1620, 8978])).
% 2.00/2.21 tff(8982,plain,
% 2.00/2.21 (c3_1(a569)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8702, 156, 8505, 8979, 8980, 8981, 1268, 1256, 85])).
% 2.00/2.21 tff(8983,plain,
% 2.00/2.21 (~c2_1(a584)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8181, 8982, 8981, 1262, 1256, 8980, 8297, 1968, 1969, 8979])).
% 2.00/2.21 tff(8984,plain,
% 2.00/2.21 (~hskp39),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8976, 946, 7925, 7860, 1])).
% 2.00/2.21 tff(8985,plain,
% 2.00/2.21 (hskp24),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[7687, 8978, 8984])).
% 2.00/2.21 tff(8986,plain,
% 2.00/2.21 (~c1_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[6663, 8985, 946, 1968, 8297, 1969])).
% 2.00/2.21 tff(8987,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c3_1(a537) | c0_1(a589) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a537) | c0_1(a589) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(8988,plain,
% 2.00/2.21 (((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584))) <=> (c0_1(a537) | c3_1(a537) | c0_1(a589) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(8989,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c3_1(a537) | c0_1(a589) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[8988])).
% 2.00/2.21 tff(8990,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a537) | c0_1(a589) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[8989, 8987])).
% 2.00/2.21 tff(8991,plain,
% 2.00/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a584) | (~c0_1(a584)) | (~c1_1(a584)))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(8992,plain,
% 2.00/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a537) | c0_1(a589) | (~ndr1_0) | (~c0_1(a584)) | (~c1_1(a584)) | c2_1(a584) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[8991, 8990])).
% 2.00/2.21 tff(8993,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8992, 156, 7925, 7860, 1968, 8979, 8980, 1969, 609, 8986, 1, 8983])).
% 2.00/2.21 tff(8994,plain,((~hskp15) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(8995,plain,
% 2.00/2.21 (~hskp15),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8994, 946, 7860, 8968, 7925])).
% 2.00/2.21 tff(8996,plain,
% 2.00/2.21 (~c3_1(a545)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1211, 1645, 58, 1644, 1667])).
% 2.00/2.21 tff(8997,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c3_1(a537) | c2_1(a555) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a537) | c2_1(a555) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(8998,plain,
% 2.00/2.21 (((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555))) <=> (c3_1(a537) | c2_1(a555) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(8999,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | (c3_1(a537) | c2_1(a555) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[8998])).
% 2.00/2.21 tff(9000,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a537) | c2_1(a555) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[8999, 8997])).
% 2.00/2.21 tff(9001,plain,
% 2.00/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c0_1(a555)) | c1_1(a537) | c3_1(a537) | (~c2_1(a537)) | (~c0_1(a555)) | c1_1(a555) | (~c3_1(a555)))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(9002,plain,
% 2.00/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c0_1(W)) | c1_1(W) | (~c3_1(W)))) | c3_1(a537) | c2_1(a555) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c3_1(a555)) | c1_1(a555) | (~c0_1(a555))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[9001, 9000])).
% 2.00/2.21 tff(9003,plain,
% 2.00/2.21 (c1_1(a555)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9002, 156, 257, 241, 7860, 233, 4778, 921, 8968])).
% 2.00/2.21 tff(9004,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1447, 156, 859, 257, 1046, 233, 97, 281, 765, 9003])).
% 2.00/2.21 tff(9005,plain,((~hskp41) | hskp39 | (~c1_1(a545)) | c0_1(a545) | c3_1(a545) | c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9006,plain,
% 2.00/2.21 (~hskp41),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9005, 1645, 859, 1667, 8996, 7860, 4778])).
% 2.00/2.21 tff(9007,plain,
% 2.00/2.21 (~hskp9),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5179, 109, 1669, 765, 1046, 111])).
% 2.00/2.21 tff(9008,plain,
% 2.00/2.21 (hskp19),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[567, 109, 332, 331, 110, 9007])).
% 2.00/2.21 tff(9009,plain,
% 2.00/2.21 (hskp28),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5069, 9008])).
% 2.00/2.21 tff(9010,plain,
% 2.00/2.21 (c2_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[171, 9009])).
% 2.00/2.21 tff(9011,plain,
% 2.00/2.21 (c3_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[185, 9009])).
% 2.00/2.21 tff(9012,plain,
% 2.00/2.21 (c1_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2044, 9011, 765, 109, 1046, 111, 9010])).
% 2.00/2.21 tff(9013,plain,
% 2.00/2.21 (~c1_1(a573)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1675, 9008])).
% 2.00/2.21 tff(9014,plain,
% 2.00/2.21 (~c0_1(a573)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1691, 9008])).
% 2.00/2.21 tff(9015,plain,
% 2.00/2.21 (~c2_1(a573)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1704, 9008])).
% 2.00/2.21 tff(9016,plain,
% 2.00/2.21 (~c0_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[177, 9009])).
% 2.00/2.21 tff(9017,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1751, 156, 1669, 9011, 9016, 9015, 9014, 9013, 1745, 9012])).
% 2.00/2.21 tff(9018,plain,(hskp15 | hskp6 | c3_1(a545) | (~c1_1(a545)) | c2_1(a545) | hskp17 | hskp41 | hskp50), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9019,plain,
% 2.00/2.21 (hskp15 | c3_1(a545) | (~c1_1(a545)) | c2_1(a545) | hskp17 | hskp41 | hskp50),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9018, 8476])).
% 2.00/2.21 tff(9020,plain,
% 2.00/2.21 (hskp17),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9019, 9006, 110, 1644, 1645, 109, 8996])).
% 2.00/2.21 tff(9021,plain,
% 2.00/2.21 (~c2_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[573, 9020])).
% 2.00/2.21 tff(9022,plain,
% 2.00/2.21 (c3_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[623, 9020])).
% 2.00/2.21 tff(9023,plain,
% 2.00/2.21 (c0_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[581, 9020])).
% 2.00/2.21 tff(9024,plain,
% 2.00/2.21 (c1_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[7896, 156, 7860, 9023, 9022, 4778, 9021, 921, 8968])).
% 2.00/2.21 tff(9025,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a571) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a571) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9026,plain,
% 2.00/2.21 ((hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp39 | c2_1(a571) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9027,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c2_1(a571) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a571)) | (~c1_1(a571))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[9026])).
% 2.00/2.21 tff(9028,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a571) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a571)) | (~c1_1(a571)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[9027, 9025])).
% 2.00/2.21 tff(9029,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(9030,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c2_1(a571) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c3_1(a571)) | (~c1_1(a571))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[9029, 9028])).
% 2.00/2.21 tff(9031,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9030, 156, 859, 9022, 1645, 9021, 1667, 281, 8996, 9024])).
% 2.00/2.21 tff(9032,plain,((~hskp4) | hskp39 | c3_1(a537) | c1_1(a537) | hskp50 | hskp15 | hskp38), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9033,plain,
% 2.00/2.21 (~hskp4),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9032, 110, 7860, 4778, 859, 109, 58])).
% 2.00/2.21 tff(9034,plain,
% 2.00/2.21 (hskp26),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8491, 5060, 23])).
% 2.00/2.21 tff(9035,plain,
% 2.00/2.21 (c1_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8573, 5060, 35, 946, 58, 109])).
% 2.00/2.21 tff(9036,plain,
% 2.00/2.21 (~hskp24),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[6663, 9035, 946, 5061, 5062, 5064])).
% 2.00/2.21 tff(9037,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[7687, 9036, 9034, 859])).
% 2.00/2.21 tff(9038,plain,((~hskp28) | hskp39 | hskp46 | hskp4 | hskp33 | hskp38 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9039,plain,
% 2.00/2.21 (~hskp28),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9038, 9033, 946, 859, 8505, 58, 109])).
% 2.00/2.21 tff(9040,plain,
% 2.00/2.21 (~hskp9),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1314, 9039])).
% 2.00/2.21 tff(9041,plain,
% 2.00/2.21 (~hskp19),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5069, 9039])).
% 2.00/2.21 tff(9042,plain,
% 2.00/2.21 (hskp27),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8477, 9033])).
% 2.00/2.21 tff(9043,plain,
% 2.00/2.21 (~c3_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3996, 9042])).
% 2.00/2.21 tff(9044,plain,
% 2.00/2.21 (c1_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[95, 9042])).
% 2.00/2.21 tff(9045,plain,
% 2.00/2.21 (~c0_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3924, 9042])).
% 2.00/2.21 tff(9046,plain,
% 2.00/2.21 (c1_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[7896, 156, 7860, 925, 924, 4778, 923, 921, 8968])).
% 2.00/2.21 tff(9047,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5409, 156, 859, 3797, 924, 87, 86, 923, 281, 9046])).
% 2.00/2.21 tff(9048,plain,((~hskp17) | hskp39 | (~c1_1(a586)) | c0_1(a586) | c3_1(a586) | c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9049,plain,
% 2.00/2.21 (~hskp17),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9048, 87, 859, 3797, 86, 7860, 4778])).
% 2.00/2.21 tff(9050,plain,
% 2.00/2.21 (hskp41),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[567, 9049, 330, 98, 109, 110])).
% 2.00/2.21 tff(9051,plain,
% 2.00/2.21 (~c2_1(a555)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[232, 9050])).
% 2.00/2.21 tff(9052,plain,
% 2.00/2.21 (c0_1(a555)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[240, 9050])).
% 2.00/2.21 tff(9053,plain,
% 2.00/2.21 (c3_1(a555)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[256, 9050])).
% 2.00/2.21 tff(9054,plain,
% 2.00/2.21 (c1_1(a555)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9002, 156, 9053, 9052, 7860, 9051, 4778, 921, 8968])).
% 2.00/2.21 tff(9055,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5583, 156, 859, 9053, 3797, 9051, 87, 86, 281, 9054])).
% 2.00/2.21 tff(9056,plain,(c0_1(a586) | hskp39 | (~c1_1(a586)) | c3_1(a586) | c3_1(a537) | c1_1(a537) | hskp9 | hskp19 | hskp15 | hskp50), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9057,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9056, 9045, 9044, 859, 9043, 7860, 4778, 330, 98, 109, 110])).
% 2.00/2.21 tff(9058,plain,(hskp50 | hskp39 | c3_1(a537) | c1_1(a537) | hskp9 | hskp19 | hskp15 | hskp38), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9059,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9058, 9041, 9040, 7860, 4778, 859, 110, 109, 58])).
% 2.00/2.21 tff(9060,plain,(hskp50 | c3_1(a537) | c1_1(a537) | hskp39 | hskp15 | hskp38 | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9061,plain,
% 2.00/2.21 (hskp50),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9060, 109, 4778, 859, 7860, 58, 946])).
% 2.00/2.21 tff(9062,plain,
% 2.00/2.21 (~hskp4),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[6209, 9061, 8505])).
% 2.00/2.21 tff(9063,plain,
% 2.00/2.21 (~hskp28),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9038, 9062, 946, 859, 8505, 58, 109])).
% 2.00/2.21 tff(9064,plain,
% 2.00/2.21 (~hskp9),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1314, 9063])).
% 2.00/2.21 tff(9065,plain,
% 2.00/2.21 (~hskp19),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5069, 9063])).
% 2.00/2.21 tff(9066,plain,
% 2.00/2.21 (hskp50),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9058, 859, 7860, 4778, 330, 98, 109, 58])).
% 2.00/2.21 tff(9067,plain,
% 2.00/2.21 (~hskp4),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[6209, 9066, 8505])).
% 2.00/2.21 tff(9068,plain,
% 2.00/2.21 (hskp27),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8477, 9067])).
% 2.00/2.21 tff(9069,plain,
% 2.00/2.21 (c1_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[95, 9068])).
% 2.00/2.21 tff(9070,plain,
% 2.00/2.21 (~c3_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3996, 9068])).
% 2.00/2.21 tff(9071,plain,
% 2.00/2.21 (~c0_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3924, 9068])).
% 2.00/2.21 tff(9072,plain,
% 2.00/2.21 (~hskp17),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9048, 9071, 859, 9069, 9070, 7860, 4778])).
% 2.00/2.21 tff(9073,plain,
% 2.00/2.21 (c2_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2766, 9071, 8505, 9066, 9070])).
% 2.00/2.21 tff(9074,plain,
% 2.00/2.21 (~hskp16),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2365, 9073, 946, 9070, 9071])).
% 2.00/2.21 tff(9075,plain,
% 2.00/2.21 (hskp18),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[382, 9074, 9072])).
% 2.00/2.21 tff(9076,plain,
% 2.00/2.21 (~c1_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[389, 9075])).
% 2.00/2.21 tff(9077,plain,
% 2.00/2.21 (~hskp35),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5310, 9069, 9067, 9071, 9070])).
% 2.00/2.21 tff(9078,plain,
% 2.00/2.21 (c0_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[397, 9075])).
% 2.00/2.21 tff(9079,plain,
% 2.00/2.21 (c2_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5426, 9078, 9077, 9073, 9070, 9076, 9069])).
% 2.00/2.21 tff(9080,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5478, 156, 946, 9069, 9078, 9071, 9076, 2215, 9073, 9079])).
% 2.00/2.21 tff(9081,plain,(hskp39 | hskp46 | c3_1(a537) | c1_1(a537) | hskp9 | hskp19 | hskp15 | hskp38), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9082,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9081, 9065, 9064, 7860, 4778, 859, 58, 109, 946])).
% 2.00/2.21 tff(9083,plain,(hskp15 | c3_1(a537) | c1_1(a537) | hskp39 | hskp38 | hskp46), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9084,plain,
% 2.00/2.21 (hskp38),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9083, 8995, 4778, 8977, 7860, 946])).
% 2.00/2.21 tff(9085,plain,
% 2.00/2.21 (c1_1(a547)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[685, 9084])).
% 2.00/2.21 tff(9086,plain,
% 2.00/2.21 (c0_1(a547)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[677, 9084])).
% 2.00/2.21 tff(9087,plain,
% 2.00/2.21 (c2_1(a547)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[693, 9084])).
% 2.00/2.21 tff(9088,plain,
% 2.00/2.21 (~c1_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[7920, 156, 946, 7925, 7860, 5062, 5061, 858, 8968])).
% 2.00/2.21 tff(9089,plain,
% 2.00/2.21 (~c3_1(a545)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1586, 1645, 859, 733, 731, 732, 1644, 1667])).
% 2.00/2.21 tff(9090,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2044, 9089, 1645, 591, 1716, 109, 1644, 625])).
% 2.00/2.21 tff(9091,plain,((~hskp4) | (~c3_1(a589)) | c1_1(a589) | hskp15 | (~c2_1(a589)) | hskp39 | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9092,plain,
% 2.00/2.21 (~hskp4),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9091, 5061, 9088, 8995, 5062, 8977, 9087, 9086, 9085])).
% 2.00/2.21 tff(9093,plain,
% 2.00/2.21 (hskp27),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8477, 9092])).
% 2.00/2.21 tff(9094,plain,
% 2.00/2.21 (c1_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[95, 9093])).
% 2.00/2.21 tff(9095,plain,
% 2.00/2.21 (hskp26),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8491, 23, 5060])).
% 2.00/2.21 tff(9096,plain,
% 2.00/2.21 (c2_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3104, 8479, 8505, 9095, 8480])).
% 2.00/2.21 tff(9097,plain,
% 2.00/2.21 (~hskp17),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9048, 8480, 859, 8489, 8479, 7860, 4778])).
% 2.00/2.21 tff(9098,plain,
% 2.00/2.21 (hskp16),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[382, 9097, 1795])).
% 2.00/2.21 tff(9099,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2365, 9098, 9096, 946, 8479, 8480])).
% 2.00/2.21 tff(9100,plain,(hskp4 | hskp46 | hskp18 | hskp39 | c3_1(a537) | c1_1(a537) | (~hskp28)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9101,plain,
% 2.00/2.21 (hskp18),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9100, 9092, 946, 8977, 7860, 4778, 5060])).
% 2.00/2.21 tff(9102,plain,
% 2.00/2.21 (~c1_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[389, 9101])).
% 2.00/2.21 tff(9103,plain,
% 2.00/2.21 (~c3_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3996, 9093])).
% 2.00/2.21 tff(9104,plain,
% 2.00/2.21 (~c0_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3924, 9093])).
% 2.00/2.21 tff(9105,plain,
% 2.00/2.21 (hskp26),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8491, 9092, 5060])).
% 2.00/2.21 tff(9106,plain,
% 2.00/2.21 (c2_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3104, 9103, 8505, 9105, 9104])).
% 2.00/2.21 tff(9107,plain,
% 2.00/2.21 (~hskp35),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5310, 9094, 9092, 9104, 9103])).
% 2.00/2.21 tff(9108,plain,
% 2.00/2.21 (c0_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[397, 9101])).
% 2.00/2.21 tff(9109,plain,
% 2.00/2.21 (c2_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5426, 9108, 9107, 9106, 9103, 9102, 9094])).
% 2.00/2.21 tff(9110,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5478, 156, 946, 9094, 9108, 9104, 9102, 2215, 9106, 9109])).
% 2.00/2.21 tff(9111,plain,((~hskp28) | hskp46 | c3_1(a537) | c1_1(a537) | c0_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9112,plain,
% 2.00/2.21 (~hskp28),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9111, 946, 7860, 4778, 7925])).
% 2.00/2.21 tff(9113,plain,
% 2.00/2.21 (~hskp19),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5069, 1213])).
% 2.00/2.21 tff(9114,assumption,(hskp27), introduced(assumption)).
% 2.00/2.21 tff(9115,plain,
% 2.00/2.21 (c1_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[95, 9114])).
% 2.00/2.21 tff(9116,plain,
% 2.00/2.21 (~c0_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3924, 9114])).
% 2.00/2.21 tff(9117,plain,
% 2.00/2.21 (~c3_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3996, 9114])).
% 2.00/2.21 tff(9118,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9056, 9117, 9116, 859, 110, 7860, 4778, 330, 98, 109, 9115])).
% 2.00/2.21 tff(9119,plain,((~hskp27) | hskp39 | hskp50 | c3_1(a537) | c1_1(a537) | hskp9 | hskp19 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9120,plain,
% 2.00/2.21 (~hskp27),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9119, 1315, 110, 7860, 4778, 859, 9113, 109])).
% 2.00/2.21 tff(9121,plain,
% 2.00/2.21 (hskp4),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8477, 9120])).
% 2.00/2.21 tff(9122,plain,
% 2.00/2.21 (~c0_1(a545)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1666, 9121])).
% 2.00/2.21 tff(9123,plain,
% 2.00/2.21 (~c2_1(a545)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1643, 9121])).
% 2.00/2.21 tff(9124,plain,
% 2.00/2.21 (c1_1(a545)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[193, 9121])).
% 2.00/2.21 tff(9125,plain,
% 2.00/2.21 (~c3_1(a545)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1586, 9124, 859, 733, 731, 732, 9123, 9122])).
% 2.00/2.21 tff(9126,plain,
% 2.00/2.21 (~hskp41),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9005, 9125, 859, 9122, 9124, 7860, 4778])).
% 2.00/2.21 tff(9127,plain,
% 2.00/2.21 (hskp17),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9019, 9126, 110, 9123, 9124, 109, 9125])).
% 2.00/2.21 tff(9128,plain,
% 2.00/2.21 (~c2_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[573, 9127])).
% 2.00/2.21 tff(9129,plain,
% 2.00/2.21 (c3_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[623, 9127])).
% 2.00/2.21 tff(9130,plain,
% 2.00/2.21 (c0_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[581, 9127])).
% 2.00/2.21 tff(9131,plain,
% 2.00/2.21 (c1_1(a571)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[7896, 156, 7860, 9130, 9129, 4778, 9128, 921, 8968])).
% 2.00/2.21 tff(9132,plain,
% 2.00/2.21 (~hskp45),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[833, 9125, 8505, 9113, 9122, 9123])).
% 2.00/2.21 tff(9133,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a571) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a571)) | (~c0_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a571) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a571)) | (~c0_1(a571)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9134,plain,
% 2.00/2.21 ((hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp45 | c2_1(a571) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a571)) | (~c0_1(a571)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9135,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a571) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a571)) | (~c0_1(a571))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[9134])).
% 2.00/2.21 tff(9136,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a571) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a571)) | (~c0_1(a571)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[9135, 9133])).
% 2.00/2.21 tff(9137,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a571) | (~c0_1(a571)) | (~c1_1(a571)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(9138,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a571) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a571)) | (~c0_1(a571))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[9137, 9136])).
% 2.00/2.21 tff(9139,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9138, 156, 9132, 9130, 9128, 9123, 9122, 757, 9125, 9131])).
% 2.00/2.21 tff(9140,plain,(hskp28 | c3_1(a537) | c1_1(a537) | hskp50 | hskp15 | hskp39 | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9141,plain,
% 2.00/2.21 (hskp50),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9140, 9112, 4778, 7860, 8995, 8977, 9087, 9086, 9085])).
% 2.00/2.21 tff(9142,plain,
% 2.00/2.21 (~hskp4),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[6209, 9141, 8505])).
% 2.00/2.21 tff(9143,plain,
% 2.00/2.21 (hskp27),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8477, 9142])).
% 2.00/2.21 tff(9144,plain,
% 2.00/2.21 (c1_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[95, 9143])).
% 2.00/2.21 tff(9145,plain,
% 2.00/2.21 (~c3_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3996, 9143])).
% 2.00/2.21 tff(9146,plain,
% 2.00/2.21 (~c0_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3924, 9143])).
% 2.00/2.21 tff(9147,plain,
% 2.00/2.21 (~hskp17),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9048, 9146, 8977, 9144, 9145, 7860, 4778])).
% 2.00/2.21 tff(9148,plain,
% 2.00/2.21 (c2_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2766, 9146, 8505, 9141, 9145])).
% 2.00/2.21 tff(9149,plain,
% 2.00/2.21 (~hskp16),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2365, 9148, 946, 9145, 9146])).
% 2.00/2.21 tff(9150,plain,
% 2.00/2.21 (hskp18),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[382, 9149, 9147])).
% 2.00/2.21 tff(9151,plain,
% 2.00/2.21 (~c1_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[389, 9150])).
% 2.00/2.21 tff(9152,plain,
% 2.00/2.21 (~hskp35),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5310, 9144, 9142, 9146, 9145])).
% 2.00/2.21 tff(9153,plain,
% 2.00/2.21 (c0_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[397, 9150])).
% 2.00/2.21 tff(9154,plain,
% 2.00/2.21 (c2_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5426, 9153, 9152, 9148, 9145, 9151, 9144])).
% 2.00/2.21 tff(9155,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5478, 156, 946, 9144, 9153, 9146, 9151, 2215, 9148, 9154])).
% 2.00/2.21 tff(9156,plain,(hskp46 | c3_1(a537) | c1_1(a537) | c0_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9157,plain,
% 2.00/2.21 (hskp46),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9156, 7925, 4778, 7860])).
% 2.00/2.21 tff(9158,plain,
% 2.00/2.21 (~c0_1(a562)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[64, 9157])).
% 2.00/2.21 tff(9159,plain,
% 2.00/2.21 (~c3_1(a562)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[270, 9157])).
% 2.00/2.21 tff(9160,plain,
% 2.00/2.21 (~c1_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[1789, 156, 8476, 1968, 1969, 1268, 1262, 1256, 1745])).
% 2.00/2.21 tff(9161,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8992, 156, 7925, 7860, 1968, 8979, 8980, 1969, 609, 9160, 1, 8983])).
% 2.00/2.21 tff(9162,plain,((~hskp15) | c0_1(a537) | c3_1(a537) | (~c2_1(a537))), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9163,plain,
% 2.00/2.21 (~hskp15),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9162, 7925, 7860, 8968])).
% 2.00/2.21 tff(9164,plain,
% 2.00/2.21 (c1_1(a562)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[288, 9157])).
% 2.00/2.21 tff(9165,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2160, 156, 3650, 973, 2771, 2770, 2769, 972, 971, 75])).
% 2.00/2.21 tff(9166,plain,((~hskp38) | hskp34 | (~c1_1(a562)) | c3_1(a562) | c0_1(a562)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9167,plain,
% 2.00/2.21 (~hskp38),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9166, 9164, 7861, 9159, 9158])).
% 2.00/2.21 tff(9168,plain,
% 2.00/2.21 (hskp50),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9119, 9113, 1315, 7860, 4778, 859, 8478, 109])).
% 2.00/2.21 tff(9169,plain,
% 2.00/2.21 (c0_1(a574)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[815, 9168])).
% 2.00/2.21 tff(9170,plain,
% 2.00/2.21 (c1_1(a574)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[807, 9168])).
% 2.00/2.21 tff(9171,plain,
% 2.00/2.21 (~hskp35),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5310, 8489, 23, 8480, 8479])).
% 2.00/2.21 tff(9172,plain,
% 2.00/2.21 (~c3_1(a574)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[799, 9168])).
% 2.00/2.21 tff(9173,plain,
% 2.00/2.21 (c2_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[2766, 9168, 8505, 8480, 8479])).
% 2.00/2.21 tff(9174,plain,
% 2.00/2.21 (~hskp25),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5379, 9173, 9172, 9171, 8489, 9170, 9169, 8479, 8505])).
% 2.00/2.21 tff(9175,plain,
% 2.00/2.21 (~hskp16),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5107, 9174, 8489, 23, 8480, 8479])).
% 2.00/2.21 tff(9176,plain,
% 2.00/2.21 (hskp18),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[382, 9175, 9097])).
% 2.00/2.21 tff(9177,plain,
% 2.00/2.21 (~c1_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[389, 9176])).
% 2.00/2.21 tff(9178,plain,
% 2.00/2.21 (c0_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[397, 9176])).
% 2.00/2.21 tff(9179,plain,
% 2.00/2.21 (c2_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5426, 9178, 9171, 9173, 8479, 9177, 8489])).
% 2.00/2.21 tff(9180,plain,
% 2.00/2.21 (~c3_1(a572)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[420, 9176])).
% 2.00/2.21 tff(9181,plain,
% 2.00/2.21 (hskp37),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[428, 156, 9178, 9180, 9177, 415, 9179])).
% 2.00/2.21 tff(9182,plain,
% 2.00/2.21 (~c3_1(a544)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[450, 9181])).
% 2.00/2.21 tff(9183,plain,
% 2.00/2.21 (~c2_1(a544)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[436, 9181])).
% 2.00/2.21 tff(9184,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a574) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a574) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9185,plain,
% 2.00/2.21 ((hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp32 | c3_1(a574) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9186,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a574) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a574)) | (~c1_1(a574))))),
% 2.00/2.21 inference(monotonicity,[status(thm)],[9185])).
% 2.00/2.21 tff(9187,plain,
% 2.00/2.21 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a574) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.00/2.21 inference(transitivity,[status(thm)],[9186, 9184])).
% 2.00/2.21 tff(9188,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 2.00/2.21 inference(quant_inst,[status(thm)],[])).
% 2.00/2.21 tff(9189,plain,
% 2.00/2.21 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a574) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a574)) | (~c1_1(a574))),
% 2.00/2.21 inference(modus_ponens,[status(thm)],[9188, 9187])).
% 2.00/2.21 tff(9190,plain,
% 2.00/2.21 (hskp32),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9189, 156, 9169, 9170, 8489, 9172, 8479, 4894, 9173])).
% 2.00/2.21 tff(9191,plain,
% 2.00/2.21 (c0_1(a596)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5522, 8343])).
% 2.00/2.21 tff(9192,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[6493, 156, 859, 6468, 9191, 8345, 8344, 3496])).
% 2.00/2.21 tff(9193,plain,((~hskp32) | hskp39 | hskp24), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9194,plain,
% 2.00/2.21 (hskp24),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9193, 9190, 859])).
% 2.00/2.21 tff(9195,plain,
% 2.00/2.21 (~c1_1(a581)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3519, 9194])).
% 2.00/2.21 tff(9196,plain,
% 2.00/2.21 (c2_1(a581)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3541, 9194])).
% 2.00/2.21 tff(9197,plain,
% 2.00/2.21 (c1_1(a544)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[444, 9181])).
% 2.00/2.21 tff(9198,plain,
% 2.00/2.21 (~c3_1(a581)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3513, 9194])).
% 2.00/2.21 tff(9199,plain,
% 2.00/2.21 (~hskp7),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5466, 9198, 109, 9197, 9196, 9195, 9183, 9182])).
% 2.00/2.21 tff(9200,plain,
% 2.00/2.21 (hskp40 | hskp7),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[521, 156, 9178, 9177, 513, 9179])).
% 2.00/2.21 tff(9201,plain,
% 2.00/2.21 (hskp40),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9200, 9199])).
% 2.00/2.21 tff(9202,plain,
% 2.00/2.21 (c3_1(a551)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[540, 9201])).
% 2.00/2.21 tff(9203,plain,
% 2.00/2.21 (c2_1(a551)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[532, 9201])).
% 2.00/2.21 tff(9204,plain,
% 2.00/2.21 (c1_1(a551)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[552, 9203, 9182, 109, 9197, 9183, 9202])).
% 2.00/2.21 tff(9205,plain,
% 2.00/2.21 (~c0_1(a551)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[558, 9201])).
% 2.00/2.21 tff(9206,plain,
% 2.00/2.21 (~hskp41),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5654, 9195, 8489, 8480, 8479, 859, 9196, 9198])).
% 2.00/2.21 tff(9207,plain,
% 2.00/2.21 ($false),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[565, 156, 9206, 1315, 9202, 9205, 342, 9204])).
% 2.00/2.21 tff(9208,plain,(hskp28 | hskp15 | hskp39 | hskp4 | c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.21 tff(9209,plain,
% 2.00/2.21 (hskp28),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[9208, 23, 859, 109, 7860, 4778])).
% 2.00/2.21 tff(9210,plain,
% 2.00/2.21 (c2_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[171, 9209])).
% 2.00/2.21 tff(9211,plain,
% 2.00/2.21 (c3_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[185, 9209])).
% 2.00/2.21 tff(9212,plain,
% 2.00/2.21 (~c1_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[6532, 9211, 9157, 23, 9210])).
% 2.00/2.21 tff(9213,plain,
% 2.00/2.21 (~c0_1(a589)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[177, 9209])).
% 2.00/2.21 tff(9214,plain,
% 2.00/2.21 (hskp26),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[8491, 9209, 23])).
% 2.00/2.21 tff(9215,plain,
% 2.00/2.21 (c2_1(a586)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[3104, 9214, 8505, 8479, 8480])).
% 2.00/2.21 tff(9216,plain,
% 2.00/2.21 (hskp47),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5700, 156, 9210, 9211, 8489, 9213, 8479, 5693, 9215])).
% 2.00/2.21 tff(9217,plain,
% 2.00/2.21 (~c2_1(a564)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5707, 9216])).
% 2.00/2.21 tff(9218,plain,
% 2.00/2.21 (c1_1(a564)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5734, 9216])).
% 2.00/2.21 tff(9219,plain,
% 2.00/2.21 (c0_1(a564)),
% 2.00/2.21 inference(unit_resolution,[status(thm)],[5742, 9216])).
% 2.00/2.21 tff(9220,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c3_1(a537) | c2_1(a564) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)) | (~c1_1(a564)) | (~c0_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a537) | c2_1(a564) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9221,plain,
% 2.00/2.21 (((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564))) <=> (c0_1(a537) | c3_1(a537) | c2_1(a564) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 2.00/2.21 inference(rewrite,[status(thm)],[])).
% 2.00/2.21 tff(9222,plain,
% 2.00/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c0_1(a537) | c3_1(a537) | c2_1(a564) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)) | (~c1_1(a564)) | (~c0_1(a564))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9221])).
% 2.00/2.22 tff(9223,plain,
% 2.00/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a537) | c2_1(a564) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)) | (~c1_1(a564)) | (~c0_1(a564)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9222, 9220])).
% 2.00/2.22 tff(9224,plain,
% 2.00/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a537) | c3_1(a537) | (~c2_1(a537)) | c1_1(a589) | c0_1(a589) | (~c3_1(a589)) | c2_1(a564) | (~c0_1(a564)) | (~c1_1(a564)))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9225,plain,
% 2.00/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c0_1(a537) | c3_1(a537) | c2_1(a564) | c0_1(a589) | (~ndr1_0) | (~c3_1(a589)) | c1_1(a589) | (~c2_1(a537)) | (~c1_1(a564)) | (~c0_1(a564))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9224, 9223])).
% 2.00/2.22 tff(9226,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9225, 156, 9219, 9218, 7925, 7860, 9211, 9217, 9213, 609, 9212, 8968])).
% 2.00/2.22 tff(9227,plain,(hskp4 | c0_1(a537) | c3_1(a537) | hskp39 | hskp15 | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9228,plain,
% 2.00/2.22 (hskp4),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9227, 109, 7860, 859, 7925, 4778])).
% 2.00/2.22 tff(9229,plain,
% 2.00/2.22 (~hskp50),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[6209, 9228, 8505])).
% 2.00/2.22 tff(9230,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9032, 9229, 9228, 7860, 4778, 9167, 859, 109])).
% 2.00/2.22 tff(9231,plain,(hskp15 | c3_1(a537) | c1_1(a537) | hskp39 | c0_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9232,plain,
% 2.00/2.22 (hskp39),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9231, 9163, 4778, 7860, 7925])).
% 2.00/2.22 tff(9233,plain,
% 2.00/2.22 (c1_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[303, 9232])).
% 2.00/2.22 tff(9234,plain,
% 2.00/2.22 (c2_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[311, 9232])).
% 2.00/2.22 tff(9235,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | (~c1_1(a562)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9236,plain,
% 2.00/2.22 ((hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562))) <=> (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | (~c1_1(a562)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9237,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | (~c1_1(a562))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9236])).
% 2.00/2.22 tff(9238,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | (~c1_1(a562)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9237, 9235])).
% 2.00/2.22 tff(9239,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a562) | c0_1(a562) | (~c1_1(a562)))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9240,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a562) | c0_1(a562) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | (~c1_1(a562))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9239, 9238])).
% 2.00/2.22 tff(9241,plain,
% 2.00/2.22 (~c0_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9240, 156, 7861, 9164, 9234, 9233, 9159, 9158, 75])).
% 2.00/2.22 tff(9242,plain,
% 2.00/2.22 (c3_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[319, 9232])).
% 2.00/2.22 tff(9243,plain,
% 2.00/2.22 (hskp4),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[326, 156, 9164, 9242, 9234, 9233, 9159, 9158, 22])).
% 2.00/2.22 tff(9244,plain,
% 2.00/2.22 (~c2_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1643, 9243])).
% 2.00/2.22 tff(9245,plain,
% 2.00/2.22 (c1_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[193, 9243])).
% 2.00/2.22 tff(9246,plain,
% 2.00/2.22 (~c0_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1666, 9243])).
% 2.00/2.22 tff(9247,plain,
% 2.00/2.22 (~c3_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1211, 9245, 9167, 9244, 9246])).
% 2.00/2.22 tff(9248,plain,
% 2.00/2.22 ((~hskp9) | hskp15 | (~c1_1(a545)) | c2_1(a545) | c3_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[5179, 8476])).
% 2.00/2.22 tff(9249,plain,
% 2.00/2.22 (~hskp9),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9248, 9247, 9245, 9163, 9244])).
% 2.00/2.22 tff(9250,plain,
% 2.00/2.22 (hskp41 | hskp9 | c0_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1513, 156, 9242, 9233, 342])).
% 2.00/2.22 tff(9251,plain,
% 2.00/2.22 (hskp41),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9250, 9249, 9241])).
% 2.00/2.22 tff(9252,plain,
% 2.00/2.22 (~c2_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[232, 9251])).
% 2.00/2.22 tff(9253,plain,
% 2.00/2.22 (c0_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[240, 9251])).
% 2.00/2.22 tff(9254,plain,
% 2.00/2.22 (c3_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[256, 9251])).
% 2.00/2.22 tff(9255,plain,
% 2.00/2.22 (c1_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9002, 156, 9254, 9253, 7860, 9252, 4778, 921, 8968])).
% 2.00/2.22 tff(9256,plain,
% 2.00/2.22 (~hskp26),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1659, 9246, 8505, 9167, 9243])).
% 2.00/2.22 tff(9257,plain,
% 2.00/2.22 ((~hskp19) | (~hskp4) | hskp26 | c3_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1753, 8476])).
% 2.00/2.22 tff(9258,plain,
% 2.00/2.22 (~hskp19),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9257, 9256, 9247, 9243])).
% 2.00/2.22 tff(9259,plain,
% 2.00/2.22 (~hskp45),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[833, 9258, 8505, 9247, 9246, 9244])).
% 2.00/2.22 tff(9260,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a555) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a555)) | (~c0_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a555)) | (~c0_1(a555)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9261,plain,
% 2.00/2.22 ((hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp45 | c2_1(a555) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a555)) | (~c0_1(a555)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9262,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a555) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a555)) | (~c0_1(a555))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9261])).
% 2.00/2.22 tff(9263,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a555)) | (~c0_1(a555)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9262, 9260])).
% 2.00/2.22 tff(9264,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9265,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a555)) | (~c0_1(a555))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9264, 9263])).
% 2.00/2.22 tff(9266,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9265, 156, 9259, 9253, 9252, 9244, 9246, 757, 9247, 9255])).
% 2.00/2.22 tff(9267,plain,(c0_1(a537) | c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9268,plain,
% 2.00/2.22 (c0_1(a537)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9267, 7860, 4778])).
% 2.00/2.22 tff(9269,plain,
% 2.00/2.22 (hskp37),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[7913, 9268, 8968, 7860])).
% 2.00/2.22 tff(9270,plain,
% 2.00/2.22 (~c3_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[450, 9269])).
% 2.00/2.22 tff(9271,plain,
% 2.00/2.22 (~c2_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[436, 9269])).
% 2.00/2.22 tff(9272,plain,
% 2.00/2.22 (c1_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[444, 9269])).
% 2.00/2.22 tff(9273,plain,
% 2.00/2.22 (c0_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[2862, 156, 35, 8979, 8980, 485, 484, 8981, 85])).
% 2.00/2.22 tff(9274,plain,
% 2.00/2.22 (c3_1(a569)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8702, 156, 35, 8979, 8980, 8981, 1268, 1256, 85])).
% 2.00/2.22 tff(9275,plain,
% 2.00/2.22 (c2_1(a586)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[3104, 9117, 35, 1615, 9116])).
% 2.00/2.22 tff(9276,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[5447, 156, 494, 485, 9116, 9117, 2785, 2775, 609, 9275, 2824, 4557])).
% 2.00/2.22 tff(9277,plain,((~hskp27) | (~c1_1(a544)) | c2_1(a544) | c0_1(a569) | c1_1(a569) | (~c3_1(a569)) | (~c0_1(a544)) | hskp33 | (~hskp26)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9278,plain,
% 2.00/2.22 (~hskp27),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9277, 1268, 485, 494, 1262, 9274, 9273, 35, 8978])).
% 2.00/2.22 tff(9279,plain,
% 2.00/2.22 (hskp4),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8477, 9278])).
% 2.00/2.22 tff(9280,plain,
% 2.00/2.22 (~c0_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1666, 9279])).
% 2.00/2.22 tff(9281,plain,
% 2.00/2.22 (hskp38),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1657, 9279, 35, 8980, 8981, 9280, 8979])).
% 2.00/2.22 tff(9282,plain,
% 2.00/2.22 (c0_1(a547)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[677, 9281])).
% 2.00/2.22 tff(9283,plain,
% 2.00/2.22 (c1_1(a547)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[685, 9281])).
% 2.00/2.22 tff(9284,plain,
% 2.00/2.22 (c2_1(a547)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[693, 9281])).
% 2.00/2.22 tff(9285,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[4212, 156, 9284, 9283, 9282, 494, 485, 1262, 1256, 707, 9274, 9273])).
% 2.00/2.22 tff(9286,plain,((~hskp15) | (~c1_1(a544)) | c2_1(a544) | hskp33 | c3_1(a544)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9287,plain,
% 2.00/2.22 (~hskp15),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9286, 9272, 9271, 8505, 9270])).
% 2.00/2.22 tff(9288,plain,
% 2.00/2.22 (hskp26),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8491, 23, 9209])).
% 2.00/2.22 tff(9289,plain,
% 2.00/2.22 (hskp24),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[7687, 9288, 859])).
% 2.00/2.22 tff(9290,plain,
% 2.00/2.22 (c1_1(a589)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[2512, 9211, 9269, 109, 9210])).
% 2.00/2.22 tff(9291,plain,
% 2.00/2.22 (~hskp46),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[6532, 9290, 23, 9211, 9210])).
% 2.00/2.22 tff(9292,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[6663, 9291, 9290, 9289, 9211, 9210, 9213])).
% 2.00/2.22 tff(9293,plain,(hskp4 | hskp15 | hskp39 | c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9294,plain,
% 2.00/2.22 (hskp4),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9293, 109, 859, 7860, 4778])).
% 2.00/2.22 tff(9295,plain,
% 2.00/2.22 (~hskp50),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[6209, 9294, 8505])).
% 2.00/2.22 tff(9296,plain,
% 2.00/2.22 (hskp38),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9032, 9295, 7860, 4778, 859, 9294, 109])).
% 2.00/2.22 tff(9297,plain,
% 2.00/2.22 (c0_1(a547)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[677, 9296])).
% 2.00/2.22 tff(9298,plain,
% 2.00/2.22 (c1_1(a547)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[685, 9296])).
% 2.00/2.22 tff(9299,plain,
% 2.00/2.22 (c2_1(a547)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[693, 9296])).
% 2.00/2.22 tff(9300,plain,
% 2.00/2.22 (c0_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[2945, 156, 7861, 9299, 9298, 9297, 9272, 9270, 75])).
% 2.00/2.22 tff(9301,plain,
% 2.00/2.22 (~c0_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1666, 9294])).
% 2.00/2.22 tff(9302,plain,
% 2.00/2.22 (~c2_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1643, 9294])).
% 2.00/2.22 tff(9303,plain,
% 2.00/2.22 (c1_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[193, 9294])).
% 2.00/2.22 tff(9304,plain,
% 2.00/2.22 (~c3_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1586, 9299, 859, 9303, 9297, 9298, 9302, 9301])).
% 2.00/2.22 tff(9305,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[4571, 156, 8505, 9272, 9270, 9302, 9301, 85, 9304, 9300])).
% 2.00/2.22 tff(9306,plain,(hskp15 | hskp39 | c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9307,plain,
% 2.00/2.22 (hskp39),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9306, 9287, 7860, 4778])).
% 2.00/2.22 tff(9308,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[5127, 8480, 8489, 1873, 23, 8479])).
% 2.00/2.22 tff(9309,plain,(hskp4 | (~hskp39)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9310,plain,
% 2.00/2.22 (hskp4),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9309, 9307])).
% 2.00/2.22 tff(9311,plain,
% 2.00/2.22 (~c2_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1643, 9310])).
% 2.00/2.22 tff(9312,plain,
% 2.00/2.22 (c1_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[193, 9310])).
% 2.00/2.22 tff(9313,plain,
% 2.00/2.22 (~c0_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1666, 9310])).
% 2.00/2.22 tff(9314,plain,
% 2.00/2.22 (~hskp50),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[6209, 9310, 8505])).
% 2.00/2.22 tff(9315,plain,
% 2.00/2.22 (~hskp7),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[502, 9113, 9272, 9287, 9270, 9314, 9271])).
% 2.00/2.22 tff(9316,plain,
% 2.00/2.22 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9317,plain,
% 2.00/2.22 ((hskp40 | hskp7 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537))) <=> (hskp40 | hskp7 | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9318,plain,
% 2.00/2.22 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9317])).
% 2.00/2.22 tff(9319,plain,
% 2.00/2.22 (((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9318, 9316])).
% 2.00/2.22 tff(9320,plain,
% 2.00/2.22 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp40 | hskp7 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9321,plain,
% 2.00/2.22 ((~![U: $i] : (hskp40 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp40 | hskp7 | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9320, 9319])).
% 2.00/2.22 tff(9322,plain,
% 2.00/2.22 (hskp40 | hskp7 | (~c2_1(a537)) | (~c0_1(a537))),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9321, 156, 4778, 513])).
% 2.00/2.22 tff(9323,plain,
% 2.00/2.22 (hskp40),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9322, 9315, 8968, 9268])).
% 2.00/2.22 tff(9324,plain,
% 2.00/2.22 (c3_1(a551)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[540, 9323])).
% 2.00/2.22 tff(9325,plain,
% 2.00/2.22 (c2_1(a551)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[532, 9323])).
% 2.00/2.22 tff(9326,plain,
% 2.00/2.22 (c1_1(a551)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[552, 9325, 9270, 9287, 9272, 9271, 9324])).
% 2.00/2.22 tff(9327,plain,
% 2.00/2.22 (~hskp25),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1301, 1213, 9314, 9113])).
% 2.00/2.22 tff(9328,plain,
% 2.00/2.22 (c1_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[303, 9307])).
% 2.00/2.22 tff(9329,plain,
% 2.00/2.22 (c2_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[311, 9307])).
% 2.00/2.22 tff(9330,plain,
% 2.00/2.22 (c3_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[319, 9307])).
% 2.00/2.22 tff(9331,plain,
% 2.00/2.22 (hskp25 | (~c3_1(a545))),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1184, 156, 9330, 9329, 9328, 9312, 9311, 55])).
% 2.00/2.22 tff(9332,plain,
% 2.00/2.22 (~c3_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9331, 9327])).
% 2.00/2.22 tff(9333,plain,
% 2.00/2.22 (c3_1(a545) | (~c0_1(a544))),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[4571, 156, 8505, 9272, 9270, 9311, 9313, 85])).
% 2.00/2.22 tff(9334,plain,
% 2.00/2.22 (~c0_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9333, 9332])).
% 2.00/2.22 tff(9335,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a544) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c0_1(a544) | (~c1_1(a544)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9336,plain,
% 2.00/2.22 ((hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544))) <=> (hskp34 | c3_1(a544) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c0_1(a544) | (~c1_1(a544)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9337,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a544) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c0_1(a544) | (~c1_1(a544))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9336])).
% 2.00/2.22 tff(9338,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c0_1(a544) | (~c1_1(a544)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9337, 9335])).
% 2.00/2.22 tff(9339,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a544) | c0_1(a544) | (~c1_1(a544)))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9340,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a544) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c0_1(a544) | (~c1_1(a544))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9339, 9338])).
% 2.00/2.22 tff(9341,plain,
% 2.00/2.22 ((~c0_1(a549)) | c0_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9340, 156, 7861, 9329, 9328, 9272, 9270, 75])).
% 2.00/2.22 tff(9342,plain,
% 2.00/2.22 (~c0_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9341, 9334])).
% 2.00/2.22 tff(9343,plain,
% 2.00/2.22 (hskp41 | hskp9 | c0_1(a549)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1513, 156, 9330, 9328, 342])).
% 2.00/2.22 tff(9344,plain,
% 2.00/2.22 (hskp41),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9343, 9342, 1315])).
% 2.00/2.22 tff(9345,plain,
% 2.00/2.22 (~c2_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[232, 9344])).
% 2.00/2.22 tff(9346,plain,
% 2.00/2.22 (c3_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[256, 9344])).
% 2.00/2.22 tff(9347,plain,
% 2.00/2.22 (~c1_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[2014, 156, 9327, 9346, 9324, 9325, 9345, 55, 9326])).
% 2.00/2.22 tff(9348,plain,
% 2.00/2.22 (c0_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[240, 9344])).
% 2.00/2.22 tff(9349,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9002, 156, 9346, 9348, 7860, 9345, 4778, 921, 8968, 9347])).
% 2.00/2.22 tff(9350,plain,(hskp28 | c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9351,plain,
% 2.00/2.22 (hskp28),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9350, 7860, 4778])).
% 2.00/2.22 tff(9352,plain,
% 2.00/2.22 (c2_1(a589)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[171, 9351])).
% 2.00/2.22 tff(9353,plain,
% 2.00/2.22 (c3_1(a589)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[185, 9351])).
% 2.00/2.22 tff(9354,plain,
% 2.00/2.22 (c1_1(a589)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[2512, 9353, 9269, 9287, 9352])).
% 2.00/2.22 tff(9355,plain,
% 2.00/2.22 (~c0_1(a589)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[177, 9351])).
% 2.00/2.22 tff(9356,plain,
% 2.00/2.22 (hskp46),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8118, 156, 9268, 9352, 4778, 9355, 2215, 9354, 8968])).
% 2.00/2.22 tff(9357,plain,
% 2.00/2.22 (~c0_1(a562)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[64, 9356])).
% 2.00/2.22 tff(9358,plain,
% 2.00/2.22 (c1_1(a562)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[288, 9356])).
% 2.00/2.22 tff(9359,plain,
% 2.00/2.22 (~c3_1(a562)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[270, 9356])).
% 2.00/2.22 tff(9360,plain,
% 2.00/2.22 (~hskp38),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9166, 9359, 7861, 9358, 9357])).
% 2.00/2.22 tff(9361,plain,
% 2.00/2.22 (~c3_1(a545)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1211, 9360, 9312, 9311, 9313])).
% 2.00/2.22 tff(9362,plain,
% 2.00/2.22 (~hskp9),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9248, 9361, 9287, 9312, 9311])).
% 2.00/2.22 tff(9363,plain,
% 2.00/2.22 (hskp41 | hskp9),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[597, 156, 9353, 9355, 342, 9354])).
% 2.00/2.22 tff(9364,plain,
% 2.00/2.22 (hskp41),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9363, 9362])).
% 2.00/2.22 tff(9365,plain,
% 2.00/2.22 (~c2_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[232, 9364])).
% 2.00/2.22 tff(9366,plain,
% 2.00/2.22 (c0_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[240, 9364])).
% 2.00/2.22 tff(9367,plain,
% 2.00/2.22 (c3_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[256, 9364])).
% 2.00/2.22 tff(9368,plain,
% 2.00/2.22 (c1_1(a555)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9002, 156, 9367, 9366, 7860, 9365, 4778, 921, 8968])).
% 2.00/2.22 tff(9369,plain,
% 2.00/2.22 (~c0_1(a544)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9333, 9361])).
% 2.00/2.22 tff(9370,plain,
% 2.00/2.22 (~hskp26),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1659, 9360, 8505, 9313, 9310])).
% 2.00/2.22 tff(9371,plain,
% 2.00/2.22 (~hskp19),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9257, 9370, 9361, 9310])).
% 2.00/2.22 tff(9372,plain,
% 2.00/2.22 (~hskp45),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[833, 9361, 8505, 9371, 9313, 9311])).
% 2.00/2.22 tff(9373,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a555) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a555)) | (~c0_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a555)) | (~c0_1(a555)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9374,plain,
% 2.00/2.22 ((hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a544) | c3_1(a544) | c0_1(a544)) <=> (hskp45 | c2_1(a555) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a555)) | (~c0_1(a555)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9375,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | c2_1(a555) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a555)) | (~c0_1(a555))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9374])).
% 2.00/2.22 tff(9376,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a544) | c3_1(a544) | c0_1(a544))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a555)) | (~c0_1(a555)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9375, 9373])).
% 2.00/2.22 tff(9377,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a555) | (~c0_1(a555)) | (~c1_1(a555)) | c2_1(a544) | c3_1(a544) | c0_1(a544))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9378,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | c2_1(a555) | c2_1(a544) | c3_1(a544) | (~ndr1_0) | c0_1(a544) | (~c1_1(a555)) | (~c0_1(a555))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9377, 9376])).
% 2.00/2.22 tff(9379,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9378, 156, 9372, 9366, 9365, 9271, 9270, 757, 9369, 9368])).
% 2.00/2.22 tff(9380,plain,(c3_1(a537) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9381,plain,
% 2.00/2.22 (c3_1(a537)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9380, 4778])).
% 2.00/2.22 tff(9382,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[6019, 156, 109, 9381, 3797, 4778, 86, 483, 653, 8968])).
% 2.00/2.22 tff(9383,plain,(c2_1(a586) | hskp15 | (~c1_1(a586)) | c1_1(a537) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9384,plain,
% 2.00/2.22 (c2_1(a586)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9383, 8489, 109, 4778, 8479])).
% 2.00/2.22 tff(9385,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9386,plain,
% 2.00/2.22 ((hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537))) <=> (hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9387,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9386])).
% 2.00/2.22 tff(9388,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9387, 9385])).
% 2.00/2.22 tff(9389,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c1_1(a586)) | c1_1(a537) | c0_1(a537) | (~c3_1(a537)))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9390,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c0_1(a537) | c1_1(a537) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9389, 9388])).
% 2.00/2.22 tff(9391,plain,
% 2.00/2.22 (hskp26 | c0_1(a537)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9390, 156, 9381, 3797, 4778, 87, 86, 1686])).
% 2.00/2.22 tff(9392,plain,
% 2.00/2.22 (c0_1(a537)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9391, 1661])).
% 2.00/2.22 tff(9393,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9394,plain,
% 2.00/2.22 ((hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp10 | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9395,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9394])).
% 2.00/2.22 tff(9396,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9395, 9393])).
% 2.00/2.22 tff(9397,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9398,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)) | (~c0_1(a537))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9397, 9396])).
% 2.00/2.22 tff(9399,plain,
% 2.00/2.22 (hskp10 | (~c2_1(a586)) | (~c0_1(a537))),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9398, 156, 9381, 3797, 87, 8092, 8968])).
% 2.00/2.22 tff(9400,plain,
% 2.00/2.22 (hskp10),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9399, 9392, 902])).
% 2.00/2.22 tff(9401,plain,
% 2.00/2.22 (~c0_1(a558)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8105, 9400])).
% 2.00/2.22 tff(9402,plain,
% 2.00/2.22 (~c1_1(a558)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8111, 9400])).
% 2.00/2.22 tff(9403,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9404,plain,
% 2.00/2.22 ((hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp46 | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(9405,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a537)) | (~c0_1(a537))))),
% 2.00/2.22 inference(monotonicity,[status(thm)],[9404])).
% 2.00/2.22 tff(9406,plain,
% 2.00/2.22 (((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.00/2.22 inference(transitivity,[status(thm)],[9405, 9403])).
% 2.00/2.22 tff(9407,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp46 | (~ndr1_0) | c1_1(a537) | (~c2_1(a537)) | (~c0_1(a537)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 2.00/2.22 inference(quant_inst,[status(thm)],[])).
% 2.00/2.22 tff(9408,plain,
% 2.00/2.22 ((~![V: $i, U: $i] : (hskp46 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp46 | c1_1(a537) | c0_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a586)) | (~c2_1(a537)) | (~c0_1(a537))),
% 2.00/2.22 inference(modus_ponens,[status(thm)],[9407, 9406])).
% 2.00/2.22 tff(9409,plain,
% 2.00/2.22 (hskp46 | (~c2_1(a586)) | (~c0_1(a537))),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9408, 156, 3797, 4778, 87, 2215, 8968])).
% 2.00/2.22 tff(9410,plain,
% 2.00/2.22 (hskp46),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9409, 9392, 902])).
% 2.00/2.22 tff(9411,plain,
% 2.00/2.22 (~c0_1(a562)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[64, 9410])).
% 2.00/2.22 tff(9412,plain,
% 2.00/2.22 (~c3_1(a562)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[270, 9410])).
% 2.00/2.22 tff(9413,plain,
% 2.00/2.22 (c3_1(a558)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8129, 9400])).
% 2.00/2.22 tff(9414,plain,
% 2.00/2.22 (c1_1(a562)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[288, 9410])).
% 2.00/2.22 tff(9415,plain,
% 2.00/2.22 ($false),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[8137, 156, 1661, 9414, 9413, 9412, 9411, 9402, 9401, 1686])).
% 2.00/2.22 tff(9416,plain,(hskp26 | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a537) | c0_1(a586) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.22 tff(9417,plain,
% 2.00/2.22 (hskp26),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[9416, 9384, 8489, 4778, 8480, 8479])).
% 2.00/2.22 tff(9418,plain,
% 2.00/2.22 (~c3_1(a584)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1620, 9417])).
% 2.00/2.22 tff(9419,plain,
% 2.00/2.22 (c1_1(a584)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1637, 9417])).
% 2.00/2.22 tff(9420,plain,
% 2.00/2.22 (c0_1(a584)),
% 2.00/2.22 inference(unit_resolution,[status(thm)],[1629, 9417])).
% 2.00/2.23 tff(9421,plain,
% 2.00/2.23 (hskp32),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5867, 156, 8489, 9420, 9419, 8479, 9418, 4894, 9384])).
% 2.00/2.23 tff(9422,plain,
% 2.00/2.23 (~c2_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5534, 9421])).
% 2.00/2.23 tff(9423,plain,
% 2.00/2.23 (~c3_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5528, 9421])).
% 2.00/2.23 tff(9424,plain,
% 2.00/2.23 (~c1_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8361, 156, 109, 9381, 4778, 9423, 9422, 483, 8968])).
% 2.00/2.23 tff(9425,plain,
% 2.00/2.23 (c0_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5522, 9421])).
% 2.00/2.23 tff(9426,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5542, 156, 9171, 9425, 8489, 9422, 8479, 3950, 9384, 9424])).
% 2.00/2.23 tff(9427,plain,(hskp4 | hskp15 | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.23 tff(9428,plain,
% 2.00/2.23 (hskp4),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9427, 109, 4778])).
% 2.00/2.23 tff(9429,plain,
% 2.00/2.23 (~c2_1(a545)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1643, 9428])).
% 2.00/2.23 tff(9430,plain,
% 2.00/2.23 (c1_1(a545)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[193, 9428])).
% 2.00/2.23 tff(9431,plain,
% 2.00/2.23 (c3_1(a545)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[2094, 156, 109, 9381, 9430, 4778, 9429, 483, 8968])).
% 2.00/2.23 tff(9432,plain,
% 2.00/2.23 (~c0_1(a545)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1666, 9428])).
% 2.00/2.23 tff(9433,plain,
% 2.00/2.23 (hskp38),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1211, 9431, 9430, 9429, 9432])).
% 2.00/2.23 tff(9434,plain,
% 2.00/2.23 (c1_1(a547)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[685, 9433])).
% 2.00/2.23 tff(9435,plain,
% 2.00/2.23 (c0_1(a547)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[677, 9433])).
% 2.00/2.23 tff(9436,plain,
% 2.00/2.23 (c2_1(a547)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[693, 9433])).
% 2.00/2.23 tff(9437,plain,
% 2.00/2.23 (hskp39),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1586, 9436, 9431, 9430, 9435, 9434, 9429, 9432])).
% 2.00/2.23 tff(9438,plain,
% 2.00/2.23 (c1_1(a549)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[303, 9437])).
% 2.00/2.23 tff(9439,plain,
% 2.00/2.23 (c2_1(a549)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[311, 9437])).
% 2.00/2.23 tff(9440,plain,
% 2.00/2.23 (c3_1(a549)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[319, 9437])).
% 2.00/2.23 tff(9441,plain,
% 2.00/2.23 (hskp25),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1184, 156, 9440, 9439, 9438, 9430, 9429, 55, 9431])).
% 2.00/2.23 tff(9442,plain,
% 2.00/2.23 (~c1_1(a582)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1190, 9441])).
% 2.00/2.23 tff(9443,plain,
% 2.00/2.23 (~c2_1(a582)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1196, 9441])).
% 2.00/2.23 tff(9444,plain,
% 2.00/2.23 (~c3_1(a582)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1202, 9441])).
% 2.00/2.23 tff(9445,plain,
% 2.00/2.23 (hskp42),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1574, 156, 9436, 9434, 9435, 9430, 9429, 1364, 9431])).
% 2.00/2.23 tff(9446,plain,
% 2.00/2.23 (~c2_1(a556)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1385, 9445])).
% 2.00/2.23 tff(9447,plain,
% 2.00/2.23 (c3_1(a556)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1403, 9445])).
% 2.00/2.23 tff(9448,plain,
% 2.00/2.23 (c1_1(a556)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1411, 9445])).
% 2.00/2.23 tff(9449,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[2192, 156, 9448, 9447, 9381, 9446, 4778, 9444, 9443, 9442, 45, 8968])).
% 2.00/2.23 tff(9450,plain,(hskp15 | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.23 tff(9451,plain,
% 2.00/2.23 (hskp15),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9450, 4778])).
% 2.00/2.23 tff(9452,plain,
% 2.00/2.23 (hskp28),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1276, 9451])).
% 2.00/2.23 tff(9453,plain,
% 2.00/2.23 (hskp26),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8580, 9451, 9452])).
% 2.00/2.23 tff(9454,plain,
% 2.00/2.23 (c0_1(a584)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1629, 9453])).
% 2.00/2.23 tff(9455,plain,
% 2.00/2.23 (~c0_1(a589)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[177, 9452])).
% 2.00/2.23 tff(9456,plain,
% 2.00/2.23 (c3_1(a589)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[185, 9452])).
% 2.00/2.23 tff(9457,plain,
% 2.00/2.23 (c2_1(a589)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[171, 9452])).
% 2.00/2.23 tff(9458,plain,
% 2.00/2.23 (c1_1(a584)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1637, 9453])).
% 2.00/2.23 tff(9459,plain,
% 2.00/2.23 (~c2_1(a569)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1255, 9451])).
% 2.00/2.23 tff(9460,plain,
% 2.00/2.23 (~c1_1(a569)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1261, 9451])).
% 2.00/2.23 tff(9461,plain,
% 2.00/2.23 (~c3_1(a584)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1620, 9453])).
% 2.00/2.23 tff(9462,plain,
% 2.00/2.23 (hskp34),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8504, 3667])).
% 2.00/2.23 tff(9463,plain,
% 2.00/2.23 (c0_1(a537)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1147, 9462])).
% 2.00/2.23 tff(9464,plain,
% 2.00/2.23 ((~hskp15) | hskp8 | (~c3_1(a537)) | (~c0_1(a537)) | c1_1(a537)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8300, 8476])).
% 2.00/2.23 tff(9465,plain,
% 2.00/2.23 (hskp8),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9464, 9463, 9381, 9451, 4778])).
% 2.00/2.23 tff(9466,plain,
% 2.00/2.23 (hskp0),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[7624, 9465, 3667])).
% 2.00/2.23 tff(9467,plain,
% 2.00/2.23 (~c2_1(a535)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[713, 9466])).
% 2.00/2.23 tff(9468,plain,
% 2.00/2.23 (hskp51),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[6599, 9465, 9463, 9381, 4778])).
% 2.00/2.23 tff(9469,plain,
% 2.00/2.23 (~c2_1(a583)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[2637, 9468])).
% 2.00/2.23 tff(9470,plain,
% 2.00/2.23 (c0_1(a535)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[721, 9466])).
% 2.00/2.23 tff(9471,plain,
% 2.00/2.23 (c1_1(a535)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[729, 9466])).
% 2.00/2.23 tff(9472,plain,
% 2.00/2.23 (c3_1(a583)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[2645, 9468])).
% 2.00/2.23 tff(9473,plain,
% 2.00/2.23 (c1_1(a583)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[3478, 156, 9472, 3672, 3671, 3670, 9471, 9470, 9469, 9467, 707])).
% 2.00/2.23 tff(9474,plain,
% 2.00/2.23 (~c2_1(a552)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[2424, 9465])).
% 2.00/2.23 tff(9475,plain,
% 2.00/2.23 (~c1_1(a552)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[2453, 9465])).
% 2.00/2.23 tff(9476,plain,
% 2.00/2.23 (~c3_1(a552)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[2430, 9465])).
% 2.00/2.23 tff(9477,plain,
% 2.00/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 2.00/2.23 inference(rewrite,[status(thm)],[])).
% 2.00/2.23 tff(9478,plain,
% 2.00/2.23 (((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552)) <=> (c2_1(a583) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 2.00/2.23 inference(rewrite,[status(thm)],[])).
% 2.00/2.23 tff(9479,plain,
% 2.00/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a583) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583))))),
% 2.00/2.23 inference(monotonicity,[status(thm)],[9478])).
% 2.00/2.23 tff(9480,plain,
% 2.00/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583)))),
% 2.00/2.23 inference(transitivity,[status(thm)],[9479, 9477])).
% 2.00/2.23 tff(9481,plain,
% 2.00/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a583) | (~c3_1(a583)) | (~c1_1(a583)) | c1_1(a537) | (~c3_1(a537)) | (~c2_1(a537)) | c2_1(a552) | c1_1(a552) | c3_1(a552))),
% 2.00/2.23 inference(quant_inst,[status(thm)],[])).
% 2.00/2.23 tff(9482,plain,
% 2.00/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a583) | c1_1(a537) | c3_1(a552) | c1_1(a552) | c2_1(a552) | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c3_1(a583)) | (~c1_1(a583))),
% 2.00/2.23 inference(modus_ponens,[status(thm)],[9481, 9480])).
% 2.00/2.23 tff(9483,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9482, 156, 9472, 9381, 9469, 4778, 9476, 9475, 9474, 45, 9473, 8968])).
% 2.00/2.23 tff(9484,plain,((~hskp33) | c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.23 tff(9485,plain,
% 2.00/2.23 (~hskp33),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9484, 4778])).
% 2.00/2.23 tff(9486,plain,
% 2.00/2.23 (~c0_1(a569)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1267, 9451])).
% 2.00/2.23 tff(9487,plain,
% 2.00/2.23 (hskp33 | c3_1(a569)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8702, 156, 9454, 9458, 9461, 9486, 9459, 85])).
% 2.00/2.23 tff(9488,plain,
% 2.00/2.23 (c3_1(a569)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9487, 9485])).
% 2.00/2.23 tff(9489,plain,
% 2.00/2.23 (~c2_1(a584)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8181, 9488, 9461, 9460, 9459, 9458, 9457, 9456, 9455, 9454])).
% 2.00/2.23 tff(9490,plain,
% 2.00/2.23 (hskp33 | c3_1(a569)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8702, 156, 1630, 1638, 1621, 2785, 2774, 85])).
% 2.00/2.23 tff(9491,plain,
% 2.00/2.23 (c3_1(a569)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9490, 35])).
% 2.00/2.23 tff(9492,plain,
% 2.00/2.23 (c2_1(a586)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[3104, 35, 1615, 86, 87])).
% 2.00/2.23 tff(9493,plain,
% 2.00/2.23 (hskp32 | (~c2_1(a586))),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5867, 156, 3797, 1630, 1638, 86, 1621, 4894])).
% 2.00/2.23 tff(9494,plain,
% 2.00/2.23 (hskp32),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9493, 9492])).
% 2.00/2.23 tff(9495,plain,
% 2.00/2.23 (~c2_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5534, 9494])).
% 2.00/2.23 tff(9496,plain,
% 2.00/2.23 (c0_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5522, 9494])).
% 2.00/2.23 tff(9497,plain,
% 2.00/2.23 (~c1_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5798, 156, 9496, 9495, 87, 86, 2785, 2775, 609, 9492, 9491])).
% 2.00/2.23 tff(9498,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5542, 156, 5363, 9496, 3797, 9495, 86, 3950, 9492, 9497])).
% 2.00/2.23 tff(9499,plain,(hskp33 | hskp35 | (~c1_1(a586)) | c3_1(a586) | c0_1(a586) | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~hskp26)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.23 tff(9500,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9499, 9171, 8489, 35, 8479, 8480, 2785, 2775, 2774, 1615])).
% 2.00/2.23 tff(9501,plain,(hskp4 | hskp33 | c0_1(a569) | c1_1(a569) | c2_1(a569) | (~hskp26)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.23 tff(9502,plain,
% 2.00/2.23 (hskp4),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9501, 9485, 9486, 9460, 9459, 9453])).
% 2.00/2.23 tff(9503,plain,
% 2.00/2.23 (~c0_1(a545)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1666, 9502])).
% 2.00/2.23 tff(9504,plain,
% 2.00/2.23 (hskp38),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1657, 9502, 9461, 9458, 9485, 9503, 9454])).
% 2.00/2.23 tff(9505,plain,
% 2.00/2.23 (c0_1(a547)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[677, 9504])).
% 2.00/2.23 tff(9506,plain,
% 2.00/2.23 (c1_1(a547)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[685, 9504])).
% 2.00/2.23 tff(9507,plain,
% 2.00/2.23 (c2_1(a547)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[693, 9504])).
% 2.00/2.23 tff(9508,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8188, 156, 9507, 9506, 9505, 9454, 9458, 9460, 9459, 707, 9488, 9489])).
% 2.00/2.23 tff(9509,plain,(c1_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.00/2.23 tff(9510,plain,
% 2.00/2.23 (~hskp34),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[1124, 9509])).
% 2.00/2.23 tff(9511,plain,
% 2.00/2.23 (~hskp33),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8504, 9510])).
% 2.00/2.23 tff(9512,plain,
% 2.00/2.23 (~hskp39),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9309, 23])).
% 2.00/2.23 tff(9513,plain,
% 2.00/2.23 (hskp24),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[7687, 1615, 9512])).
% 2.00/2.23 tff(9514,plain,
% 2.00/2.23 (~c3_1(a581)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[3513, 9513])).
% 2.00/2.23 tff(9515,plain,
% 2.00/2.23 (c2_1(a581)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[3541, 9513])).
% 2.00/2.23 tff(9516,plain,
% 2.00/2.23 (~c1_1(a581)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[3519, 9513])).
% 2.00/2.23 tff(9517,plain,
% 2.00/2.23 (~hskp17),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5411, 9516, 8489, 8479, 8480, 9512, 9515, 9514])).
% 2.00/2.23 tff(9518,plain,
% 2.00/2.23 (~hskp41),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5654, 9516, 8489, 8480, 8479, 9512, 9515, 9514])).
% 2.00/2.23 tff(9519,plain,
% 2.00/2.23 (c2_1(a586)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[3104, 1615, 8479, 9511, 8480])).
% 2.00/2.23 tff(9520,plain,
% 2.00/2.23 (hskp32),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5867, 156, 8489, 1630, 1638, 8479, 1621, 4894, 9519])).
% 2.00/2.23 tff(9521,plain,
% 2.00/2.23 (c0_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5522, 9520])).
% 2.00/2.23 tff(9522,plain,
% 2.00/2.23 (~c3_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5528, 9520])).
% 2.00/2.23 tff(9523,plain,
% 2.00/2.23 (~c2_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5534, 9520])).
% 2.00/2.23 tff(9524,plain,
% 2.00/2.23 (c1_1(a596)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5542, 156, 9171, 9521, 8489, 9523, 8479, 3950, 9519])).
% 2.00/2.23 tff(9525,plain,
% 2.00/2.23 (~hskp9),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5562, 9524, 8479, 8480, 9523, 9519, 9522, 9511, 9521])).
% 2.00/2.23 tff(9526,plain,
% 2.00/2.23 (~hskp16),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[373, 9525, 9518])).
% 2.00/2.23 tff(9527,plain,
% 2.00/2.23 (hskp18),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[382, 9526, 9517])).
% 2.00/2.23 tff(9528,plain,
% 2.00/2.23 (~c1_1(a572)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[389, 9527])).
% 2.00/2.23 tff(9529,plain,
% 2.00/2.23 (c0_1(a572)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[397, 9527])).
% 2.00/2.23 tff(9530,plain,
% 2.00/2.23 (c2_1(a572)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5426, 9529, 9171, 9519, 8479, 9528, 8489])).
% 2.00/2.23 tff(9531,plain,
% 2.00/2.23 (~c3_1(a572)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[420, 9527])).
% 2.00/2.23 tff(9532,plain,
% 2.00/2.23 (hskp37),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[428, 156, 9529, 9531, 9528, 415, 9530])).
% 2.00/2.23 tff(9533,plain,
% 2.00/2.23 (~c3_1(a544)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[450, 9532])).
% 2.00/2.23 tff(9534,plain,
% 2.00/2.23 (c1_1(a544)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[444, 9532])).
% 2.00/2.23 tff(9535,plain,
% 2.00/2.23 (~c2_1(a544)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[436, 9532])).
% 2.00/2.23 tff(9536,plain,
% 2.00/2.23 (~hskp7),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5466, 9535, 9514, 109, 9515, 9516, 9534, 9533])).
% 2.00/2.23 tff(9537,plain,
% 2.00/2.23 (hskp40 | hskp7),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[521, 156, 9529, 9528, 513, 9530])).
% 2.00/2.23 tff(9538,plain,
% 2.00/2.23 (hskp40),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9537, 9536])).
% 2.00/2.23 tff(9539,plain,
% 2.00/2.23 (c3_1(a551)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[540, 9538])).
% 2.00/2.23 tff(9540,plain,
% 2.00/2.23 (c2_1(a551)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[532, 9538])).
% 2.00/2.23 tff(9541,plain,
% 2.00/2.23 (c1_1(a551)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[552, 9540, 9533, 109, 9534, 9535, 9539])).
% 2.00/2.23 tff(9542,plain,
% 2.00/2.23 (hskp46),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5478, 156, 8489, 9529, 8480, 9528, 2215, 9519, 9530])).
% 2.00/2.23 tff(9543,plain,
% 2.00/2.23 (~c0_1(a562)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[64, 9542])).
% 2.00/2.23 tff(9544,plain,
% 2.00/2.23 (~c3_1(a562)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[270, 9542])).
% 2.00/2.23 tff(9545,plain,
% 2.00/2.23 (c1_1(a562)),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[288, 9542])).
% 2.00/2.23 tff(9546,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5488, 156, 23, 9545, 9539, 9540, 9544, 9543, 22, 9541])).
% 2.00/2.23 tff(9547,plain,((~hskp26) | hskp4 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.00/2.23 tff(9548,plain,
% 2.00/2.23 (~hskp26),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[9547, 23, 109])).
% 2.00/2.23 tff(9549,plain,
% 2.00/2.23 (~hskp28),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8491, 9548, 23])).
% 2.00/2.23 tff(9550,plain,
% 2.00/2.23 (~hskp40),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5159, 9548, 23, 8489, 8479, 8480])).
% 2.00/2.23 tff(9551,plain,
% 2.00/2.23 (~hskp28),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[8491, 1661, 23])).
% 2.00/2.23 tff(9552,plain,
% 2.00/2.23 (~hskp40),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[5159, 1661, 23, 8489, 8479, 8480])).
% 2.00/2.23 tff(9553,plain,
% 2.00/2.23 (hskp7),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[524, 384, 110, 515, 98])).
% 2.00/2.23 tff(9554,plain,
% 2.00/2.23 ($false),
% 2.00/2.23 inference(unit_resolution,[status(thm)],[502, 888, 9553, 98, 109, 889, 110, 887])).
% 2.08/2.23 tff(9555,plain,((~hskp18) | hskp19 | hskp15 | hskp50 | hskp40), inference(lemma,lemma(discharge,[]))).
% 2.08/2.23 tff(9556,plain,
% 2.08/2.23 (~hskp18),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9555, 110, 515, 109, 9113])).
% 2.08/2.23 tff(9557,plain,
% 2.08/2.23 (~hskp25),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[1301, 110, 1213, 9113])).
% 2.08/2.23 tff(9558,plain,
% 2.08/2.23 (~hskp16),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5107, 9557, 8489, 23, 8480, 8479])).
% 2.08/2.23 tff(9559,plain,
% 2.08/2.23 (hskp17),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[382, 9558, 9556])).
% 2.08/2.23 tff(9560,plain,
% 2.08/2.23 (~c2_1(a571)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[573, 9559])).
% 2.08/2.23 tff(9561,plain,
% 2.08/2.23 (c0_1(a571)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[581, 9559])).
% 2.08/2.23 tff(9562,plain,
% 2.08/2.23 (c1_1(a571)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[588, 156, 110, 9113, 9561, 9560, 34])).
% 2.08/2.23 tff(9563,plain,
% 2.08/2.23 (c3_1(a571)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[623, 9559])).
% 2.08/2.23 tff(9564,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9565,plain,
% 2.08/2.23 ((hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537))) <=> (hskp39 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9566,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571))))),
% 2.08/2.23 inference(monotonicity,[status(thm)],[9565])).
% 2.08/2.23 tff(9567,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571)))),
% 2.08/2.23 inference(transitivity,[status(thm)],[9566, 9564])).
% 2.08/2.23 tff(9568,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a571) | (~c3_1(a571)) | (~c1_1(a571)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))),
% 2.08/2.23 inference(quant_inst,[status(thm)],[])).
% 2.08/2.23 tff(9569,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | c2_1(a571) | (~ndr1_0) | (~c3_1(a571)) | (~c1_1(a571))),
% 2.08/2.23 inference(modus_ponens,[status(thm)],[9568, 9567])).
% 2.08/2.23 tff(9570,plain,
% 2.08/2.23 ($false),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9569, 156, 9512, 7925, 7860, 9563, 9509, 9560, 281, 9562])).
% 2.08/2.23 tff(9571,plain,(hskp50 | c0_1(a537) | c3_1(a537) | hskp4 | hskp40 | hskp15 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.08/2.23 tff(9572,plain,
% 2.08/2.23 (hskp50),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9571, 7925, 7860, 23, 515, 109, 1213])).
% 2.08/2.23 tff(9573,plain,
% 2.08/2.23 (~c3_1(a574)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[799, 9572])).
% 2.08/2.23 tff(9574,plain,
% 2.08/2.23 (c1_1(a574)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[807, 9572])).
% 2.08/2.23 tff(9575,plain,
% 2.08/2.23 (c0_1(a574)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[815, 9572])).
% 2.08/2.23 tff(9576,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a574) | (~ndr1_0) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a574) | (~ndr1_0) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9577,plain,
% 2.08/2.23 ((hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c3_1(a537) | c0_1(a537)) <=> (hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a574) | (~ndr1_0) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9578,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c3_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a574) | (~ndr1_0) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574))))),
% 2.08/2.23 inference(monotonicity,[status(thm)],[9577])).
% 2.08/2.23 tff(9579,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c3_1(a537) | c0_1(a537))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a574) | (~ndr1_0) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.08/2.23 inference(transitivity,[status(thm)],[9578, 9576])).
% 2.08/2.23 tff(9580,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c2_1(a537) | c3_1(a537) | c0_1(a537))),
% 2.08/2.23 inference(quant_inst,[status(thm)],[])).
% 2.08/2.23 tff(9581,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c0_1(a537) | c3_1(a537) | c3_1(a574) | (~ndr1_0) | c2_1(a537) | (~c0_1(a574)) | (~c1_1(a574))),
% 2.08/2.23 inference(modus_ponens,[status(thm)],[9580, 9579])).
% 2.08/2.23 tff(9582,plain,
% 2.08/2.23 ($false),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9581, 156, 9511, 9575, 9574, 7925, 7860, 9573, 85, 4777])).
% 2.08/2.23 tff(9583,plain,(c0_1(a537) | c3_1(a537) | c2_1(a537) | hskp4 | hskp40 | hskp15 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.08/2.23 tff(9584,plain,
% 2.08/2.23 (c0_1(a537)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9583, 9552, 4777, 23, 7860, 109, 9551])).
% 2.08/2.23 tff(9585,plain,
% 2.08/2.23 (hskp39 | hskp24 | c2_1(a537) | (~c0_1(a537))),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[8519, 156, 7860, 3496])).
% 2.08/2.23 tff(9586,plain,
% 2.08/2.23 (hskp24),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9585, 9584, 9512, 4777])).
% 2.08/2.23 tff(9587,plain,
% 2.08/2.23 (~c3_1(a581)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[3513, 9586])).
% 2.08/2.23 tff(9588,plain,
% 2.08/2.23 (c2_1(a581)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[3541, 9586])).
% 2.08/2.23 tff(9589,plain,
% 2.08/2.23 (~c1_1(a581)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[3519, 9586])).
% 2.08/2.23 tff(9590,plain,
% 2.08/2.23 (~hskp17),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5411, 9589, 8489, 8479, 8480, 9512, 9588, 9587])).
% 2.08/2.23 tff(9591,plain,
% 2.08/2.23 (~hskp9),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[1314, 9551])).
% 2.08/2.23 tff(9592,plain,
% 2.08/2.23 (~hskp41),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5654, 9589, 8489, 8480, 8479, 9512, 9588, 9587])).
% 2.08/2.23 tff(9593,plain,
% 2.08/2.23 (~hskp16),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[373, 9592, 9591])).
% 2.08/2.23 tff(9594,plain,
% 2.08/2.23 (hskp18),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[382, 9593, 9590])).
% 2.08/2.23 tff(9595,plain,
% 2.08/2.23 (~c1_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[389, 9594])).
% 2.08/2.23 tff(9596,plain,
% 2.08/2.23 (~hskp19),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5069, 9551])).
% 2.08/2.23 tff(9597,plain,
% 2.08/2.23 (hskp50),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[567, 9592, 109, 9596, 9590, 9591])).
% 2.08/2.23 tff(9598,plain,
% 2.08/2.23 (c2_1(a586)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[2766, 9597, 9511, 8480, 8479])).
% 2.08/2.23 tff(9599,plain,
% 2.08/2.23 (c0_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[397, 9594])).
% 2.08/2.23 tff(9600,plain,
% 2.08/2.23 (c2_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5426, 9599, 9171, 9598, 8479, 9595, 8489])).
% 2.08/2.23 tff(9601,plain,
% 2.08/2.23 (~c3_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[420, 9594])).
% 2.08/2.23 tff(9602,plain,
% 2.08/2.23 (hskp37),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[428, 156, 9599, 9601, 9595, 415, 9600])).
% 2.08/2.23 tff(9603,plain,
% 2.08/2.23 (~c3_1(a544)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[450, 9602])).
% 2.08/2.23 tff(9604,plain,
% 2.08/2.23 (hskp7),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[521, 156, 9552, 9599, 9595, 513, 9600])).
% 2.08/2.23 tff(9605,plain,
% 2.08/2.23 (c1_1(a544)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[444, 9602])).
% 2.08/2.23 tff(9606,plain,
% 2.08/2.23 (~c2_1(a544)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[436, 9602])).
% 2.08/2.23 tff(9607,plain,
% 2.08/2.23 ($false),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5466, 9606, 9605, 9587, 109, 9588, 9589, 9604, 9603])).
% 2.08/2.23 tff(9608,plain,(hskp26 | hskp15 | c2_1(a537) | c3_1(a537) | hskp4), inference(lemma,lemma(discharge,[]))).
% 2.08/2.23 tff(9609,plain,
% 2.08/2.23 (c2_1(a537)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9608, 9548, 109, 7860, 23])).
% 2.08/2.23 tff(9610,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9611,plain,
% 2.08/2.23 ((hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp34 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9612,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a537)) | (~c0_1(a537))))),
% 2.08/2.23 inference(monotonicity,[status(thm)],[9611])).
% 2.08/2.23 tff(9613,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.08/2.23 inference(transitivity,[status(thm)],[9612, 9610])).
% 2.08/2.23 tff(9614,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 2.08/2.23 inference(quant_inst,[status(thm)],[])).
% 2.08/2.23 tff(9615,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c2_1(a537)) | (~c0_1(a537))),
% 2.08/2.23 inference(modus_ponens,[status(thm)],[9614, 9613])).
% 2.08/2.23 tff(9616,plain,
% 2.08/2.23 (~c0_1(a537)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9615, 156, 9510, 8489, 9509, 8480, 8479, 75, 9609])).
% 2.08/2.23 tff(9617,plain,
% 2.08/2.23 (hskp50),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9571, 9616, 7860, 23, 9550, 109, 9549])).
% 2.08/2.23 tff(9618,plain,
% 2.08/2.23 (c0_1(a574)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[815, 9617])).
% 2.08/2.23 tff(9619,plain,
% 2.08/2.23 (c1_1(a574)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[807, 9617])).
% 2.08/2.23 tff(9620,plain,
% 2.08/2.23 (c2_1(a586)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[2766, 9617, 9511, 8480, 8479])).
% 2.08/2.23 tff(9621,plain,
% 2.08/2.23 (~c3_1(a574)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[799, 9617])).
% 2.08/2.23 tff(9622,plain,
% 2.08/2.23 (~hskp25),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5379, 9621, 9620, 9171, 8489, 9619, 9618, 8479, 9511])).
% 2.08/2.23 tff(9623,plain,
% 2.08/2.23 (~hskp16),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5107, 9622, 8489, 23, 8480, 8479])).
% 2.08/2.23 tff(9624,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a537) | c3_1(a574) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a574)) | (~c1_1(a574)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a537) | c3_1(a574) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9625,plain,
% 2.08/2.23 ((hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a537) | (~c1_1(a537)) | (~c2_1(a537))) <=> (hskp32 | c3_1(a537) | c3_1(a574) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9626,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a537) | (~c1_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | c3_1(a537) | c3_1(a574) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a574)) | (~c1_1(a574))))),
% 2.08/2.23 inference(monotonicity,[status(thm)],[9625])).
% 2.08/2.23 tff(9627,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a537) | (~c1_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a537) | c3_1(a574) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a574)) | (~c1_1(a574)))),
% 2.08/2.23 inference(transitivity,[status(thm)],[9626, 9624])).
% 2.08/2.23 tff(9628,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp32 | (~ndr1_0) | c3_1(a574) | (~c0_1(a574)) | (~c1_1(a574)) | c3_1(a537) | (~c1_1(a537)) | (~c2_1(a537)))),
% 2.08/2.23 inference(quant_inst,[status(thm)],[])).
% 2.08/2.23 tff(9629,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp32 | c3_1(a537) | c3_1(a574) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a574)) | (~c1_1(a574))),
% 2.08/2.23 inference(modus_ponens,[status(thm)],[9628, 9627])).
% 2.08/2.23 tff(9630,plain,
% 2.08/2.23 (hskp32),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9629, 156, 9618, 9619, 7860, 9621, 9509, 4894, 9609])).
% 2.08/2.23 tff(9631,plain,
% 2.08/2.23 (hskp24),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9193, 9630, 9512])).
% 2.08/2.23 tff(9632,plain,
% 2.08/2.23 (~c3_1(a581)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[3513, 9631])).
% 2.08/2.23 tff(9633,plain,
% 2.08/2.23 (c2_1(a581)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[3541, 9631])).
% 2.08/2.23 tff(9634,plain,
% 2.08/2.23 (~c1_1(a581)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[3519, 9631])).
% 2.08/2.23 tff(9635,plain,
% 2.08/2.23 (~hskp17),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5411, 9634, 8489, 8479, 8480, 9512, 9633, 9632])).
% 2.08/2.23 tff(9636,plain,
% 2.08/2.23 (hskp18),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[382, 9635, 9623])).
% 2.08/2.23 tff(9637,plain,
% 2.08/2.23 (~c1_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[389, 9636])).
% 2.08/2.23 tff(9638,plain,
% 2.08/2.23 (c0_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[397, 9636])).
% 2.08/2.23 tff(9639,plain,
% 2.08/2.23 (c2_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5426, 9638, 9171, 9620, 8479, 9637, 8489])).
% 2.08/2.23 tff(9640,plain,
% 2.08/2.23 (~c3_1(a572)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[420, 9636])).
% 2.08/2.23 tff(9641,plain,
% 2.08/2.23 (hskp37),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[428, 156, 9638, 9640, 9637, 415, 9639])).
% 2.08/2.23 tff(9642,plain,
% 2.08/2.23 (~c3_1(a544)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[450, 9641])).
% 2.08/2.23 tff(9643,plain,
% 2.08/2.23 (hskp7),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[521, 156, 9550, 9638, 9637, 513, 9639])).
% 2.08/2.23 tff(9644,plain,
% 2.08/2.23 (c1_1(a544)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[444, 9641])).
% 2.08/2.23 tff(9645,plain,
% 2.08/2.23 (~c2_1(a544)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[436, 9641])).
% 2.08/2.23 tff(9646,plain,
% 2.08/2.23 ($false),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[5466, 9645, 9644, 9632, 109, 9633, 9634, 9643, 9642])).
% 2.08/2.23 tff(9647,plain,(hskp4 | hskp15 | c3_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.23 tff(9648,plain,
% 2.08/2.23 (hskp4),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9647, 109, 7860])).
% 2.08/2.23 tff(9649,plain,
% 2.08/2.23 (~c2_1(a545)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[1643, 9648])).
% 2.08/2.23 tff(9650,plain,
% 2.08/2.23 (c1_1(a545)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[193, 9648])).
% 2.08/2.23 tff(9651,plain,
% 2.08/2.23 (~c0_1(a545)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[1666, 9648])).
% 2.08/2.23 tff(9652,plain,
% 2.08/2.23 (~c3_1(a545)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[1586, 2771, 859, 1046, 2769, 2770, 111, 97])).
% 2.08/2.23 tff(9653,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a537) | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a537) | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a537)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9654,plain,
% 2.08/2.23 ((hskp33 | (~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp33 | c3_1(a537) | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a537)))),
% 2.08/2.23 inference(rewrite,[status(thm)],[])).
% 2.08/2.23 tff(9655,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | c3_1(a537) | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a537))))),
% 2.08/2.23 inference(monotonicity,[status(thm)],[9654])).
% 2.08/2.23 tff(9656,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a537) | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a537)))),
% 2.08/2.23 inference(transitivity,[status(thm)],[9655, 9653])).
% 2.08/2.23 tff(9657,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp33 | (~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 2.08/2.23 inference(quant_inst,[status(thm)],[])).
% 2.08/2.23 tff(9658,plain,
% 2.08/2.23 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp33 | c3_1(a537) | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c0_1(a537))),
% 2.08/2.23 inference(modus_ponens,[status(thm)],[9657, 9656])).
% 2.08/2.23 tff(9659,plain,
% 2.08/2.23 (c3_1(a545) | (~c0_1(a537))),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9658, 156, 9511, 7860, 9509, 111, 97, 85])).
% 2.08/2.23 tff(9660,plain,
% 2.08/2.23 (~c0_1(a537)),
% 2.08/2.23 inference(unit_resolution,[status(thm)],[9659, 9652])).
% 2.08/2.23 tff(9661,plain,
% 2.08/2.23 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9662,plain,
% 2.08/2.24 ((hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537))) <=> (hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9663,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9662])).
% 2.08/2.24 tff(9664,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)))),
% 2.08/2.24 inference(transitivity,[status(thm)],[9663, 9661])).
% 2.08/2.24 tff(9665,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))),
% 2.08/2.24 inference(quant_inst,[status(thm)],[])).
% 2.08/2.24 tff(9666,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a547)) | (~c0_1(a547)) | (~c1_1(a547))),
% 2.08/2.24 inference(modus_ponens,[status(thm)],[9665, 9664])).
% 2.08/2.24 tff(9667,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9666, 156, 9510, 2771, 2770, 2769, 9660, 7860, 9509, 75])).
% 2.08/2.24 tff(9668,plain,((~hskp38) | c3_1(a537) | c2_1(a545) | c0_1(a545) | hskp39 | (~c1_1(a545))), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9669,plain,
% 2.08/2.24 (~hskp38),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9668, 859, 9649, 9651, 7860, 9650])).
% 2.08/2.24 tff(9670,plain,
% 2.08/2.24 (~c3_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1211, 9669, 9650, 9649, 9651])).
% 2.08/2.24 tff(9671,plain,
% 2.08/2.24 (~hskp9),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9248, 9670, 109, 9650, 9649])).
% 2.08/2.24 tff(9672,plain,
% 2.08/2.24 (~hskp26),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1659, 9669, 9511, 9648, 9651])).
% 2.08/2.24 tff(9673,plain,
% 2.08/2.24 (~hskp19),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9257, 9670, 9672, 9648])).
% 2.08/2.24 tff(9674,plain,
% 2.08/2.24 (~hskp50),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[6209, 9648, 9511])).
% 2.08/2.24 tff(9675,plain,
% 2.08/2.24 (c3_1(a545) | (~c0_1(a537))),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9658, 156, 9511, 7860, 9509, 9649, 9651, 85])).
% 2.08/2.24 tff(9676,plain,
% 2.08/2.24 (~c0_1(a537)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9675, 9670])).
% 2.08/2.24 tff(9677,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a537) | c3_1(a537) | c2_1(a555) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a537) | c3_1(a537) | c2_1(a555) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9678,plain,
% 2.08/2.24 ((hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537))) <=> (hskp39 | c0_1(a537) | c3_1(a537) | c2_1(a555) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9679,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | c0_1(a537) | c3_1(a537) | c2_1(a555) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555))))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9678])).
% 2.08/2.24 tff(9680,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a537) | c3_1(a537) | c2_1(a555) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555)))),
% 2.08/2.24 inference(transitivity,[status(thm)],[9679, 9677])).
% 2.08/2.24 tff(9681,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a555) | (~c3_1(a555)) | (~c1_1(a555)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))),
% 2.08/2.24 inference(quant_inst,[status(thm)],[])).
% 2.08/2.24 tff(9682,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | c0_1(a537) | c3_1(a537) | c2_1(a555) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a555)) | (~c1_1(a555))),
% 2.08/2.24 inference(modus_ponens,[status(thm)],[9681, 9680])).
% 2.08/2.24 tff(9683,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9682, 156, 859, 257, 7925, 7860, 233, 9509, 281, 248])).
% 2.08/2.24 tff(9684,plain,((~hskp41) | hskp39 | c0_1(a537) | c3_1(a537) | hskp50 | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9685,plain,
% 2.08/2.24 (~hskp41),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9684, 859, 9676, 7860, 9674, 9673])).
% 2.08/2.24 tff(9686,plain,
% 2.08/2.24 (hskp17),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[567, 9685, 109, 9674, 9673, 9671])).
% 2.08/2.24 tff(9687,plain,
% 2.08/2.24 (~c2_1(a571)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[573, 9686])).
% 2.08/2.24 tff(9688,plain,
% 2.08/2.24 (c0_1(a571)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[581, 9686])).
% 2.08/2.24 tff(9689,plain,
% 2.08/2.24 (c1_1(a571)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[588, 156, 9674, 9673, 9688, 9687, 34])).
% 2.08/2.24 tff(9690,plain,
% 2.08/2.24 (c3_1(a571)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[623, 9686])).
% 2.08/2.24 tff(9691,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9569, 156, 859, 9676, 7860, 9690, 9509, 9687, 281, 9689])).
% 2.08/2.24 tff(9692,plain,(hskp39 | c3_1(a537) | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9693,plain,
% 2.08/2.24 (hskp39),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9692, 109, 7860])).
% 2.08/2.24 tff(9694,plain,
% 2.08/2.24 (c1_1(a549)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[303, 9693])).
% 2.08/2.24 tff(9695,plain,
% 2.08/2.24 (c2_1(a549)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[311, 9693])).
% 2.08/2.24 tff(9696,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9697,plain,
% 2.08/2.24 ((hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537))) <=> (hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9698,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549))))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9697])).
% 2.08/2.24 tff(9699,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)))),
% 2.08/2.24 inference(transitivity,[status(thm)],[9698, 9696])).
% 2.08/2.24 tff(9700,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549)) | c3_1(a537) | c0_1(a537) | (~c1_1(a537)))),
% 2.08/2.24 inference(quant_inst,[status(thm)],[])).
% 2.08/2.24 tff(9701,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | c0_1(a537) | c3_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c2_1(a549)) | (~c0_1(a549)) | (~c1_1(a549))),
% 2.08/2.24 inference(modus_ponens,[status(thm)],[9700, 9699])).
% 2.08/2.24 tff(9702,plain,
% 2.08/2.24 (c0_1(a537) | (~c0_1(a549))),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9701, 156, 9510, 9695, 9694, 7860, 9509, 75])).
% 2.08/2.24 tff(9703,plain,
% 2.08/2.24 (~c0_1(a549)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9702, 7925])).
% 2.08/2.24 tff(9704,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9666, 156, 9510, 2771, 2770, 2769, 7925, 7860, 9509, 75])).
% 2.08/2.24 tff(9705,plain,((~hskp38) | c0_1(a537) | c3_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9706,plain,
% 2.08/2.24 (~hskp38),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9705, 7925, 7860])).
% 2.08/2.24 tff(9707,plain,
% 2.08/2.24 (~c3_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1211, 9706, 9650, 9649, 9651])).
% 2.08/2.24 tff(9708,plain,
% 2.08/2.24 (~hskp9),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9248, 9707, 109, 9650, 9649])).
% 2.08/2.24 tff(9709,plain,
% 2.08/2.24 (c3_1(a549)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[319, 9693])).
% 2.08/2.24 tff(9710,plain,
% 2.08/2.24 (hskp41 | hskp9 | c0_1(a549)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1513, 156, 9709, 9694, 342])).
% 2.08/2.24 tff(9711,plain,
% 2.08/2.24 (hskp41),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9710, 9708, 9703])).
% 2.08/2.24 tff(9712,plain,
% 2.08/2.24 (~c2_1(a555)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[232, 9711])).
% 2.08/2.24 tff(9713,plain,
% 2.08/2.24 (c0_1(a555)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[240, 9711])).
% 2.08/2.24 tff(9714,plain,
% 2.08/2.24 (~hskp26),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1659, 9706, 9511, 9648, 9651])).
% 2.08/2.24 tff(9715,plain,
% 2.08/2.24 (~hskp19),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9257, 9707, 9714, 9648])).
% 2.08/2.24 tff(9716,plain,
% 2.08/2.24 (c1_1(a555)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[247, 156, 9674, 9715, 9713, 9712, 34])).
% 2.08/2.24 tff(9717,plain,
% 2.08/2.24 (~hskp45),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[833, 9707, 9511, 9715, 9651, 9649])).
% 2.08/2.24 tff(9718,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9265, 156, 9717, 9713, 9712, 9649, 9651, 757, 9707, 9716])).
% 2.08/2.24 tff(9719,plain,(c0_1(a537) | hskp15 | c3_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9720,plain,
% 2.08/2.24 (c0_1(a537)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9719, 109, 7860])).
% 2.08/2.24 tff(9721,plain,
% 2.08/2.24 (c3_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9675, 9720])).
% 2.08/2.24 tff(9722,plain,
% 2.08/2.24 (hskp46 | (~c3_1(a545))),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1163, 156, 9650, 9649, 9651, 12])).
% 2.08/2.24 tff(9723,plain,
% 2.08/2.24 (hskp46),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9722, 9721])).
% 2.08/2.24 tff(9724,plain,
% 2.08/2.24 (~c0_1(a562)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[64, 9723])).
% 2.08/2.24 tff(9725,plain,
% 2.08/2.24 (hskp38),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1211, 9721, 9650, 9649, 9651])).
% 2.08/2.24 tff(9726,plain,
% 2.08/2.24 (c1_1(a562)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[288, 9723])).
% 2.08/2.24 tff(9727,plain,
% 2.08/2.24 (~c3_1(a562)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[270, 9723])).
% 2.08/2.24 tff(9728,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9166, 9727, 9726, 9510, 9725, 9724])).
% 2.08/2.24 tff(9729,plain,(hskp15 | c3_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9730,plain,
% 2.08/2.24 (hskp15),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9729, 7860])).
% 2.08/2.24 tff(9731,plain,
% 2.08/2.24 (hskp28),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1276, 9730])).
% 2.08/2.24 tff(9732,plain,
% 2.08/2.24 (hskp26),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[8580, 9730, 9731])).
% 2.08/2.24 tff(9733,plain,
% 2.08/2.24 (~c2_1(a569)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1255, 9730])).
% 2.08/2.24 tff(9734,plain,
% 2.08/2.24 (~c0_1(a569)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1267, 9730])).
% 2.08/2.24 tff(9735,plain,
% 2.08/2.24 (~c1_1(a569)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1261, 9730])).
% 2.08/2.24 tff(9736,plain,
% 2.08/2.24 (hskp4),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9501, 9735, 9511, 9734, 9733, 9732])).
% 2.08/2.24 tff(9737,plain,
% 2.08/2.24 (~c0_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1666, 9736])).
% 2.08/2.24 tff(9738,plain,
% 2.08/2.24 (c1_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[193, 9736])).
% 2.08/2.24 tff(9739,plain,
% 2.08/2.24 (~c3_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1782, 156, 8476, 9738, 9734, 9735, 9733, 9737, 1745])).
% 2.08/2.24 tff(9740,plain,
% 2.08/2.24 (~c2_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1643, 9736])).
% 2.08/2.24 tff(9741,plain,
% 2.08/2.24 (c0_1(a584)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1629, 9732])).
% 2.08/2.24 tff(9742,plain,
% 2.08/2.24 (c1_1(a584)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1637, 9732])).
% 2.08/2.24 tff(9743,plain,
% 2.08/2.24 (~c3_1(a584)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1620, 9732])).
% 2.08/2.24 tff(9744,plain,
% 2.08/2.24 (hskp38),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1657, 9743, 9736, 9742, 9511, 9737, 9741])).
% 2.08/2.24 tff(9745,plain,
% 2.08/2.24 (c0_1(a537)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9705, 9744, 7860])).
% 2.08/2.24 tff(9746,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9658, 156, 9511, 9745, 7860, 9509, 9740, 9737, 85, 9739])).
% 2.08/2.24 tff(9747,plain,(c3_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9748,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9749,plain,
% 2.08/2.24 ((hskp4 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp4 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9750,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | (~c2_1(a537))))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9749])).
% 2.08/2.24 tff(9751,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | (~c2_1(a537)))),
% 2.08/2.24 inference(transitivity,[status(thm)],[9750, 9748])).
% 2.08/2.24 tff(9752,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a537)) | (~c2_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 2.08/2.24 inference(quant_inst,[status(thm)],[])).
% 2.08/2.24 tff(9753,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | (~c2_1(a537))),
% 2.08/2.24 inference(modus_ponens,[status(thm)],[9752, 9751])).
% 2.08/2.24 tff(9754,plain,
% 2.08/2.24 (~c2_1(a537)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9753, 156, 23, 9747, 8489, 9509, 8480, 8479, 22])).
% 2.08/2.24 tff(9755,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | c2_1(a537))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | c2_1(a537))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9756,plain,
% 2.08/2.24 ((hskp39 | (~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (hskp39 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | c2_1(a537))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9757,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | c2_1(a537)))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9756])).
% 2.08/2.24 tff(9758,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | c2_1(a537))),
% 2.08/2.24 inference(transitivity,[status(thm)],[9757, 9755])).
% 2.08/2.24 tff(9759,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp39 | (~ndr1_0) | c2_1(a537) | (~c3_1(a537)) | (~c1_1(a537)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 2.08/2.24 inference(quant_inst,[status(thm)],[])).
% 2.08/2.24 tff(9760,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp39 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp39 | (~c1_1(a537)) | c0_1(a586) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c3_1(a537)) | c2_1(a537)),
% 2.08/2.24 inference(modus_ponens,[status(thm)],[9759, 9758])).
% 2.08/2.24 tff(9761,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9760, 156, 9512, 9747, 8489, 9509, 8480, 8479, 281, 9754])).
% 2.08/2.24 tff(9762,plain,(hskp4), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9763,plain,
% 2.08/2.24 (~c0_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1666, 9762])).
% 2.08/2.24 tff(9764,plain,
% 2.08/2.24 (~c2_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1643, 9762])).
% 2.08/2.24 tff(9765,plain,
% 2.08/2.24 (c1_1(a545)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[193, 9762])).
% 2.08/2.24 tff(9766,plain,
% 2.08/2.24 (hskp46 | (~c3_1(a545))),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1163, 156, 9765, 9764, 9763, 12])).
% 2.08/2.24 tff(9767,plain,
% 2.08/2.24 (hskp46),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9766, 2])).
% 2.08/2.24 tff(9768,plain,
% 2.08/2.24 (~c0_1(a562)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[64, 9767])).
% 2.08/2.24 tff(9769,plain,
% 2.08/2.24 (hskp38),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1211, 2, 9765, 9764, 9763])).
% 2.08/2.24 tff(9770,plain,
% 2.08/2.24 (c1_1(a562)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[288, 9767])).
% 2.08/2.24 tff(9771,plain,
% 2.08/2.24 (~c3_1(a562)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[270, 9767])).
% 2.08/2.24 tff(9772,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9166, 9771, 9770, 9510, 9769, 9768])).
% 2.08/2.24 tff(9773,plain,(~c3_1(a545)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9774,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[1655, 156, 9511, 1630, 1638, 1621, 9764, 9763, 85, 9773])).
% 2.08/2.24 tff(9775,plain,(~hskp26), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9776,plain,
% 2.08/2.24 (~hskp15),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[8578, 9775, 9765, 9763])).
% 2.08/2.24 tff(9777,plain,
% 2.08/2.24 (~hskp9),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9248, 765, 109, 9765, 9764])).
% 2.08/2.24 tff(9778,plain,
% 2.08/2.24 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a537)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9779,plain,
% 2.08/2.24 ((hskp41 | hskp9 | (~ndr1_0) | c0_1(a537) | (~c3_1(a537)) | (~c1_1(a537))) <=> (hskp41 | hskp9 | c0_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9780,plain,
% 2.08/2.24 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a537) | (~c3_1(a537)) | (~c1_1(a537)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | c0_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a537))))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9779])).
% 2.08/2.24 tff(9781,plain,
% 2.08/2.24 (((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a537) | (~c3_1(a537)) | (~c1_1(a537)))) <=> ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a537)))),
% 2.08/2.24 inference(transitivity,[status(thm)],[9780, 9778])).
% 2.08/2.24 tff(9782,plain,
% 2.08/2.24 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp41 | hskp9 | (~ndr1_0) | c0_1(a537) | (~c3_1(a537)) | (~c1_1(a537)))),
% 2.08/2.24 inference(quant_inst,[status(thm)],[])).
% 2.08/2.24 tff(9783,plain,
% 2.08/2.24 ((~![U: $i] : (hskp41 | hskp9 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp41 | hskp9 | c0_1(a537) | (~c1_1(a537)) | (~ndr1_0) | (~c3_1(a537))),
% 2.08/2.24 inference(modus_ponens,[status(thm)],[9782, 9781])).
% 2.08/2.24 tff(9784,plain,
% 2.08/2.24 (hskp41 | hskp9 | c0_1(a537) | (~c3_1(a537))),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9783, 156, 9509, 342])).
% 2.08/2.24 tff(9785,plain,
% 2.08/2.24 (hskp41),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9784, 9777, 9747, 7925])).
% 2.08/2.24 tff(9786,plain,
% 2.08/2.24 (~c2_1(a555)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[232, 9785])).
% 2.08/2.24 tff(9787,plain,
% 2.08/2.24 (c0_1(a555)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[240, 9785])).
% 2.08/2.24 tff(9788,plain,
% 2.08/2.24 (~hskp19),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9257, 765, 1661, 9762])).
% 2.08/2.24 tff(9789,plain,
% 2.08/2.24 (~hskp50),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[6209, 9762, 9511])).
% 2.08/2.24 tff(9790,plain,
% 2.08/2.24 (c1_1(a555)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[247, 156, 9789, 9788, 9787, 9786, 34])).
% 2.08/2.24 tff(9791,plain,
% 2.08/2.24 (~hskp45),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[833, 9788, 9511, 765, 9763, 9764])).
% 2.08/2.24 tff(9792,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9265, 156, 9791, 9787, 9786, 9764, 9763, 757, 765, 9790])).
% 2.08/2.24 tff(9793,plain,(c3_1(a545) | c0_1(a537) | hskp26 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9794,plain,
% 2.08/2.24 (c0_1(a537)),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9793, 9775, 9773, 9776])).
% 2.08/2.24 tff(9795,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~c1_1(a537)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a537)) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | (~c1_1(a537)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9796,plain,
% 2.08/2.24 ((hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545))) <=> (hskp34 | (~c1_1(a537)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9797,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~c1_1(a537)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a537)) | (~c0_1(a537))))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9796])).
% 2.08/2.24 tff(9798,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | (~c1_1(a537)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a537)) | (~c0_1(a537)))),
% 2.08/2.24 inference(transitivity,[status(thm)],[9797, 9795])).
% 2.08/2.24 tff(9799,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c1_1(a537)) | c3_1(a545) | c0_1(a545) | (~c1_1(a545)))),
% 2.08/2.24 inference(quant_inst,[status(thm)],[])).
% 2.08/2.24 tff(9800,plain,
% 2.08/2.24 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp34 | (~c1_1(a537)) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | (~c1_1(a545)) | (~c2_1(a537)) | (~c0_1(a537))),
% 2.08/2.24 inference(modus_ponens,[status(thm)],[9799, 9798])).
% 2.08/2.24 tff(9801,plain,
% 2.08/2.24 ($false),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9800, 156, 9510, 9794, 9765, 9509, 9763, 75, 9773, 1])).
% 2.08/2.24 tff(9802,plain,(~c2_1(a537)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.24 tff(9803,plain,
% 2.08/2.24 (~hskp19),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[9257, 9775, 9773, 9762])).
% 2.08/2.24 tff(9804,plain,
% 2.08/2.24 (~hskp45),
% 2.08/2.24 inference(unit_resolution,[status(thm)],[833, 9803, 9511, 9773, 9763, 9764])).
% 2.08/2.24 tff(9805,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | c2_1(a537) | (~c0_1(a537)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | c2_1(a537) | (~c0_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9806,plain,
% 2.08/2.24 ((hskp45 | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545)) <=> (hskp45 | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | c2_1(a537) | (~c0_1(a537)))),
% 2.08/2.24 inference(rewrite,[status(thm)],[])).
% 2.08/2.24 tff(9807,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | c2_1(a537) | (~c0_1(a537))))),
% 2.08/2.24 inference(monotonicity,[status(thm)],[9806])).
% 2.08/2.24 tff(9808,plain,
% 2.08/2.24 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | c2_1(a537) | (~c0_1(a537)))),
% 2.08/2.25 inference(transitivity,[status(thm)],[9807, 9805])).
% 2.08/2.25 tff(9809,plain,
% 2.08/2.25 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | (hskp45 | (~ndr1_0) | c2_1(a537) | (~c0_1(a537)) | (~c1_1(a537)) | c2_1(a545) | c3_1(a545) | c0_1(a545))),
% 2.08/2.25 inference(quant_inst,[status(thm)],[])).
% 2.08/2.25 tff(9810,plain,
% 2.08/2.25 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | c0_1(V))) | hskp45 | (~c1_1(a537)) | c2_1(a545) | c0_1(a545) | (~ndr1_0) | c3_1(a545) | c2_1(a537) | (~c0_1(a537))),
% 2.08/2.25 inference(modus_ponens,[status(thm)],[9809, 9808])).
% 2.08/2.25 tff(9811,plain,
% 2.08/2.25 ($false),
% 2.08/2.25 inference(unit_resolution,[status(thm)],[9810, 156, 9804, 9794, 9509, 9764, 9763, 757, 9773, 9802])).
% 2.08/2.25 % SZS output end Proof
% 2.08/2.25 % E exiting
%------------------------------------------------------------------------------