%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN474-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:39:15 AM UTC 2025
% Result : Unsatisfiable 1.82s 2.00s
% Output : Proof 2.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN474-1 : TPTP v9.0.0. Released v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:36:54 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.82/2.00 % SZS status Unsatisfiable
% 1.82/2.00 % SZS output start Proof
% 1.82/2.00 tff(c1_1_type, type, (
% 1.82/2.00 c1_1: $i > $o)).
% 1.82/2.00 tff(a938_type, type, (
% 1.82/2.00 a938: $i)).
% 1.82/2.00 tff(a912_type, type, (
% 1.82/2.00 a912: $i)).
% 1.82/2.00 tff(hskp11_type, type, (
% 1.82/2.00 hskp11: $o)).
% 1.82/2.00 tff(c2_1_type, type, (
% 1.82/2.00 c2_1: $i > $o)).
% 1.82/2.00 tff(a910_type, type, (
% 1.82/2.00 a910: $i)).
% 1.82/2.00 tff(hskp10_type, type, (
% 1.82/2.00 hskp10: $o)).
% 1.82/2.00 tff(hskp16_type, type, (
% 1.82/2.00 hskp16: $o)).
% 1.82/2.00 tff(c0_1_type, type, (
% 1.82/2.00 c0_1: $i > $o)).
% 1.82/2.00 tff(hskp21_type, type, (
% 1.82/2.00 hskp21: $o)).
% 1.82/2.00 tff(a958_type, type, (
% 1.82/2.00 a958: $i)).
% 1.82/2.00 tff(a907_type, type, (
% 1.82/2.00 a907: $i)).
% 1.82/2.00 tff(a928_type, type, (
% 1.82/2.00 a928: $i)).
% 1.82/2.00 tff(a957_type, type, (
% 1.82/2.00 a957: $i)).
% 1.82/2.00 tff(hskp31_type, type, (
% 1.82/2.00 hskp31: $o)).
% 1.82/2.00 tff(c3_1_type, type, (
% 1.82/2.00 c3_1: $i > $o)).
% 1.82/2.00 tff(ndr1_0_type, type, (
% 1.82/2.00 ndr1_0: $o)).
% 1.82/2.00 tff(a898_type, type, (
% 1.82/2.00 a898: $i)).
% 1.82/2.00 tff(hskp0_type, type, (
% 1.82/2.00 hskp0: $o)).
% 1.82/2.00 tff(hskp1_type, type, (
% 1.82/2.00 hskp1: $o)).
% 1.82/2.00 tff(hskp25_type, type, (
% 1.82/2.00 hskp25: $o)).
% 1.82/2.00 tff(hskp17_type, type, (
% 1.82/2.00 hskp17: $o)).
% 1.82/2.00 tff(hskp7_type, type, (
% 1.82/2.00 hskp7: $o)).
% 1.82/2.00 tff(hskp20_type, type, (
% 1.82/2.00 hskp20: $o)).
% 1.82/2.00 tff(a899_type, type, (
% 1.82/2.00 a899: $i)).
% 1.82/2.00 tff(a978_type, type, (
% 1.82/2.00 a978: $i)).
% 1.82/2.00 tff(hskp27_type, type, (
% 1.82/2.00 hskp27: $o)).
% 1.82/2.00 tff(hskp22_type, type, (
% 1.82/2.00 hskp22: $o)).
% 1.82/2.00 tff(hskp2_type, type, (
% 1.82/2.00 hskp2: $o)).
% 1.82/2.00 tff(a901_type, type, (
% 1.82/2.00 a901: $i)).
% 1.82/2.00 tff(a909_type, type, (
% 1.82/2.00 a909: $i)).
% 1.82/2.00 tff(hskp9_type, type, (
% 1.82/2.00 hskp9: $o)).
% 1.82/2.00 tff(a918_type, type, (
% 1.82/2.00 a918: $i)).
% 1.82/2.00 tff(hskp14_type, type, (
% 1.82/2.00 hskp14: $o)).
% 1.82/2.00 tff(hskp29_type, type, (
% 1.82/2.00 hskp29: $o)).
% 1.82/2.00 tff(a929_type, type, (
% 1.82/2.00 a929: $i)).
% 1.82/2.00 tff(hskp18_type, type, (
% 1.82/2.00 hskp18: $o)).
% 1.82/2.00 tff(a914_type, type, (
% 1.82/2.00 a914: $i)).
% 1.82/2.00 tff(hskp13_type, type, (
% 1.82/2.00 hskp13: $o)).
% 1.82/2.00 tff(a905_type, type, (
% 1.82/2.00 a905: $i)).
% 1.82/2.00 tff(hskp5_type, type, (
% 1.82/2.00 hskp5: $o)).
% 1.82/2.00 tff(a913_type, type, (
% 1.82/2.00 a913: $i)).
% 1.82/2.00 tff(hskp12_type, type, (
% 1.82/2.00 hskp12: $o)).
% 1.82/2.00 tff(a904_type, type, (
% 1.82/2.00 a904: $i)).
% 1.82/2.00 tff(hskp4_type, type, (
% 1.82/2.00 hskp4: $o)).
% 1.82/2.00 tff(a906_type, type, (
% 1.82/2.00 a906: $i)).
% 1.82/2.00 tff(hskp6_type, type, (
% 1.82/2.00 hskp6: $o)).
% 1.82/2.00 tff(a908_type, type, (
% 1.82/2.00 a908: $i)).
% 1.82/2.00 tff(hskp8_type, type, (
% 1.82/2.00 hskp8: $o)).
% 1.82/2.00 tff(a953_type, type, (
% 1.82/2.00 a953: $i)).
% 1.82/2.00 tff(hskp24_type, type, (
% 1.82/2.00 hskp24: $o)).
% 1.82/2.00 tff(a900_type, type, (
% 1.82/2.00 a900: $i)).
% 1.82/2.00 tff(hskp28_type, type, (
% 1.82/2.00 hskp28: $o)).
% 1.82/2.00 tff(a937_type, type, (
% 1.82/2.00 a937: $i)).
% 1.82/2.00 tff(hskp3_type, type, (
% 1.82/2.00 hskp3: $o)).
% 1.82/2.00 tff(a903_type, type, (
% 1.82/2.00 a903: $i)).
% 1.82/2.00 tff(a939_type, type, (
% 1.82/2.00 a939: $i)).
% 1.82/2.00 tff(a911_type, type, (
% 1.82/2.00 a911: $i)).
% 1.82/2.00 tff(a923_type, type, (
% 1.82/2.00 a923: $i)).
% 1.82/2.00 tff(a921_type, type, (
% 1.82/2.00 a921: $i)).
% 1.82/2.00 tff(hskp15_type, type, (
% 1.82/2.00 hskp15: $o)).
% 1.82/2.00 tff(a919_type, type, (
% 1.82/2.00 a919: $i)).
% 1.82/2.00 tff(hskp30_type, type, (
% 1.82/2.00 hskp30: $o)).
% 1.82/2.00 tff(a969_type, type, (
% 1.82/2.00 a969: $i)).
% 1.82/2.00 tff(hskp26_type, type, (
% 1.82/2.00 hskp26: $o)).
% 1.82/2.00 tff(1,plain,
% 1.82/2.00 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(2,plain,
% 1.82/2.00 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[1])).
% 1.82/2.00 tff(3,plain,
% 1.82/2.00 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(4,plain,
% 1.82/2.00 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp31) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp31))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(5,plain,
% 1.82/2.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[4])).
% 1.82/2.00 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.82/2.00 tff(7,plain,
% 1.82/2.00 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.82/2.00 tff(8,plain,
% 1.82/2.00 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.82/2.00 tff(9,plain,(
% 1.82/2.00 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.82/2.00 inference(skolemize,[status(sab)],[8])).
% 1.82/2.00 tff(10,plain,
% 1.82/2.00 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.82/2.00 tff(11,plain,
% 1.82/2.00 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(12,plain,
% 1.82/2.00 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[11])).
% 1.82/2.00 tff(13,plain,
% 1.82/2.00 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(14,plain,
% 1.82/2.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(15,plain,
% 1.82/2.00 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[14])).
% 1.82/2.00 tff(16,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.82/2.00 tff(17,plain,
% 1.82/2.00 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.82/2.00 tff(18,plain,
% 1.82/2.00 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.82/2.00 tff(19,plain,(
% 1.82/2.00 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.82/2.00 inference(skolemize,[status(sab)],[18])).
% 1.82/2.00 tff(20,plain,
% 1.82/2.00 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.82/2.00 tff(21,plain,
% 1.82/2.00 (^[U: $i] : refl((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(22,plain,
% 1.82/2.00 (![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[21])).
% 1.82/2.00 tff(23,plain,
% 1.82/2.00 (![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(24,plain,
% 1.82/2.00 (^[U: $i] : 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)) | 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) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(25,plain,
% 1.82/2.00 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[24])).
% 1.82/2.00 tff(26,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.82/2.00 tff(27,plain,
% 1.82/2.00 (![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.82/2.00 tff(28,plain,
% 1.82/2.00 (![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.82/2.00 tff(29,plain,(
% 1.82/2.00 ![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.82/2.00 inference(skolemize,[status(sab)],[28])).
% 1.82/2.00 tff(30,plain,
% 1.82/2.00 (![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.82/2.00 tff(31,assumption,(~hskp0), introduced(assumption)).
% 1.82/2.00 tff(32,assumption,(~hskp17), introduced(assumption)).
% 1.82/2.00 tff(33,plain,
% 1.82/2.00 (^[U: $i] : refl((hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(34,plain,
% 1.82/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[33])).
% 1.82/2.00 tff(35,plain,
% 1.82/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(36,plain,
% 1.82/2.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp20) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp20) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.82/2.00 inference(bind,[status(th)],[])).
% 1.82/2.00 tff(37,plain,
% 1.82/2.00 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp20) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.00 inference(quant_intro,[status(thm)],[36])).
% 1.82/2.00 tff(38,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.82/2.00 tff(39,plain,
% 1.82/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.82/2.00 tff(40,plain,
% 1.82/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.82/2.00 tff(41,plain,(
% 1.82/2.00 ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.00 inference(skolemize,[status(sab)],[40])).
% 1.82/2.00 tff(42,plain,
% 1.82/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.82/2.00 tff(43,assumption,(~c0_1(a899)), introduced(assumption)).
% 1.82/2.00 tff(44,assumption,(~c0_1(a907)), introduced(assumption)).
% 1.82/2.00 tff(45,assumption,(~c1_1(a907)), introduced(assumption)).
% 1.82/2.00 tff(46,assumption,(~hskp31), introduced(assumption)).
% 1.82/2.00 tff(47,assumption,(~c2_1(a901)), introduced(assumption)).
% 1.82/2.00 tff(48,assumption,(~c3_1(a901)), introduced(assumption)).
% 1.82/2.00 tff(49,assumption,(~c1_1(a901)), introduced(assumption)).
% 1.82/2.00 tff(50,assumption,(~hskp10), introduced(assumption)).
% 1.82/2.00 tff(51,assumption,(~c0_1(a901)), introduced(assumption)).
% 1.82/2.00 tff(52,assumption,(hskp0), introduced(assumption)).
% 1.82/2.00 tff(53,plain,
% 1.82/2.00 (((~hskp0) | c1_1(a898)) <=> ((~hskp0) | c1_1(a898))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(54,axiom,((~hskp0) | c1_1(a898)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.82/2.00 tff(55,plain,
% 1.82/2.00 ((~hskp0) | c1_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.82/2.00 tff(56,plain,
% 1.82/2.00 ((~hskp0) | c1_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[55, 53])).
% 1.82/2.00 tff(57,plain,
% 1.82/2.00 ((~hskp0) | c1_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[56, 53])).
% 1.82/2.00 tff(58,plain,
% 1.82/2.00 ((~hskp0) | c1_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.82/2.00 tff(59,plain,
% 1.82/2.00 ((~hskp0) | c1_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[58, 53])).
% 1.82/2.00 tff(60,plain,
% 1.82/2.00 (c1_1(a898)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[59, 52])).
% 1.82/2.00 tff(61,plain,
% 1.82/2.00 (((~hskp0) | (~c2_1(a898))) <=> ((~hskp0) | (~c2_1(a898)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(62,plain,
% 1.82/2.00 (((~c2_1(a898)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a898)))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(63,axiom,((~c2_1(a898)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.82/2.00 tff(64,plain,
% 1.82/2.00 ((~hskp0) | (~c2_1(a898))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.82/2.00 tff(65,plain,
% 1.82/2.00 ((~hskp0) | (~c2_1(a898))),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[64, 61])).
% 1.82/2.00 tff(66,plain,
% 1.82/2.00 (~c2_1(a898)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[65, 52])).
% 1.82/2.00 tff(67,plain,
% 1.82/2.00 (((~hskp0) | c0_1(a898)) <=> ((~hskp0) | c0_1(a898))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(68,axiom,((~hskp0) | c0_1(a898)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.82/2.00 tff(69,plain,
% 1.82/2.00 ((~hskp0) | c0_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.82/2.00 tff(70,plain,
% 1.82/2.00 ((~hskp0) | c0_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[69, 67])).
% 1.82/2.00 tff(71,plain,
% 1.82/2.00 ((~hskp0) | c0_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[70, 67])).
% 1.82/2.00 tff(72,plain,
% 1.82/2.00 ((~hskp0) | c0_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.82/2.00 tff(73,plain,
% 1.82/2.00 ((~hskp0) | c0_1(a898)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[72, 67])).
% 1.82/2.00 tff(74,plain,
% 1.82/2.00 (c0_1(a898)),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[73, 52])).
% 1.82/2.00 tff(75,assumption,(~c3_1(a898)), introduced(assumption)).
% 1.82/2.00 tff(76,assumption,(~c2_1(a898)), introduced(assumption)).
% 1.82/2.00 tff(77,assumption,(c1_1(a898)), introduced(assumption)).
% 1.82/2.00 tff(78,assumption,(c0_1(a898)), introduced(assumption)).
% 1.82/2.00 tff(79,assumption,(~ndr1_0), introduced(assumption)).
% 1.82/2.00 tff(80,plain,
% 1.82/2.00 ((ndr1_0 | (~hskp29)) <=> (ndr1_0 | (~hskp29))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(81,plain,
% 1.82/2.00 (((~hskp29) | ndr1_0) <=> (ndr1_0 | (~hskp29))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(82,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 1.82/2.00 tff(83,plain,
% 1.82/2.00 (ndr1_0 | (~hskp29)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.82/2.00 tff(84,plain,
% 1.82/2.00 (ndr1_0 | (~hskp29)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[83, 80])).
% 1.82/2.00 tff(85,plain,
% 1.82/2.00 (~hskp29),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[84, 79])).
% 1.82/2.00 tff(86,assumption,(~hskp29), introduced(assumption)).
% 1.82/2.00 tff(87,plain,
% 1.82/2.00 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(88,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.82/2.00 tff(89,plain,
% 1.82/2.00 ((~hskp31) | ndr1_0),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.82/2.00 tff(90,plain,
% 1.82/2.00 ((~hskp31) | ndr1_0),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[89, 87])).
% 1.82/2.00 tff(91,plain,
% 1.82/2.00 ((~hskp31) | ndr1_0),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[90, 87])).
% 1.82/2.00 tff(92,plain,
% 1.82/2.00 ((~hskp31) | ndr1_0),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[91, 87])).
% 1.82/2.00 tff(93,plain,
% 1.82/2.00 ((~hskp31) | ndr1_0),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[92, 87])).
% 1.82/2.00 tff(94,plain,
% 1.82/2.00 (~hskp31),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[93, 79])).
% 1.82/2.00 tff(95,plain,
% 1.82/2.00 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(96,plain,
% 1.82/2.00 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(97,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.82/2.00 tff(98,plain,
% 1.82/2.00 (ndr1_0 | (~hskp27)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.82/2.00 tff(99,plain,
% 1.82/2.00 (ndr1_0 | (~hskp27)),
% 1.82/2.00 inference(modus_ponens,[status(thm)],[98, 95])).
% 1.82/2.00 tff(100,plain,
% 1.82/2.00 (~hskp27),
% 1.82/2.00 inference(unit_resolution,[status(thm)],[99, 79])).
% 1.82/2.00 tff(101,plain,
% 1.82/2.00 ((hskp31 | hskp29 | hskp27) <=> (hskp31 | hskp29 | hskp27)),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(102,plain,
% 1.82/2.00 (((hskp29 | hskp31) | hskp27) <=> (hskp31 | hskp29 | hskp27)),
% 1.82/2.00 inference(rewrite,[status(thm)],[])).
% 1.82/2.00 tff(103,axiom,((hskp29 | hskp31) | hskp27), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.82/2.01 tff(104,plain,
% 1.82/2.01 (hskp31 | hskp29 | hskp27),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.82/2.01 tff(105,plain,
% 1.82/2.01 (hskp31 | hskp29 | hskp27),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[104, 101])).
% 1.82/2.01 tff(106,plain,
% 1.82/2.01 (hskp31 | hskp29 | hskp27),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.82/2.01 tff(107,plain,
% 1.82/2.01 (hskp31 | hskp29 | hskp27),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[106, 101])).
% 1.82/2.01 tff(108,plain,
% 1.82/2.01 (hskp31 | hskp29 | hskp27),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[107, 101])).
% 1.82/2.01 tff(109,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[108, 100, 94, 86])).
% 1.82/2.01 tff(110,plain,(ndr1_0 | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(111,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[110, 85, 79])).
% 1.82/2.01 tff(112,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(113,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(114,plain,
% 1.82/2.01 ((hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a898) | c2_1(a898) | (~c1_1(a898))) <=> (hskp31 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(115,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a898) | c2_1(a898) | (~c1_1(a898)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[114])).
% 1.82/2.01 tff(116,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a898) | c2_1(a898) | (~c1_1(a898)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[115, 113])).
% 1.82/2.01 tff(117,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a898) | c2_1(a898) | (~c1_1(a898)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(118,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.82/2.01 tff(119,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[118, 46, 112, 78, 77, 76, 10, 75])).
% 1.82/2.01 tff(120,plain,(c3_1(a898) | hskp31 | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a898)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(121,plain,
% 1.82/2.01 (c3_1(a898)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[120, 74, 66, 60, 46])).
% 1.82/2.01 tff(122,plain,
% 1.82/2.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(123,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[122])).
% 1.82/2.01 tff(124,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(125,plain,
% 1.82/2.01 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(126,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[125])).
% 1.82/2.01 tff(127,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.82/2.01 tff(128,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.82/2.01 tff(129,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[128, 124])).
% 1.82/2.01 tff(130,plain,(
% 1.82/2.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.82/2.01 inference(skolemize,[status(sab)],[129])).
% 1.82/2.01 tff(131,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[130, 123])).
% 1.82/2.01 tff(132,assumption,(c1_1(a901)), introduced(assumption)).
% 1.82/2.01 tff(133,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(134,plain,
% 1.82/2.01 ((hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901))) <=> (hskp31 | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(135,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[134])).
% 1.82/2.01 tff(136,plain,
% 1.82/2.01 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[135, 133])).
% 1.82/2.01 tff(137,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(138,plain,
% 1.82/2.01 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.82/2.01 tff(139,plain,
% 1.82/2.01 ($false),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[138, 46, 112, 74, 60, 47, 48, 66, 10, 132])).
% 1.82/2.01 tff(140,plain,((~hskp0) | hskp31 | c2_1(a901) | c3_1(a901) | (~c1_1(a901))), inference(lemma,lemma(discharge,[]))).
% 1.82/2.01 tff(141,plain,
% 1.82/2.01 (~c1_1(a901)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[140, 52, 47, 48, 46])).
% 1.82/2.01 tff(142,plain,
% 1.82/2.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(143,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[142])).
% 1.82/2.01 tff(144,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(145,plain,
% 1.82/2.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(146,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_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) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[145])).
% 1.82/2.01 tff(147,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.82/2.01 tff(148,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.82/2.01 tff(149,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[148, 144])).
% 1.82/2.01 tff(150,plain,(
% 1.82/2.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/2.01 inference(skolemize,[status(sab)],[149])).
% 1.82/2.01 tff(151,plain,
% 1.82/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[150, 143])).
% 1.82/2.01 tff(152,assumption,(~hskp1), introduced(assumption)).
% 1.82/2.01 tff(153,plain,
% 1.82/2.01 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | c1_1(a901))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | c1_1(a901))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(154,plain,
% 1.82/2.01 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c0_1(a901)) <=> (hskp1 | hskp0 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | c1_1(a901))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(155,plain,
% 1.82/2.01 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | c1_1(a901)))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[154])).
% 1.82/2.01 tff(156,plain,
% 1.82/2.01 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | c1_1(a901))),
% 1.82/2.01 inference(transitivity,[status(thm)],[155, 153])).
% 1.82/2.01 tff(157,plain,
% 1.82/2.01 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(158,plain,
% 1.82/2.01 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | c1_1(a901)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.82/2.01 tff(159,plain,
% 1.82/2.01 (hskp1 | hskp0 | c0_1(a901) | c1_1(a901)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[158, 112, 47, 20])).
% 1.82/2.01 tff(160,plain,
% 1.82/2.01 (hskp0),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[159, 152, 51, 49])).
% 1.82/2.01 tff(161,plain,
% 1.82/2.01 (~c2_1(a898)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[65, 160])).
% 1.82/2.01 tff(162,plain,
% 1.82/2.01 (c1_1(a898)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[59, 160])).
% 1.82/2.01 tff(163,plain,
% 1.82/2.01 (c0_1(a898)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[73, 160])).
% 1.82/2.01 tff(164,plain,
% 1.82/2.01 (c3_1(a898)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[120, 163, 46, 162, 161])).
% 1.82/2.01 tff(165,plain,
% 1.82/2.01 (^[U: $i] : refl((hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(166,plain,
% 1.82/2.01 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[165])).
% 1.82/2.01 tff(167,plain,
% 1.82/2.01 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(168,plain,
% 1.82/2.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp13) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp13) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(169,plain,
% 1.82/2.01 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp13) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[168])).
% 1.82/2.01 tff(170,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.82/2.01 tff(171,plain,
% 1.82/2.01 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.82/2.01 tff(172,plain,
% 1.82/2.01 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.82/2.01 tff(173,plain,(
% 1.82/2.01 ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.01 inference(skolemize,[status(sab)],[172])).
% 1.82/2.01 tff(174,plain,
% 1.82/2.01 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[173, 166])).
% 1.82/2.01 tff(175,plain,
% 1.82/2.01 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(176,plain,
% 1.82/2.01 ((hskp13 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898))) <=> (hskp13 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(177,plain,
% 1.82/2.01 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898))))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[176])).
% 1.82/2.01 tff(178,plain,
% 1.82/2.01 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))),
% 1.82/2.01 inference(transitivity,[status(thm)],[177, 175])).
% 1.82/2.01 tff(179,plain,
% 1.82/2.01 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(180,plain,
% 1.82/2.01 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.82/2.01 tff(181,plain,
% 1.82/2.01 (hskp13 | (~c3_1(a898))),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[180, 112, 152, 162, 161, 174])).
% 1.82/2.01 tff(182,plain,
% 1.82/2.01 (hskp13),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[181, 164])).
% 1.82/2.01 tff(183,plain,
% 1.82/2.01 (((~hskp13) | (~c2_1(a914))) <=> ((~hskp13) | (~c2_1(a914)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(184,plain,
% 1.82/2.01 (((~c2_1(a914)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a914)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(185,axiom,((~c2_1(a914)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.82/2.01 tff(186,plain,
% 1.82/2.01 ((~hskp13) | (~c2_1(a914))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.82/2.01 tff(187,plain,
% 1.82/2.01 ((~hskp13) | (~c2_1(a914))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[186, 183])).
% 1.82/2.01 tff(188,plain,
% 1.82/2.01 (~c2_1(a914)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[187, 182])).
% 1.82/2.01 tff(189,plain,
% 1.82/2.01 (((~hskp13) | (~c1_1(a914))) <=> ((~hskp13) | (~c1_1(a914)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(190,plain,
% 1.82/2.01 (((~c1_1(a914)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a914)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(191,axiom,((~c1_1(a914)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.82/2.01 tff(192,plain,
% 1.82/2.01 ((~hskp13) | (~c1_1(a914))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.82/2.01 tff(193,plain,
% 1.82/2.01 ((~hskp13) | (~c1_1(a914))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[192, 189])).
% 1.82/2.01 tff(194,plain,
% 1.82/2.01 (~c1_1(a914)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[193, 182])).
% 1.82/2.01 tff(195,plain,
% 1.82/2.01 (((~hskp13) | c3_1(a914)) <=> ((~hskp13) | c3_1(a914))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(196,axiom,((~hskp13) | c3_1(a914)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.82/2.01 tff(197,plain,
% 1.82/2.01 ((~hskp13) | c3_1(a914)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.82/2.01 tff(198,plain,
% 1.82/2.01 ((~hskp13) | c3_1(a914)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[197, 195])).
% 1.82/2.01 tff(199,plain,
% 1.82/2.01 ((~hskp13) | c3_1(a914)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[198, 195])).
% 1.82/2.01 tff(200,plain,
% 1.82/2.01 ((~hskp13) | c3_1(a914)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[199, 195])).
% 1.82/2.01 tff(201,plain,
% 1.82/2.01 ((~hskp13) | c3_1(a914)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[200, 195])).
% 1.82/2.01 tff(202,plain,
% 1.82/2.01 (c3_1(a914)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[201, 182])).
% 1.82/2.01 tff(203,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a914) | c2_1(a914) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c3_1(a914)) | c0_1(a914))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a914) | c2_1(a914) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c3_1(a914)) | c0_1(a914))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(204,plain,
% 1.82/2.01 (((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c1_1(a914) | c2_1(a914) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c3_1(a914)) | c0_1(a914))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(205,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a914) | c2_1(a914) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c3_1(a914)) | c0_1(a914)))),
% 1.82/2.01 inference(monotonicity,[status(thm)],[204])).
% 1.82/2.01 tff(206,plain,
% 1.82/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a914) | c2_1(a914) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c3_1(a914)) | c0_1(a914))),
% 1.82/2.01 inference(transitivity,[status(thm)],[205, 203])).
% 1.82/2.01 tff(207,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.82/2.01 inference(quant_inst,[status(thm)],[])).
% 1.82/2.01 tff(208,plain,
% 1.82/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a914) | c2_1(a914) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c3_1(a914)) | c0_1(a914)),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.82/2.01 tff(209,plain,
% 1.82/2.01 (c0_1(a914)),
% 1.82/2.01 inference(unit_resolution,[status(thm)],[208, 112, 202, 194, 188, 51, 48, 151, 49])).
% 1.82/2.01 tff(210,plain,
% 1.82/2.01 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(211,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[210])).
% 1.82/2.01 tff(212,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(213,plain,
% 1.82/2.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(214,plain,
% 1.82/2.01 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[213])).
% 1.82/2.01 tff(215,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.82/2.01 tff(216,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.82/2.01 tff(217,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[216, 212])).
% 1.82/2.01 tff(218,plain,(
% 1.82/2.01 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.82/2.01 inference(skolemize,[status(sab)],[217])).
% 1.82/2.01 tff(219,plain,
% 1.82/2.01 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[218, 211])).
% 1.82/2.01 tff(220,plain,
% 1.82/2.01 (^[U: $i] : refl((hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(221,plain,
% 1.82/2.01 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[220])).
% 1.82/2.01 tff(222,plain,
% 1.82/2.01 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(rewrite,[status(thm)],[])).
% 1.82/2.01 tff(223,plain,
% 1.82/2.01 (^[U: $i] : 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(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)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp5) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp5) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.82/2.01 inference(bind,[status(th)],[])).
% 1.82/2.01 tff(224,plain,
% 1.82/2.01 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp5) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(quant_intro,[status(thm)],[223])).
% 1.82/2.01 tff(225,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.82/2.01 tff(226,plain,
% 1.82/2.01 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.82/2.01 tff(227,plain,
% 1.82/2.01 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.82/2.01 tff(228,plain,(
% 1.82/2.01 ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/2.01 inference(skolemize,[status(sab)],[227])).
% 1.82/2.01 tff(229,plain,
% 1.82/2.01 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[228, 221])).
% 1.82/2.02 tff(230,plain,
% 1.82/2.02 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(231,plain,
% 1.82/2.02 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898))) <=> (hskp5 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(232,plain,
% 1.82/2.02 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[231])).
% 1.82/2.02 tff(233,plain,
% 1.82/2.02 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[232, 230])).
% 1.82/2.02 tff(234,plain,
% 1.82/2.02 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(235,plain,
% 1.82/2.02 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.82/2.02 tff(236,plain,
% 1.82/2.02 (hskp5 | (~c3_1(a898))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[235, 112, 152, 163, 161, 229])).
% 1.82/2.02 tff(237,plain,
% 1.82/2.02 (hskp5),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[236, 164])).
% 1.82/2.02 tff(238,plain,
% 1.82/2.02 (((~hskp5) | c3_1(a905)) <=> ((~hskp5) | c3_1(a905))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(239,axiom,((~hskp5) | c3_1(a905)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.82/2.02 tff(240,plain,
% 1.82/2.02 ((~hskp5) | c3_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.82/2.02 tff(241,plain,
% 1.82/2.02 ((~hskp5) | c3_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[240, 238])).
% 1.82/2.02 tff(242,plain,
% 1.82/2.02 ((~hskp5) | c3_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[241, 238])).
% 1.82/2.02 tff(243,plain,
% 1.82/2.02 ((~hskp5) | c3_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[242, 238])).
% 1.82/2.02 tff(244,plain,
% 1.82/2.02 ((~hskp5) | c3_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[243, 238])).
% 1.82/2.02 tff(245,plain,
% 1.82/2.02 (c3_1(a905)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[244, 237])).
% 1.82/2.02 tff(246,plain,
% 1.82/2.02 (((~hskp5) | c1_1(a905)) <=> ((~hskp5) | c1_1(a905))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(247,axiom,((~hskp5) | c1_1(a905)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.82/2.02 tff(248,plain,
% 1.82/2.02 ((~hskp5) | c1_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.82/2.02 tff(249,plain,
% 1.82/2.02 ((~hskp5) | c1_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[248, 246])).
% 1.82/2.02 tff(250,plain,
% 1.82/2.02 ((~hskp5) | c1_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[249, 246])).
% 1.82/2.02 tff(251,plain,
% 1.82/2.02 ((~hskp5) | c1_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[250, 246])).
% 1.82/2.02 tff(252,plain,
% 1.82/2.02 ((~hskp5) | c1_1(a905)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[251, 246])).
% 1.82/2.02 tff(253,plain,
% 1.82/2.02 (c1_1(a905)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[252, 237])).
% 1.82/2.02 tff(254,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a905)) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a905)) | (~c0_1(a914)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(255,plain,
% 1.82/2.02 ((hskp1 | (~ndr1_0) | (~c1_1(a905)) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914))) <=> (hskp1 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a905)) | (~c0_1(a914)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(256,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a905)) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a905)) | (~c0_1(a914))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[255])).
% 1.82/2.02 tff(257,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a905)) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a905)) | (~c0_1(a914)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[256, 254])).
% 1.82/2.02 tff(258,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a905)) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(259,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a905)) | (~c0_1(a914))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.82/2.02 tff(260,plain,
% 1.82/2.02 ((~c2_1(a905)) | (~c0_1(a914))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[259, 112, 152, 253, 245, 194, 188, 219])).
% 1.82/2.02 tff(261,plain,
% 1.82/2.02 (~c2_1(a905)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[260, 209])).
% 1.82/2.02 tff(262,plain,
% 1.82/2.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(263,plain,
% 1.82/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[262])).
% 1.82/2.02 tff(264,plain,
% 1.82/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(265,plain,
% 1.82/2.02 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(266,plain,
% 1.82/2.02 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[265])).
% 1.82/2.02 tff(267,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.82/2.02 tff(268,plain,
% 1.82/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.82/2.02 tff(269,plain,
% 1.82/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[268, 264])).
% 1.82/2.02 tff(270,plain,(
% 1.82/2.02 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.02 inference(skolemize,[status(sab)],[269])).
% 1.82/2.02 tff(271,plain,
% 1.82/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[270, 263])).
% 1.82/2.02 tff(272,plain,
% 1.82/2.02 (((~hskp5) | (~c0_1(a905))) <=> ((~hskp5) | (~c0_1(a905)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(273,plain,
% 1.82/2.02 (((~c0_1(a905)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a905)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(274,axiom,((~c0_1(a905)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.82/2.02 tff(275,plain,
% 1.82/2.02 ((~hskp5) | (~c0_1(a905))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[274, 273])).
% 1.82/2.02 tff(276,plain,
% 1.82/2.02 ((~hskp5) | (~c0_1(a905))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[275, 272])).
% 1.82/2.02 tff(277,plain,
% 1.82/2.02 (~c0_1(a905)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[276, 237])).
% 1.82/2.02 tff(278,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a914) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a914) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(279,plain,
% 1.82/2.02 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905))) <=> (c1_1(a914) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(280,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a914) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c3_1(a914)) | (~c0_1(a914))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[279])).
% 1.82/2.02 tff(281,plain,
% 1.82/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a914) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[280, 278])).
% 1.82/2.02 tff(282,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(283,plain,
% 1.82/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a914) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c3_1(a914)) | (~c0_1(a914))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.82/2.02 tff(284,plain,
% 1.82/2.02 (c2_1(a905) | (~c0_1(a914))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[283, 112, 202, 245, 163, 162, 194, 277, 161, 271])).
% 1.82/2.02 tff(285,plain,
% 1.82/2.02 ($false),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[284, 261, 209])).
% 1.82/2.02 tff(286,plain,(hskp1 | c0_1(a901) | c3_1(a901) | c1_1(a901) | hskp31 | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.02 tff(287,plain,
% 1.82/2.02 (hskp1),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[286, 141, 48, 51, 46, 47])).
% 1.82/2.02 tff(288,plain,
% 1.82/2.02 (((~hskp1) | (~c0_1(a899))) <=> ((~hskp1) | (~c0_1(a899)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(289,plain,
% 1.82/2.02 (((~c0_1(a899)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a899)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(290,axiom,((~c0_1(a899)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.82/2.02 tff(291,plain,
% 1.82/2.02 ((~hskp1) | (~c0_1(a899))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.82/2.02 tff(292,plain,
% 1.82/2.02 ((~hskp1) | (~c0_1(a899))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[291, 288])).
% 1.82/2.02 tff(293,plain,
% 1.82/2.02 (~c0_1(a899)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[292, 287])).
% 1.82/2.02 tff(294,plain,
% 1.82/2.02 (((~hskp1) | c2_1(a899)) <=> ((~hskp1) | c2_1(a899))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(295,axiom,((~hskp1) | c2_1(a899)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.82/2.02 tff(296,plain,
% 1.82/2.02 ((~hskp1) | c2_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.82/2.02 tff(297,plain,
% 1.82/2.02 ((~hskp1) | c2_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[296, 294])).
% 1.82/2.02 tff(298,plain,
% 1.82/2.02 ((~hskp1) | c2_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[297, 294])).
% 1.82/2.02 tff(299,plain,
% 1.82/2.02 ((~hskp1) | c2_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[298, 294])).
% 1.82/2.02 tff(300,plain,
% 1.82/2.02 ((~hskp1) | c2_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[299, 294])).
% 1.82/2.02 tff(301,plain,
% 1.82/2.02 (c2_1(a899)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[300, 287])).
% 1.82/2.02 tff(302,plain,
% 1.82/2.02 (((~hskp1) | c1_1(a899)) <=> ((~hskp1) | c1_1(a899))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(303,axiom,((~hskp1) | c1_1(a899)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.82/2.02 tff(304,plain,
% 1.82/2.02 ((~hskp1) | c1_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.82/2.02 tff(305,plain,
% 1.82/2.02 ((~hskp1) | c1_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[304, 302])).
% 1.82/2.02 tff(306,plain,
% 1.82/2.02 ((~hskp1) | c1_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[305, 302])).
% 1.82/2.02 tff(307,plain,
% 1.82/2.02 ((~hskp1) | c1_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[306, 302])).
% 1.82/2.02 tff(308,plain,
% 1.82/2.02 ((~hskp1) | c1_1(a899)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[307, 302])).
% 1.82/2.02 tff(309,plain,
% 1.82/2.02 (c1_1(a899)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[308, 287])).
% 1.82/2.02 tff(310,assumption,(c3_1(a898)), introduced(assumption)).
% 1.82/2.02 tff(311,assumption,(c1_1(a899)), introduced(assumption)).
% 1.82/2.02 tff(312,assumption,(c2_1(a899)), introduced(assumption)).
% 1.82/2.02 tff(313,assumption,(~hskp14), introduced(assumption)).
% 1.82/2.02 tff(314,assumption,(c3_1(a899)), introduced(assumption)).
% 1.82/2.02 tff(315,plain,
% 1.82/2.02 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(316,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[315])).
% 1.82/2.02 tff(317,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(318,plain,
% 1.82/2.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(319,plain,
% 1.82/2.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[318])).
% 1.82/2.02 tff(320,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.82/2.02 tff(321,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[320, 319])).
% 1.82/2.02 tff(322,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[321, 317])).
% 1.82/2.02 tff(323,plain,(
% 1.82/2.02 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(skolemize,[status(sab)],[322])).
% 1.82/2.02 tff(324,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[323, 316])).
% 1.82/2.02 tff(325,plain,
% 1.82/2.02 (^[U: $i] : refl((hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(326,plain,
% 1.82/2.02 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[325])).
% 1.82/2.02 tff(327,plain,
% 1.82/2.02 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(328,plain,
% 1.82/2.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp10) <=> ((hskp12 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp10))), rewrite(((hskp12 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp10) <=> (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp10) <=> (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(329,plain,
% 1.82/2.02 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp10) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[328])).
% 1.82/2.02 tff(330,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.82/2.02 tff(331,plain,
% 1.82/2.02 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.82/2.02 tff(332,plain,
% 1.82/2.02 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[331, 327])).
% 1.82/2.02 tff(333,plain,(
% 1.82/2.02 ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.02 inference(skolemize,[status(sab)],[332])).
% 1.82/2.02 tff(334,plain,
% 1.82/2.02 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[333, 326])).
% 1.82/2.02 tff(335,plain,
% 1.82/2.02 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(336,plain,
% 1.82/2.02 ((hskp12 | hskp10 | (~ndr1_0) | c0_1(a899) | (~c1_1(a899)) | (~c3_1(a899))) <=> (hskp12 | hskp10 | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(337,plain,
% 1.82/2.02 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a899) | (~c1_1(a899)) | (~c3_1(a899)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[336])).
% 1.82/2.02 tff(338,plain,
% 1.82/2.02 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a899) | (~c1_1(a899)) | (~c3_1(a899)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[337, 335])).
% 1.82/2.02 tff(339,plain,
% 1.82/2.02 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a899) | (~c1_1(a899)) | (~c3_1(a899)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(340,plain,
% 1.82/2.02 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.82/2.02 tff(341,plain,
% 1.82/2.02 (hskp12 | (~c3_1(a899)) | (~c1_1(a899))),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[340, 112, 50, 43, 334])).
% 1.82/2.02 tff(342,plain,
% 1.82/2.02 (hskp12),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[341, 314, 311])).
% 1.82/2.02 tff(343,plain,
% 1.82/2.02 (((~hskp12) | (~c3_1(a913))) <=> ((~hskp12) | (~c3_1(a913)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(344,plain,
% 1.82/2.02 (((~c3_1(a913)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a913)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(345,axiom,((~c3_1(a913)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.82/2.02 tff(346,plain,
% 1.82/2.02 ((~hskp12) | (~c3_1(a913))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.82/2.02 tff(347,plain,
% 1.82/2.02 ((~hskp12) | (~c3_1(a913))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[346, 343])).
% 1.82/2.02 tff(348,plain,
% 1.82/2.02 (~c3_1(a913)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[347, 342])).
% 1.82/2.02 tff(349,plain,
% 1.82/2.02 (((~hskp12) | c0_1(a913)) <=> ((~hskp12) | c0_1(a913))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(350,axiom,((~hskp12) | c0_1(a913)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.82/2.02 tff(351,plain,
% 1.82/2.02 ((~hskp12) | c0_1(a913)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.82/2.02 tff(352,plain,
% 1.82/2.02 ((~hskp12) | c0_1(a913)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[351, 349])).
% 1.82/2.02 tff(353,plain,
% 1.82/2.02 ((~hskp12) | c0_1(a913)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[352, 349])).
% 1.82/2.02 tff(354,plain,
% 1.82/2.02 ((~hskp12) | c0_1(a913)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[353, 349])).
% 1.82/2.02 tff(355,plain,
% 1.82/2.02 ((~hskp12) | c0_1(a913)),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[354, 349])).
% 1.82/2.02 tff(356,plain,
% 1.82/2.02 (c0_1(a913)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[355, 342])).
% 1.82/2.02 tff(357,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(358,plain,
% 1.82/2.02 ((hskp14 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c1_1(a899))) <=> (hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(359,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913))))),
% 1.82/2.02 inference(monotonicity,[status(thm)],[358])).
% 1.82/2.02 tff(360,plain,
% 1.82/2.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.82/2.02 inference(transitivity,[status(thm)],[359, 357])).
% 1.82/2.02 tff(361,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c1_1(a899)))),
% 1.82/2.02 inference(quant_inst,[status(thm)],[])).
% 1.82/2.02 tff(362,plain,
% 1.82/2.02 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913))),
% 1.82/2.02 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.82/2.02 tff(363,plain,
% 1.82/2.02 (~c2_1(a913)),
% 1.82/2.02 inference(unit_resolution,[status(thm)],[362, 112, 313, 356, 311, 348, 43, 324, 314])).
% 1.82/2.02 tff(364,plain,
% 1.82/2.02 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.82/2.02 inference(bind,[status(th)],[])).
% 1.82/2.02 tff(365,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(quant_intro,[status(thm)],[364])).
% 1.82/2.02 tff(366,plain,
% 1.82/2.02 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.82/2.02 inference(rewrite,[status(thm)],[])).
% 1.82/2.02 tff(367,plain,
% 1.82/2.02 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(368,plain,
% 1.82/2.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[367])).
% 1.82/2.03 tff(369,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.82/2.03 tff(370,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.82/2.03 tff(371,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[370, 366])).
% 1.82/2.03 tff(372,plain,(
% 1.82/2.03 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.82/2.03 inference(skolemize,[status(sab)],[371])).
% 1.82/2.03 tff(373,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[372, 365])).
% 1.82/2.03 tff(374,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | c2_1(a913) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | c2_1(a913) | (~c0_1(a913)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(375,plain,
% 1.82/2.03 ((hskp14 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | c2_1(a913) | (~c0_1(a913)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(376,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | c2_1(a913) | (~c0_1(a913))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[375])).
% 1.82/2.03 tff(377,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | c2_1(a913) | (~c0_1(a913)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[376, 374])).
% 1.82/2.03 tff(378,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(379,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | c2_1(a913) | (~c0_1(a913))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.82/2.03 tff(380,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[379, 112, 313, 356, 311, 312, 348, 43, 373, 363])).
% 1.82/2.03 tff(381,plain,((~c3_1(a899)) | hskp14 | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(382,plain,
% 1.82/2.03 (~c3_1(a899)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[381, 313, 312, 311, 43, 50])).
% 1.82/2.03 tff(383,plain,
% 1.82/2.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(384,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[383])).
% 1.82/2.03 tff(385,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(386,plain,
% 1.82/2.03 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(387,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[386])).
% 1.82/2.03 tff(388,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.82/2.03 tff(389,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.82/2.03 tff(390,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[389, 385])).
% 1.82/2.03 tff(391,plain,(
% 1.82/2.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.82/2.03 inference(skolemize,[status(sab)],[390])).
% 1.82/2.03 tff(392,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[391, 384])).
% 1.82/2.03 tff(393,plain,
% 1.82/2.03 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(394,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[393])).
% 1.82/2.03 tff(395,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(396,plain,
% 1.82/2.03 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_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)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(397,plain,
% 1.82/2.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[396])).
% 1.82/2.03 tff(398,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.82/2.03 tff(399,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.82/2.03 tff(400,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[399, 395])).
% 1.82/2.03 tff(401,plain,(
% 1.82/2.03 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.03 inference(skolemize,[status(sab)],[400])).
% 1.82/2.03 tff(402,plain,
% 1.82/2.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[401, 394])).
% 1.82/2.03 tff(403,assumption,(hskp12), introduced(assumption)).
% 1.82/2.03 tff(404,plain,
% 1.82/2.03 (~c3_1(a913)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[347, 403])).
% 1.82/2.03 tff(405,plain,
% 1.82/2.03 (((~hskp12) | (~c1_1(a913))) <=> ((~hskp12) | (~c1_1(a913)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(406,plain,
% 1.82/2.03 (((~c1_1(a913)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a913)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(407,axiom,((~c1_1(a913)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.82/2.03 tff(408,plain,
% 1.82/2.03 ((~hskp12) | (~c1_1(a913))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.82/2.03 tff(409,plain,
% 1.82/2.03 ((~hskp12) | (~c1_1(a913))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[408, 405])).
% 1.82/2.03 tff(410,plain,
% 1.82/2.03 (~c1_1(a913)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[409, 403])).
% 1.82/2.03 tff(411,assumption,(hskp21), introduced(assumption)).
% 1.82/2.03 tff(412,plain,
% 1.82/2.03 (((~hskp21) | (~c3_1(a938))) <=> ((~hskp21) | (~c3_1(a938)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(413,plain,
% 1.82/2.03 (((~c3_1(a938)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a938)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(414,axiom,((~c3_1(a938)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.82/2.03 tff(415,plain,
% 1.82/2.03 ((~hskp21) | (~c3_1(a938))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.82/2.03 tff(416,plain,
% 1.82/2.03 ((~hskp21) | (~c3_1(a938))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[415, 412])).
% 1.82/2.03 tff(417,plain,
% 1.82/2.03 (~c3_1(a938)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[416, 411])).
% 1.82/2.03 tff(418,plain,
% 1.82/2.03 (((~hskp21) | (~c2_1(a938))) <=> ((~hskp21) | (~c2_1(a938)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(419,plain,
% 1.82/2.03 (((~c2_1(a938)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a938)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(420,axiom,((~c2_1(a938)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.82/2.03 tff(421,plain,
% 1.82/2.03 ((~hskp21) | (~c2_1(a938))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.82/2.03 tff(422,plain,
% 1.82/2.03 ((~hskp21) | (~c2_1(a938))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[421, 418])).
% 1.82/2.03 tff(423,plain,
% 1.82/2.03 (~c2_1(a938)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[422, 411])).
% 1.82/2.03 tff(424,plain,
% 1.82/2.03 (((~hskp21) | c0_1(a938)) <=> ((~hskp21) | c0_1(a938))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(425,axiom,((~hskp21) | c0_1(a938)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.82/2.03 tff(426,plain,
% 1.82/2.03 ((~hskp21) | c0_1(a938)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[425, 424])).
% 1.82/2.03 tff(427,plain,
% 1.82/2.03 ((~hskp21) | c0_1(a938)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[426, 424])).
% 1.82/2.03 tff(428,plain,
% 1.82/2.03 ((~hskp21) | c0_1(a938)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[427, 424])).
% 1.82/2.03 tff(429,plain,
% 1.82/2.03 ((~hskp21) | c0_1(a938)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[428, 424])).
% 1.82/2.03 tff(430,plain,
% 1.82/2.03 ((~hskp21) | c0_1(a938)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[429, 424])).
% 1.82/2.03 tff(431,plain,
% 1.82/2.03 (c0_1(a938)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[430, 411])).
% 1.82/2.03 tff(432,assumption,(ndr1_0), introduced(assumption)).
% 1.82/2.03 tff(433,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a938)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(434,plain,
% 1.82/2.03 ((hskp14 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp14 | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a938)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(435,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a938))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[434])).
% 1.82/2.03 tff(436,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a938)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[435, 433])).
% 1.82/2.03 tff(437,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(438,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a938))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.82/2.03 tff(439,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[438, 432, 313, 431, 311, 312, 423, 417, 43, 373])).
% 1.82/2.03 tff(440,plain,((~hskp21) | (~ndr1_0) | hskp14 | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(441,plain,
% 1.82/2.03 ((~hskp21) | hskp14 | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[440, 112])).
% 1.82/2.03 tff(442,plain,
% 1.82/2.03 (~hskp21),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[441, 313, 311, 312, 43])).
% 1.82/2.03 tff(443,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a913) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a913) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a913)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(444,plain,
% 1.82/2.03 ((hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913))) <=> (hskp21 | c1_1(a913) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a913)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(445,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a913) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a913))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[444])).
% 1.82/2.03 tff(446,plain,
% 1.82/2.03 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a913) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a913)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[445, 443])).
% 1.82/2.03 tff(447,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(448,plain,
% 1.82/2.03 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a913) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a913))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.82/2.03 tff(449,plain,
% 1.82/2.03 (~c2_1(a913)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[448, 112, 442, 78, 77, 410, 404, 76, 402])).
% 1.82/2.03 tff(450,plain,
% 1.82/2.03 (c0_1(a913)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[355, 403])).
% 1.82/2.03 tff(451,plain,
% 1.82/2.03 ($false),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[379, 112, 313, 450, 311, 312, 404, 43, 373, 449])).
% 1.82/2.03 tff(452,plain,((~hskp12) | hskp14 | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a898)), inference(lemma,lemma(discharge,[]))).
% 1.82/2.03 tff(453,plain,
% 1.82/2.03 (~hskp12),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[452, 313, 78, 311, 43, 312, 77, 76])).
% 1.82/2.03 tff(454,plain,
% 1.82/2.03 (^[U: $i] : refl((hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(455,plain,
% 1.82/2.03 (![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[454])).
% 1.82/2.03 tff(456,plain,
% 1.82/2.03 (![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(457,plain,
% 1.82/2.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp6) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp6))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp6) <=> (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp6) <=> (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(458,plain,
% 1.82/2.03 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp6) <=> ![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[457])).
% 1.82/2.03 tff(459,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.82/2.03 tff(460,plain,
% 1.82/2.03 (![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.82/2.03 tff(461,plain,
% 1.82/2.03 (![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[460, 456])).
% 1.82/2.03 tff(462,plain,(
% 1.82/2.03 ![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.03 inference(skolemize,[status(sab)],[461])).
% 1.82/2.03 tff(463,plain,
% 1.82/2.03 (![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[462, 455])).
% 1.82/2.03 tff(464,plain,
% 1.82/2.03 (((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))) <=> ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp6 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(465,plain,
% 1.82/2.03 ((hskp12 | hskp6 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898))) <=> (hskp12 | hskp6 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(466,plain,
% 1.82/2.03 (((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)))) <=> ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898))))),
% 1.82/2.03 inference(monotonicity,[status(thm)],[465])).
% 1.82/2.03 tff(467,plain,
% 1.82/2.03 (((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)))) <=> ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp6 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)))),
% 1.82/2.03 inference(transitivity,[status(thm)],[466, 464])).
% 1.82/2.03 tff(468,plain,
% 1.82/2.03 ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)))),
% 1.82/2.03 inference(quant_inst,[status(thm)],[])).
% 1.82/2.03 tff(469,plain,
% 1.82/2.03 ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp6 | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.82/2.03 tff(470,plain,
% 1.82/2.03 (hskp12 | hskp6),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[469, 112, 77, 76, 463, 310])).
% 1.82/2.03 tff(471,plain,
% 1.82/2.03 (hskp6),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[470, 453])).
% 1.82/2.03 tff(472,plain,
% 1.82/2.03 (((~hskp6) | c3_1(a906)) <=> ((~hskp6) | c3_1(a906))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(473,axiom,((~hskp6) | c3_1(a906)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.82/2.03 tff(474,plain,
% 1.82/2.03 ((~hskp6) | c3_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.82/2.03 tff(475,plain,
% 1.82/2.03 ((~hskp6) | c3_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[474, 472])).
% 1.82/2.03 tff(476,plain,
% 1.82/2.03 ((~hskp6) | c3_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[475, 472])).
% 1.82/2.03 tff(477,plain,
% 1.82/2.03 ((~hskp6) | c3_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[476, 472])).
% 1.82/2.03 tff(478,plain,
% 1.82/2.03 ((~hskp6) | c3_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[477, 472])).
% 1.82/2.03 tff(479,plain,
% 1.82/2.03 (c3_1(a906)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[478, 471])).
% 1.82/2.03 tff(480,plain,
% 1.82/2.03 (((~hskp6) | c2_1(a906)) <=> ((~hskp6) | c2_1(a906))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(481,axiom,((~hskp6) | c2_1(a906)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.82/2.03 tff(482,plain,
% 1.82/2.03 ((~hskp6) | c2_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[481, 480])).
% 1.82/2.03 tff(483,plain,
% 1.82/2.03 ((~hskp6) | c2_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[482, 480])).
% 1.82/2.03 tff(484,plain,
% 1.82/2.03 ((~hskp6) | c2_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[483, 480])).
% 1.82/2.03 tff(485,plain,
% 1.82/2.03 ((~hskp6) | c2_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[484, 480])).
% 1.82/2.03 tff(486,plain,
% 1.82/2.03 ((~hskp6) | c2_1(a906)),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[485, 480])).
% 1.82/2.03 tff(487,plain,
% 1.82/2.03 (c2_1(a906)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[486, 471])).
% 1.82/2.03 tff(488,plain,
% 1.82/2.03 (((~hskp6) | (~c1_1(a906))) <=> ((~hskp6) | (~c1_1(a906)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(489,plain,
% 1.82/2.03 (((~c1_1(a906)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a906)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(490,axiom,((~c1_1(a906)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.82/2.03 tff(491,plain,
% 1.82/2.03 ((~hskp6) | (~c1_1(a906))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.82/2.03 tff(492,plain,
% 1.82/2.03 ((~hskp6) | (~c1_1(a906))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[491, 488])).
% 1.82/2.03 tff(493,plain,
% 1.82/2.03 (~c1_1(a906)),
% 1.82/2.03 inference(unit_resolution,[status(thm)],[492, 471])).
% 1.82/2.03 tff(494,plain,
% 1.82/2.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(495,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[494])).
% 1.82/2.03 tff(496,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.03 tff(497,plain,
% 1.82/2.03 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | 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(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_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(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.82/2.03 inference(bind,[status(th)],[])).
% 1.82/2.03 tff(498,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.03 inference(quant_intro,[status(thm)],[497])).
% 1.82/2.03 tff(499,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.82/2.03 tff(500,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.82/2.03 tff(501,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[500, 496])).
% 1.82/2.03 tff(502,plain,(
% 1.82/2.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.03 inference(skolemize,[status(sab)],[501])).
% 1.82/2.03 tff(503,plain,
% 1.82/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/2.03 inference(modus_ponens,[status(thm)],[502, 495])).
% 1.82/2.03 tff(504,assumption,(~c3_1(a899)), introduced(assumption)).
% 1.82/2.03 tff(505,assumption,(~c3_1(a907)), introduced(assumption)).
% 1.82/2.03 tff(506,plain,
% 1.82/2.03 (((~hskp7) | c3_1(a907)) <=> ((~hskp7) | c3_1(a907))),
% 1.82/2.03 inference(rewrite,[status(thm)],[])).
% 1.82/2.04 tff(507,axiom,((~hskp7) | c3_1(a907)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.82/2.04 tff(508,plain,
% 1.82/2.04 ((~hskp7) | c3_1(a907)),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.82/2.04 tff(509,plain,
% 1.82/2.04 ((~hskp7) | c3_1(a907)),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[508, 506])).
% 1.82/2.04 tff(510,plain,
% 1.82/2.04 ((~hskp7) | c3_1(a907)),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[509, 506])).
% 1.82/2.04 tff(511,plain,
% 1.82/2.04 ((~hskp7) | c3_1(a907)),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[510, 506])).
% 1.82/2.04 tff(512,plain,
% 1.82/2.04 ((~hskp7) | c3_1(a907)),
% 1.82/2.04 inference(modus_ponens,[status(thm)],[511, 506])).
% 1.82/2.04 tff(513,plain,
% 1.82/2.04 (~hskp7),
% 1.82/2.04 inference(unit_resolution,[status(thm)],[512, 505])).
% 1.82/2.04 tff(514,plain,
% 1.82/2.04 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.82/2.04 inference(bind,[status(th)],[])).
% 1.82/2.04 tff(515,plain,
% 1.82/2.04 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[514])).
% 1.88/2.04 tff(516,plain,
% 1.88/2.04 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(517,plain,
% 1.88/2.04 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp7) <=> ((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.88/2.04 inference(bind,[status(th)],[])).
% 1.88/2.04 tff(518,plain,
% 1.88/2.04 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp7) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[517])).
% 1.88/2.04 tff(519,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp4) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.88/2.04 tff(520,plain,
% 1.88/2.04 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.88/2.04 tff(521,plain,
% 1.88/2.04 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[520, 516])).
% 1.88/2.04 tff(522,plain,(
% 1.88/2.04 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.88/2.04 inference(skolemize,[status(sab)],[521])).
% 1.88/2.04 tff(523,plain,
% 1.88/2.04 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[522, 515])).
% 1.88/2.04 tff(524,plain,
% 1.88/2.04 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(525,plain,
% 1.88/2.04 ((hskp7 | hskp4 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c1_1(a899))) <=> (hskp7 | hskp4 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(526,plain,
% 1.88/2.04 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c1_1(a899)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899))))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[525])).
% 1.88/2.04 tff(527,plain,
% 1.88/2.04 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c1_1(a899)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)))),
% 1.88/2.04 inference(transitivity,[status(thm)],[526, 524])).
% 1.88/2.04 tff(528,plain,
% 1.88/2.04 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c1_1(a899)))),
% 1.88/2.04 inference(quant_inst,[status(thm)],[])).
% 1.88/2.04 tff(529,plain,
% 1.88/2.04 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.88/2.04 tff(530,plain,
% 1.88/2.04 (hskp7 | hskp4 | c3_1(a899) | (~c1_1(a899))),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[529, 112, 43, 523])).
% 1.88/2.04 tff(531,plain,
% 1.88/2.04 (hskp4),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[530, 513, 311, 504])).
% 1.88/2.04 tff(532,plain,
% 1.88/2.04 (((~hskp4) | (~c3_1(a904))) <=> ((~hskp4) | (~c3_1(a904)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(533,plain,
% 1.88/2.04 (((~c3_1(a904)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a904)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(534,axiom,((~c3_1(a904)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.88/2.04 tff(535,plain,
% 1.88/2.04 ((~hskp4) | (~c3_1(a904))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.88/2.04 tff(536,plain,
% 1.88/2.04 ((~hskp4) | (~c3_1(a904))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[535, 532])).
% 1.88/2.04 tff(537,plain,
% 1.88/2.04 (~c3_1(a904)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[536, 531])).
% 1.88/2.04 tff(538,plain,
% 1.88/2.04 (((~hskp4) | (~c1_1(a904))) <=> ((~hskp4) | (~c1_1(a904)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(539,plain,
% 1.88/2.04 (((~c1_1(a904)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a904)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(540,axiom,((~c1_1(a904)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.88/2.04 tff(541,plain,
% 1.88/2.04 ((~hskp4) | (~c1_1(a904))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[540, 539])).
% 1.88/2.04 tff(542,plain,
% 1.88/2.04 ((~hskp4) | (~c1_1(a904))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[541, 538])).
% 1.88/2.04 tff(543,plain,
% 1.88/2.04 (~c1_1(a904)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[542, 531])).
% 1.88/2.04 tff(544,assumption,(c3_1(a906)), introduced(assumption)).
% 1.88/2.04 tff(545,assumption,(c2_1(a906)), introduced(assumption)).
% 1.88/2.04 tff(546,assumption,(~c1_1(a906)), introduced(assumption)).
% 1.88/2.04 tff(547,assumption,(~hskp7), introduced(assumption)).
% 1.88/2.04 tff(548,plain,
% 1.88/2.04 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.88/2.04 inference(bind,[status(th)],[])).
% 1.88/2.04 tff(549,plain,
% 1.88/2.04 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[548])).
% 1.88/2.04 tff(550,plain,
% 1.88/2.04 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(551,plain,
% 1.88/2.04 (^[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)) | 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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.88/2.04 inference(bind,[status(th)],[])).
% 1.88/2.04 tff(552,plain,
% 1.88/2.04 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[551])).
% 1.88/2.04 tff(553,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.88/2.04 tff(554,plain,
% 1.88/2.04 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[553, 552])).
% 1.88/2.04 tff(555,plain,
% 1.88/2.04 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[554, 550])).
% 1.88/2.04 tff(556,plain,(
% 1.88/2.04 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.88/2.04 inference(skolemize,[status(sab)],[555])).
% 1.88/2.04 tff(557,plain,
% 1.88/2.04 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[556, 549])).
% 1.88/2.04 tff(558,assumption,(~hskp8), introduced(assumption)).
% 1.88/2.04 tff(559,plain,
% 1.88/2.04 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c1_1(a906) | (~ndr1_0) | c0_1(a906) | (~c3_1(a906)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a906) | (~ndr1_0) | c0_1(a906) | (~c3_1(a906)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(560,plain,
% 1.88/2.04 ((hskp8 | hskp7 | (~ndr1_0) | c1_1(a906) | c0_1(a906) | (~c3_1(a906))) <=> (hskp8 | hskp7 | c1_1(a906) | (~ndr1_0) | c0_1(a906) | (~c3_1(a906)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(561,plain,
% 1.88/2.04 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a906) | c0_1(a906) | (~c3_1(a906)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c1_1(a906) | (~ndr1_0) | c0_1(a906) | (~c3_1(a906))))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[560])).
% 1.88/2.04 tff(562,plain,
% 1.88/2.04 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a906) | c0_1(a906) | (~c3_1(a906)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a906) | (~ndr1_0) | c0_1(a906) | (~c3_1(a906)))),
% 1.88/2.04 inference(transitivity,[status(thm)],[561, 559])).
% 1.88/2.04 tff(563,plain,
% 1.88/2.04 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a906) | c0_1(a906) | (~c3_1(a906)))),
% 1.88/2.04 inference(quant_inst,[status(thm)],[])).
% 1.88/2.04 tff(564,plain,
% 1.88/2.04 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a906) | (~ndr1_0) | c0_1(a906) | (~c3_1(a906))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.88/2.04 tff(565,plain,
% 1.88/2.04 (hskp7 | c0_1(a906)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[564, 112, 558, 544, 546, 557])).
% 1.88/2.04 tff(566,plain,
% 1.88/2.04 (c0_1(a906)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[565, 547])).
% 1.88/2.04 tff(567,plain,
% 1.88/2.04 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.88/2.04 inference(bind,[status(th)],[])).
% 1.88/2.04 tff(568,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[567])).
% 1.88/2.04 tff(569,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(570,plain,
% 1.88/2.04 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.88/2.04 inference(bind,[status(th)],[])).
% 1.88/2.04 tff(571,plain,
% 1.88/2.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[570])).
% 1.88/2.04 tff(572,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.88/2.04 tff(573,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.88/2.04 tff(574,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[573, 569])).
% 1.88/2.04 tff(575,plain,(
% 1.88/2.04 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/2.04 inference(skolemize,[status(sab)],[574])).
% 1.88/2.04 tff(576,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[575, 568])).
% 1.88/2.04 tff(577,plain,
% 1.88/2.04 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(578,plain,
% 1.88/2.04 ((hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906))) <=> (hskp7 | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(579,plain,
% 1.88/2.04 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906))))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[578])).
% 1.88/2.04 tff(580,plain,
% 1.88/2.04 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)))),
% 1.88/2.04 inference(transitivity,[status(thm)],[579, 577])).
% 1.88/2.04 tff(581,plain,
% 1.88/2.04 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906)))),
% 1.88/2.04 inference(quant_inst,[status(thm)],[])).
% 1.88/2.04 tff(582,plain,
% 1.88/2.04 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[581, 580])).
% 1.88/2.04 tff(583,plain,
% 1.88/2.04 (hskp7 | (~c0_1(a906))),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[582, 112, 545, 78, 77, 546, 76, 576])).
% 1.88/2.04 tff(584,plain,
% 1.88/2.04 ($false),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[583, 566, 547])).
% 1.88/2.04 tff(585,plain,(hskp7 | (~c2_1(a906)) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a906) | c2_1(a898) | hskp8 | (~c3_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.88/2.04 tff(586,plain,
% 1.88/2.04 (hskp8),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[585, 513, 78, 77, 546, 76, 545, 544])).
% 1.88/2.04 tff(587,plain,
% 1.88/2.04 (((~hskp8) | (~c2_1(a908))) <=> ((~hskp8) | (~c2_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(588,plain,
% 1.88/2.04 (((~c2_1(a908)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(589,axiom,((~c2_1(a908)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.88/2.04 tff(590,plain,
% 1.88/2.04 ((~hskp8) | (~c2_1(a908))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.88/2.04 tff(591,plain,
% 1.88/2.04 ((~hskp8) | (~c2_1(a908))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[590, 587])).
% 1.88/2.04 tff(592,plain,
% 1.88/2.04 (~c2_1(a908)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[591, 586])).
% 1.88/2.04 tff(593,plain,
% 1.88/2.04 (((~hskp8) | (~c0_1(a908))) <=> ((~hskp8) | (~c0_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(594,plain,
% 1.88/2.04 (((~c0_1(a908)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(595,axiom,((~c0_1(a908)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.88/2.04 tff(596,plain,
% 1.88/2.04 ((~hskp8) | (~c0_1(a908))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.88/2.04 tff(597,plain,
% 1.88/2.04 ((~hskp8) | (~c0_1(a908))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[596, 593])).
% 1.88/2.04 tff(598,plain,
% 1.88/2.04 (~c0_1(a908)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[597, 586])).
% 1.88/2.04 tff(599,plain,
% 1.88/2.04 (((~hskp4) | c2_1(a904)) <=> ((~hskp4) | c2_1(a904))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(600,axiom,((~hskp4) | c2_1(a904)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.88/2.04 tff(601,plain,
% 1.88/2.04 ((~hskp4) | c2_1(a904)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.88/2.04 tff(602,plain,
% 1.88/2.04 ((~hskp4) | c2_1(a904)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[601, 599])).
% 1.88/2.04 tff(603,plain,
% 1.88/2.04 ((~hskp4) | c2_1(a904)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[602, 599])).
% 1.88/2.04 tff(604,plain,
% 1.88/2.04 ((~hskp4) | c2_1(a904)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[603, 599])).
% 1.88/2.04 tff(605,plain,
% 1.88/2.04 ((~hskp4) | c2_1(a904)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[604, 599])).
% 1.88/2.04 tff(606,plain,
% 1.88/2.04 (c2_1(a904)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[605, 531])).
% 1.88/2.04 tff(607,plain,
% 1.88/2.04 (((~hskp8) | c3_1(a908)) <=> ((~hskp8) | c3_1(a908))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(608,axiom,((~hskp8) | c3_1(a908)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.88/2.04 tff(609,plain,
% 1.88/2.04 ((~hskp8) | c3_1(a908)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.88/2.04 tff(610,plain,
% 1.88/2.04 ((~hskp8) | c3_1(a908)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[609, 607])).
% 1.88/2.04 tff(611,plain,
% 1.88/2.04 ((~hskp8) | c3_1(a908)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[610, 607])).
% 1.88/2.04 tff(612,plain,
% 1.88/2.04 ((~hskp8) | c3_1(a908)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[611, 607])).
% 1.88/2.04 tff(613,plain,
% 1.88/2.04 ((~hskp8) | c3_1(a908)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[612, 607])).
% 1.88/2.04 tff(614,plain,
% 1.88/2.04 (c3_1(a908)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[613, 586])).
% 1.88/2.04 tff(615,plain,
% 1.88/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a908) | c2_1(a908) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a908)) | (~c3_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a908) | c2_1(a908) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a908)) | (~c3_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(616,plain,
% 1.88/2.04 (((~ndr1_0) | c2_1(a908) | (~c1_1(a908)) | (~c3_1(a908)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908))) <=> (c0_1(a908) | c2_1(a908) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a908)) | (~c3_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(617,plain,
% 1.88/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a908) | (~c1_1(a908)) | (~c3_1(a908)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a908) | c2_1(a908) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a908)) | (~c3_1(a908))))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[616])).
% 1.88/2.04 tff(618,plain,
% 1.88/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a908) | (~c1_1(a908)) | (~c3_1(a908)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a908) | c2_1(a908) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a908)) | (~c3_1(a908)))),
% 1.88/2.04 inference(transitivity,[status(thm)],[617, 615])).
% 1.88/2.04 tff(619,plain,
% 1.88/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a908) | (~c1_1(a908)) | (~c3_1(a908)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908)))),
% 1.88/2.04 inference(quant_inst,[status(thm)],[])).
% 1.88/2.04 tff(620,plain,
% 1.88/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a908) | c2_1(a908) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a908)) | (~c3_1(a908))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[619, 618])).
% 1.88/2.04 tff(621,plain,
% 1.88/2.04 (~c1_1(a908)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[620, 112, 614, 606, 598, 592, 543, 537, 503])).
% 1.88/2.04 tff(622,plain,
% 1.88/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c1_1(a908) | (~c3_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c1_1(a908) | (~c3_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(623,plain,
% 1.88/2.04 (((~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c3_1(a908)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907)) <=> (c3_1(a907) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c1_1(a908) | (~c3_1(a908)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(624,plain,
% 1.88/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c3_1(a908)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c1_1(a908) | (~c3_1(a908))))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[623])).
% 1.88/2.04 tff(625,plain,
% 1.88/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c3_1(a908)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c1_1(a908) | (~c3_1(a908)))),
% 1.88/2.04 inference(transitivity,[status(thm)],[624, 622])).
% 1.88/2.04 tff(626,plain,
% 1.88/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c3_1(a908)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907))),
% 1.88/2.04 inference(quant_inst,[status(thm)],[])).
% 1.88/2.04 tff(627,plain,
% 1.88/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c1_1(a908) | (~c3_1(a908))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[626, 625])).
% 1.88/2.04 tff(628,plain,
% 1.88/2.04 ($false),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[627, 112, 614, 505, 598, 592, 44, 45, 151, 621])).
% 1.88/2.04 tff(629,plain,(c3_1(a907) | c0_1(a907) | c1_1(a907) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a906) | c2_1(a898) | (~c2_1(a906)) | (~c3_1(a906)) | (~c1_1(a899)) | c3_1(a899) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.04 tff(630,plain,
% 1.88/2.04 (c3_1(a907)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[629, 493, 45, 78, 77, 44, 76, 487, 479, 311, 382, 43])).
% 1.88/2.04 tff(631,plain,
% 1.88/2.04 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.88/2.04 inference(bind,[status(th)],[])).
% 1.88/2.04 tff(632,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[631])).
% 1.88/2.04 tff(633,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.88/2.04 inference(rewrite,[status(thm)],[])).
% 1.88/2.04 tff(634,plain,
% 1.88/2.04 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.88/2.04 inference(bind,[status(th)],[])).
% 1.88/2.04 tff(635,plain,
% 1.88/2.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.88/2.04 inference(quant_intro,[status(thm)],[634])).
% 1.88/2.04 tff(636,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.88/2.04 tff(637,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.88/2.04 tff(638,plain,
% 1.88/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[637, 633])).
% 1.88/2.05 tff(639,plain,(
% 1.88/2.05 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.88/2.05 inference(skolemize,[status(sab)],[638])).
% 1.88/2.05 tff(640,plain,
% 1.88/2.05 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[639, 632])).
% 1.88/2.05 tff(641,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c3_1(a907)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(642,plain,
% 1.88/2.05 ((hskp4 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907))) <=> (hskp4 | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c3_1(a907)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(643,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c3_1(a907))))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[642])).
% 1.88/2.05 tff(644,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c3_1(a907)))),
% 1.88/2.05 inference(transitivity,[status(thm)],[643, 641])).
% 1.88/2.05 tff(645,plain,
% 1.88/2.05 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))),
% 1.88/2.05 inference(quant_inst,[status(thm)],[])).
% 1.88/2.05 tff(646,plain,
% 1.88/2.05 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c3_1(a907))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.88/2.05 tff(647,plain,
% 1.88/2.05 (hskp4 | (~c3_1(a907))),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[646, 112, 78, 44, 45, 76, 640, 310])).
% 1.88/2.05 tff(648,plain,
% 1.88/2.05 (hskp4),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[647, 630])).
% 1.88/2.05 tff(649,plain,
% 1.88/2.05 (~c3_1(a904)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[536, 648])).
% 1.88/2.05 tff(650,plain,
% 1.88/2.05 (~c1_1(a904)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[542, 648])).
% 1.88/2.05 tff(651,plain,
% 1.88/2.05 (c2_1(a904)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[605, 648])).
% 1.88/2.05 tff(652,plain,
% 1.88/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a907) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a907) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(653,plain,
% 1.88/2.05 (((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899))) <=> (c0_1(a907) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(654,plain,
% 1.88/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a907) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907))))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[653])).
% 1.88/2.05 tff(655,plain,
% 1.88/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a907) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.88/2.05 inference(transitivity,[status(thm)],[654, 652])).
% 1.88/2.05 tff(656,plain,
% 1.88/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))),
% 1.88/2.05 inference(quant_inst,[status(thm)],[])).
% 1.88/2.05 tff(657,plain,
% 1.88/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a907) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.88/2.05 tff(658,plain,
% 1.88/2.05 (~c2_1(a907)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[657, 112, 630, 651, 311, 44, 650, 649, 43, 392, 382])).
% 1.88/2.05 tff(659,plain,
% 1.88/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a907) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a907) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | c2_1(a907) | (~c3_1(a907)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(660,plain,
% 1.88/2.05 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907))) <=> (c0_1(a907) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | c2_1(a907) | (~c3_1(a907)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(661,plain,
% 1.88/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a907) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | c2_1(a907) | (~c3_1(a907))))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[660])).
% 1.88/2.05 tff(662,plain,
% 1.88/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a907) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | c2_1(a907) | (~c3_1(a907)))),
% 1.88/2.05 inference(transitivity,[status(thm)],[661, 659])).
% 1.88/2.05 tff(663,plain,
% 1.88/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))),
% 1.88/2.05 inference(quant_inst,[status(thm)],[])).
% 1.88/2.05 tff(664,plain,
% 1.88/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a907) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | c2_1(a907) | (~c3_1(a907))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[663, 662])).
% 1.88/2.05 tff(665,plain,
% 1.88/2.05 ($false),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[664, 112, 630, 651, 77, 44, 650, 649, 76, 503, 658, 310])).
% 1.88/2.05 tff(666,plain,(hskp14 | (~c1_1(a898)) | c0_1(a907) | c2_1(a898) | (~c3_1(a898)) | (~c1_1(a899)) | c0_1(a899) | (~c0_1(a898)) | c1_1(a907) | (~c2_1(a899)) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.88/2.05 tff(667,plain,
% 1.88/2.05 (hskp14),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[666, 60, 44, 66, 121, 309, 293, 74, 45, 301, 50])).
% 1.88/2.05 tff(668,plain,
% 1.88/2.05 (((~hskp14) | (~c1_1(a918))) <=> ((~hskp14) | (~c1_1(a918)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(669,plain,
% 1.88/2.05 (((~c1_1(a918)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a918)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(670,axiom,((~c1_1(a918)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.88/2.05 tff(671,plain,
% 1.88/2.05 ((~hskp14) | (~c1_1(a918))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[670, 669])).
% 1.88/2.05 tff(672,plain,
% 1.88/2.05 ((~hskp14) | (~c1_1(a918))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[671, 668])).
% 1.88/2.05 tff(673,plain,
% 1.88/2.05 (~c1_1(a918)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[672, 667])).
% 1.88/2.05 tff(674,assumption,(~hskp4), introduced(assumption)).
% 1.88/2.05 tff(675,plain,
% 1.88/2.05 (~c3_1(a907)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[647, 674])).
% 1.88/2.05 tff(676,plain,
% 1.88/2.05 (~hskp7),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[512, 675])).
% 1.88/2.05 tff(677,plain,
% 1.88/2.05 (hskp7 | hskp4 | c3_1(a899)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[529, 112, 311, 43, 523])).
% 1.88/2.05 tff(678,plain,
% 1.88/2.05 (c3_1(a899)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[677, 676, 674])).
% 1.88/2.05 tff(679,plain,
% 1.88/2.05 (hskp12 | (~c3_1(a899))),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[340, 112, 50, 311, 43, 334])).
% 1.88/2.05 tff(680,plain,
% 1.88/2.05 (hskp12),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[679, 678])).
% 1.88/2.05 tff(681,plain,
% 1.88/2.05 (~c3_1(a913)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[347, 680])).
% 1.88/2.05 tff(682,plain,
% 1.88/2.05 (c0_1(a913)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[355, 680])).
% 1.88/2.05 tff(683,plain,
% 1.88/2.05 (~c1_1(a913)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[409, 680])).
% 1.88/2.05 tff(684,plain,
% 1.88/2.05 (^[U: $i] : refl((hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.88/2.05 inference(bind,[status(th)],[])).
% 1.88/2.05 tff(685,plain,
% 1.88/2.05 (![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.88/2.05 inference(quant_intro,[status(thm)],[684])).
% 1.88/2.05 tff(686,plain,
% 1.88/2.05 (![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(687,plain,
% 1.88/2.05 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp7) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7) <=> (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp7) <=> (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.88/2.05 inference(bind,[status(th)],[])).
% 1.88/2.05 tff(688,plain,
% 1.88/2.05 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp7) <=> ![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.88/2.05 inference(quant_intro,[status(thm)],[687])).
% 1.88/2.05 tff(689,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.88/2.05 tff(690,plain,
% 1.88/2.05 (![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[689, 688])).
% 1.88/2.05 tff(691,plain,
% 1.88/2.05 (![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[690, 686])).
% 1.88/2.05 tff(692,plain,(
% 1.88/2.05 ![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.88/2.05 inference(skolemize,[status(sab)],[691])).
% 1.88/2.05 tff(693,plain,
% 1.88/2.05 (![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[692, 685])).
% 1.88/2.05 tff(694,assumption,(~c3_1(a913)), introduced(assumption)).
% 1.88/2.05 tff(695,assumption,(c0_1(a913)), introduced(assumption)).
% 1.88/2.05 tff(696,plain,
% 1.88/2.05 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(697,plain,
% 1.88/2.05 ((hskp10 | hskp7 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913))) <=> (hskp10 | hskp7 | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(698,plain,
% 1.88/2.05 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913))))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[697])).
% 1.88/2.05 tff(699,plain,
% 1.88/2.05 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)))),
% 1.88/2.05 inference(transitivity,[status(thm)],[698, 696])).
% 1.88/2.05 tff(700,plain,
% 1.88/2.05 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)))),
% 1.88/2.05 inference(quant_inst,[status(thm)],[])).
% 1.88/2.05 tff(701,plain,
% 1.88/2.05 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.88/2.05 tff(702,plain,
% 1.88/2.05 (hskp7 | c2_1(a913)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[701, 112, 50, 695, 694, 693])).
% 1.88/2.05 tff(703,plain,
% 1.88/2.05 (c2_1(a913)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[702, 547])).
% 1.88/2.05 tff(704,assumption,(~c1_1(a913)), introduced(assumption)).
% 1.88/2.05 tff(705,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(706,plain,
% 1.88/2.05 ((hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913))) <=> (hskp7 | c1_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(707,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c0_1(a913)) | (~c2_1(a913))))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[706])).
% 1.88/2.05 tff(708,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.88/2.05 inference(transitivity,[status(thm)],[707, 705])).
% 1.88/2.05 tff(709,plain,
% 1.88/2.05 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))),
% 1.88/2.05 inference(quant_inst,[status(thm)],[])).
% 1.88/2.05 tff(710,plain,
% 1.88/2.05 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a913) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c0_1(a913)) | (~c2_1(a913))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[709, 708])).
% 1.88/2.05 tff(711,plain,
% 1.88/2.05 (hskp7 | (~c2_1(a913))),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[710, 112, 695, 78, 77, 704, 76, 576])).
% 1.88/2.05 tff(712,plain,
% 1.88/2.05 ($false),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[711, 703, 547])).
% 1.88/2.05 tff(713,plain,(hskp7 | (~c0_1(a913)) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a913) | c2_1(a898) | hskp10 | c3_1(a913)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.05 tff(714,plain,
% 1.88/2.05 ($false),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[713, 683, 682, 78, 77, 676, 76, 50, 681])).
% 1.88/2.05 tff(715,plain,(hskp4 | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a898) | hskp10 | (~c1_1(a899)) | c0_1(a899) | c0_1(a907) | c1_1(a907) | (~c3_1(a898))), inference(lemma,lemma(discharge,[]))).
% 1.88/2.05 tff(716,plain,
% 1.88/2.05 (hskp4),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[715, 74, 60, 66, 50, 309, 293, 44, 45, 121])).
% 1.88/2.05 tff(717,plain,
% 1.88/2.05 (~c3_1(a904)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[536, 716])).
% 1.88/2.05 tff(718,plain,
% 1.88/2.05 (~c1_1(a904)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[542, 716])).
% 1.88/2.05 tff(719,plain,
% 1.88/2.05 (c2_1(a904)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[605, 716])).
% 1.88/2.05 tff(720,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(721,plain,
% 1.88/2.05 ((hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904))) <=> (hskp21 | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(722,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a904))))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[721])).
% 1.88/2.05 tff(723,plain,
% 1.88/2.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)))),
% 1.88/2.05 inference(transitivity,[status(thm)],[722, 720])).
% 1.88/2.05 tff(724,plain,
% 1.88/2.05 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)))),
% 1.88/2.05 inference(quant_inst,[status(thm)],[])).
% 1.88/2.05 tff(725,plain,
% 1.88/2.05 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a904))),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.88/2.05 tff(726,plain,
% 1.88/2.05 (hskp21),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[725, 112, 719, 74, 60, 718, 717, 66, 402])).
% 1.88/2.05 tff(727,plain,
% 1.88/2.05 (hskp14),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[438, 432, 431, 311, 312, 423, 417, 43, 373])).
% 1.88/2.05 tff(728,plain,
% 1.88/2.05 (((~hskp14) | c0_1(a918)) <=> ((~hskp14) | c0_1(a918))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(729,axiom,((~hskp14) | c0_1(a918)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.88/2.05 tff(730,plain,
% 1.88/2.05 ((~hskp14) | c0_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[729, 728])).
% 1.88/2.05 tff(731,plain,
% 1.88/2.05 ((~hskp14) | c0_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[730, 728])).
% 1.88/2.05 tff(732,plain,
% 1.88/2.05 ((~hskp14) | c0_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[731, 728])).
% 1.88/2.05 tff(733,plain,
% 1.88/2.05 ((~hskp14) | c0_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[732, 728])).
% 1.88/2.05 tff(734,plain,
% 1.88/2.05 ((~hskp14) | c0_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[733, 728])).
% 1.88/2.05 tff(735,plain,
% 1.88/2.05 (c0_1(a918)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[734, 727])).
% 1.88/2.05 tff(736,plain,
% 1.88/2.05 (((~hskp14) | c3_1(a918)) <=> ((~hskp14) | c3_1(a918))),
% 1.88/2.05 inference(rewrite,[status(thm)],[])).
% 1.88/2.05 tff(737,axiom,((~hskp14) | c3_1(a918)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.88/2.05 tff(738,plain,
% 1.88/2.05 ((~hskp14) | c3_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[737, 736])).
% 1.88/2.05 tff(739,plain,
% 1.88/2.05 ((~hskp14) | c3_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[738, 736])).
% 1.88/2.05 tff(740,plain,
% 1.88/2.05 ((~hskp14) | c3_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[739, 736])).
% 1.88/2.05 tff(741,plain,
% 1.88/2.05 ((~hskp14) | c3_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[740, 736])).
% 1.88/2.05 tff(742,plain,
% 1.88/2.05 ((~hskp14) | c3_1(a918)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[741, 736])).
% 1.89/2.05 tff(743,plain,
% 1.89/2.05 (c3_1(a918)),
% 1.89/2.05 inference(unit_resolution,[status(thm)],[742, 727])).
% 1.89/2.05 tff(744,plain,
% 1.89/2.05 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.89/2.05 inference(bind,[status(th)],[])).
% 1.89/2.05 tff(745,plain,
% 1.89/2.05 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.05 inference(quant_intro,[status(thm)],[744])).
% 1.89/2.05 tff(746,plain,
% 1.89/2.05 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.05 inference(rewrite,[status(thm)],[])).
% 1.89/2.05 tff(747,plain,
% 1.89/2.05 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_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)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_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)) | c1_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_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)) | c1_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.89/2.05 inference(bind,[status(th)],[])).
% 1.89/2.05 tff(748,plain,
% 1.89/2.05 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.05 inference(quant_intro,[status(thm)],[747])).
% 1.89/2.05 tff(749,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.89/2.05 tff(750,plain,
% 1.89/2.05 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.05 inference(modus_ponens,[status(thm)],[749, 748])).
% 1.89/2.05 tff(751,plain,
% 1.89/2.05 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.05 inference(modus_ponens,[status(thm)],[750, 746])).
% 1.89/2.05 tff(752,plain,(
% 1.89/2.05 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.05 inference(skolemize,[status(sab)],[751])).
% 1.89/2.05 tff(753,plain,
% 1.89/2.05 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.05 inference(modus_ponens,[status(thm)],[752, 745])).
% 1.89/2.05 tff(754,assumption,(~c1_1(a918)), introduced(assumption)).
% 1.89/2.05 tff(755,assumption,(~hskp18), introduced(assumption)).
% 1.89/2.05 tff(756,plain,
% 1.89/2.05 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a938) | c3_1(a938) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a938) | c3_1(a938) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)))),
% 1.89/2.05 inference(rewrite,[status(thm)],[])).
% 1.89/2.05 tff(757,plain,
% 1.89/2.05 ((hskp18 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918))) <=> (hskp18 | c2_1(a938) | c3_1(a938) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)))),
% 1.89/2.05 inference(rewrite,[status(thm)],[])).
% 1.89/2.05 tff(758,plain,
% 1.89/2.05 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a938) | c3_1(a938) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938))))),
% 1.89/2.05 inference(monotonicity,[status(thm)],[757])).
% 1.89/2.05 tff(759,plain,
% 1.89/2.05 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a938) | c3_1(a938) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)))),
% 1.89/2.05 inference(transitivity,[status(thm)],[758, 756])).
% 1.89/2.05 tff(760,plain,
% 1.89/2.05 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))),
% 1.89/2.06 inference(quant_inst,[status(thm)],[])).
% 1.89/2.06 tff(761,plain,
% 1.89/2.06 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a938) | c3_1(a938) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.89/2.06 tff(762,plain,
% 1.89/2.06 ((~c0_1(a918)) | (~c3_1(a918))),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[761, 432, 755, 431, 423, 417, 754, 753])).
% 1.89/2.06 tff(763,plain,
% 1.89/2.06 ($false),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[762, 743, 735])).
% 1.89/2.06 tff(764,plain,((~hskp21) | (~ndr1_0) | hskp18 | c1_1(a918) | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.06 tff(765,plain,
% 1.89/2.06 ((~hskp21) | hskp18 | c1_1(a918) | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[764, 112])).
% 1.89/2.06 tff(766,plain,
% 1.89/2.06 (hskp18),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[765, 726, 673, 309, 301, 293])).
% 1.89/2.06 tff(767,plain,
% 1.89/2.06 (((~hskp18) | (~c1_1(a929))) <=> ((~hskp18) | (~c1_1(a929)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(768,plain,
% 1.89/2.06 (((~c1_1(a929)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a929)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(769,axiom,((~c1_1(a929)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.89/2.06 tff(770,plain,
% 1.89/2.06 ((~hskp18) | (~c1_1(a929))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.89/2.06 tff(771,plain,
% 1.89/2.06 ((~hskp18) | (~c1_1(a929))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[770, 767])).
% 1.89/2.06 tff(772,plain,
% 1.89/2.06 (~c1_1(a929)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[771, 766])).
% 1.89/2.06 tff(773,plain,
% 1.89/2.06 (~c3_1(a938)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[416, 726])).
% 1.89/2.06 tff(774,plain,
% 1.89/2.06 (~c2_1(a938)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[422, 726])).
% 1.89/2.06 tff(775,plain,
% 1.89/2.06 (((~hskp18) | c2_1(a929)) <=> ((~hskp18) | c2_1(a929))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(776,axiom,((~hskp18) | c2_1(a929)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.89/2.06 tff(777,plain,
% 1.89/2.06 ((~hskp18) | c2_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[776, 775])).
% 1.89/2.06 tff(778,plain,
% 1.89/2.06 ((~hskp18) | c2_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[777, 775])).
% 1.89/2.06 tff(779,plain,
% 1.89/2.06 ((~hskp18) | c2_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[778, 775])).
% 1.89/2.06 tff(780,plain,
% 1.89/2.06 ((~hskp18) | c2_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[779, 775])).
% 1.89/2.06 tff(781,plain,
% 1.89/2.06 ((~hskp18) | c2_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[780, 775])).
% 1.89/2.06 tff(782,plain,
% 1.89/2.06 (c2_1(a929)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[781, 766])).
% 1.89/2.06 tff(783,plain,
% 1.89/2.06 (((~hskp18) | c0_1(a929)) <=> ((~hskp18) | c0_1(a929))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(784,axiom,((~hskp18) | c0_1(a929)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.89/2.06 tff(785,plain,
% 1.89/2.06 ((~hskp18) | c0_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.89/2.06 tff(786,plain,
% 1.89/2.06 ((~hskp18) | c0_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[785, 783])).
% 1.89/2.06 tff(787,plain,
% 1.89/2.06 ((~hskp18) | c0_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[786, 783])).
% 1.89/2.06 tff(788,plain,
% 1.89/2.06 ((~hskp18) | c0_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[787, 783])).
% 1.89/2.06 tff(789,plain,
% 1.89/2.06 ((~hskp18) | c0_1(a929)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[788, 783])).
% 1.89/2.06 tff(790,plain,
% 1.89/2.06 (c0_1(a929)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[789, 766])).
% 1.89/2.06 tff(791,plain,
% 1.89/2.06 (c0_1(a938)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[430, 726])).
% 1.89/2.06 tff(792,plain,
% 1.89/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(793,plain,
% 1.89/2.06 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929))) <=> (c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(794,plain,
% 1.89/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938))))),
% 1.89/2.06 inference(monotonicity,[status(thm)],[793])).
% 1.89/2.06 tff(795,plain,
% 1.89/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))),
% 1.89/2.06 inference(transitivity,[status(thm)],[794, 792])).
% 1.89/2.06 tff(796,plain,
% 1.89/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))),
% 1.89/2.06 inference(quant_inst,[status(thm)],[])).
% 1.89/2.06 tff(797,plain,
% 1.89/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[796, 795])).
% 1.89/2.06 tff(798,plain,
% 1.89/2.06 ($false),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[797, 112, 791, 790, 782, 60, 774, 773, 772, 66, 131, 121])).
% 1.89/2.06 tff(799,plain,((~hskp0) | hskp10 | c0_1(a907) | c1_1(a907) | c3_1(a901) | c0_1(a901) | hskp31 | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.06 tff(800,plain,
% 1.89/2.06 (~hskp0),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[799, 51, 44, 45, 48, 50, 46, 47])).
% 1.89/2.06 tff(801,assumption,(~c1_1(a912)), introduced(assumption)).
% 1.89/2.06 tff(802,assumption,(~c2_1(a912)), introduced(assumption)).
% 1.89/2.06 tff(803,plain,
% 1.89/2.06 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.89/2.06 inference(bind,[status(th)],[])).
% 1.89/2.06 tff(804,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.06 inference(quant_intro,[status(thm)],[803])).
% 1.89/2.06 tff(805,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(806,plain,
% 1.89/2.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.89/2.06 inference(bind,[status(th)],[])).
% 1.89/2.06 tff(807,plain,
% 1.89/2.06 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.06 inference(quant_intro,[status(thm)],[806])).
% 1.89/2.06 tff(808,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.89/2.06 tff(809,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.89/2.06 tff(810,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[809, 805])).
% 1.89/2.06 tff(811,plain,(
% 1.89/2.06 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.06 inference(skolemize,[status(sab)],[810])).
% 1.89/2.06 tff(812,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[811, 804])).
% 1.89/2.06 tff(813,assumption,(~c3_1(a912)), introduced(assumption)).
% 1.89/2.06 tff(814,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(815,plain,
% 1.89/2.06 ((hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a912) | c2_1(a912) | c1_1(a912)) <=> (hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(816,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901))))),
% 1.89/2.06 inference(monotonicity,[status(thm)],[815])).
% 1.89/2.06 tff(817,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.89/2.06 inference(transitivity,[status(thm)],[816, 814])).
% 1.89/2.06 tff(818,plain,
% 1.89/2.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a912) | c2_1(a912) | c1_1(a912))),
% 1.89/2.06 inference(quant_inst,[status(thm)],[])).
% 1.89/2.06 tff(819,plain,
% 1.89/2.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[818, 817])).
% 1.89/2.06 tff(820,plain,
% 1.89/2.06 (~c1_1(a901)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[819, 112, 50, 801, 802, 813, 51, 47, 812])).
% 1.89/2.06 tff(821,plain,
% 1.89/2.06 (hskp1),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[286, 820, 48, 51, 46, 47])).
% 1.89/2.06 tff(822,plain,
% 1.89/2.06 (c2_1(a899)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[300, 821])).
% 1.89/2.06 tff(823,assumption,(hskp17), introduced(assumption)).
% 1.89/2.06 tff(824,plain,
% 1.89/2.06 (((~hskp17) | (~c3_1(a928))) <=> ((~hskp17) | (~c3_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(825,plain,
% 1.89/2.06 (((~c3_1(a928)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(826,axiom,((~c3_1(a928)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.89/2.06 tff(827,plain,
% 1.89/2.06 ((~hskp17) | (~c3_1(a928))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[826, 825])).
% 1.89/2.06 tff(828,plain,
% 1.89/2.06 ((~hskp17) | (~c3_1(a928))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[827, 824])).
% 1.89/2.06 tff(829,plain,
% 1.89/2.06 (~c3_1(a928)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[828, 823])).
% 1.89/2.06 tff(830,plain,
% 1.89/2.06 (((~hskp17) | (~c2_1(a928))) <=> ((~hskp17) | (~c2_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(831,plain,
% 1.89/2.06 (((~c2_1(a928)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(832,axiom,((~c2_1(a928)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.89/2.06 tff(833,plain,
% 1.89/2.06 ((~hskp17) | (~c2_1(a928))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.89/2.06 tff(834,plain,
% 1.89/2.06 ((~hskp17) | (~c2_1(a928))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[833, 830])).
% 1.89/2.06 tff(835,plain,
% 1.89/2.06 (~c2_1(a928)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[834, 823])).
% 1.89/2.06 tff(836,plain,
% 1.89/2.06 (((~hskp17) | c1_1(a928)) <=> ((~hskp17) | c1_1(a928))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(837,axiom,((~hskp17) | c1_1(a928)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.89/2.06 tff(838,plain,
% 1.89/2.06 ((~hskp17) | c1_1(a928)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.89/2.06 tff(839,plain,
% 1.89/2.06 ((~hskp17) | c1_1(a928)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[838, 836])).
% 1.89/2.06 tff(840,plain,
% 1.89/2.06 ((~hskp17) | c1_1(a928)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[839, 836])).
% 1.89/2.06 tff(841,plain,
% 1.89/2.06 ((~hskp17) | c1_1(a928)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[840, 836])).
% 1.89/2.06 tff(842,plain,
% 1.89/2.06 ((~hskp17) | c1_1(a928)),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[841, 836])).
% 1.89/2.06 tff(843,plain,
% 1.89/2.06 (c1_1(a928)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[842, 823])).
% 1.89/2.06 tff(844,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(845,plain,
% 1.89/2.06 ((hskp31 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928))) <=> (hskp31 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(846,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928))))),
% 1.89/2.06 inference(monotonicity,[status(thm)],[845])).
% 1.89/2.06 tff(847,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)))),
% 1.89/2.06 inference(transitivity,[status(thm)],[846, 844])).
% 1.89/2.06 tff(848,plain,
% 1.89/2.06 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928)))),
% 1.89/2.06 inference(quant_inst,[status(thm)],[])).
% 1.89/2.06 tff(849,plain,
% 1.89/2.06 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.89/2.06 tff(850,plain,
% 1.89/2.06 (~c0_1(a928)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[849, 46, 112, 843, 835, 829, 10])).
% 1.89/2.06 tff(851,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(852,plain,
% 1.89/2.06 ((hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c2_1(a912) | c1_1(a912)) <=> (hskp10 | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(853,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928))))),
% 1.89/2.06 inference(monotonicity,[status(thm)],[852])).
% 1.89/2.06 tff(854,plain,
% 1.89/2.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))),
% 1.89/2.06 inference(transitivity,[status(thm)],[853, 851])).
% 1.89/2.06 tff(855,plain,
% 1.89/2.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c2_1(a912) | c1_1(a912))),
% 1.89/2.06 inference(quant_inst,[status(thm)],[])).
% 1.89/2.06 tff(856,plain,
% 1.89/2.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[855, 854])).
% 1.89/2.06 tff(857,plain,
% 1.89/2.06 ($false),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[856, 112, 50, 843, 835, 801, 802, 813, 812, 850])).
% 1.89/2.06 tff(858,plain,((~hskp17) | hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.89/2.06 tff(859,plain,
% 1.89/2.06 (~hskp17),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[858, 813, 801, 802, 50, 46])).
% 1.89/2.06 tff(860,plain,
% 1.89/2.06 (c1_1(a899)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[308, 821])).
% 1.89/2.06 tff(861,plain,
% 1.89/2.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.89/2.06 inference(bind,[status(th)],[])).
% 1.89/2.06 tff(862,plain,
% 1.89/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.89/2.06 inference(quant_intro,[status(thm)],[861])).
% 1.89/2.06 tff(863,plain,
% 1.89/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(864,plain,
% 1.89/2.06 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_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)) | (~c2_1(U))) | (~c3_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.89/2.06 inference(bind,[status(th)],[])).
% 1.89/2.06 tff(865,plain,
% 1.89/2.06 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.89/2.06 inference(quant_intro,[status(thm)],[864])).
% 1.89/2.06 tff(866,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.89/2.06 tff(867,plain,
% 1.89/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.89/2.06 tff(868,plain,
% 1.89/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[867, 863])).
% 1.89/2.06 tff(869,plain,(
% 1.89/2.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.89/2.06 inference(skolemize,[status(sab)],[868])).
% 1.89/2.06 tff(870,plain,
% 1.89/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[869, 862])).
% 1.89/2.06 tff(871,plain,
% 1.89/2.06 (~c3_1(a899)),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[381, 313, 311, 312, 43, 50])).
% 1.89/2.06 tff(872,plain,
% 1.89/2.06 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.89/2.06 inference(bind,[status(th)],[])).
% 1.89/2.06 tff(873,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.89/2.06 inference(quant_intro,[status(thm)],[872])).
% 1.89/2.06 tff(874,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(875,plain,
% 1.89/2.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.89/2.06 inference(bind,[status(th)],[])).
% 1.89/2.06 tff(876,plain,
% 1.89/2.06 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.89/2.06 inference(quant_intro,[status(thm)],[875])).
% 1.89/2.06 tff(877,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.89/2.06 tff(878,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[877, 876])).
% 1.89/2.06 tff(879,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[878, 874])).
% 1.89/2.06 tff(880,plain,(
% 1.89/2.06 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.89/2.06 inference(skolemize,[status(sab)],[879])).
% 1.89/2.06 tff(881,plain,
% 1.89/2.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[880, 873])).
% 1.89/2.06 tff(882,plain,
% 1.89/2.06 (^[U: $i] : refl((hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.89/2.06 inference(bind,[status(th)],[])).
% 1.89/2.06 tff(883,plain,
% 1.89/2.06 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.89/2.06 inference(quant_intro,[status(thm)],[882])).
% 1.89/2.06 tff(884,plain,
% 1.89/2.06 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(885,plain,
% 1.89/2.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp17) <=> ((hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp17))), rewrite(((hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp17) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp17) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.89/2.07 inference(bind,[status(th)],[])).
% 1.89/2.07 tff(886,plain,
% 1.89/2.07 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp17) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.89/2.07 inference(quant_intro,[status(thm)],[885])).
% 1.89/2.07 tff(887,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.89/2.07 tff(888,plain,
% 1.89/2.07 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.89/2.07 tff(889,plain,
% 1.89/2.07 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[888, 884])).
% 1.89/2.07 tff(890,plain,(
% 1.89/2.07 ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.89/2.07 inference(skolemize,[status(sab)],[889])).
% 1.89/2.07 tff(891,plain,
% 1.89/2.07 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[890, 883])).
% 1.89/2.07 tff(892,plain,
% 1.89/2.07 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(893,plain,
% 1.89/2.07 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c2_1(a899))) <=> (hskp17 | hskp0 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(894,plain,
% 1.89/2.07 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c2_1(a899)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899))))),
% 1.89/2.07 inference(monotonicity,[status(thm)],[893])).
% 1.89/2.07 tff(895,plain,
% 1.89/2.07 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c2_1(a899)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)))),
% 1.89/2.07 inference(transitivity,[status(thm)],[894, 892])).
% 1.89/2.07 tff(896,plain,
% 1.89/2.07 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a899) | c3_1(a899) | (~c2_1(a899)))),
% 1.89/2.07 inference(quant_inst,[status(thm)],[])).
% 1.89/2.07 tff(897,plain,
% 1.89/2.07 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[896, 895])).
% 1.89/2.07 tff(898,plain,
% 1.89/2.07 (hskp17 | hskp0 | c3_1(a899) | (~c2_1(a899))),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[897, 112, 43, 891])).
% 1.89/2.07 tff(899,plain,
% 1.89/2.07 (hskp0),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[898, 871, 312, 859])).
% 1.89/2.07 tff(900,plain,
% 1.89/2.07 (c1_1(a898)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[59, 899])).
% 1.89/2.07 tff(901,plain,
% 1.89/2.07 (c0_1(a898)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[73, 899])).
% 1.89/2.07 tff(902,plain,
% 1.89/2.07 (c3_1(a898)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[120, 901, 76, 900, 46])).
% 1.89/2.07 tff(903,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a912)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(904,plain,
% 1.89/2.07 ((hskp14 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c0_1(a912)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp14 | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a912)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(905,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c0_1(a912)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a912))))),
% 1.89/2.07 inference(monotonicity,[status(thm)],[904])).
% 1.89/2.07 tff(906,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c0_1(a912)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a912)))),
% 1.89/2.07 inference(transitivity,[status(thm)],[905, 903])).
% 1.89/2.07 tff(907,plain,
% 1.89/2.07 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c0_1(a912)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.89/2.07 inference(quant_inst,[status(thm)],[])).
% 1.89/2.07 tff(908,plain,
% 1.89/2.07 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a912))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[907, 906])).
% 1.89/2.07 tff(909,plain,
% 1.89/2.07 (hskp14 | c3_1(a912) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a912))),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[908, 112, 802, 43, 373])).
% 1.89/2.07 tff(910,plain,
% 1.89/2.07 (~c0_1(a912)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[909, 313, 312, 813, 311])).
% 1.89/2.07 tff(911,plain,
% 1.89/2.07 (~hskp12),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[452, 313, 311, 312, 43, 901, 900, 76])).
% 1.89/2.07 tff(912,plain,
% 1.89/2.07 (hskp12 | hskp6 | (~c3_1(a898)) | (~c1_1(a898))),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[469, 112, 76, 463])).
% 1.89/2.07 tff(913,plain,
% 1.89/2.07 (hskp6),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[912, 911, 900, 902])).
% 1.89/2.07 tff(914,assumption,(~c0_1(a912)), introduced(assumption)).
% 1.89/2.07 tff(915,assumption,(hskp6), introduced(assumption)).
% 1.89/2.07 tff(916,plain,
% 1.89/2.07 (c3_1(a906)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[478, 915])).
% 1.89/2.07 tff(917,plain,
% 1.89/2.07 (~c1_1(a906)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[492, 915])).
% 1.89/2.07 tff(918,plain,
% 1.89/2.07 (c2_1(a906)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[486, 915])).
% 1.89/2.07 tff(919,plain,
% 1.89/2.07 (hskp7),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[585, 918, 78, 77, 917, 76, 558, 916])).
% 1.89/2.07 tff(920,plain,
% 1.89/2.07 (c3_1(a907)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[512, 919])).
% 1.89/2.07 tff(921,plain,
% 1.89/2.07 (hskp4 | (~c3_1(a898)) | (~c0_1(a898)) | (~c3_1(a907))),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[646, 112, 44, 45, 76, 640])).
% 1.89/2.07 tff(922,plain,
% 1.89/2.07 (hskp4),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[921, 920, 78, 310])).
% 1.89/2.07 tff(923,plain,
% 1.89/2.07 (~c3_1(a904)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[536, 922])).
% 1.89/2.07 tff(924,plain,
% 1.89/2.07 (~c1_1(a904)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[542, 922])).
% 1.89/2.07 tff(925,plain,
% 1.89/2.07 (c2_1(a904)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[605, 922])).
% 1.89/2.07 tff(926,plain,
% 1.89/2.07 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.89/2.07 inference(bind,[status(th)],[])).
% 1.89/2.07 tff(927,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.89/2.07 inference(quant_intro,[status(thm)],[926])).
% 1.89/2.07 tff(928,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(929,plain,
% 1.89/2.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.89/2.07 inference(bind,[status(th)],[])).
% 1.89/2.07 tff(930,plain,
% 1.89/2.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.89/2.07 inference(quant_intro,[status(thm)],[929])).
% 1.89/2.07 tff(931,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.89/2.07 tff(932,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[931, 930])).
% 1.89/2.07 tff(933,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[932, 928])).
% 1.89/2.07 tff(934,plain,(
% 1.89/2.07 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.89/2.07 inference(skolemize,[status(sab)],[933])).
% 1.89/2.07 tff(935,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[934, 927])).
% 1.89/2.07 tff(936,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a906) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c3_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a906) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c3_1(a906)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(937,plain,
% 1.89/2.07 ((hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906))) <=> (hskp28 | c1_1(a906) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c3_1(a906)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(938,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a906) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c3_1(a906))))),
% 1.89/2.07 inference(monotonicity,[status(thm)],[937])).
% 1.89/2.07 tff(939,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a906) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c3_1(a906)))),
% 1.89/2.07 inference(transitivity,[status(thm)],[938, 936])).
% 1.89/2.07 tff(940,plain,
% 1.89/2.07 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906)))),
% 1.89/2.07 inference(quant_inst,[status(thm)],[])).
% 1.89/2.07 tff(941,plain,
% 1.89/2.07 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a906) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c3_1(a906))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.89/2.07 tff(942,plain,
% 1.89/2.07 (hskp28),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[941, 112, 918, 916, 78, 77, 917, 935, 310])).
% 1.89/2.07 tff(943,plain,
% 1.89/2.07 (((~hskp28) | c3_1(a900)) <=> ((~hskp28) | c3_1(a900))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(944,axiom,((~hskp28) | c3_1(a900)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.89/2.07 tff(945,plain,
% 1.89/2.07 ((~hskp28) | c3_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[944, 943])).
% 1.89/2.07 tff(946,plain,
% 1.89/2.07 ((~hskp28) | c3_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[945, 943])).
% 1.89/2.07 tff(947,plain,
% 1.89/2.07 ((~hskp28) | c3_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[946, 943])).
% 1.89/2.07 tff(948,plain,
% 1.89/2.07 ((~hskp28) | c3_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[947, 943])).
% 1.89/2.07 tff(949,plain,
% 1.89/2.07 ((~hskp28) | c3_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[948, 943])).
% 1.89/2.07 tff(950,plain,
% 1.89/2.07 (c3_1(a900)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[949, 942])).
% 1.89/2.07 tff(951,plain,
% 1.89/2.07 (((~hskp28) | c2_1(a900)) <=> ((~hskp28) | c2_1(a900))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(952,axiom,((~hskp28) | c2_1(a900)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.89/2.07 tff(953,plain,
% 1.89/2.07 ((~hskp28) | c2_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[952, 951])).
% 1.89/2.07 tff(954,plain,
% 1.89/2.07 ((~hskp28) | c2_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[953, 951])).
% 1.89/2.07 tff(955,plain,
% 1.89/2.07 ((~hskp28) | c2_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[954, 951])).
% 1.89/2.07 tff(956,plain,
% 1.89/2.07 ((~hskp28) | c2_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[955, 951])).
% 1.89/2.07 tff(957,plain,
% 1.89/2.07 ((~hskp28) | c2_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[956, 951])).
% 1.89/2.07 tff(958,plain,
% 1.89/2.07 (c2_1(a900)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[957, 942])).
% 1.89/2.07 tff(959,plain,
% 1.89/2.07 (((~hskp28) | c0_1(a900)) <=> ((~hskp28) | c0_1(a900))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(960,axiom,((~hskp28) | c0_1(a900)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.89/2.07 tff(961,plain,
% 1.89/2.07 ((~hskp28) | c0_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[960, 959])).
% 1.89/2.07 tff(962,plain,
% 1.89/2.07 ((~hskp28) | c0_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[961, 959])).
% 1.89/2.07 tff(963,plain,
% 1.89/2.07 ((~hskp28) | c0_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[962, 959])).
% 1.89/2.07 tff(964,plain,
% 1.89/2.07 ((~hskp28) | c0_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[963, 959])).
% 1.89/2.07 tff(965,plain,
% 1.89/2.07 ((~hskp28) | c0_1(a900)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[964, 959])).
% 1.89/2.07 tff(966,plain,
% 1.89/2.07 (c0_1(a900)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[965, 942])).
% 1.89/2.07 tff(967,plain,
% 1.89/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a912) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a912) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(968,plain,
% 1.89/2.07 (((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a912) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(969,plain,
% 1.89/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a912) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900))))),
% 1.89/2.07 inference(monotonicity,[status(thm)],[968])).
% 1.89/2.07 tff(970,plain,
% 1.89/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a912) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 1.89/2.07 inference(transitivity,[status(thm)],[969, 967])).
% 1.89/2.07 tff(971,plain,
% 1.89/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.89/2.07 inference(quant_inst,[status(thm)],[])).
% 1.89/2.07 tff(972,plain,
% 1.89/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a912) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[971, 970])).
% 1.89/2.07 tff(973,plain,
% 1.89/2.07 ($false),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[972, 112, 966, 958, 950, 925, 801, 802, 924, 923, 870, 914])).
% 1.89/2.07 tff(974,plain,((~hskp6) | c1_1(a912) | c2_1(a912) | c0_1(a912) | (~c0_1(a898)) | (~c3_1(a898)) | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~c1_1(a898)) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.89/2.07 tff(975,plain,
% 1.89/2.07 (hskp8),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[974, 913, 802, 910, 901, 902, 44, 45, 76, 900, 801])).
% 1.89/2.07 tff(976,plain,
% 1.89/2.07 (~c2_1(a908)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[591, 975])).
% 1.89/2.07 tff(977,plain,
% 1.89/2.07 (~c0_1(a908)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[597, 975])).
% 1.89/2.07 tff(978,plain,
% 1.89/2.07 (c3_1(a908)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[613, 975])).
% 1.89/2.07 tff(979,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a908) | c2_1(a908) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a908) | c2_1(a908) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a908)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(980,plain,
% 1.89/2.07 ((hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908))) <=> (hskp14 | c0_1(a908) | c2_1(a908) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a908)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(981,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a908) | c2_1(a908) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a908))))),
% 1.89/2.07 inference(monotonicity,[status(thm)],[980])).
% 1.89/2.07 tff(982,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a908) | c2_1(a908) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a908)))),
% 1.89/2.07 inference(transitivity,[status(thm)],[981, 979])).
% 1.89/2.07 tff(983,plain,
% 1.89/2.07 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)))),
% 1.89/2.07 inference(quant_inst,[status(thm)],[])).
% 1.89/2.07 tff(984,plain,
% 1.89/2.07 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a908) | c2_1(a908) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a908))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[983, 982])).
% 1.89/2.07 tff(985,plain,
% 1.89/2.07 ($false),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[984, 112, 313, 978, 311, 312, 977, 976, 881, 871])).
% 1.89/2.07 tff(986,plain,(hskp14 | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a912) | c0_1(a907) | c1_1(a907) | c2_1(a898) | c1_1(a912) | c0_1(a899) | hskp31 | hskp10 | c3_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.07 tff(987,plain,
% 1.89/2.07 (hskp14),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[986, 76, 822, 802, 44, 45, 860, 801, 43, 46, 50, 813])).
% 1.89/2.07 tff(988,plain,
% 1.89/2.07 (~c1_1(a918)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[672, 987])).
% 1.89/2.07 tff(989,plain,
% 1.89/2.07 (c0_1(a918)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[734, 987])).
% 1.89/2.07 tff(990,plain,
% 1.89/2.07 (c3_1(a918)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[742, 987])).
% 1.89/2.07 tff(991,assumption,(~c0_1(a898)), introduced(assumption)).
% 1.89/2.07 tff(992,plain,
% 1.89/2.07 (~hskp0),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[73, 991])).
% 1.89/2.07 tff(993,assumption,(hskp20), introduced(assumption)).
% 1.89/2.07 tff(994,plain,
% 1.89/2.07 (((~hskp20) | (~c3_1(a937))) <=> ((~hskp20) | (~c3_1(a937)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(995,plain,
% 1.89/2.07 (((~c3_1(a937)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a937)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(996,axiom,((~c3_1(a937)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.89/2.07 tff(997,plain,
% 1.89/2.07 ((~hskp20) | (~c3_1(a937))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[996, 995])).
% 1.89/2.07 tff(998,plain,
% 1.89/2.07 ((~hskp20) | (~c3_1(a937))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[997, 994])).
% 1.89/2.07 tff(999,plain,
% 1.89/2.07 (~c3_1(a937)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[998, 993])).
% 1.89/2.07 tff(1000,plain,
% 1.89/2.07 (((~hskp20) | (~c0_1(a937))) <=> ((~hskp20) | (~c0_1(a937)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1001,plain,
% 1.89/2.07 (((~c0_1(a937)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a937)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1002,axiom,((~c0_1(a937)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.89/2.07 tff(1003,plain,
% 1.89/2.07 ((~hskp20) | (~c0_1(a937))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 1.89/2.07 tff(1004,plain,
% 1.89/2.07 ((~hskp20) | (~c0_1(a937))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1003, 1000])).
% 1.89/2.07 tff(1005,plain,
% 1.89/2.07 (~c0_1(a937)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[1004, 993])).
% 1.89/2.07 tff(1006,plain,
% 1.89/2.07 (((~hskp20) | c2_1(a937)) <=> ((~hskp20) | c2_1(a937))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1007,axiom,((~hskp20) | c2_1(a937)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.89/2.07 tff(1008,plain,
% 1.89/2.07 ((~hskp20) | c2_1(a937)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.89/2.07 tff(1009,plain,
% 1.89/2.07 ((~hskp20) | c2_1(a937)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1008, 1006])).
% 1.89/2.07 tff(1010,plain,
% 1.89/2.07 ((~hskp20) | c2_1(a937)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1009, 1006])).
% 1.89/2.07 tff(1011,plain,
% 1.89/2.07 ((~hskp20) | c2_1(a937)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1010, 1006])).
% 1.89/2.07 tff(1012,plain,
% 1.89/2.07 ((~hskp20) | c2_1(a937)),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1011, 1006])).
% 1.89/2.07 tff(1013,plain,
% 1.89/2.07 (c2_1(a937)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[1012, 993])).
% 1.89/2.07 tff(1014,plain,
% 1.89/2.07 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a937) | c3_1(a937) | (~ndr1_0) | (~c2_1(a937)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a937) | c3_1(a937) | (~ndr1_0) | (~c2_1(a937)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1015,plain,
% 1.89/2.07 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a937) | c3_1(a937) | (~c2_1(a937))) <=> (hskp17 | hskp0 | c0_1(a937) | c3_1(a937) | (~ndr1_0) | (~c2_1(a937)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1016,plain,
% 1.89/2.07 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a937) | c3_1(a937) | (~c2_1(a937)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a937) | c3_1(a937) | (~ndr1_0) | (~c2_1(a937))))),
% 1.89/2.07 inference(monotonicity,[status(thm)],[1015])).
% 1.89/2.07 tff(1017,plain,
% 1.89/2.07 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a937) | c3_1(a937) | (~c2_1(a937)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a937) | c3_1(a937) | (~ndr1_0) | (~c2_1(a937)))),
% 1.89/2.07 inference(transitivity,[status(thm)],[1016, 1014])).
% 1.89/2.07 tff(1018,plain,
% 1.89/2.07 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a937) | c3_1(a937) | (~c2_1(a937)))),
% 1.89/2.07 inference(quant_inst,[status(thm)],[])).
% 1.89/2.07 tff(1019,plain,
% 1.89/2.07 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a937) | c3_1(a937) | (~ndr1_0) | (~c2_1(a937))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 1.89/2.07 tff(1020,plain,
% 1.89/2.07 ($false),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[1019, 112, 32, 31, 1013, 1005, 999, 891])).
% 1.89/2.07 tff(1021,plain,((~hskp20) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.89/2.07 tff(1022,plain,
% 1.89/2.07 (~hskp20),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[1021, 992, 32])).
% 1.89/2.07 tff(1023,plain,
% 1.89/2.07 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.89/2.07 inference(bind,[status(th)],[])).
% 1.89/2.07 tff(1024,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.89/2.07 inference(quant_intro,[status(thm)],[1023])).
% 1.89/2.07 tff(1025,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1026,plain,
% 1.89/2.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.89/2.07 inference(bind,[status(th)],[])).
% 1.89/2.07 tff(1027,plain,
% 1.89/2.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.89/2.07 inference(quant_intro,[status(thm)],[1026])).
% 1.89/2.07 tff(1028,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.89/2.07 tff(1029,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.89/2.07 tff(1030,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1029, 1025])).
% 1.89/2.07 tff(1031,plain,(
% 1.89/2.07 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.89/2.07 inference(skolemize,[status(sab)],[1030])).
% 1.89/2.07 tff(1032,plain,
% 1.89/2.07 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.89/2.07 inference(modus_ponens,[status(thm)],[1031, 1024])).
% 1.89/2.07 tff(1033,assumption,(c0_1(a918)), introduced(assumption)).
% 1.89/2.07 tff(1034,plain,
% 1.89/2.07 (c3_1(a899)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[898, 992, 312, 32])).
% 1.89/2.07 tff(1035,plain,
% 1.89/2.07 (hskp12),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[341, 1034, 311])).
% 1.89/2.07 tff(1036,plain,
% 1.89/2.07 (~c3_1(a913)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[347, 1035])).
% 1.89/2.07 tff(1037,plain,
% 1.89/2.07 (c0_1(a913)),
% 1.89/2.07 inference(unit_resolution,[status(thm)],[355, 1035])).
% 1.89/2.07 tff(1038,assumption,(c3_1(a918)), introduced(assumption)).
% 1.89/2.07 tff(1039,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c0_1(a898) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c0_1(a898) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1040,plain,
% 1.89/2.07 ((hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a912) | c2_1(a912) | c1_1(a912)) <=> (hskp10 | c0_1(a898) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)))),
% 1.89/2.07 inference(rewrite,[status(thm)],[])).
% 1.89/2.07 tff(1041,plain,
% 1.89/2.07 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c0_1(a898) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898))))),
% 1.89/2.08 inference(monotonicity,[status(thm)],[1040])).
% 1.89/2.08 tff(1042,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c0_1(a898) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)))),
% 1.89/2.08 inference(transitivity,[status(thm)],[1041, 1039])).
% 1.89/2.08 tff(1043,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a912) | c2_1(a912) | c1_1(a912))),
% 1.89/2.08 inference(quant_inst,[status(thm)],[])).
% 1.89/2.08 tff(1044,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c0_1(a898) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.89/2.08 tff(1045,plain,
% 1.89/2.08 (c0_1(a898) | (~c1_1(a898))),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1044, 112, 50, 801, 802, 813, 76, 812])).
% 1.89/2.08 tff(1046,plain,
% 1.89/2.08 (~c1_1(a898)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1045, 991])).
% 1.89/2.08 tff(1047,plain,
% 1.89/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a898) | c1_1(a898) | c0_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c1_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a898) | c1_1(a898) | c0_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c1_1(a901))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1048,plain,
% 1.89/2.08 (((~ndr1_0) | c2_1(a898) | c1_1(a898) | (~c3_1(a898)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c0_1(a898) | c1_1(a898) | c0_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c1_1(a901))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1049,plain,
% 1.89/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a898) | c1_1(a898) | (~c3_1(a898)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a898) | c1_1(a898) | c0_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c1_1(a901)))),
% 1.89/2.08 inference(monotonicity,[status(thm)],[1048])).
% 1.89/2.08 tff(1050,plain,
% 1.89/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a898) | c1_1(a898) | (~c3_1(a898)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a898) | c1_1(a898) | c0_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c1_1(a901))),
% 1.89/2.08 inference(transitivity,[status(thm)],[1049, 1047])).
% 1.89/2.08 tff(1051,plain,
% 1.89/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a898) | c1_1(a898) | (~c3_1(a898)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.89/2.08 inference(quant_inst,[status(thm)],[])).
% 1.89/2.08 tff(1052,plain,
% 1.89/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a898) | c1_1(a898) | c0_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c1_1(a901)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.89/2.08 tff(1053,plain,
% 1.89/2.08 (c0_1(a898) | c1_1(a898) | (~c3_1(a898))),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1052, 112, 51, 48, 76, 151, 820])).
% 1.89/2.08 tff(1054,plain,
% 1.89/2.08 (~c3_1(a898)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1053, 1046, 991])).
% 1.89/2.08 tff(1055,plain,
% 1.89/2.08 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.89/2.08 inference(bind,[status(th)],[])).
% 1.89/2.08 tff(1056,plain,
% 1.89/2.08 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.08 inference(quant_intro,[status(thm)],[1055])).
% 1.89/2.08 tff(1057,plain,
% 1.89/2.08 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1058,plain,
% 1.89/2.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.89/2.08 inference(bind,[status(th)],[])).
% 1.89/2.08 tff(1059,plain,
% 1.89/2.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.08 inference(quant_intro,[status(thm)],[1058])).
% 1.89/2.08 tff(1060,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.89/2.08 tff(1061,plain,
% 1.89/2.08 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 1.89/2.08 tff(1062,plain,
% 1.89/2.08 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1061, 1057])).
% 1.89/2.08 tff(1063,plain,(
% 1.89/2.08 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.08 inference(skolemize,[status(sab)],[1062])).
% 1.89/2.08 tff(1064,plain,
% 1.89/2.08 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1063, 1056])).
% 1.89/2.08 tff(1065,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a898) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a898) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1066,plain,
% 1.89/2.08 ((hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a898) | c2_1(a898) | c1_1(a898)) <=> (hskp20 | c1_1(a898) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1067,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a898) | c2_1(a898) | c1_1(a898))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a898) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a913)) | (~c2_1(a913))))),
% 1.89/2.08 inference(monotonicity,[status(thm)],[1066])).
% 1.89/2.08 tff(1068,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a898) | c2_1(a898) | c1_1(a898))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a898) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.89/2.08 inference(transitivity,[status(thm)],[1067, 1065])).
% 1.89/2.08 tff(1069,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a898) | c2_1(a898) | c1_1(a898))),
% 1.89/2.08 inference(quant_inst,[status(thm)],[])).
% 1.89/2.08 tff(1070,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a898) | c3_1(a913) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a913)) | (~c2_1(a913))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 1.89/2.08 tff(1071,plain,
% 1.89/2.08 (hskp20 | (~c2_1(a913))),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1070, 112, 1037, 1046, 1036, 76, 1064, 1054])).
% 1.89/2.08 tff(1072,plain,
% 1.89/2.08 (~c2_1(a913)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1071, 1022])).
% 1.89/2.08 tff(1073,assumption,(~c2_1(a913)), introduced(assumption)).
% 1.89/2.08 tff(1074,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c1_1(a918) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c1_1(a918) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1075,plain,
% 1.89/2.08 ((hskp18 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918))) <=> (hskp18 | c1_1(a918) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1076,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c1_1(a918) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 1.89/2.08 inference(monotonicity,[status(thm)],[1075])).
% 1.89/2.08 tff(1077,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c1_1(a918) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.08 inference(transitivity,[status(thm)],[1076, 1074])).
% 1.89/2.08 tff(1078,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c0_1(a913)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))),
% 1.89/2.08 inference(quant_inst,[status(thm)],[])).
% 1.89/2.08 tff(1079,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c1_1(a918) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c0_1(a913)) | (~c0_1(a918)) | (~c3_1(a918))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.89/2.08 tff(1080,plain,
% 1.89/2.08 ($false),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1079, 432, 755, 1033, 1038, 695, 754, 694, 753, 1073])).
% 1.89/2.08 tff(1081,plain,(c2_1(a913) | (~ndr1_0) | hskp18 | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a913)) | c1_1(a918) | c3_1(a913)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.08 tff(1082,plain,
% 1.89/2.08 (c2_1(a913) | hskp18 | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a913)) | c1_1(a918) | c3_1(a913)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1081, 112])).
% 1.89/2.08 tff(1083,plain,
% 1.89/2.08 (hskp18),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1082, 1072, 1038, 1037, 1036, 1033, 754])).
% 1.89/2.08 tff(1084,plain,
% 1.89/2.08 (~c1_1(a929)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[771, 1083])).
% 1.89/2.08 tff(1085,plain,
% 1.89/2.08 (hskp7 | c2_1(a913)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[701, 112, 50, 1037, 1036, 693])).
% 1.89/2.08 tff(1086,plain,
% 1.89/2.08 (hskp7),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1085, 1072])).
% 1.89/2.08 tff(1087,plain,
% 1.89/2.08 (c3_1(a907)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[512, 1086])).
% 1.89/2.08 tff(1088,plain,
% 1.89/2.08 (c2_1(a929)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[781, 1083])).
% 1.89/2.08 tff(1089,plain,
% 1.89/2.08 (c0_1(a929)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[789, 1083])).
% 1.89/2.08 tff(1090,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a929) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a929) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1091,plain,
% 1.89/2.08 ((hskp3 | (~ndr1_0) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907))) <=> (hskp3 | c1_1(a929) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1092,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a929) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c2_1(a929)) | (~c0_1(a929))))),
% 1.89/2.08 inference(monotonicity,[status(thm)],[1091])).
% 1.89/2.08 tff(1093,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a929) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 1.89/2.08 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.89/2.08 tff(1094,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))),
% 1.89/2.08 inference(quant_inst,[status(thm)],[])).
% 1.89/2.08 tff(1095,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a929) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c2_1(a929)) | (~c0_1(a929))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.89/2.08 tff(1096,plain,
% 1.89/2.08 (hskp3),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1095, 112, 1089, 1088, 1087, 1084, 44, 45, 1032])).
% 1.89/2.08 tff(1097,plain,
% 1.89/2.08 (((~hskp3) | (~c3_1(a903))) <=> ((~hskp3) | (~c3_1(a903)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1098,plain,
% 1.89/2.08 (((~c3_1(a903)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a903)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1099,axiom,((~c3_1(a903)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.89/2.08 tff(1100,plain,
% 1.89/2.08 ((~hskp3) | (~c3_1(a903))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 1.89/2.08 tff(1101,plain,
% 1.89/2.08 ((~hskp3) | (~c3_1(a903))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1100, 1097])).
% 1.89/2.08 tff(1102,plain,
% 1.89/2.08 (~c3_1(a903)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1101, 1096])).
% 1.89/2.08 tff(1103,assumption,(~hskp20), introduced(assumption)).
% 1.89/2.08 tff(1104,assumption,(hskp3), introduced(assumption)).
% 1.89/2.08 tff(1105,plain,
% 1.89/2.08 (((~hskp3) | c0_1(a903)) <=> ((~hskp3) | c0_1(a903))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1106,axiom,((~hskp3) | c0_1(a903)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.89/2.08 tff(1107,plain,
% 1.89/2.08 ((~hskp3) | c0_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 1.89/2.08 tff(1108,plain,
% 1.89/2.08 ((~hskp3) | c0_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1107, 1105])).
% 1.89/2.08 tff(1109,plain,
% 1.89/2.08 ((~hskp3) | c0_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1108, 1105])).
% 1.89/2.08 tff(1110,plain,
% 1.89/2.08 ((~hskp3) | c0_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1109, 1105])).
% 1.89/2.08 tff(1111,plain,
% 1.89/2.08 ((~hskp3) | c0_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1110, 1105])).
% 1.89/2.08 tff(1112,plain,
% 1.89/2.08 (c0_1(a903)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1111, 1104])).
% 1.89/2.08 tff(1113,plain,
% 1.89/2.08 (((~hskp3) | c2_1(a903)) <=> ((~hskp3) | c2_1(a903))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1114,axiom,((~hskp3) | c2_1(a903)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.89/2.08 tff(1115,plain,
% 1.89/2.08 ((~hskp3) | c2_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 1.89/2.08 tff(1116,plain,
% 1.89/2.08 ((~hskp3) | c2_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1115, 1113])).
% 1.89/2.08 tff(1117,plain,
% 1.89/2.08 ((~hskp3) | c2_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1116, 1113])).
% 1.89/2.08 tff(1118,plain,
% 1.89/2.08 ((~hskp3) | c2_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1117, 1113])).
% 1.89/2.08 tff(1119,plain,
% 1.89/2.08 ((~hskp3) | c2_1(a903)),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1118, 1113])).
% 1.89/2.08 tff(1120,plain,
% 1.89/2.08 (c2_1(a903)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1119, 1104])).
% 1.89/2.08 tff(1121,assumption,(~c3_1(a903)), introduced(assumption)).
% 1.89/2.08 tff(1122,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a903) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a903)) | (~c0_1(a903)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a903) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a903)) | (~c0_1(a903)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1123,plain,
% 1.89/2.08 ((hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a901) | c2_1(a901) | c1_1(a901)) <=> (hskp20 | c3_1(a903) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a903)) | (~c0_1(a903)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1124,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a903) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a903)) | (~c0_1(a903))))),
% 1.89/2.08 inference(monotonicity,[status(thm)],[1123])).
% 1.89/2.08 tff(1125,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a903) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a903)) | (~c0_1(a903)))),
% 1.89/2.08 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.89/2.08 tff(1126,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a901) | c2_1(a901) | c1_1(a901))),
% 1.89/2.08 inference(quant_inst,[status(thm)],[])).
% 1.89/2.08 tff(1127,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a903) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a903)) | (~c0_1(a903))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.89/2.08 tff(1128,plain,
% 1.89/2.08 (hskp20 | (~ndr1_0) | c1_1(a901) | (~c2_1(a903)) | (~c0_1(a903))),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1127, 1121, 47, 48, 1064])).
% 1.89/2.08 tff(1129,plain,
% 1.89/2.08 ($false),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1128, 1120, 1112, 432, 1103, 49])).
% 1.89/2.08 tff(1130,plain,((~hskp3) | (~ndr1_0) | hskp20 | c1_1(a901) | c3_1(a903) | c2_1(a901) | c3_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.08 tff(1131,plain,
% 1.89/2.08 ((~hskp3) | hskp20 | c1_1(a901) | c3_1(a903) | c2_1(a901) | c3_1(a901)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1130, 112])).
% 1.89/2.08 tff(1132,plain,
% 1.89/2.08 ($false),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1131, 1102, 1096, 48, 820, 1022, 47])).
% 1.89/2.08 tff(1133,plain,(c0_1(a898) | c3_1(a901) | c2_1(a901) | c0_1(a907) | c1_1(a907) | hskp10 | (~c3_1(a918)) | (~c0_1(a918)) | c1_1(a918) | c2_1(a898) | hskp17 | (~c1_1(a899)) | c0_1(a899) | c0_1(a901) | (~c2_1(a899)) | c1_1(a912) | c2_1(a912) | c3_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.08 tff(1134,plain,
% 1.89/2.08 (c0_1(a898)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1133, 990, 47, 44, 45, 50, 48, 989, 988, 76, 859, 860, 43, 51, 822, 801, 802, 813])).
% 1.89/2.08 tff(1135,plain,
% 1.89/2.08 (~hskp20),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1021, 31, 32])).
% 1.89/2.08 tff(1136,plain,
% 1.89/2.08 (c3_1(a899)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[898, 31, 312, 32])).
% 1.89/2.08 tff(1137,plain,
% 1.89/2.08 (hskp12),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[341, 1136, 311])).
% 1.89/2.08 tff(1138,plain,
% 1.89/2.08 (~c3_1(a913)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[347, 1137])).
% 1.89/2.08 tff(1139,plain,
% 1.89/2.08 (c0_1(a913)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[355, 1137])).
% 1.89/2.08 tff(1140,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a913) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a913) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1141,plain,
% 1.89/2.08 ((hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a912) | c2_1(a912) | c1_1(a912)) <=> (hskp20 | c3_1(a913) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1142,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a913) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913))))),
% 1.89/2.08 inference(monotonicity,[status(thm)],[1141])).
% 1.89/2.08 tff(1143,plain,
% 1.89/2.08 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a913) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.89/2.08 inference(transitivity,[status(thm)],[1142, 1140])).
% 1.89/2.08 tff(1144,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a912) | c2_1(a912) | c1_1(a912))),
% 1.89/2.08 inference(quant_inst,[status(thm)],[])).
% 1.89/2.08 tff(1145,plain,
% 1.89/2.08 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a913) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 1.89/2.08 tff(1146,plain,
% 1.89/2.08 (~c2_1(a913)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1145, 112, 1135, 1139, 1138, 801, 802, 813, 1064])).
% 1.89/2.08 tff(1147,plain,
% 1.89/2.08 (hskp18),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1082, 1146, 1038, 1139, 1138, 1033, 754])).
% 1.89/2.08 tff(1148,plain,
% 1.89/2.08 (~c1_1(a929)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[771, 1147])).
% 1.89/2.08 tff(1149,plain,
% 1.89/2.08 (hskp7),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[701, 112, 50, 1139, 1138, 693, 1146])).
% 1.89/2.08 tff(1150,plain,
% 1.89/2.08 (c3_1(a907)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[512, 1149])).
% 1.89/2.08 tff(1151,plain,
% 1.89/2.08 (c2_1(a929)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[781, 1147])).
% 1.89/2.08 tff(1152,plain,
% 1.89/2.08 (c0_1(a929)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[789, 1147])).
% 1.89/2.08 tff(1153,plain,
% 1.89/2.08 (hskp3),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1095, 112, 1152, 1151, 1150, 1148, 44, 45, 1032])).
% 1.89/2.08 tff(1154,plain,
% 1.89/2.08 (~c3_1(a903)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1101, 1153])).
% 1.89/2.08 tff(1155,plain,
% 1.89/2.08 ($false),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1131, 1154, 1153, 48, 49, 1135, 47])).
% 1.89/2.08 tff(1156,plain,(hskp0 | c3_1(a901) | c1_1(a901) | c2_1(a901) | c0_1(a907) | c1_1(a907) | (~c3_1(a918)) | (~c0_1(a918)) | c1_1(a918) | hskp10 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~c1_1(a899)) | c0_1(a899) | hskp17 | (~c2_1(a899))), inference(lemma,lemma(discharge,[]))).
% 1.89/2.08 tff(1157,plain,
% 1.89/2.08 (hskp0),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[1156, 990, 820, 47, 44, 45, 48, 989, 988, 50, 801, 802, 813, 860, 43, 859, 822])).
% 1.89/2.08 tff(1158,plain,
% 1.89/2.08 (c1_1(a898)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[59, 1157])).
% 1.89/2.08 tff(1159,plain,
% 1.89/2.08 (c3_1(a898)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[120, 1158, 76, 1134, 46])).
% 1.89/2.08 tff(1160,plain,
% 1.89/2.08 (^[U: $i] : refl((hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.89/2.08 inference(bind,[status(th)],[])).
% 1.89/2.08 tff(1161,plain,
% 1.89/2.08 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.89/2.08 inference(quant_intro,[status(thm)],[1160])).
% 1.89/2.08 tff(1162,plain,
% 1.89/2.08 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1163,plain,
% 1.89/2.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp17) <=> ((hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp17))), rewrite(((hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp17) <=> (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.89/2.08 inference(bind,[status(th)],[])).
% 1.89/2.08 tff(1164,plain,
% 1.89/2.08 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp17) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.89/2.08 inference(quant_intro,[status(thm)],[1163])).
% 1.89/2.08 tff(1165,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.89/2.08 tff(1166,plain,
% 1.89/2.08 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 1.89/2.08 tff(1167,plain,
% 1.89/2.08 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1166, 1162])).
% 1.89/2.08 tff(1168,plain,(
% 1.89/2.08 ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.89/2.08 inference(skolemize,[status(sab)],[1167])).
% 1.89/2.08 tff(1169,plain,
% 1.89/2.08 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.89/2.08 inference(modus_ponens,[status(thm)],[1168, 1161])).
% 1.89/2.08 tff(1170,assumption,(~hskp12), introduced(assumption)).
% 1.89/2.08 tff(1171,plain,
% 1.89/2.08 (hskp6),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[912, 1170, 77, 310])).
% 1.89/2.08 tff(1172,plain,
% 1.89/2.08 (~c1_1(a906)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[492, 1171])).
% 1.89/2.08 tff(1173,plain,
% 1.89/2.08 (c3_1(a906)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[478, 1171])).
% 1.89/2.08 tff(1174,plain,
% 1.89/2.08 (c2_1(a906)),
% 1.89/2.08 inference(unit_resolution,[status(thm)],[486, 1171])).
% 1.89/2.08 tff(1175,plain,
% 1.89/2.08 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c3_1(a906)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c3_1(a906)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1176,plain,
% 1.89/2.08 ((hskp24 | hskp17 | (~ndr1_0) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906))) <=> (hskp24 | hskp17 | c1_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c3_1(a906)))),
% 1.89/2.08 inference(rewrite,[status(thm)],[])).
% 1.89/2.08 tff(1177,plain,
% 1.89/2.08 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c3_1(a906))))),
% 1.89/2.09 inference(monotonicity,[status(thm)],[1176])).
% 1.89/2.09 tff(1178,plain,
% 1.89/2.09 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c3_1(a906)))),
% 1.89/2.09 inference(transitivity,[status(thm)],[1177, 1175])).
% 1.89/2.09 tff(1179,plain,
% 1.89/2.09 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a906) | (~c3_1(a906)) | (~c2_1(a906)))),
% 1.89/2.09 inference(quant_inst,[status(thm)],[])).
% 1.89/2.09 tff(1180,plain,
% 1.89/2.09 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c3_1(a906))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 1.89/2.09 tff(1181,plain,
% 1.89/2.09 (hskp24),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1180, 112, 32, 1174, 1173, 1172, 1169])).
% 1.89/2.09 tff(1182,plain,
% 1.89/2.09 (((~hskp24) | c3_1(a953)) <=> ((~hskp24) | c3_1(a953))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1183,axiom,((~hskp24) | c3_1(a953)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.89/2.09 tff(1184,plain,
% 1.89/2.09 ((~hskp24) | c3_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.89/2.09 tff(1185,plain,
% 1.89/2.09 ((~hskp24) | c3_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1184, 1182])).
% 1.89/2.09 tff(1186,plain,
% 1.89/2.09 ((~hskp24) | c3_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1185, 1182])).
% 1.89/2.09 tff(1187,plain,
% 1.89/2.09 ((~hskp24) | c3_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1186, 1182])).
% 1.89/2.09 tff(1188,plain,
% 1.89/2.09 ((~hskp24) | c3_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1187, 1182])).
% 1.89/2.09 tff(1189,plain,
% 1.89/2.09 (c3_1(a953)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1188, 1181])).
% 1.89/2.09 tff(1190,plain,
% 1.89/2.09 (((~hskp24) | c1_1(a953)) <=> ((~hskp24) | c1_1(a953))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1191,axiom,((~hskp24) | c1_1(a953)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.89/2.09 tff(1192,plain,
% 1.89/2.09 ((~hskp24) | c1_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 1.89/2.09 tff(1193,plain,
% 1.89/2.09 ((~hskp24) | c1_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1192, 1190])).
% 1.89/2.09 tff(1194,plain,
% 1.89/2.09 ((~hskp24) | c1_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1193, 1190])).
% 1.89/2.09 tff(1195,plain,
% 1.89/2.09 ((~hskp24) | c1_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1194, 1190])).
% 1.89/2.09 tff(1196,plain,
% 1.89/2.09 ((~hskp24) | c1_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1195, 1190])).
% 1.89/2.09 tff(1197,plain,
% 1.89/2.09 (c1_1(a953)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1196, 1181])).
% 1.89/2.09 tff(1198,plain,
% 1.89/2.09 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1199,plain,
% 1.89/2.09 ((hskp12 | hskp10 | (~ndr1_0) | c0_1(a953) | (~c1_1(a953)) | (~c3_1(a953))) <=> (hskp12 | hskp10 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1200,plain,
% 1.89/2.09 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a953) | (~c1_1(a953)) | (~c3_1(a953)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953)))),
% 1.89/2.09 inference(monotonicity,[status(thm)],[1199])).
% 1.89/2.09 tff(1201,plain,
% 1.89/2.09 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a953) | (~c1_1(a953)) | (~c3_1(a953)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))),
% 1.89/2.09 inference(transitivity,[status(thm)],[1200, 1198])).
% 1.89/2.09 tff(1202,plain,
% 1.89/2.09 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a953) | (~c1_1(a953)) | (~c3_1(a953)))),
% 1.89/2.09 inference(quant_inst,[status(thm)],[])).
% 1.89/2.09 tff(1203,plain,
% 1.89/2.09 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.89/2.09 tff(1204,plain,
% 1.89/2.09 (c0_1(a953)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1203, 112, 1170, 50, 1197, 1189, 334])).
% 1.89/2.09 tff(1205,plain,
% 1.89/2.09 (((~hskp24) | (~c2_1(a953))) <=> ((~hskp24) | (~c2_1(a953)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1206,plain,
% 1.89/2.09 (((~c2_1(a953)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a953)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1207,axiom,((~c2_1(a953)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.89/2.09 tff(1208,plain,
% 1.89/2.09 ((~hskp24) | (~c2_1(a953))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.89/2.09 tff(1209,plain,
% 1.89/2.09 ((~hskp24) | (~c2_1(a953))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1208, 1205])).
% 1.89/2.09 tff(1210,plain,
% 1.89/2.09 (~c2_1(a953)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1209, 1181])).
% 1.89/2.09 tff(1211,plain,
% 1.89/2.09 (c0_1(a912)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[974, 558, 802, 78, 915, 310, 44, 45, 76, 77, 801])).
% 1.89/2.09 tff(1212,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a912) | c3_1(a912) | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c0_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a912) | c3_1(a912) | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c0_1(a912)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1213,plain,
% 1.89/2.09 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a912) | c2_1(a912) | (~c0_1(a912)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906))) <=> (c2_1(a912) | c3_1(a912) | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c0_1(a912)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1214,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a912) | c2_1(a912) | (~c0_1(a912)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a912) | c3_1(a912) | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c0_1(a912))))),
% 1.89/2.09 inference(monotonicity,[status(thm)],[1213])).
% 1.89/2.09 tff(1215,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a912) | c2_1(a912) | (~c0_1(a912)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a912) | c3_1(a912) | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c0_1(a912)))),
% 1.89/2.09 inference(transitivity,[status(thm)],[1214, 1212])).
% 1.89/2.09 tff(1216,plain,
% 1.89/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a912) | c2_1(a912) | (~c0_1(a912)) | c1_1(a906) | (~c2_1(a906)) | (~c0_1(a906)))),
% 1.89/2.09 inference(quant_inst,[status(thm)],[])).
% 1.89/2.09 tff(1217,plain,
% 1.89/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a912) | c3_1(a912) | c1_1(a906) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c0_1(a912))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 1.89/2.09 tff(1218,plain,
% 1.89/2.09 ((~c0_1(a906)) | (~c0_1(a912))),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1217, 112, 918, 77, 802, 813, 917, 76, 131, 310])).
% 1.89/2.09 tff(1219,plain,
% 1.89/2.09 (~c0_1(a906)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1218, 1211])).
% 1.89/2.09 tff(1220,plain,
% 1.89/2.09 (hskp7),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[585, 558, 78, 77, 917, 76, 918, 916])).
% 1.89/2.09 tff(1221,plain,
% 1.89/2.09 (c3_1(a907)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[512, 1220])).
% 1.89/2.09 tff(1222,plain,
% 1.89/2.09 (hskp4),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[921, 1221, 78, 310])).
% 1.89/2.09 tff(1223,plain,
% 1.89/2.09 (~c3_1(a904)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[536, 1222])).
% 1.89/2.09 tff(1224,plain,
% 1.89/2.09 (~c1_1(a904)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[542, 1222])).
% 1.89/2.09 tff(1225,plain,
% 1.89/2.09 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.89/2.09 inference(bind,[status(th)],[])).
% 1.89/2.09 tff(1226,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.89/2.09 inference(quant_intro,[status(thm)],[1225])).
% 1.89/2.09 tff(1227,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1228,plain,
% 1.89/2.09 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.89/2.09 inference(bind,[status(th)],[])).
% 1.89/2.09 tff(1229,plain,
% 1.89/2.09 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.89/2.09 inference(quant_intro,[status(thm)],[1228])).
% 1.89/2.09 tff(1230,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.89/2.09 tff(1231,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 1.89/2.09 tff(1232,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1231, 1227])).
% 1.89/2.09 tff(1233,plain,(
% 1.89/2.09 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.89/2.09 inference(skolemize,[status(sab)],[1232])).
% 1.89/2.09 tff(1234,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1233, 1226])).
% 1.89/2.09 tff(1235,plain,
% 1.89/2.09 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a912) | c2_1(a912) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c0_1(a912)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1236,plain,
% 1.89/2.09 ((hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912))) <=> (hskp22 | c1_1(a912) | c2_1(a912) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c0_1(a912)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1237,plain,
% 1.89/2.09 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a912) | c2_1(a912) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c0_1(a912))))),
% 1.89/2.09 inference(monotonicity,[status(thm)],[1236])).
% 1.89/2.09 tff(1238,plain,
% 1.89/2.09 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c0_1(a912)))),
% 1.89/2.09 inference(transitivity,[status(thm)],[1237, 1235])).
% 1.89/2.09 tff(1239,plain,
% 1.89/2.09 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))),
% 1.89/2.09 inference(quant_inst,[status(thm)],[])).
% 1.89/2.09 tff(1240,plain,
% 1.89/2.09 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c0_1(a912))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 1.89/2.09 tff(1241,plain,
% 1.89/2.09 (hskp22 | (~c3_1(a898)) | (~c0_1(a898)) | (~c0_1(a912))),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1240, 112, 801, 802, 76, 1234])).
% 1.89/2.09 tff(1242,plain,
% 1.89/2.09 (hskp22),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1241, 1211, 78, 310])).
% 1.89/2.09 tff(1243,plain,
% 1.89/2.09 (((~hskp22) | (~c3_1(a939))) <=> ((~hskp22) | (~c3_1(a939)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1244,plain,
% 1.89/2.09 (((~c3_1(a939)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a939)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1245,axiom,((~c3_1(a939)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.89/2.09 tff(1246,plain,
% 1.89/2.09 ((~hskp22) | (~c3_1(a939))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 1.89/2.09 tff(1247,plain,
% 1.89/2.09 ((~hskp22) | (~c3_1(a939))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1246, 1243])).
% 1.89/2.09 tff(1248,plain,
% 1.89/2.09 (~c3_1(a939)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1247, 1242])).
% 1.89/2.09 tff(1249,plain,
% 1.89/2.09 (((~hskp22) | (~c0_1(a939))) <=> ((~hskp22) | (~c0_1(a939)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1250,plain,
% 1.89/2.09 (((~c0_1(a939)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a939)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1251,axiom,((~c0_1(a939)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.89/2.09 tff(1252,plain,
% 1.89/2.09 ((~hskp22) | (~c0_1(a939))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 1.89/2.09 tff(1253,plain,
% 1.89/2.09 ((~hskp22) | (~c0_1(a939))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1252, 1249])).
% 1.89/2.09 tff(1254,plain,
% 1.89/2.09 (~c0_1(a939)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1253, 1242])).
% 1.89/2.09 tff(1255,plain,
% 1.89/2.09 (c2_1(a904)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[605, 1222])).
% 1.89/2.09 tff(1256,plain,
% 1.89/2.09 (((~hskp22) | c1_1(a939)) <=> ((~hskp22) | c1_1(a939))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1257,axiom,((~hskp22) | c1_1(a939)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.89/2.09 tff(1258,plain,
% 1.89/2.09 ((~hskp22) | c1_1(a939)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 1.89/2.09 tff(1259,plain,
% 1.89/2.09 ((~hskp22) | c1_1(a939)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1258, 1256])).
% 1.89/2.09 tff(1260,plain,
% 1.89/2.09 ((~hskp22) | c1_1(a939)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1259, 1256])).
% 1.89/2.09 tff(1261,plain,
% 1.89/2.09 ((~hskp22) | c1_1(a939)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1260, 1256])).
% 1.89/2.09 tff(1262,plain,
% 1.89/2.09 ((~hskp22) | c1_1(a939)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1261, 1256])).
% 1.89/2.09 tff(1263,plain,
% 1.89/2.09 (c1_1(a939)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1262, 1242])).
% 1.89/2.09 tff(1264,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a906)) | c0_1(a906) | (~c3_1(a906)) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a906)) | c0_1(a906) | (~c3_1(a906)) | (~c1_1(a939)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1265,plain,
% 1.89/2.09 (((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a906) | (~c3_1(a906)) | (~c2_1(a906)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a906)) | c0_1(a906) | (~c3_1(a906)) | (~c1_1(a939)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1266,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a906) | (~c3_1(a906)) | (~c2_1(a906)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a906)) | c0_1(a906) | (~c3_1(a906)) | (~c1_1(a939))))),
% 1.89/2.09 inference(monotonicity,[status(thm)],[1265])).
% 1.89/2.09 tff(1267,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a906) | (~c3_1(a906)) | (~c2_1(a906)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a906)) | c0_1(a906) | (~c3_1(a906)) | (~c1_1(a939)))),
% 1.89/2.09 inference(transitivity,[status(thm)],[1266, 1264])).
% 1.89/2.09 tff(1268,plain,
% 1.89/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a906) | (~c3_1(a906)) | (~c2_1(a906)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 1.89/2.09 inference(quant_inst,[status(thm)],[])).
% 1.89/2.09 tff(1269,plain,
% 1.89/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a906)) | c0_1(a906) | (~c3_1(a906)) | (~c1_1(a939))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 1.89/2.09 tff(1270,plain,
% 1.89/2.09 ($false),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1269, 112, 1263, 918, 916, 1255, 1254, 1248, 1224, 1223, 392, 1219])).
% 1.89/2.09 tff(1271,plain,(hskp8 | (~c0_1(a898)) | (~c3_1(a898)) | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~c1_1(a898)) | c2_1(a912) | c3_1(a912) | c1_1(a912) | (~hskp6)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.09 tff(1272,plain,
% 1.89/2.09 (hskp8),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1271, 1171, 310, 44, 45, 76, 77, 802, 813, 801, 78])).
% 1.89/2.09 tff(1273,plain,
% 1.89/2.09 (~c0_1(a908)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[597, 1272])).
% 1.89/2.09 tff(1274,assumption,(hskp8), introduced(assumption)).
% 1.89/2.09 tff(1275,plain,
% 1.89/2.09 (c3_1(a908)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[613, 1274])).
% 1.89/2.09 tff(1276,plain,
% 1.89/2.09 (~c2_1(a908)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[591, 1274])).
% 1.89/2.09 tff(1277,assumption,(c0_1(a953)), introduced(assumption)).
% 1.89/2.09 tff(1278,assumption,(~c0_1(a908)), introduced(assumption)).
% 1.89/2.09 tff(1279,assumption,(~c2_1(a953)), introduced(assumption)).
% 1.89/2.09 tff(1280,assumption,(c1_1(a953)), introduced(assumption)).
% 1.89/2.09 tff(1281,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a953) | c1_1(a918) | c0_1(a908) | c2_1(a908) | (~ndr1_0) | (~c3_1(a908)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c1_1(a953)) | (~c0_1(a953)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c1_1(a918) | c0_1(a908) | c2_1(a908) | (~ndr1_0) | (~c3_1(a908)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c1_1(a953)) | (~c0_1(a953)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1282,plain,
% 1.89/2.09 (((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908))) <=> (c2_1(a953) | c1_1(a918) | c0_1(a908) | c2_1(a908) | (~ndr1_0) | (~c3_1(a908)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c1_1(a953)) | (~c0_1(a953)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1283,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a953) | c1_1(a918) | c0_1(a908) | c2_1(a908) | (~ndr1_0) | (~c3_1(a908)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c1_1(a953)) | (~c0_1(a953))))),
% 1.89/2.09 inference(monotonicity,[status(thm)],[1282])).
% 1.89/2.09 tff(1284,plain,
% 1.89/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c1_1(a918) | c0_1(a908) | c2_1(a908) | (~ndr1_0) | (~c3_1(a908)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c1_1(a953)) | (~c0_1(a953)))),
% 1.89/2.09 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.89/2.09 tff(1285,plain,
% 1.89/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a908) | c2_1(a908) | (~c3_1(a908)))),
% 1.89/2.09 inference(quant_inst,[status(thm)],[])).
% 1.89/2.09 tff(1286,plain,
% 1.89/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c1_1(a918) | c0_1(a908) | c2_1(a908) | (~ndr1_0) | (~c3_1(a908)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c1_1(a953)) | (~c0_1(a953))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.89/2.09 tff(1287,plain,
% 1.89/2.09 (c2_1(a908) | (~c3_1(a908))),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1286, 112, 1280, 1033, 1038, 1279, 754, 1278, 271, 1277])).
% 1.89/2.09 tff(1288,plain,
% 1.89/2.09 ($false),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1287, 1276, 1275])).
% 1.89/2.09 tff(1289,plain,((~hskp8) | (~c1_1(a953)) | (~c0_1(a918)) | (~c3_1(a918)) | c2_1(a953) | c1_1(a918) | c0_1(a908) | (~c0_1(a953))), inference(lemma,lemma(discharge,[]))).
% 1.89/2.09 tff(1290,plain,
% 1.89/2.09 ($false),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1289, 1273, 1272, 1033, 1038, 1210, 754, 1197, 1204])).
% 1.89/2.09 tff(1291,plain,(hskp12 | (~c0_1(a918)) | (~c3_1(a918)) | c1_1(a918) | (~c3_1(a898)) | c0_1(a907) | c1_1(a907) | c2_1(a898) | (~c1_1(a898)) | c2_1(a912) | c3_1(a912) | c1_1(a912) | (~c0_1(a898)) | hskp10 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.89/2.09 tff(1292,plain,
% 1.89/2.09 (hskp12),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1291, 989, 990, 988, 1159, 44, 45, 76, 1158, 802, 813, 801, 1134, 50, 859])).
% 1.89/2.09 tff(1293,plain,
% 1.89/2.09 (~c3_1(a913)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[347, 1292])).
% 1.89/2.09 tff(1294,plain,
% 1.89/2.09 (~c1_1(a913)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[409, 1292])).
% 1.89/2.09 tff(1295,plain,
% 1.89/2.09 (c0_1(a913)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[355, 1292])).
% 1.89/2.09 tff(1296,plain,
% 1.89/2.09 (hskp7),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[713, 1295, 1134, 1158, 1294, 76, 50, 1293])).
% 1.89/2.09 tff(1297,plain,
% 1.89/2.09 (c3_1(a907)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[512, 1296])).
% 1.89/2.09 tff(1298,plain,
% 1.89/2.09 (hskp4),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[921, 1297, 1134, 1159])).
% 1.89/2.09 tff(1299,plain,
% 1.89/2.09 (~c3_1(a904)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[536, 1298])).
% 1.89/2.09 tff(1300,plain,
% 1.89/2.09 (~c1_1(a904)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[542, 1298])).
% 1.89/2.09 tff(1301,plain,
% 1.89/2.09 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.89/2.09 inference(bind,[status(th)],[])).
% 1.89/2.09 tff(1302,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.89/2.09 inference(quant_intro,[status(thm)],[1301])).
% 1.89/2.09 tff(1303,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1304,plain,
% 1.89/2.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | 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))), ((((~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) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.89/2.09 inference(bind,[status(th)],[])).
% 1.89/2.09 tff(1305,plain,
% 1.89/2.09 (![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.89/2.09 inference(quant_intro,[status(thm)],[1304])).
% 1.89/2.09 tff(1306,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.89/2.09 tff(1307,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 1.89/2.09 tff(1308,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1307, 1303])).
% 1.89/2.09 tff(1309,plain,(
% 1.89/2.09 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.89/2.09 inference(skolemize,[status(sab)],[1308])).
% 1.89/2.09 tff(1310,plain,
% 1.89/2.09 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1309, 1302])).
% 1.89/2.09 tff(1311,plain,
% 1.89/2.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1312,plain,
% 1.89/2.09 ((hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a901) | c2_1(a901) | c0_1(a901)) <=> (hskp9 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1313,plain,
% 1.89/2.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a901) | c2_1(a901) | c0_1(a901))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0)))),
% 1.89/2.09 inference(monotonicity,[status(thm)],[1312])).
% 1.89/2.09 tff(1314,plain,
% 1.89/2.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a901) | c2_1(a901) | c0_1(a901))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0))),
% 1.89/2.09 inference(transitivity,[status(thm)],[1313, 1311])).
% 1.89/2.09 tff(1315,plain,
% 1.89/2.09 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a901) | c2_1(a901) | c0_1(a901))),
% 1.89/2.09 inference(quant_inst,[status(thm)],[])).
% 1.89/2.09 tff(1316,plain,
% 1.89/2.09 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0)),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.89/2.09 tff(1317,plain,
% 1.89/2.09 (hskp9 | c3_1(a912)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1316, 112, 801, 802, 51, 47, 48, 1310])).
% 1.89/2.09 tff(1318,plain,
% 1.89/2.09 (hskp9),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1317, 813])).
% 1.89/2.09 tff(1319,plain,
% 1.89/2.09 (((~hskp9) | (~c2_1(a909))) <=> ((~hskp9) | (~c2_1(a909)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1320,plain,
% 1.89/2.09 (((~c2_1(a909)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a909)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1321,axiom,((~c2_1(a909)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.89/2.09 tff(1322,plain,
% 1.89/2.09 ((~hskp9) | (~c2_1(a909))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 1.89/2.09 tff(1323,plain,
% 1.89/2.09 ((~hskp9) | (~c2_1(a909))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1322, 1319])).
% 1.89/2.09 tff(1324,plain,
% 1.89/2.09 (~c2_1(a909)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1323, 1318])).
% 1.89/2.09 tff(1325,plain,
% 1.89/2.09 (((~hskp9) | (~c1_1(a909))) <=> ((~hskp9) | (~c1_1(a909)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1326,plain,
% 1.89/2.09 (((~c1_1(a909)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a909)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1327,axiom,((~c1_1(a909)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.89/2.09 tff(1328,plain,
% 1.89/2.09 ((~hskp9) | (~c1_1(a909))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.89/2.09 tff(1329,plain,
% 1.89/2.09 ((~hskp9) | (~c1_1(a909))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1328, 1325])).
% 1.89/2.09 tff(1330,plain,
% 1.89/2.09 (~c1_1(a909)),
% 1.89/2.09 inference(unit_resolution,[status(thm)],[1329, 1318])).
% 1.89/2.09 tff(1331,plain,
% 1.89/2.09 (((~hskp9) | (~c0_1(a909))) <=> ((~hskp9) | (~c0_1(a909)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1332,plain,
% 1.89/2.09 (((~c0_1(a909)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a909)))),
% 1.89/2.09 inference(rewrite,[status(thm)],[])).
% 1.89/2.09 tff(1333,axiom,((~c0_1(a909)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.89/2.09 tff(1334,plain,
% 1.89/2.09 ((~hskp9) | (~c0_1(a909))),
% 1.89/2.09 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.89/2.09 tff(1335,plain,
% 1.89/2.09 ((~hskp9) | (~c0_1(a909))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1334, 1331])).
% 1.89/2.10 tff(1336,plain,
% 1.89/2.10 (~c0_1(a909)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1335, 1318])).
% 1.89/2.10 tff(1337,plain,
% 1.89/2.10 (c2_1(a904)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[605, 1298])).
% 1.89/2.10 tff(1338,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1339,plain,
% 1.89/2.10 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907))) <=> (c1_1(a918) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1340,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 1.89/2.10 inference(monotonicity,[status(thm)],[1339])).
% 1.89/2.10 tff(1341,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.10 inference(transitivity,[status(thm)],[1340, 1338])).
% 1.89/2.10 tff(1342,plain,
% 1.89/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))),
% 1.89/2.10 inference(quant_inst,[status(thm)],[])).
% 1.89/2.10 tff(1343,plain,
% 1.89/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 1.89/2.10 tff(1344,plain,
% 1.89/2.10 ((~c0_1(a898)) | (~c1_1(a898)) | c2_1(a907) | (~c3_1(a907))),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1343, 112, 989, 990, 988, 44, 76, 271])).
% 1.89/2.10 tff(1345,plain,
% 1.89/2.10 (c2_1(a907)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1344, 1297, 1134, 1158])).
% 1.89/2.10 tff(1346,plain,
% 1.89/2.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a907) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a907) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1347,plain,
% 1.89/2.10 ((hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907))) <=> (hskp28 | c1_1(a907) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1348,plain,
% 1.89/2.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a907) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907))))),
% 1.89/2.10 inference(monotonicity,[status(thm)],[1347])).
% 1.89/2.10 tff(1349,plain,
% 1.89/2.10 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a907) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.89/2.10 inference(transitivity,[status(thm)],[1348, 1346])).
% 1.89/2.10 tff(1350,plain,
% 1.89/2.10 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))),
% 1.89/2.10 inference(quant_inst,[status(thm)],[])).
% 1.89/2.10 tff(1351,plain,
% 1.89/2.10 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a907) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 1.89/2.10 tff(1352,plain,
% 1.89/2.10 (hskp28 | (~c2_1(a907)) | (~c3_1(a907))),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1351, 112, 1134, 1158, 45, 935, 1159])).
% 1.89/2.10 tff(1353,plain,
% 1.89/2.10 (hskp28),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1352, 1297, 1345])).
% 1.89/2.10 tff(1354,plain,
% 1.89/2.10 (c3_1(a900)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[949, 1353])).
% 1.89/2.10 tff(1355,plain,
% 1.89/2.10 (c2_1(a900)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[957, 1353])).
% 1.89/2.10 tff(1356,plain,
% 1.89/2.10 (c0_1(a900)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[965, 1353])).
% 1.89/2.10 tff(1357,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1358,plain,
% 1.89/2.10 (((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909)) <=> (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1359,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900))))),
% 1.89/2.10 inference(monotonicity,[status(thm)],[1358])).
% 1.89/2.10 tff(1360,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 1.89/2.10 inference(transitivity,[status(thm)],[1359, 1357])).
% 1.89/2.10 tff(1361,plain,
% 1.89/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))),
% 1.89/2.10 inference(quant_inst,[status(thm)],[])).
% 1.89/2.10 tff(1362,plain,
% 1.89/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 1.89/2.10 tff(1363,plain,
% 1.89/2.10 ($false),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1362, 112, 1356, 1355, 1354, 1337, 1336, 1330, 1324, 1300, 1299, 870])).
% 1.89/2.10 tff(1364,plain,(c2_1(a898) | c1_1(a907) | c0_1(a907) | hskp10 | c2_1(a912) | c3_1(a912) | c1_1(a912) | hskp31 | c2_1(a901) | c3_1(a901) | c0_1(a899) | c0_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.10 tff(1365,plain,
% 1.89/2.10 (c2_1(a898)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1364, 813, 44, 50, 802, 45, 801, 46, 47, 48, 43, 51])).
% 1.89/2.10 tff(1366,plain,
% 1.89/2.10 (~hskp0),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[65, 1365])).
% 1.89/2.10 tff(1367,plain,
% 1.89/2.10 (c3_1(a899)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[898, 1366, 822, 859])).
% 1.89/2.10 tff(1368,plain,
% 1.89/2.10 (hskp14),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[381, 1367, 860, 822, 43, 50])).
% 1.89/2.10 tff(1369,plain,
% 1.89/2.10 (~c1_1(a918)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[672, 1368])).
% 1.89/2.10 tff(1370,plain,
% 1.89/2.10 (c0_1(a918)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[734, 1368])).
% 1.89/2.10 tff(1371,plain,
% 1.89/2.10 (c3_1(a918)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[742, 1368])).
% 1.89/2.10 tff(1372,plain,
% 1.89/2.10 ($false),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1156, 1371, 1370, 820, 47, 44, 45, 48, 1366, 1369, 50, 801, 802, 813, 860, 43, 859, 822])).
% 1.89/2.10 tff(1373,plain,(c3_1(a912) | c2_1(a901) | c0_1(a907) | c1_1(a907) | c3_1(a901) | hskp10 | c1_1(a912) | c2_1(a912) | c0_1(a899) | hskp31 | c0_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.10 tff(1374,plain,
% 1.89/2.10 (c3_1(a912)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1373, 802, 44, 45, 48, 50, 801, 47, 43, 46, 51])).
% 1.89/2.10 tff(1375,plain,
% 1.89/2.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.89/2.10 inference(bind,[status(th)],[])).
% 1.89/2.10 tff(1376,plain,
% 1.89/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.89/2.10 inference(quant_intro,[status(thm)],[1375])).
% 1.89/2.10 tff(1377,plain,
% 1.89/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1378,plain,
% 1.89/2.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_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(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.89/2.10 inference(bind,[status(th)],[])).
% 1.89/2.10 tff(1379,plain,
% 1.89/2.10 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.89/2.10 inference(quant_intro,[status(thm)],[1378])).
% 1.89/2.10 tff(1380,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.89/2.10 tff(1381,plain,
% 1.89/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.89/2.10 tff(1382,plain,
% 1.89/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1381, 1377])).
% 1.89/2.10 tff(1383,plain,(
% 1.89/2.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.89/2.10 inference(skolemize,[status(sab)],[1382])).
% 1.89/2.10 tff(1384,plain,
% 1.89/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1383, 1376])).
% 1.89/2.10 tff(1385,assumption,(c3_1(a912)), introduced(assumption)).
% 1.89/2.10 tff(1386,plain,
% 1.89/2.10 (((~hskp11) | (~c3_1(a912))) <=> ((~hskp11) | (~c3_1(a912)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1387,plain,
% 1.89/2.10 (((~c3_1(a912)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a912)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1388,axiom,((~c3_1(a912)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.89/2.10 tff(1389,plain,
% 1.89/2.10 ((~hskp11) | (~c3_1(a912))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.89/2.10 tff(1390,plain,
% 1.89/2.10 ((~hskp11) | (~c3_1(a912))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1389, 1386])).
% 1.89/2.10 tff(1391,plain,
% 1.89/2.10 (~hskp11),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1390, 1385])).
% 1.89/2.10 tff(1392,assumption,(~c0_1(a928)), introduced(assumption)).
% 1.89/2.10 tff(1393,plain,
% 1.89/2.10 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.89/2.10 inference(bind,[status(th)],[])).
% 1.89/2.10 tff(1394,plain,
% 1.89/2.10 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.89/2.10 inference(quant_intro,[status(thm)],[1393])).
% 1.89/2.10 tff(1395,plain,
% 1.89/2.10 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1396,plain,
% 1.89/2.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.89/2.10 inference(bind,[status(th)],[])).
% 1.89/2.10 tff(1397,plain,
% 1.89/2.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.89/2.10 inference(quant_intro,[status(thm)],[1396])).
% 1.89/2.10 tff(1398,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.89/2.10 tff(1399,plain,
% 1.89/2.10 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 1.89/2.10 tff(1400,plain,
% 1.89/2.10 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1399, 1395])).
% 1.89/2.10 tff(1401,plain,(
% 1.89/2.10 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.89/2.10 inference(skolemize,[status(sab)],[1400])).
% 1.89/2.10 tff(1402,plain,
% 1.89/2.10 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1401, 1394])).
% 1.89/2.10 tff(1403,assumption,(~c2_1(a928)), introduced(assumption)).
% 1.89/2.10 tff(1404,assumption,(c1_1(a928)), introduced(assumption)).
% 1.89/2.10 tff(1405,assumption,(hskp29), introduced(assumption)).
% 1.89/2.10 tff(1406,plain,
% 1.89/2.10 (((~hskp29) | c3_1(a911)) <=> ((~hskp29) | c3_1(a911))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1407,axiom,((~hskp29) | c3_1(a911)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.89/2.10 tff(1408,plain,
% 1.89/2.10 ((~hskp29) | c3_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 1.89/2.10 tff(1409,plain,
% 1.89/2.10 ((~hskp29) | c3_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1408, 1406])).
% 1.89/2.10 tff(1410,plain,
% 1.89/2.10 ((~hskp29) | c3_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1409, 1406])).
% 1.89/2.10 tff(1411,plain,
% 1.89/2.10 ((~hskp29) | c3_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1410, 1406])).
% 1.89/2.10 tff(1412,plain,
% 1.89/2.10 ((~hskp29) | c3_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1411, 1406])).
% 1.89/2.10 tff(1413,plain,
% 1.89/2.10 (c3_1(a911)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1412, 1405])).
% 1.89/2.10 tff(1414,plain,
% 1.89/2.10 (((~hskp29) | c1_1(a911)) <=> ((~hskp29) | c1_1(a911))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1415,axiom,((~hskp29) | c1_1(a911)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.89/2.10 tff(1416,plain,
% 1.89/2.10 ((~hskp29) | c1_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 1.89/2.10 tff(1417,plain,
% 1.89/2.10 ((~hskp29) | c1_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1416, 1414])).
% 1.89/2.10 tff(1418,plain,
% 1.89/2.10 ((~hskp29) | c1_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1417, 1414])).
% 1.89/2.10 tff(1419,plain,
% 1.89/2.10 ((~hskp29) | c1_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1418, 1414])).
% 1.89/2.10 tff(1420,plain,
% 1.89/2.10 ((~hskp29) | c1_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1419, 1414])).
% 1.89/2.10 tff(1421,plain,
% 1.89/2.10 (c1_1(a911)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1420, 1405])).
% 1.89/2.10 tff(1422,plain,
% 1.89/2.10 (((~hskp29) | c0_1(a911)) <=> ((~hskp29) | c0_1(a911))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1423,axiom,((~hskp29) | c0_1(a911)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.89/2.10 tff(1424,plain,
% 1.89/2.10 ((~hskp29) | c0_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 1.89/2.10 tff(1425,plain,
% 1.89/2.10 ((~hskp29) | c0_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1424, 1422])).
% 1.89/2.10 tff(1426,plain,
% 1.89/2.10 ((~hskp29) | c0_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1425, 1422])).
% 1.89/2.10 tff(1427,plain,
% 1.89/2.10 ((~hskp29) | c0_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1426, 1422])).
% 1.89/2.10 tff(1428,plain,
% 1.89/2.10 ((~hskp29) | c0_1(a911)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1427, 1422])).
% 1.89/2.10 tff(1429,plain,
% 1.89/2.10 (c0_1(a911)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1428, 1405])).
% 1.89/2.10 tff(1430,assumption,(~hskp11), introduced(assumption)).
% 1.89/2.10 tff(1431,plain,
% 1.89/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a928) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a928) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | c0_1(a928) | (~c1_1(a928)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1432,plain,
% 1.89/2.10 ((hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (hskp11 | c2_1(a928) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | c0_1(a928) | (~c1_1(a928)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1433,plain,
% 1.89/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a928) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | c0_1(a928) | (~c1_1(a928))))),
% 1.89/2.10 inference(monotonicity,[status(thm)],[1432])).
% 1.89/2.10 tff(1434,plain,
% 1.89/2.10 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a928) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | c0_1(a928) | (~c1_1(a928)))),
% 1.89/2.10 inference(transitivity,[status(thm)],[1433, 1431])).
% 1.89/2.10 tff(1435,plain,
% 1.89/2.10 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 1.89/2.10 inference(quant_inst,[status(thm)],[])).
% 1.89/2.10 tff(1436,plain,
% 1.89/2.10 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a928) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | c0_1(a928) | (~c1_1(a928))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 1.89/2.10 tff(1437,plain,
% 1.89/2.10 ($false),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1436, 112, 1430, 1429, 1421, 1413, 1404, 1403, 1402, 1392])).
% 1.89/2.10 tff(1438,plain,((~hskp29) | hskp11 | (~c1_1(a928)) | c2_1(a928) | c0_1(a928)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.10 tff(1439,plain,
% 1.89/2.10 (~hskp29),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1438, 850, 1391, 835, 843])).
% 1.89/2.10 tff(1440,plain,
% 1.89/2.10 (hskp27),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[108, 1439, 46])).
% 1.89/2.10 tff(1441,plain,
% 1.89/2.10 (((~hskp27) | (~c0_1(a978))) <=> ((~hskp27) | (~c0_1(a978)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1442,plain,
% 1.89/2.10 (((~c0_1(a978)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a978)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1443,axiom,((~c0_1(a978)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.89/2.10 tff(1444,plain,
% 1.89/2.10 ((~hskp27) | (~c0_1(a978))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.89/2.10 tff(1445,plain,
% 1.89/2.10 ((~hskp27) | (~c0_1(a978))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1444, 1441])).
% 1.89/2.10 tff(1446,plain,
% 1.89/2.10 (~c0_1(a978)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1445, 1440])).
% 1.89/2.10 tff(1447,plain,
% 1.89/2.10 (((~hskp27) | c3_1(a978)) <=> ((~hskp27) | c3_1(a978))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1448,axiom,((~hskp27) | c3_1(a978)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.89/2.10 tff(1449,plain,
% 1.89/2.10 ((~hskp27) | c3_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 1.89/2.10 tff(1450,plain,
% 1.89/2.10 ((~hskp27) | c3_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1449, 1447])).
% 1.89/2.10 tff(1451,plain,
% 1.89/2.10 ((~hskp27) | c3_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1450, 1447])).
% 1.89/2.10 tff(1452,plain,
% 1.89/2.10 ((~hskp27) | c3_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1451, 1447])).
% 1.89/2.10 tff(1453,plain,
% 1.89/2.10 ((~hskp27) | c3_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1452, 1447])).
% 1.89/2.10 tff(1454,plain,
% 1.89/2.10 (c3_1(a978)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1453, 1440])).
% 1.89/2.10 tff(1455,plain,
% 1.89/2.10 (((~hskp27) | c2_1(a978)) <=> ((~hskp27) | c2_1(a978))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1456,axiom,((~hskp27) | c2_1(a978)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.89/2.10 tff(1457,plain,
% 1.89/2.10 ((~hskp27) | c2_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 1.89/2.10 tff(1458,plain,
% 1.89/2.10 ((~hskp27) | c2_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1457, 1455])).
% 1.89/2.10 tff(1459,plain,
% 1.89/2.10 ((~hskp27) | c2_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1458, 1455])).
% 1.89/2.10 tff(1460,plain,
% 1.89/2.10 ((~hskp27) | c2_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1459, 1455])).
% 1.89/2.10 tff(1461,plain,
% 1.89/2.10 ((~hskp27) | c2_1(a978)),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1460, 1455])).
% 1.89/2.10 tff(1462,plain,
% 1.89/2.10 (c2_1(a978)),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1461, 1440])).
% 1.89/2.10 tff(1463,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1464,plain,
% 1.89/2.10 (((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978))) <=> (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1465,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 1.89/2.10 inference(monotonicity,[status(thm)],[1464])).
% 1.89/2.10 tff(1466,plain,
% 1.89/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.89/2.10 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.89/2.10 tff(1467,plain,
% 1.89/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.89/2.10 inference(quant_inst,[status(thm)],[])).
% 1.89/2.10 tff(1468,plain,
% 1.89/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))),
% 1.89/2.10 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.89/2.10 tff(1469,plain,
% 1.89/2.10 ($false),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1468, 112, 1462, 1454, 843, 1446, 835, 829, 801, 802, 1385, 1384])).
% 1.89/2.10 tff(1470,plain,((~hskp17) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.89/2.10 tff(1471,plain,
% 1.89/2.10 (~hskp17),
% 1.89/2.10 inference(unit_resolution,[status(thm)],[1470, 802, 801, 1374, 46])).
% 1.89/2.10 tff(1472,plain,
% 1.89/2.10 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1473,plain,
% 1.89/2.10 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a907) | c1_1(a907) | c0_1(a907)) <=> (hskp1 | hskp0 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907))),
% 1.89/2.10 inference(rewrite,[status(thm)],[])).
% 1.89/2.10 tff(1474,plain,
% 1.89/2.10 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907)))),
% 1.89/2.10 inference(monotonicity,[status(thm)],[1473])).
% 1.89/2.10 tff(1475,plain,
% 1.89/2.10 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907))),
% 1.89/2.10 inference(transitivity,[status(thm)],[1474, 1472])).
% 1.89/2.10 tff(1476,plain,
% 1.89/2.10 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a907) | c1_1(a907) | c0_1(a907))),
% 1.89/2.10 inference(quant_inst,[status(thm)],[])).
% 1.89/2.10 tff(1477,plain,
% 1.89/2.10 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907)),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.89/2.11 tff(1478,plain,
% 1.89/2.11 (hskp1 | hskp0 | c1_1(a907) | c2_1(a907)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1477, 112, 44, 20])).
% 1.89/2.11 tff(1479,plain,
% 1.89/2.11 (c2_1(a907)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1478, 152, 45, 31])).
% 1.89/2.11 tff(1480,plain,
% 1.89/2.11 (c1_1(a901)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[159, 152, 51, 31])).
% 1.89/2.11 tff(1481,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1482,plain,
% 1.89/2.11 (((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907))) <=> (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1483,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907))))),
% 1.89/2.11 inference(monotonicity,[status(thm)],[1482])).
% 1.89/2.11 tff(1484,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.89/2.11 inference(transitivity,[status(thm)],[1483, 1481])).
% 1.89/2.11 tff(1485,plain,
% 1.89/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))),
% 1.89/2.11 inference(quant_inst,[status(thm)],[])).
% 1.89/2.11 tff(1486,plain,
% 1.89/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907))),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 1.89/2.11 tff(1487,plain,
% 1.89/2.11 ((~c3_1(a912)) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907))),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1486, 112, 801, 802, 44, 47, 48, 1384])).
% 1.89/2.11 tff(1488,plain,
% 1.89/2.11 (~c3_1(a907)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1487, 1479, 1385, 1480])).
% 1.89/2.11 tff(1489,plain,
% 1.89/2.11 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c3_1(a907) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a907) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1490,plain,
% 1.89/2.11 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c2_1(a907))) <=> (hskp17 | hskp0 | c3_1(a907) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1491,plain,
% 1.89/2.11 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c2_1(a907)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c3_1(a907) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907))))),
% 1.89/2.11 inference(monotonicity,[status(thm)],[1490])).
% 1.89/2.11 tff(1492,plain,
% 1.89/2.11 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c2_1(a907)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a907) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)))),
% 1.89/2.11 inference(transitivity,[status(thm)],[1491, 1489])).
% 1.89/2.11 tff(1493,plain,
% 1.89/2.11 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c2_1(a907)))),
% 1.89/2.11 inference(quant_inst,[status(thm)],[])).
% 1.89/2.11 tff(1494,plain,
% 1.89/2.11 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a907) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907))),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 1.89/2.11 tff(1495,plain,
% 1.89/2.11 (hskp17 | hskp0 | c3_1(a907) | (~c2_1(a907))),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1494, 112, 44, 891])).
% 1.89/2.11 tff(1496,plain,
% 1.89/2.11 ($false),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1495, 1488, 1479, 31, 32])).
% 1.89/2.11 tff(1497,plain,(hskp1 | hskp0 | hskp17 | c0_1(a907) | (~c3_1(a912)) | c1_1(a912) | c2_1(a912) | c2_1(a901) | c3_1(a901) | c1_1(a907) | c0_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.11 tff(1498,plain,
% 1.89/2.11 (hskp1),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1497, 32, 31, 44, 1385, 801, 802, 47, 48, 45, 51])).
% 1.89/2.11 tff(1499,plain,
% 1.89/2.11 (c2_1(a899)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[300, 1498])).
% 1.89/2.11 tff(1500,plain,
% 1.89/2.11 (c3_1(a899)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[898, 1499, 31, 32])).
% 1.89/2.11 tff(1501,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1502,plain,
% 1.89/2.11 (((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899))) <=> (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1503,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901))))),
% 1.89/2.11 inference(monotonicity,[status(thm)],[1502])).
% 1.89/2.11 tff(1504,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)))),
% 1.89/2.11 inference(transitivity,[status(thm)],[1503, 1501])).
% 1.89/2.11 tff(1505,plain,
% 1.89/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))),
% 1.89/2.11 inference(quant_inst,[status(thm)],[])).
% 1.89/2.11 tff(1506,plain,
% 1.89/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901))),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 1.89/2.11 tff(1507,plain,
% 1.89/2.11 ((~c3_1(a912)) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901))),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1506, 112, 801, 802, 47, 48, 43, 1384])).
% 1.89/2.11 tff(1508,plain,
% 1.89/2.11 (~c1_1(a901)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1507, 1500, 1385, 1499])).
% 1.89/2.11 tff(1509,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | c0_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | c0_1(a912))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1510,plain,
% 1.89/2.11 (((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | c0_1(a912))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1511,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | c0_1(a912)))),
% 1.89/2.11 inference(monotonicity,[status(thm)],[1510])).
% 1.89/2.11 tff(1512,plain,
% 1.89/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | c0_1(a912))),
% 1.89/2.11 inference(transitivity,[status(thm)],[1511, 1509])).
% 1.89/2.11 tff(1513,plain,
% 1.89/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.89/2.11 inference(quant_inst,[status(thm)],[])).
% 1.89/2.11 tff(1514,plain,
% 1.89/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | c0_1(a912)),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 1.89/2.11 tff(1515,plain,
% 1.89/2.11 ((~c3_1(a912)) | c1_1(a901) | c0_1(a912)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1514, 112, 801, 802, 51, 48, 151])).
% 1.89/2.11 tff(1516,plain,
% 1.89/2.11 (c0_1(a912)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1515, 1508, 1385])).
% 1.89/2.11 tff(1517,plain,
% 1.89/2.11 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.89/2.11 inference(bind,[status(th)],[])).
% 1.89/2.11 tff(1518,plain,
% 1.89/2.11 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.11 inference(quant_intro,[status(thm)],[1517])).
% 1.89/2.11 tff(1519,plain,
% 1.89/2.11 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1520,plain,
% 1.89/2.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.89/2.11 inference(bind,[status(th)],[])).
% 1.89/2.11 tff(1521,plain,
% 1.89/2.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.11 inference(quant_intro,[status(thm)],[1520])).
% 1.89/2.11 tff(1522,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.89/2.11 tff(1523,plain,
% 1.89/2.11 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 1.89/2.11 tff(1524,plain,
% 1.89/2.11 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1523, 1519])).
% 1.89/2.11 tff(1525,plain,(
% 1.89/2.11 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.11 inference(skolemize,[status(sab)],[1524])).
% 1.89/2.11 tff(1526,plain,
% 1.89/2.11 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1525, 1518])).
% 1.89/2.11 tff(1527,plain,
% 1.89/2.11 (c1_1(a899)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[308, 1498])).
% 1.89/2.11 tff(1528,plain,
% 1.89/2.11 (hskp14),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[381, 1500, 1499, 1527, 43, 50])).
% 1.89/2.11 tff(1529,plain,
% 1.89/2.11 (c3_1(a918)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[742, 1528])).
% 1.89/2.11 tff(1530,plain,
% 1.89/2.11 (c0_1(a918)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[734, 1528])).
% 1.89/2.11 tff(1531,plain,
% 1.89/2.11 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1532,plain,
% 1.89/2.11 ((hskp0 | (~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912))) <=> (hskp0 | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.11 inference(rewrite,[status(thm)],[])).
% 1.89/2.11 tff(1533,plain,
% 1.89/2.11 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 1.89/2.11 inference(monotonicity,[status(thm)],[1532])).
% 1.89/2.11 tff(1534,plain,
% 1.89/2.11 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.89/2.11 inference(transitivity,[status(thm)],[1533, 1531])).
% 1.89/2.11 tff(1535,plain,
% 1.89/2.11 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)))),
% 1.89/2.11 inference(quant_inst,[status(thm)],[])).
% 1.89/2.11 tff(1536,plain,
% 1.89/2.11 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))),
% 1.89/2.11 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 1.89/2.11 tff(1537,plain,
% 1.89/2.11 (~c2_1(a918)),
% 1.89/2.11 inference(unit_resolution,[status(thm)],[1536, 112, 31, 1530, 1529, 802, 1385, 1526, 1516])).
% 1.95/2.11 tff(1538,plain,
% 1.95/2.11 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(1539,plain,
% 1.95/2.11 ((hskp22 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912))) <=> (hskp22 | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(1540,plain,
% 1.95/2.11 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[1539])).
% 1.95/2.11 tff(1541,plain,
% 1.95/2.11 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)))),
% 1.95/2.11 inference(transitivity,[status(thm)],[1540, 1538])).
% 1.95/2.11 tff(1542,plain,
% 1.95/2.11 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(1543,plain,
% 1.95/2.11 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.95/2.11 tff(1544,plain,
% 1.95/2.11 (hskp22 | (~c3_1(a912)) | (~c0_1(a912))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1543, 112, 801, 802, 1234])).
% 1.95/2.11 tff(1545,plain,
% 1.95/2.11 (hskp22),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1544, 1516, 1385])).
% 1.95/2.11 tff(1546,plain,
% 1.95/2.11 (~c3_1(a939)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1247, 1545])).
% 1.95/2.11 tff(1547,plain,
% 1.95/2.11 (~c0_1(a939)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1253, 1545])).
% 1.95/2.11 tff(1548,plain,
% 1.95/2.11 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a939) | c3_1(a939) | (~ndr1_0) | (~c2_1(a939)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a939) | c3_1(a939) | (~ndr1_0) | (~c2_1(a939)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(1549,plain,
% 1.95/2.11 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a939) | c3_1(a939) | (~c2_1(a939))) <=> (hskp17 | hskp0 | c0_1(a939) | c3_1(a939) | (~ndr1_0) | (~c2_1(a939)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(1550,plain,
% 1.95/2.11 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a939) | c3_1(a939) | (~c2_1(a939)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a939) | c3_1(a939) | (~ndr1_0) | (~c2_1(a939))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[1549])).
% 1.95/2.11 tff(1551,plain,
% 1.95/2.11 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a939) | c3_1(a939) | (~c2_1(a939)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a939) | c3_1(a939) | (~ndr1_0) | (~c2_1(a939)))),
% 1.95/2.11 inference(transitivity,[status(thm)],[1550, 1548])).
% 1.95/2.11 tff(1552,plain,
% 1.95/2.11 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a939) | c3_1(a939) | (~c2_1(a939)))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(1553,plain,
% 1.95/2.11 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a939) | c3_1(a939) | (~ndr1_0) | (~c2_1(a939))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.95/2.11 tff(1554,plain,
% 1.95/2.11 (~c2_1(a939)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1553, 112, 32, 31, 1547, 1546, 891])).
% 1.95/2.11 tff(1555,plain,
% 1.95/2.11 (~c1_1(a918)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[672, 1528])).
% 1.95/2.11 tff(1556,plain,
% 1.95/2.11 (c1_1(a939)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1262, 1545])).
% 1.95/2.11 tff(1557,plain,
% 1.95/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a939) | c1_1(a918) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a918) | (~c3_1(a918)) | c2_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a939) | c1_1(a918) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a918) | (~c3_1(a918)) | c2_1(a939) | (~c1_1(a939)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(1558,plain,
% 1.95/2.11 (((~ndr1_0) | c2_1(a939) | c3_1(a939) | (~c1_1(a939)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899))) <=> (c3_1(a939) | c1_1(a918) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a918) | (~c3_1(a918)) | c2_1(a939) | (~c1_1(a939)))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(1559,plain,
% 1.95/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a939) | c3_1(a939) | (~c1_1(a939)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a939) | c1_1(a918) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a918) | (~c3_1(a918)) | c2_1(a939) | (~c1_1(a939))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[1558])).
% 1.95/2.11 tff(1560,plain,
% 1.95/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a939) | c3_1(a939) | (~c1_1(a939)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a939) | c1_1(a918) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a918) | (~c3_1(a918)) | c2_1(a939) | (~c1_1(a939)))),
% 1.95/2.11 inference(transitivity,[status(thm)],[1559, 1557])).
% 1.95/2.11 tff(1561,plain,
% 1.95/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a939) | c3_1(a939) | (~c1_1(a939)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(1562,plain,
% 1.95/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a939) | c1_1(a918) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a918) | (~c3_1(a918)) | c2_1(a939) | (~c1_1(a939))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 1.95/2.11 tff(1563,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1562, 112, 1556, 1529, 1499, 1546, 1555, 43, 1384, 1500, 1554, 1537])).
% 1.95/2.11 tff(1564,plain,(hskp17 | c0_1(a899) | hskp0 | c2_1(a912) | (~c3_1(a912)) | c1_1(a912) | c0_1(a901) | c3_1(a901) | c2_1(a901) | hskp10 | c0_1(a907) | c1_1(a907)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(1565,plain,
% 1.95/2.12 (hskp0),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1564, 1471, 43, 802, 1374, 801, 51, 48, 47, 50, 44, 45])).
% 1.95/2.12 tff(1566,plain,
% 1.95/2.12 (~c2_1(a898)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[65, 1565])).
% 1.95/2.12 tff(1567,plain,
% 1.95/2.12 (c0_1(a898)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[73, 1565])).
% 1.95/2.12 tff(1568,plain,
% 1.95/2.12 (c1_1(a898)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[59, 1565])).
% 1.95/2.12 tff(1569,plain,
% 1.95/2.12 (c3_1(a898)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[120, 1568, 1566, 1567, 46])).
% 1.95/2.12 tff(1570,plain,
% 1.95/2.12 (~hskp11),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1390, 1374])).
% 1.95/2.12 tff(1571,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1572,plain,
% 1.95/2.12 ((hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901))) <=> (hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1573,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1572])).
% 1.95/2.12 tff(1574,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1573, 1571])).
% 1.95/2.12 tff(1575,plain,
% 1.95/2.12 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1576,plain,
% 1.95/2.12 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 1.95/2.12 tff(1577,plain,
% 1.95/2.12 (~c1_1(a901)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1576, 112, 1570, 1567, 1568, 51, 47, 1402, 1569])).
% 1.95/2.12 tff(1578,plain,
% 1.95/2.12 (c0_1(a912)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1515, 1577, 1374])).
% 1.95/2.12 tff(1579,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1580,plain,
% 1.95/2.12 ((hskp9 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c3_1(a901) | c3_1(a901) | c2_1(a901) | c0_1(a901)) <=> (hskp9 | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1581,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c3_1(a901) | c3_1(a901) | c2_1(a901) | c0_1(a901))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901)))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1580])).
% 1.95/2.12 tff(1582,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c3_1(a901) | c3_1(a901) | c2_1(a901) | c0_1(a901))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.95/2.12 tff(1583,plain,
% 1.95/2.12 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a901) | c1_1(a901) | c3_1(a901) | c3_1(a901) | c2_1(a901) | c0_1(a901))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1584,plain,
% 1.95/2.12 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a901) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.95/2.12 tff(1585,plain,
% 1.95/2.12 (hskp9 | c0_1(a901) | c1_1(a901)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1584, 112, 47, 48, 1310])).
% 1.95/2.12 tff(1586,plain,
% 1.95/2.12 (hskp9),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1585, 1577, 51])).
% 1.95/2.12 tff(1587,plain,
% 1.95/2.12 (~c2_1(a909)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1323, 1586])).
% 1.95/2.12 tff(1588,plain,
% 1.95/2.12 (~c1_1(a909)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1329, 1586])).
% 1.95/2.12 tff(1589,plain,
% 1.95/2.12 (~c0_1(a909)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1335, 1586])).
% 1.95/2.12 tff(1590,assumption,(c0_1(a912)), introduced(assumption)).
% 1.95/2.12 tff(1591,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a908)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1592,plain,
% 1.95/2.12 (((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907)) <=> (c3_1(a907) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a908)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1593,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a908))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1592])).
% 1.95/2.12 tff(1594,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a908)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.95/2.12 tff(1595,plain,
% 1.95/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a908) | c0_1(a908) | (~c3_1(a908)) | c3_1(a907) | c1_1(a907) | c0_1(a907))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1596,plain,
% 1.95/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a908) | c2_1(a908) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a908))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.95/2.12 tff(1597,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1596, 112, 614, 505, 801, 802, 1385, 598, 592, 44, 45, 151])).
% 1.95/2.12 tff(1598,plain,(c3_1(a907) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c1_1(a907) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a906) | c2_1(a898) | (~c2_1(a906)) | (~c3_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(1599,plain,
% 1.95/2.12 (c3_1(a907)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1598, 917, 802, 1385, 44, 45, 78, 77, 801, 76, 918, 916])).
% 1.95/2.12 tff(1600,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c0_1(a912)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1601,plain,
% 1.95/2.12 ((hskp4 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907))) <=> (hskp4 | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c0_1(a912)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1602,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c0_1(a912))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1601])).
% 1.95/2.12 tff(1603,plain,
% 1.95/2.12 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c0_1(a912)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1602, 1600])).
% 1.95/2.12 tff(1604,plain,
% 1.95/2.12 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c0_1(a912)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1605,plain,
% 1.95/2.12 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c0_1(a912))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.95/2.12 tff(1606,plain,
% 1.95/2.12 (hskp4 | (~c3_1(a912)) | (~c3_1(a907)) | (~c0_1(a912))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1605, 112, 802, 44, 45, 640])).
% 1.95/2.12 tff(1607,plain,
% 1.95/2.12 (hskp4),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1606, 1599, 1385, 1590])).
% 1.95/2.12 tff(1608,plain,
% 1.95/2.12 (~c3_1(a904)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[536, 1607])).
% 1.95/2.12 tff(1609,plain,
% 1.95/2.12 (~c1_1(a904)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[542, 1607])).
% 1.95/2.12 tff(1610,assumption,(~c2_1(a909)), introduced(assumption)).
% 1.95/2.12 tff(1611,assumption,(~c1_1(a909)), introduced(assumption)).
% 1.95/2.12 tff(1612,assumption,(~c0_1(a909)), introduced(assumption)).
% 1.95/2.12 tff(1613,plain,
% 1.95/2.12 (c2_1(a904)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[605, 1607])).
% 1.95/2.12 tff(1614,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1362, 112, 966, 958, 950, 1613, 1612, 1611, 1610, 1609, 1608, 870])).
% 1.95/2.12 tff(1615,plain,((~hskp6) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~c3_1(a912)) | (~c0_1(a912)) | c2_1(a912) | c0_1(a907) | c1_1(a907) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a912) | c2_1(a898) | (~c3_1(a898))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(1616,plain,
% 1.95/2.12 (~hskp6),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1615, 1589, 1588, 1587, 1374, 1578, 802, 44, 45, 1567, 1568, 801, 1566, 1569])).
% 1.95/2.12 tff(1617,plain,
% 1.95/2.12 (hskp12 | hskp6),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[469, 112, 1568, 1566, 463, 1569])).
% 1.95/2.12 tff(1618,plain,
% 1.95/2.12 (hskp12),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1617, 1616])).
% 1.95/2.12 tff(1619,plain,
% 1.95/2.12 (~c3_1(a913)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[347, 1618])).
% 1.95/2.12 tff(1620,plain,
% 1.95/2.12 (c0_1(a913)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[355, 1618])).
% 1.95/2.12 tff(1621,plain,
% 1.95/2.12 (~c1_1(a913)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[409, 1618])).
% 1.95/2.12 tff(1622,plain,
% 1.95/2.12 (hskp7),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[713, 1621, 1567, 1568, 1620, 1566, 50, 1619])).
% 1.95/2.12 tff(1623,plain,
% 1.95/2.12 (c3_1(a907)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[512, 1622])).
% 1.95/2.12 tff(1624,plain,
% 1.95/2.12 (^[U: $i] : refl((hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.95/2.12 inference(bind,[status(th)],[])).
% 1.95/2.12 tff(1625,plain,
% 1.95/2.12 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.95/2.12 inference(quant_intro,[status(thm)],[1624])).
% 1.95/2.12 tff(1626,plain,
% 1.95/2.12 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1627,plain,
% 1.95/2.12 (^[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)) | 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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.95/2.12 inference(bind,[status(th)],[])).
% 1.95/2.12 tff(1628,plain,
% 1.95/2.12 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.95/2.12 inference(quant_intro,[status(thm)],[1627])).
% 1.95/2.12 tff(1629,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.95/2.12 tff(1630,plain,
% 1.95/2.12 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 1.95/2.12 tff(1631,plain,
% 1.95/2.12 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1630, 1626])).
% 1.95/2.12 tff(1632,plain,(
% 1.95/2.12 ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.95/2.12 inference(skolemize,[status(sab)],[1631])).
% 1.95/2.12 tff(1633,plain,
% 1.95/2.12 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1632, 1625])).
% 1.95/2.12 tff(1634,plain,
% 1.95/2.12 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp5 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp5 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1635,plain,
% 1.95/2.12 ((hskp6 | hskp5 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | (~c3_1(a907))) <=> (hskp6 | hskp5 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1636,plain,
% 1.95/2.12 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp5 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1635])).
% 1.95/2.12 tff(1637,plain,
% 1.95/2.12 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp5 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.95/2.12 tff(1638,plain,
% 1.95/2.12 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | (~c3_1(a907)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1639,plain,
% 1.95/2.12 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp6 | hskp5 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.95/2.12 tff(1640,plain,
% 1.95/2.12 (hskp6 | hskp5 | c1_1(a907) | (~c3_1(a907))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1639, 112, 44, 1633])).
% 1.95/2.12 tff(1641,plain,
% 1.95/2.12 (hskp5),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1640, 1623, 1616, 45])).
% 1.95/2.12 tff(1642,plain,
% 1.95/2.12 (~c0_1(a905)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[276, 1641])).
% 1.95/2.12 tff(1643,plain,
% 1.95/2.12 (hskp1),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[286, 1577, 48, 51, 46, 47])).
% 1.95/2.12 tff(1644,plain,
% 1.95/2.12 (c2_1(a899)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[300, 1643])).
% 1.95/2.12 tff(1645,plain,
% 1.95/2.12 (c1_1(a899)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[308, 1643])).
% 1.95/2.12 tff(1646,plain,
% 1.95/2.12 (hskp14),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[452, 1618, 1567, 1645, 43, 1644, 1568, 1566])).
% 1.95/2.12 tff(1647,plain,
% 1.95/2.12 (~c1_1(a918)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[672, 1646])).
% 1.95/2.12 tff(1648,plain,
% 1.95/2.12 (c3_1(a905)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[244, 1641])).
% 1.95/2.12 tff(1649,plain,
% 1.95/2.12 (c3_1(a918)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[742, 1646])).
% 1.95/2.12 tff(1650,plain,
% 1.95/2.12 (c0_1(a918)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[734, 1646])).
% 1.95/2.12 tff(1651,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1652,plain,
% 1.95/2.12 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905))) <=> (c1_1(a918) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1653,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c0_1(a918)) | (~c3_1(a918))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1652])).
% 1.95/2.12 tff(1654,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1653, 1651])).
% 1.95/2.12 tff(1655,plain,
% 1.95/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1656,plain,
% 1.95/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a905) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a905)) | c2_1(a905) | (~c0_1(a918)) | (~c3_1(a918))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 1.95/2.12 tff(1657,plain,
% 1.95/2.12 (c2_1(a905)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1656, 112, 1650, 1649, 1648, 1567, 1568, 1647, 1642, 1566, 271])).
% 1.95/2.12 tff(1658,plain,
% 1.95/2.12 (hskp4),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1606, 1623, 1374, 1578])).
% 1.95/2.12 tff(1659,plain,
% 1.95/2.12 (~c3_1(a904)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[536, 1658])).
% 1.95/2.12 tff(1660,plain,
% 1.95/2.12 (~c1_1(a904)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[542, 1658])).
% 1.95/2.12 tff(1661,plain,
% 1.95/2.12 (hskp22),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1544, 1578, 1374])).
% 1.95/2.12 tff(1662,plain,
% 1.95/2.12 (~c3_1(a939)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1247, 1661])).
% 1.95/2.12 tff(1663,plain,
% 1.95/2.12 (~c0_1(a939)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1253, 1661])).
% 1.95/2.12 tff(1664,plain,
% 1.95/2.12 (c2_1(a904)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[605, 1658])).
% 1.95/2.12 tff(1665,plain,
% 1.95/2.12 (c1_1(a939)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1262, 1661])).
% 1.95/2.12 tff(1666,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a939)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1667,plain,
% 1.95/2.12 (((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c0_1(a939) | c3_1(a939) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a939)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1668,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a939))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1667])).
% 1.95/2.12 tff(1669,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a939)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1668, 1666])).
% 1.95/2.12 tff(1670,plain,
% 1.95/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1671,plain,
% 1.95/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a939))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 1.95/2.12 tff(1672,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1671, 112, 1665, 1648, 1664, 1663, 1662, 1642, 1660, 1659, 392, 1657])).
% 1.95/2.12 tff(1673,plain,(c2_1(a912) | c1_1(a907) | c0_1(a907) | hskp10 | c0_1(a899) | c1_1(a912) | c3_1(a901) | c0_1(a901) | hskp31 | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(1674,plain,
% 1.95/2.12 (c2_1(a912)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1673, 43, 44, 50, 45, 801, 48, 51, 46, 47])).
% 1.95/2.12 tff(1675,plain,
% 1.95/2.12 (((~hskp11) | (~c2_1(a912))) <=> ((~hskp11) | (~c2_1(a912)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1676,plain,
% 1.95/2.12 (((~c2_1(a912)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a912)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1677,axiom,((~c2_1(a912)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.95/2.12 tff(1678,plain,
% 1.95/2.12 ((~hskp11) | (~c2_1(a912))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 1.95/2.12 tff(1679,plain,
% 1.95/2.12 ((~hskp11) | (~c2_1(a912))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1678, 1675])).
% 1.95/2.12 tff(1680,plain,
% 1.95/2.12 (~hskp11),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1679, 1674])).
% 1.95/2.12 tff(1681,plain,
% 1.95/2.12 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c1_1(a928)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c1_1(a928)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1682,plain,
% 1.95/2.12 ((hskp25 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928))) <=> (hskp25 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c1_1(a928)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1683,plain,
% 1.95/2.12 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c1_1(a928))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1682])).
% 1.95/2.12 tff(1684,plain,
% 1.95/2.12 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c1_1(a928)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[1683, 1681])).
% 1.95/2.12 tff(1685,plain,
% 1.95/2.12 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(1686,plain,
% 1.95/2.12 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c1_1(a928))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.95/2.12 tff(1687,plain,
% 1.95/2.12 (hskp25),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1686, 112, 843, 835, 829, 30])).
% 1.95/2.12 tff(1688,plain,
% 1.95/2.12 (((~hskp25) | (~c3_1(a958))) <=> ((~hskp25) | (~c3_1(a958)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1689,plain,
% 1.95/2.12 (((~c3_1(a958)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a958)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1690,axiom,((~c3_1(a958)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.95/2.12 tff(1691,plain,
% 1.95/2.12 ((~hskp25) | (~c3_1(a958))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 1.95/2.12 tff(1692,plain,
% 1.95/2.12 ((~hskp25) | (~c3_1(a958))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1691, 1688])).
% 1.95/2.12 tff(1693,plain,
% 1.95/2.12 (~c3_1(a958)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1692, 1687])).
% 1.95/2.12 tff(1694,plain,
% 1.95/2.12 (((~hskp25) | (~c1_1(a958))) <=> ((~hskp25) | (~c1_1(a958)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1695,plain,
% 1.95/2.12 (((~c1_1(a958)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a958)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1696,axiom,((~c1_1(a958)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.95/2.12 tff(1697,plain,
% 1.95/2.12 ((~hskp25) | (~c1_1(a958))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 1.95/2.12 tff(1698,plain,
% 1.95/2.12 ((~hskp25) | (~c1_1(a958))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1697, 1694])).
% 1.95/2.12 tff(1699,plain,
% 1.95/2.12 (~c1_1(a958)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1698, 1687])).
% 1.95/2.12 tff(1700,plain,
% 1.95/2.12 (~hskp29),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1438, 850, 1430, 835, 843])).
% 1.95/2.12 tff(1701,plain,
% 1.95/2.12 (hskp27),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[108, 1700, 46])).
% 1.95/2.12 tff(1702,plain,
% 1.95/2.12 (~c0_1(a978)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1445, 1701])).
% 1.95/2.12 tff(1703,plain,
% 1.95/2.12 (c3_1(a978)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1453, 1701])).
% 1.95/2.12 tff(1704,plain,
% 1.95/2.12 (c2_1(a978)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1461, 1701])).
% 1.95/2.12 tff(1705,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1706,plain,
% 1.95/2.12 (((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (c0_1(a978) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(1707,plain,
% 1.95/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1706])).
% 1.95/2.13 tff(1708,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1707, 1705])).
% 1.95/2.13 tff(1709,plain,
% 1.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1710,plain,
% 1.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)) | (~c3_1(a978)) | (~c2_1(a978))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.95/2.13 tff(1711,plain,
% 1.95/2.13 (~c2_1(a958)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1710, 112, 1704, 1703, 843, 1702, 1699, 1693, 829, 392, 850])).
% 1.95/2.13 tff(1712,plain,
% 1.95/2.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.95/2.13 inference(bind,[status(th)],[])).
% 1.95/2.13 tff(1713,plain,
% 1.95/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.95/2.13 inference(quant_intro,[status(thm)],[1712])).
% 1.95/2.13 tff(1714,plain,
% 1.95/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1715,plain,
% 1.95/2.13 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.95/2.13 inference(bind,[status(th)],[])).
% 1.95/2.13 tff(1716,plain,
% 1.95/2.13 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.95/2.13 inference(quant_intro,[status(thm)],[1715])).
% 1.95/2.13 tff(1717,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | (~c1_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c2_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.95/2.13 tff(1718,plain,
% 1.95/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.95/2.13 tff(1719,plain,
% 1.95/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1718, 1714])).
% 1.95/2.13 tff(1720,plain,(
% 1.95/2.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.95/2.13 inference(skolemize,[status(sab)],[1719])).
% 1.95/2.13 tff(1721,plain,
% 1.95/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1720, 1713])).
% 1.95/2.13 tff(1722,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1723,plain,
% 1.95/2.13 (((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c0_1(a978) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1724,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1723])).
% 1.95/2.13 tff(1725,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1724, 1722])).
% 1.95/2.13 tff(1726,plain,
% 1.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1727,plain,
% 1.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 1.95/2.13 tff(1728,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1727, 112, 1704, 1703, 843, 1702, 1699, 1693, 835, 1721, 850, 1711])).
% 1.95/2.13 tff(1729,plain,((~hskp17) | hskp31 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(1730,plain,
% 1.95/2.13 (~hskp17),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1729, 1680, 46])).
% 1.95/2.13 tff(1731,assumption,(c2_1(a912)), introduced(assumption)).
% 1.95/2.13 tff(1732,assumption,(~c1_1(a898)), introduced(assumption)).
% 1.95/2.13 tff(1733,plain,
% 1.95/2.13 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a898) | c1_1(a898) | c2_1(a898) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a898) | c1_1(a898) | c2_1(a898) | (~ndr1_0))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1734,plain,
% 1.95/2.13 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a898) | c1_1(a898) | c0_1(a898)) <=> (hskp1 | hskp0 | c0_1(a898) | c1_1(a898) | c2_1(a898) | (~ndr1_0))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1735,plain,
% 1.95/2.13 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a898) | c1_1(a898) | c0_1(a898))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a898) | c1_1(a898) | c2_1(a898) | (~ndr1_0)))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1734])).
% 1.95/2.13 tff(1736,plain,
% 1.95/2.13 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a898) | c1_1(a898) | c0_1(a898))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a898) | c1_1(a898) | c2_1(a898) | (~ndr1_0))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1735, 1733])).
% 1.95/2.13 tff(1737,plain,
% 1.95/2.13 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a898) | c1_1(a898) | c0_1(a898))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1738,plain,
% 1.95/2.13 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a898) | c1_1(a898) | c2_1(a898) | (~ndr1_0)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 1.95/2.13 tff(1739,plain,
% 1.95/2.13 (hskp1 | hskp0 | c0_1(a898) | c1_1(a898)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1738, 112, 76, 20])).
% 1.95/2.13 tff(1740,plain,
% 1.95/2.13 (hskp1),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1739, 1732, 991, 992])).
% 1.95/2.13 tff(1741,plain,
% 1.95/2.13 (c2_1(a899)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[300, 1740])).
% 1.95/2.13 tff(1742,plain,
% 1.95/2.13 (c1_1(a899)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[308, 1740])).
% 1.95/2.13 tff(1743,plain,
% 1.95/2.13 (~c3_1(a899)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[381, 313, 1742, 1741, 43, 50])).
% 1.95/2.13 tff(1744,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a898) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a898) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1745,plain,
% 1.95/2.13 ((hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898))) <=> (hskp14 | c0_1(a898) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1746,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a898) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1745])).
% 1.95/2.13 tff(1747,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a898) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1746, 1744])).
% 1.95/2.13 tff(1748,plain,
% 1.95/2.13 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a898) | c0_1(a898) | (~c3_1(a898)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1749,plain,
% 1.95/2.13 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a898) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 1.95/2.13 tff(1750,plain,
% 1.95/2.13 (~c3_1(a898)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1749, 112, 313, 1742, 1741, 991, 76, 881, 1743])).
% 1.95/2.13 tff(1751,plain,
% 1.95/2.13 (hskp17),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[898, 1743, 992, 1741])).
% 1.95/2.13 tff(1752,plain,
% 1.95/2.13 (~c3_1(a928)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[828, 1751])).
% 1.95/2.13 tff(1753,plain,
% 1.95/2.13 (~c2_1(a928)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[834, 1751])).
% 1.95/2.13 tff(1754,plain,
% 1.95/2.13 (c1_1(a928)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[842, 1751])).
% 1.95/2.13 tff(1755,plain,
% 1.95/2.13 (~c0_1(a928)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[849, 46, 112, 1754, 1753, 1752, 10])).
% 1.95/2.13 tff(1756,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c1_1(a898) | c2_1(a928) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a898) | c2_1(a928) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | c0_1(a928) | (~c1_1(a928)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1757,plain,
% 1.95/2.13 ((hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a898) | c2_1(a898) | c1_1(a898)) <=> (hskp10 | c1_1(a898) | c2_1(a928) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | c0_1(a928) | (~c1_1(a928)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1758,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a898) | c2_1(a898) | c1_1(a898))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c1_1(a898) | c2_1(a928) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | c0_1(a928) | (~c1_1(a928))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1757])).
% 1.95/2.13 tff(1759,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a898) | c2_1(a898) | c1_1(a898))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a898) | c2_1(a928) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | c0_1(a928) | (~c1_1(a928)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.95/2.13 tff(1760,plain,
% 1.95/2.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a898) | c2_1(a898) | c1_1(a898))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1761,plain,
% 1.95/2.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a898) | c2_1(a928) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | c0_1(a928) | (~c1_1(a928))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.95/2.13 tff(1762,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1761, 112, 50, 1754, 1732, 1753, 76, 812, 1755, 1750])).
% 1.95/2.13 tff(1763,plain,(hskp14 | hskp10 | c1_1(a898) | c2_1(a898) | hskp31 | c0_1(a898) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(1764,plain,
% 1.95/2.13 (hskp14),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1763, 1732, 50, 76, 46, 991, 43])).
% 1.95/2.13 tff(1765,plain,
% 1.95/2.13 (c3_1(a918)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[742, 1764])).
% 1.95/2.13 tff(1766,plain,
% 1.95/2.13 (c0_1(a918)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[734, 1764])).
% 1.95/2.13 tff(1767,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a898) | c1_1(a898) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a898) | c1_1(a898) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1768,plain,
% 1.95/2.13 (((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c1_1(a898) | c0_1(a898) | c2_1(a898)) <=> (c0_1(a898) | c1_1(a898) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1769,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c1_1(a898) | c0_1(a898) | c2_1(a898))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a898) | c1_1(a898) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1768])).
% 1.95/2.13 tff(1770,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c1_1(a898) | c0_1(a898) | c2_1(a898))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a898) | c1_1(a898) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1769, 1767])).
% 1.95/2.13 tff(1771,plain,
% 1.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c1_1(a898) | c0_1(a898) | c2_1(a898))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1772,plain,
% 1.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a898) | c1_1(a898) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 1.95/2.13 tff(1773,plain,
% 1.95/2.13 (~c2_1(a918)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1772, 112, 1766, 1765, 991, 1732, 801, 1731, 813, 76, 870])).
% 1.95/2.13 tff(1774,plain,
% 1.95/2.13 (~c1_1(a918)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[672, 1764])).
% 1.95/2.13 tff(1775,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1776,plain,
% 1.95/2.13 ((hskp22 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c2_1(a918) | c1_1(a918) | (~c0_1(a918))) <=> (hskp22 | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1777,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c2_1(a918) | c1_1(a918) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1776])).
% 1.95/2.13 tff(1778,plain,
% 1.95/2.13 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c2_1(a918) | c1_1(a918) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1777, 1775])).
% 1.95/2.13 tff(1779,plain,
% 1.95/2.13 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c2_1(a918) | c1_1(a918) | (~c0_1(a918)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(1780,plain,
% 1.95/2.13 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 1.95/2.13 tff(1781,plain,
% 1.95/2.13 (hskp22),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1780, 112, 1766, 1765, 1774, 1234, 1773])).
% 1.95/2.13 tff(1782,plain,
% 1.95/2.13 (~c3_1(a939)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1247, 1781])).
% 1.95/2.13 tff(1783,plain,
% 1.95/2.13 (~c0_1(a939)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1253, 1781])).
% 1.95/2.13 tff(1784,plain,
% 1.95/2.13 (c1_1(a939)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1262, 1781])).
% 1.95/2.13 tff(1785,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a939)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1786,plain,
% 1.95/2.13 (((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c0_1(a939) | c3_1(a939) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a939)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(1787,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a939))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[1786])).
% 1.95/2.13 tff(1788,plain,
% 1.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a939)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[1787, 1785])).
% 1.95/2.13 tff(1789,plain,
% 1.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1790,plain,
% 1.95/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a939))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.95/2.14 tff(1791,plain,
% 1.95/2.14 (~c3_1(a899)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1790, 112, 1784, 1741, 1783, 1782, 801, 1731, 813, 43, 392])).
% 1.95/2.14 tff(1792,plain,
% 1.95/2.14 (hskp17),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[898, 1791, 992, 1741])).
% 1.95/2.14 tff(1793,plain,
% 1.95/2.14 (~c3_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[828, 1792])).
% 1.95/2.14 tff(1794,plain,
% 1.95/2.14 (~c2_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[834, 1792])).
% 1.95/2.14 tff(1795,plain,
% 1.95/2.14 (c1_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[842, 1792])).
% 1.95/2.14 tff(1796,plain,
% 1.95/2.14 (~hskp11),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1679, 1731])).
% 1.95/2.14 tff(1797,plain,
% 1.95/2.14 (~c0_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[849, 46, 112, 1795, 1794, 1793, 10])).
% 1.95/2.14 tff(1798,plain,
% 1.95/2.14 (~hskp29),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1438, 1797, 1796, 1794, 1795])).
% 1.95/2.14 tff(1799,plain,
% 1.95/2.14 (hskp27),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[108, 1798, 46])).
% 1.95/2.14 tff(1800,plain,
% 1.95/2.14 (~c0_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1445, 1799])).
% 1.95/2.14 tff(1801,plain,
% 1.95/2.14 (c3_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1453, 1799])).
% 1.95/2.14 tff(1802,plain,
% 1.95/2.14 (c2_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1461, 1799])).
% 1.95/2.14 tff(1803,plain,
% 1.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1804,plain,
% 1.95/2.14 (((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978))) <=> (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1805,plain,
% 1.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1804])).
% 1.95/2.14 tff(1806,plain,
% 1.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1805, 1803])).
% 1.95/2.14 tff(1807,plain,
% 1.95/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1808,plain,
% 1.95/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 1.95/2.14 tff(1809,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1808, 112, 1802, 1801, 1795, 1765, 1800, 1794, 1793, 1774, 1384, 1773])).
% 1.95/2.14 tff(1810,plain,(c1_1(a898) | hskp31 | c0_1(a899) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a898) | c2_1(a898) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1811,plain,
% 1.95/2.14 (c1_1(a898)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1810, 991, 43, 801, 1731, 813, 46, 76, 50])).
% 1.95/2.14 tff(1812,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c0_1(a898) | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c0_1(a898) | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)) | c1_1(a901))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1813,plain,
% 1.95/2.14 ((hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a901) | c2_1(a901) | c1_1(a901)) <=> (hskp10 | c0_1(a898) | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)) | c1_1(a901))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1814,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c0_1(a898) | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)) | c1_1(a901)))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1813])).
% 1.95/2.14 tff(1815,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c0_1(a898) | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)) | c1_1(a901))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1814, 1812])).
% 1.95/2.14 tff(1816,plain,
% 1.95/2.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a898) | c0_1(a898) | (~c1_1(a898)) | c3_1(a901) | c2_1(a901) | c1_1(a901))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1817,plain,
% 1.95/2.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c0_1(a898) | c2_1(a901) | c3_1(a901) | c2_1(a898) | (~ndr1_0) | (~c1_1(a898)) | c1_1(a901)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 1.95/2.14 tff(1818,plain,
% 1.95/2.14 (c0_1(a898) | (~c1_1(a898)) | c1_1(a901)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1817, 112, 50, 47, 48, 76, 812])).
% 1.95/2.14 tff(1819,plain,
% 1.95/2.14 (c1_1(a901)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1818, 1811, 991])).
% 1.95/2.14 tff(1820,plain,
% 1.95/2.14 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1821,plain,
% 1.95/2.14 ((hskp25 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901))) <=> (hskp25 | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1822,plain,
% 1.95/2.14 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1821])).
% 1.95/2.14 tff(1823,plain,
% 1.95/2.14 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1822, 1820])).
% 1.95/2.14 tff(1824,plain,
% 1.95/2.14 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c1_1(a901)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1825,plain,
% 1.95/2.14 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.95/2.14 tff(1826,plain,
% 1.95/2.14 (hskp25 | c3_1(a901) | (~c1_1(a901))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1825, 112, 47, 30])).
% 1.95/2.14 tff(1827,plain,
% 1.95/2.14 (hskp25),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1826, 1819, 48])).
% 1.95/2.14 tff(1828,plain,
% 1.95/2.14 (~c3_1(a958)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1692, 1827])).
% 1.95/2.14 tff(1829,plain,
% 1.95/2.14 (~c1_1(a958)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1698, 1827])).
% 1.95/2.14 tff(1830,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c1_1(a958) | c3_1(a958) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a958))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a958) | c3_1(a958) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a958))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1831,plain,
% 1.95/2.14 ((hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c2_1(a958) | c1_1(a958)) <=> (hskp10 | c1_1(a958) | c3_1(a958) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a958))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1832,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c2_1(a958) | c1_1(a958))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c1_1(a958) | c3_1(a958) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a958)))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1831])).
% 1.95/2.14 tff(1833,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c2_1(a958) | c1_1(a958))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a958) | c3_1(a958) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a958))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1832, 1830])).
% 1.95/2.14 tff(1834,plain,
% 1.95/2.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c2_1(a958) | c1_1(a958))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1835,plain,
% 1.95/2.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c1_1(a958) | c3_1(a958) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a958)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 1.95/2.14 tff(1836,plain,
% 1.95/2.14 (c2_1(a958)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1835, 112, 50, 1829, 1828, 51, 47, 812, 1819])).
% 1.95/2.14 tff(1837,plain,
% 1.95/2.14 (((~hskp25) | (~c0_1(a958))) <=> ((~hskp25) | (~c0_1(a958)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1838,plain,
% 1.95/2.14 (((~c0_1(a958)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a958)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1839,axiom,((~c0_1(a958)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.95/2.14 tff(1840,plain,
% 1.95/2.14 ((~hskp25) | (~c0_1(a958))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.95/2.14 tff(1841,plain,
% 1.95/2.14 ((~hskp25) | (~c0_1(a958))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1840, 1837])).
% 1.95/2.14 tff(1842,plain,
% 1.95/2.14 (~c0_1(a958)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1841, 1827])).
% 1.95/2.14 tff(1843,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1844,plain,
% 1.95/2.14 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a958) | c3_1(a958) | (~c2_1(a958))) <=> (hskp17 | hskp0 | c0_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1845,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a958) | c3_1(a958) | (~c2_1(a958)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1844])).
% 1.95/2.14 tff(1846,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a958) | c3_1(a958) | (~c2_1(a958)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1845, 1843])).
% 1.95/2.14 tff(1847,plain,
% 1.95/2.14 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a958) | c3_1(a958) | (~c2_1(a958)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1848,plain,
% 1.95/2.14 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 1.95/2.14 tff(1849,plain,
% 1.95/2.14 (hskp17),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1848, 112, 992, 1842, 1828, 891, 1836])).
% 1.95/2.14 tff(1850,plain,
% 1.95/2.14 (~c3_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[828, 1849])).
% 1.95/2.14 tff(1851,plain,
% 1.95/2.14 (~c2_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[834, 1849])).
% 1.95/2.14 tff(1852,plain,
% 1.95/2.14 (c1_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[842, 1849])).
% 1.95/2.14 tff(1853,plain,
% 1.95/2.14 (~c0_1(a928)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[849, 46, 112, 1852, 1851, 1850, 10])).
% 1.95/2.14 tff(1854,plain,
% 1.95/2.14 (~hskp29),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1438, 1853, 1796, 1851, 1852])).
% 1.95/2.14 tff(1855,plain,
% 1.95/2.14 (hskp27),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[108, 1854, 46])).
% 1.95/2.14 tff(1856,plain,
% 1.95/2.14 (~c0_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1445, 1855])).
% 1.95/2.14 tff(1857,plain,
% 1.95/2.14 (c3_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1453, 1855])).
% 1.95/2.14 tff(1858,plain,
% 1.95/2.14 (c2_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1461, 1855])).
% 1.95/2.14 tff(1859,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1710, 112, 1858, 1857, 1852, 1856, 1829, 1828, 1850, 392, 1853, 1836])).
% 1.95/2.14 tff(1860,plain,(c0_1(a898) | hskp31 | hskp10 | c0_1(a901) | c2_1(a901) | c3_1(a901) | c2_1(a898) | c0_1(a899) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1861,plain,
% 1.95/2.14 (c0_1(a898)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1860, 813, 50, 51, 47, 48, 76, 43, 801, 1731, 46])).
% 1.95/2.14 tff(1862,plain,
% 1.95/2.14 (~hskp29),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1438, 850, 1796, 835, 843])).
% 1.95/2.14 tff(1863,plain,
% 1.95/2.14 (hskp27),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[108, 1862, 46])).
% 1.95/2.14 tff(1864,plain,
% 1.95/2.14 (~c0_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1445, 1863])).
% 1.95/2.14 tff(1865,plain,
% 1.95/2.14 (c3_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1453, 1863])).
% 1.95/2.14 tff(1866,plain,
% 1.95/2.14 (c2_1(a978)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1461, 1863])).
% 1.95/2.14 tff(1867,plain,
% 1.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c3_1(a928) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c3_1(a928) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1868,plain,
% 1.95/2.14 (((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (c0_1(a978) | c3_1(a928) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1869,plain,
% 1.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c3_1(a928) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1868])).
% 1.95/2.14 tff(1870,plain,
% 1.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c3_1(a928) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1869, 1867])).
% 1.95/2.14 tff(1871,plain,
% 1.95/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1872,plain,
% 1.95/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c3_1(a928) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.95/2.14 tff(1873,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1872, 112, 1866, 1865, 843, 1864, 829, 801, 1731, 813, 392, 850])).
% 1.95/2.14 tff(1874,plain,((~hskp17) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(1875,plain,
% 1.95/2.14 (~hskp17),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1874, 813, 1731, 801, 46])).
% 1.95/2.14 tff(1876,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a912))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a912))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1877,plain,
% 1.95/2.14 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912))) <=> (hskp17 | hskp0 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a912))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1878,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a912)))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1877])).
% 1.95/2.14 tff(1879,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a912))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1878, 1876])).
% 1.95/2.14 tff(1880,plain,
% 1.95/2.14 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1881,plain,
% 1.95/2.14 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | c0_1(a912)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 1.95/2.14 tff(1882,plain,
% 1.95/2.14 (hskp17 | hskp0 | c3_1(a912) | c0_1(a912)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1881, 112, 1731, 891])).
% 1.95/2.14 tff(1883,plain,
% 1.95/2.14 (c0_1(a912)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1882, 32, 813, 31])).
% 1.95/2.14 tff(1884,plain,
% 1.95/2.14 (~hskp20),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1021, 32, 31])).
% 1.95/2.14 tff(1885,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~c2_1(a912)) | c3_1(a912) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | (~c2_1(a912)) | c3_1(a912) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a912)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1886,plain,
% 1.95/2.14 ((hskp20 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912)) | c3_1(a901) | c2_1(a901) | c1_1(a901)) <=> (hskp20 | (~c2_1(a912)) | c3_1(a912) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a912)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1887,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~c2_1(a912)) | c3_1(a912) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a912))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1886])).
% 1.95/2.14 tff(1888,plain,
% 1.95/2.14 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | (~c2_1(a912)) | c3_1(a912) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a912)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1887, 1885])).
% 1.95/2.14 tff(1889,plain,
% 1.95/2.14 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912)) | c3_1(a901) | c2_1(a901) | c1_1(a901))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1890,plain,
% 1.95/2.14 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | (~c2_1(a912)) | c3_1(a912) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a912))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 1.95/2.14 tff(1891,plain,
% 1.95/2.14 (hskp20 | c1_1(a901) | (~c0_1(a912))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1890, 112, 1731, 813, 47, 48, 1064])).
% 1.95/2.14 tff(1892,plain,
% 1.95/2.14 (c1_1(a901)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1891, 1884, 1883])).
% 1.95/2.14 tff(1893,plain,
% 1.95/2.14 (hskp25),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1826, 1892, 48])).
% 1.95/2.14 tff(1894,plain,
% 1.95/2.14 (~c3_1(a958)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1692, 1893])).
% 1.95/2.14 tff(1895,plain,
% 1.95/2.14 (~c0_1(a958)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1841, 1893])).
% 1.95/2.14 tff(1896,plain,
% 1.95/2.14 (~c2_1(a958)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1848, 112, 32, 31, 1895, 1894, 891])).
% 1.95/2.14 tff(1897,plain,
% 1.95/2.14 (^[U: $i] : refl((hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.95/2.14 inference(bind,[status(th)],[])).
% 1.95/2.14 tff(1898,plain,
% 1.95/2.14 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.95/2.14 inference(quant_intro,[status(thm)],[1897])).
% 1.95/2.14 tff(1899,plain,
% 1.95/2.14 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1900,plain,
% 1.95/2.14 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp10) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp10) <=> (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.95/2.14 inference(bind,[status(th)],[])).
% 1.95/2.14 tff(1901,plain,
% 1.95/2.14 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp10) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.95/2.14 inference(quant_intro,[status(thm)],[1900])).
% 1.95/2.14 tff(1902,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.95/2.14 tff(1903,plain,
% 1.95/2.14 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.95/2.14 tff(1904,plain,
% 1.95/2.14 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1903, 1899])).
% 1.95/2.14 tff(1905,plain,(
% 1.95/2.14 ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.95/2.14 inference(skolemize,[status(sab)],[1904])).
% 1.95/2.14 tff(1906,plain,
% 1.95/2.14 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1905, 1898])).
% 1.95/2.14 tff(1907,plain,
% 1.95/2.14 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | (~c0_1(a912)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | (~c0_1(a912)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1908,plain,
% 1.95/2.14 ((hskp16 | hskp10 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912))) <=> (hskp16 | hskp10 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | (~c0_1(a912)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1909,plain,
% 1.95/2.14 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | (~c0_1(a912))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1908])).
% 1.95/2.14 tff(1910,plain,
% 1.95/2.14 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | (~c0_1(a912)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[1909, 1907])).
% 1.95/2.14 tff(1911,plain,
% 1.95/2.14 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a912) | (~c2_1(a912)) | (~c0_1(a912)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(1912,plain,
% 1.95/2.14 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | (~c2_1(a912)) | c3_1(a912) | (~ndr1_0) | (~c0_1(a912))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 1.95/2.14 tff(1913,plain,
% 1.95/2.14 (hskp16 | c3_1(a912) | (~c0_1(a912))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1912, 112, 50, 1731, 1906])).
% 1.95/2.14 tff(1914,plain,
% 1.95/2.14 (hskp16),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1913, 1883, 813])).
% 1.95/2.14 tff(1915,plain,
% 1.95/2.14 (((~hskp16) | (~c3_1(a923))) <=> ((~hskp16) | (~c3_1(a923)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1916,plain,
% 1.95/2.14 (((~c3_1(a923)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a923)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1917,axiom,((~c3_1(a923)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.95/2.14 tff(1918,plain,
% 1.95/2.14 ((~hskp16) | (~c3_1(a923))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 1.95/2.14 tff(1919,plain,
% 1.95/2.14 ((~hskp16) | (~c3_1(a923))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1918, 1915])).
% 1.95/2.14 tff(1920,plain,
% 1.95/2.14 (~c3_1(a923)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1919, 1914])).
% 1.95/2.14 tff(1921,plain,
% 1.95/2.14 (((~hskp16) | c2_1(a923)) <=> ((~hskp16) | c2_1(a923))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1922,axiom,((~hskp16) | c2_1(a923)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.95/2.14 tff(1923,plain,
% 1.95/2.14 ((~hskp16) | c2_1(a923)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.95/2.14 tff(1924,plain,
% 1.95/2.14 ((~hskp16) | c2_1(a923)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1923, 1921])).
% 1.95/2.14 tff(1925,plain,
% 1.95/2.14 ((~hskp16) | c2_1(a923)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1924, 1921])).
% 1.95/2.14 tff(1926,plain,
% 1.95/2.14 ((~hskp16) | c2_1(a923)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1925, 1921])).
% 1.95/2.14 tff(1927,plain,
% 1.95/2.14 ((~hskp16) | c2_1(a923)),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[1926, 1921])).
% 1.95/2.14 tff(1928,plain,
% 1.95/2.14 (c2_1(a923)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1927, 1914])).
% 1.95/2.14 tff(1929,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c3_1(a923) | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a923) | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1930,plain,
% 1.95/2.14 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a923) | c3_1(a923) | (~c2_1(a923))) <=> (hskp17 | hskp0 | c3_1(a923) | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(1931,plain,
% 1.95/2.14 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a923) | c3_1(a923) | (~c2_1(a923)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c3_1(a923) | (~ndr1_0) | c0_1(a923) | (~c2_1(a923))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[1930])).
% 1.95/2.15 tff(1932,plain,
% 1.95/2.15 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a923) | c3_1(a923) | (~c2_1(a923)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a923) | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1931, 1929])).
% 1.95/2.15 tff(1933,plain,
% 1.95/2.15 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a923) | c3_1(a923) | (~c2_1(a923)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1934,plain,
% 1.95/2.15 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a923) | (~ndr1_0) | c0_1(a923) | (~c2_1(a923))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1933, 1932])).
% 1.95/2.15 tff(1935,plain,
% 1.95/2.15 (c0_1(a923)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1934, 112, 32, 31, 1928, 1920, 891])).
% 1.95/2.15 tff(1936,plain,
% 1.95/2.15 (~c1_1(a958)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1698, 1893])).
% 1.95/2.15 tff(1937,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c2_1(a923)) | c2_1(a958))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c2_1(a923)) | c2_1(a958))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1938,plain,
% 1.95/2.15 ((hskp20 | (~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a958) | c2_1(a958) | c1_1(a958)) <=> (hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c2_1(a923)) | c2_1(a958))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1939,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a958) | c2_1(a958) | c1_1(a958))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c2_1(a923)) | c2_1(a958)))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[1938])).
% 1.95/2.15 tff(1940,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a958) | c2_1(a958) | c1_1(a958))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c2_1(a923)) | c2_1(a958))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1939, 1937])).
% 1.95/2.15 tff(1941,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a958) | c2_1(a958) | c1_1(a958))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1942,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c2_1(a923)) | c2_1(a958)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1941, 1940])).
% 1.95/2.15 tff(1943,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1942, 112, 1884, 1928, 1936, 1894, 1920, 1064, 1935, 1896])).
% 1.95/2.15 tff(1944,plain,(hskp17 | hskp0 | c3_1(a901) | c2_1(a901) | (~c2_1(a912)) | c3_1(a912) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(1945,plain,
% 1.95/2.15 (hskp0),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1944, 1875, 48, 47, 1731, 813, 50])).
% 1.95/2.15 tff(1946,plain,
% 1.95/2.15 (c1_1(a898)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[59, 1945])).
% 1.95/2.15 tff(1947,plain,
% 1.95/2.15 (c3_1(a898)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[120, 1946, 76, 1861, 46])).
% 1.95/2.15 tff(1948,plain,
% 1.95/2.15 ((~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a901))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[138, 46, 112, 47, 48, 76, 10])).
% 1.95/2.15 tff(1949,plain,
% 1.95/2.15 (~c1_1(a901)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1948, 1946, 1861])).
% 1.95/2.15 tff(1950,plain,
% 1.95/2.15 (hskp1),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[286, 1949, 48, 51, 46, 47])).
% 1.95/2.15 tff(1951,plain,
% 1.95/2.15 (c2_1(a899)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[300, 1950])).
% 1.95/2.15 tff(1952,plain,
% 1.95/2.15 (c1_1(a899)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[308, 1950])).
% 1.95/2.15 tff(1953,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1954,plain,
% 1.95/2.15 ((hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912))) <=> (hskp21 | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1955,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[1954])).
% 1.95/2.15 tff(1956,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1955, 1953])).
% 1.95/2.15 tff(1957,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1958,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.95/2.15 tff(1959,plain,
% 1.95/2.15 (hskp21 | (~c0_1(a898)) | (~c1_1(a898))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1958, 112, 801, 1731, 813, 76, 402])).
% 1.95/2.15 tff(1960,plain,
% 1.95/2.15 (hskp21),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1959, 1946, 1861])).
% 1.95/2.15 tff(1961,plain,
% 1.95/2.15 (hskp14),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[441, 1951, 1960, 1952, 43])).
% 1.95/2.15 tff(1962,plain,
% 1.95/2.15 (~c1_1(a918)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[672, 1961])).
% 1.95/2.15 tff(1963,plain,
% 1.95/2.15 (hskp18),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[765, 1962, 1960, 1952, 1951, 43])).
% 1.95/2.15 tff(1964,plain,
% 1.95/2.15 (~c1_1(a929)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[771, 1963])).
% 1.95/2.15 tff(1965,plain,
% 1.95/2.15 (~c3_1(a938)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[416, 1960])).
% 1.95/2.15 tff(1966,plain,
% 1.95/2.15 (~c2_1(a938)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[422, 1960])).
% 1.95/2.15 tff(1967,plain,
% 1.95/2.15 (c2_1(a929)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[781, 1963])).
% 1.95/2.15 tff(1968,plain,
% 1.95/2.15 (c0_1(a929)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[789, 1963])).
% 1.95/2.15 tff(1969,plain,
% 1.95/2.15 (c0_1(a938)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[430, 1960])).
% 1.95/2.15 tff(1970,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[797, 112, 1969, 1968, 1967, 1946, 1966, 1965, 1964, 76, 131, 1947])).
% 1.95/2.15 tff(1971,plain,(c3_1(a912) | c2_1(a898) | c0_1(a899) | c3_1(a901) | c0_1(a901) | hskp31 | c2_1(a901) | c1_1(a912) | (~c2_1(a912)) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(1972,plain,
% 1.95/2.15 (c2_1(a898)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1971, 813, 43, 48, 51, 46, 47, 801, 1731, 50])).
% 1.95/2.15 tff(1973,plain,
% 1.95/2.15 (~hskp17),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1729, 1796, 46])).
% 1.95/2.15 tff(1974,plain,
% 1.95/2.15 (hskp0),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1944, 813, 48, 47, 1731, 1973, 50])).
% 1.95/2.15 tff(1975,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[65, 1974, 1972])).
% 1.95/2.15 tff(1976,plain,(c3_1(a912) | c3_1(a901) | c2_1(a901) | (~c2_1(a912)) | hskp10 | c0_1(a899) | c0_1(a901) | hskp31 | c1_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(1977,plain,
% 1.95/2.15 (c3_1(a912)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1976, 1674, 47, 48, 50, 43, 51, 46, 801])).
% 1.95/2.15 tff(1978,plain,
% 1.95/2.15 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1979,plain,
% 1.95/2.15 ((hskp24 | hskp17 | (~ndr1_0) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912))) <=> (hskp24 | hskp17 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1980,plain,
% 1.95/2.15 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0)))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[1979])).
% 1.95/2.15 tff(1981,plain,
% 1.95/2.15 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1980, 1978])).
% 1.95/2.15 tff(1982,plain,
% 1.95/2.15 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(1983,plain,
% 1.95/2.15 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 1.95/2.15 tff(1984,plain,
% 1.95/2.15 (hskp24 | hskp17 | (~c2_1(a912)) | (~c3_1(a912))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1983, 112, 801, 1169])).
% 1.95/2.15 tff(1985,plain,
% 1.95/2.15 (hskp24),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1984, 1977, 1674, 1730])).
% 1.95/2.15 tff(1986,plain,
% 1.95/2.15 (c1_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1196, 1985])).
% 1.95/2.15 tff(1987,plain,
% 1.95/2.15 (c3_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1188, 1985])).
% 1.95/2.15 tff(1988,plain,
% 1.95/2.15 (~c2_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1209, 1985])).
% 1.95/2.15 tff(1989,assumption,(~c0_1(a953)), introduced(assumption)).
% 1.95/2.15 tff(1990,assumption,(c3_1(a953)), introduced(assumption)).
% 1.95/2.15 tff(1991,plain,
% 1.95/2.15 (hskp12 | c0_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1203, 112, 50, 1280, 1990, 334])).
% 1.95/2.15 tff(1992,plain,
% 1.95/2.15 (hskp12),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1991, 1989])).
% 1.95/2.15 tff(1993,plain,
% 1.95/2.15 (~c3_1(a913)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[347, 1992])).
% 1.95/2.15 tff(1994,plain,
% 1.95/2.15 (~c1_1(a913)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[409, 1992])).
% 1.95/2.15 tff(1995,plain,
% 1.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1996,plain,
% 1.95/2.15 (((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a953) | c2_1(a953) | (~c3_1(a953))) <=> (c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(1997,plain,
% 1.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a953) | c2_1(a953) | (~c3_1(a953)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953)))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[1996])).
% 1.95/2.15 tff(1998,plain,
% 1.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a953) | c2_1(a953) | (~c3_1(a953)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953))),
% 1.95/2.15 inference(transitivity,[status(thm)],[1997, 1995])).
% 1.95/2.15 tff(1999,plain,
% 1.95/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a953) | c2_1(a953) | (~c3_1(a953)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(2000,plain,
% 1.95/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | (~c1_1(a953)) | (~c3_1(a953)) | c0_1(a953)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.95/2.15 tff(2001,plain,
% 1.95/2.15 (~c2_1(a913)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2000, 112, 1280, 1990, 1279, 1994, 1993, 503, 1989])).
% 1.95/2.15 tff(2002,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c1_1(a953)) | c0_1(a953))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c1_1(a953)) | c0_1(a953))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2003,plain,
% 1.95/2.15 ((hskp10 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a913) | c2_1(a913) | c1_1(a913)) <=> (hskp10 | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c1_1(a953)) | c0_1(a953))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2004,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a913) | c2_1(a913) | c1_1(a913))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c1_1(a953)) | c0_1(a953)))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[2003])).
% 1.95/2.15 tff(2005,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a913) | c2_1(a913) | c1_1(a913))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c1_1(a953)) | c0_1(a953))),
% 1.95/2.15 inference(transitivity,[status(thm)],[2004, 2002])).
% 1.95/2.15 tff(2006,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp10 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a913) | c2_1(a913) | c1_1(a913))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(2007,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp10 | c2_1(a953) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | c2_1(a913) | (~c1_1(a953)) | c0_1(a953)),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 1.95/2.15 tff(2008,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2007, 112, 50, 1280, 1279, 1994, 1993, 812, 2001, 1989])).
% 1.95/2.15 tff(2009,plain,(c0_1(a953) | hskp10 | (~c1_1(a953)) | c2_1(a953) | (~c3_1(a953))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(2010,plain,
% 1.95/2.15 (c0_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2009, 1986, 50, 1988, 1987])).
% 1.95/2.15 tff(2011,assumption,(hskp24), introduced(assumption)).
% 1.95/2.15 tff(2012,plain,
% 1.95/2.15 (c3_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1188, 2011])).
% 1.95/2.15 tff(2013,plain,
% 1.95/2.15 (~c2_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1209, 2011])).
% 1.95/2.15 tff(2014,plain,
% 1.95/2.15 (c1_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1196, 2011])).
% 1.95/2.15 tff(2015,plain,
% 1.95/2.15 (c0_1(a953)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2009, 2014, 50, 2013, 2012])).
% 1.95/2.15 tff(2016,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2017,plain,
% 1.95/2.15 ((hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901))) <=> (hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2018,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[2017])).
% 1.95/2.15 tff(2019,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[2018, 2016])).
% 1.95/2.15 tff(2020,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(2021,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 1.95/2.15 tff(2022,plain,
% 1.95/2.15 ((~c1_1(a901)) | (~c0_1(a953))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2021, 112, 1680, 2014, 2012, 51, 47, 1402])).
% 1.95/2.15 tff(2023,plain,
% 1.95/2.15 (~c1_1(a901)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2022, 2015])).
% 1.95/2.15 tff(2024,plain,
% 1.95/2.15 (hskp1),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[286, 2023, 48, 51, 46, 47])).
% 1.95/2.15 tff(2025,plain,
% 1.95/2.15 (c1_1(a899)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[308, 2024])).
% 1.95/2.15 tff(2026,plain,
% 1.95/2.15 (hskp9),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1585, 2023, 51])).
% 1.95/2.15 tff(2027,plain,
% 1.95/2.15 (~c2_1(a909)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1323, 2026])).
% 1.95/2.15 tff(2028,plain,
% 1.95/2.15 (~c1_1(a909)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1329, 2026])).
% 1.95/2.15 tff(2029,plain,
% 1.95/2.15 (~c0_1(a909)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1335, 2026])).
% 1.95/2.15 tff(2030,plain,
% 1.95/2.15 (c3_1(a912)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1971, 76, 43, 48, 51, 46, 47, 801, 1674, 50])).
% 1.95/2.15 tff(2031,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2032,plain,
% 1.95/2.15 ((hskp28 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912))) <=> (hskp28 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2033,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[2032])).
% 1.95/2.15 tff(2034,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[2033, 2031])).
% 1.95/2.15 tff(2035,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c1_1(a912) | (~c3_1(a912)) | (~c2_1(a912)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(2036,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a912) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 1.95/2.15 tff(2037,plain,
% 1.95/2.15 (hskp28 | (~c0_1(a953))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2036, 112, 2014, 2012, 801, 1674, 2030, 935])).
% 1.95/2.15 tff(2038,plain,
% 1.95/2.15 (hskp28),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2037, 2015])).
% 1.95/2.15 tff(2039,plain,
% 1.95/2.15 (c3_1(a900)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[949, 2038])).
% 1.95/2.15 tff(2040,plain,
% 1.95/2.15 (c2_1(a900)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[957, 2038])).
% 1.95/2.15 tff(2041,plain,
% 1.95/2.15 (c0_1(a900)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[965, 2038])).
% 1.95/2.15 tff(2042,assumption,(hskp4), introduced(assumption)).
% 1.95/2.15 tff(2043,plain,
% 1.95/2.15 (~c3_1(a904)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[536, 2042])).
% 1.95/2.15 tff(2044,plain,
% 1.95/2.15 (~c1_1(a904)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[542, 2042])).
% 1.95/2.15 tff(2045,plain,
% 1.95/2.15 (c2_1(a904)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[605, 2042])).
% 1.95/2.15 tff(2046,assumption,(c3_1(a900)), introduced(assumption)).
% 1.95/2.15 tff(2047,assumption,(c2_1(a900)), introduced(assumption)).
% 1.95/2.15 tff(2048,assumption,(c0_1(a900)), introduced(assumption)).
% 1.95/2.15 tff(2049,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1362, 112, 2048, 2047, 2046, 2045, 1612, 1611, 1610, 2044, 2043, 870])).
% 1.95/2.15 tff(2050,plain,((~hskp4) | (~c0_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a909) | c1_1(a909) | c2_1(a909)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(2051,plain,
% 1.95/2.15 (~hskp4),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2050, 2041, 2040, 2039, 2029, 2028, 2027])).
% 1.95/2.15 tff(2052,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a953) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a953) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2053,plain,
% 1.95/2.15 ((hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953))) <=> (hskp0 | c2_1(a953) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2054,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a953) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a953)) | (~c0_1(a953))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[2053])).
% 1.95/2.15 tff(2055,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a953) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[2054, 2052])).
% 1.95/2.15 tff(2056,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(2057,plain,
% 1.95/2.15 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a953) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a953)) | (~c0_1(a953))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.95/2.15 tff(2058,plain,
% 1.95/2.15 (hskp0),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2057, 112, 2041, 2040, 2039, 2012, 2013, 1526, 2015])).
% 1.95/2.15 tff(2059,plain,
% 1.95/2.15 (c1_1(a898)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[59, 2058])).
% 1.95/2.15 tff(2060,plain,
% 1.95/2.15 (c0_1(a898)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[73, 2058])).
% 1.95/2.15 tff(2061,plain,
% 1.95/2.15 (c3_1(a898)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[120, 2060, 76, 2059, 46])).
% 1.95/2.15 tff(2062,plain,
% 1.95/2.15 (~c3_1(a907)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[921, 2051, 2060, 2061])).
% 1.95/2.15 tff(2063,plain,
% 1.95/2.15 (~hskp7),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[512, 2062])).
% 1.95/2.15 tff(2064,plain,
% 1.95/2.15 (c3_1(a899)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[530, 2063, 2025, 2051])).
% 1.95/2.15 tff(2065,plain,
% 1.95/2.15 (hskp12),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[341, 2064, 2025])).
% 1.95/2.15 tff(2066,plain,
% 1.95/2.15 (~c3_1(a913)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[347, 2065])).
% 1.95/2.15 tff(2067,plain,
% 1.95/2.15 (c0_1(a913)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[355, 2065])).
% 1.95/2.15 tff(2068,plain,
% 1.95/2.15 (~c1_1(a913)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[409, 2065])).
% 1.95/2.15 tff(2069,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[713, 2068, 2067, 2060, 2059, 2063, 76, 50, 2066])).
% 1.95/2.15 tff(2070,plain,((~hskp24) | c2_1(a898) | hskp10 | c0_1(a899) | c0_1(a907) | c1_1(a907) | hskp31 | c3_1(a901) | c0_1(a901) | c2_1(a901) | c1_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(2071,plain,
% 1.95/2.15 (c2_1(a898)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2070, 1985, 50, 43, 44, 45, 46, 48, 51, 47, 801])).
% 1.95/2.15 tff(2072,plain,
% 1.95/2.15 (~hskp0),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[65, 2071])).
% 1.95/2.15 tff(2073,plain,
% 1.95/2.15 (~hskp20),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1021, 2072, 1730])).
% 1.95/2.15 tff(2074,plain,
% 1.95/2.15 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c0_1(a953)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2075,plain,
% 1.95/2.15 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953))) <=> (hskp20 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(2076,plain,
% 1.95/2.15 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c0_1(a953))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[2075])).
% 1.95/2.15 tff(2077,plain,
% 1.95/2.15 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[2076, 2074])).
% 1.95/2.15 tff(2078,plain,
% 1.95/2.15 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c0_1(a953)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(2079,plain,
% 1.95/2.15 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c0_1(a953))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 1.95/2.15 tff(2080,plain,
% 1.95/2.15 (hskp1),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2079, 112, 2073, 1986, 1988, 42, 2010])).
% 1.95/2.15 tff(2081,plain,
% 1.95/2.15 (c1_1(a899)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[308, 2080])).
% 1.95/2.15 tff(2082,plain,
% 1.95/2.15 (c2_1(a899)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[300, 2080])).
% 1.95/2.15 tff(2083,plain,
% 1.95/2.15 (c3_1(a899)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[898, 2082, 2072, 1730])).
% 1.95/2.15 tff(2084,plain,
% 1.95/2.15 (hskp14),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[381, 2083, 2082, 2081, 43, 50])).
% 1.95/2.15 tff(2085,plain,
% 1.95/2.15 (~c1_1(a918)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[672, 2084])).
% 1.95/2.15 tff(2086,plain,
% 1.95/2.15 (c3_1(a918)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[742, 2084])).
% 1.95/2.15 tff(2087,plain,
% 1.95/2.15 (c0_1(a918)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[734, 2084])).
% 1.95/2.15 tff(2088,plain,
% 1.95/2.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a953) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a953) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2089,plain,
% 1.95/2.16 ((hskp0 | (~ndr1_0) | (~c3_1(a912)) | (~c2_1(a912)) | (~c0_1(a912)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953))) <=> (hskp0 | c2_1(a953) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2090,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a912)) | (~c2_1(a912)) | (~c0_1(a912)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a953) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c3_1(a953)) | (~c0_1(a953))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[2089])).
% 1.95/2.16 tff(2091,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a912)) | (~c2_1(a912)) | (~c0_1(a912)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a953) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[2090, 2088])).
% 1.95/2.16 tff(2092,plain,
% 1.95/2.16 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a912)) | (~c2_1(a912)) | (~c0_1(a912)) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(2093,plain,
% 1.95/2.16 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a953) | (~c2_1(a912)) | (~c3_1(a912)) | (~ndr1_0) | (~c0_1(a912)) | (~c3_1(a953)) | (~c0_1(a953))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.95/2.16 tff(2094,plain,
% 1.95/2.16 (~c0_1(a912)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2093, 112, 2072, 1987, 1988, 1674, 1977, 1526, 2010])).
% 1.95/2.16 tff(2095,plain,
% 1.95/2.16 (~c1_1(a901)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2021, 112, 1680, 1986, 1987, 51, 47, 1402, 2010])).
% 1.95/2.16 tff(2096,plain,
% 1.95/2.16 (hskp9),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1585, 2095, 51])).
% 1.95/2.16 tff(2097,plain,
% 1.95/2.16 (~c2_1(a909)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1323, 2096])).
% 1.95/2.16 tff(2098,plain,
% 1.95/2.16 (~c1_1(a909)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1329, 2096])).
% 1.95/2.16 tff(2099,plain,
% 1.95/2.16 (hskp28),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2036, 112, 1986, 1987, 801, 1674, 1977, 935, 2010])).
% 1.95/2.16 tff(2100,plain,
% 1.95/2.16 (c0_1(a900)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[965, 2099])).
% 1.95/2.16 tff(2101,plain,
% 1.95/2.16 (c3_1(a900)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[949, 2099])).
% 1.95/2.16 tff(2102,plain,
% 1.95/2.16 (c2_1(a900)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[957, 2099])).
% 1.95/2.16 tff(2103,plain,
% 1.95/2.16 (~c0_1(a909)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1335, 2096])).
% 1.95/2.16 tff(2104,plain,
% 1.95/2.16 (~hskp4),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2050, 2103, 2102, 2101, 2100, 2098, 2097])).
% 1.95/2.16 tff(2105,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a953) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a953) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2106,plain,
% 1.95/2.16 ((hskp4 | (~ndr1_0) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907))) <=> (hskp4 | c2_1(a953) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2107,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a953) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a953)) | (~c0_1(a953))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[2106])).
% 1.95/2.16 tff(2108,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a953) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[2107, 2105])).
% 1.95/2.16 tff(2109,plain,
% 1.95/2.16 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a953) | (~c3_1(a953)) | (~c0_1(a953)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(2110,plain,
% 1.95/2.16 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a953) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a953)) | (~c0_1(a953))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 1.95/2.16 tff(2111,plain,
% 1.95/2.16 (hskp4 | (~c3_1(a907))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2110, 112, 1987, 1988, 44, 45, 640, 2010])).
% 1.95/2.16 tff(2112,plain,
% 1.95/2.16 (~c3_1(a907)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2111, 2104])).
% 1.95/2.16 tff(2113,plain,
% 1.95/2.16 (~hskp7),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[512, 2112])).
% 1.95/2.16 tff(2114,plain,
% 1.95/2.16 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c1_1(a912) | (~c3_1(a912)) | (~ndr1_0) | c0_1(a912))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a912) | (~c3_1(a912)) | (~ndr1_0) | c0_1(a912))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2115,plain,
% 1.95/2.16 ((hskp8 | hskp7 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912))) <=> (hskp8 | hskp7 | c1_1(a912) | (~c3_1(a912)) | (~ndr1_0) | c0_1(a912))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2116,plain,
% 1.95/2.16 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c1_1(a912) | (~c3_1(a912)) | (~ndr1_0) | c0_1(a912)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[2115])).
% 1.95/2.16 tff(2117,plain,
% 1.95/2.16 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a912) | (~c3_1(a912)) | (~ndr1_0) | c0_1(a912))),
% 1.95/2.16 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.95/2.16 tff(2118,plain,
% 1.95/2.16 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(2119,plain,
% 1.95/2.16 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a912) | (~c3_1(a912)) | (~ndr1_0) | c0_1(a912)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.95/2.16 tff(2120,plain,
% 1.95/2.16 (hskp8 | hskp7 | (~c3_1(a912)) | c0_1(a912)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2119, 112, 801, 557])).
% 1.95/2.16 tff(2121,plain,
% 1.95/2.16 (hskp8),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2120, 2113, 1977, 2094])).
% 1.95/2.16 tff(2122,plain,
% 1.95/2.16 (~c0_1(a908)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[597, 2121])).
% 1.95/2.16 tff(2123,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1289, 2122, 2121, 2087, 2086, 1988, 2085, 2010, 1986])).
% 1.95/2.16 tff(2124,plain,(c0_1(a899) | c1_1(a912) | c0_1(a907) | c1_1(a907) | hskp10 | c0_1(a901) | c2_1(a901) | c3_1(a901) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(2125,plain,
% 1.95/2.16 (c0_1(a899)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2124, 801, 44, 45, 50, 51, 47, 48, 46])).
% 1.95/2.16 tff(2126,plain,
% 1.95/2.16 (~hskp1),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[292, 2125])).
% 1.95/2.16 tff(2127,plain,
% 1.95/2.16 (c1_1(a901)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[286, 2126, 48, 51, 46, 47])).
% 1.95/2.16 tff(2128,plain,
% 1.95/2.16 (hskp25),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1826, 2127, 48])).
% 1.95/2.16 tff(2129,plain,
% 1.95/2.16 (~c3_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1692, 2128])).
% 1.95/2.16 tff(2130,plain,
% 1.95/2.16 (~c1_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1698, 2128])).
% 1.95/2.16 tff(2131,plain,
% 1.95/2.16 (c2_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1835, 112, 50, 2130, 2129, 51, 47, 812, 2127])).
% 1.95/2.16 tff(2132,plain,
% 1.95/2.16 (~hskp0),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[140, 2127, 47, 48, 46])).
% 1.95/2.16 tff(2133,plain,
% 1.95/2.16 (~c0_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1841, 2128])).
% 1.95/2.16 tff(2134,plain,
% 1.95/2.16 (hskp17 | hskp0 | (~c2_1(a958))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1848, 112, 2133, 2129, 891])).
% 1.95/2.16 tff(2135,plain,
% 1.95/2.16 (hskp17),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2134, 2132, 2131])).
% 1.95/2.16 tff(2136,plain,
% 1.95/2.16 (hskp11),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1729, 2135, 46])).
% 1.95/2.16 tff(2137,plain,
% 1.95/2.16 (~c2_1(a912)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1679, 2136])).
% 1.95/2.16 tff(2138,plain,
% 1.95/2.16 (~c3_1(a912)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1390, 2136])).
% 1.95/2.16 tff(2139,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[858, 2138, 2137, 801, 2135, 50, 46])).
% 1.95/2.16 tff(2140,plain,(c1_1(a912) | hskp10 | hskp31 | c2_1(a901) | c3_1(a901) | c0_1(a901) | c0_1(a907) | c1_1(a907)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(2141,plain,
% 1.95/2.16 (c1_1(a912)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2140, 51, 46, 47, 48, 50, 44, 45])).
% 1.95/2.16 tff(2142,plain,
% 1.95/2.16 (((~hskp11) | (~c1_1(a912))) <=> ((~hskp11) | (~c1_1(a912)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2143,plain,
% 1.95/2.16 (((~c1_1(a912)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a912)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2144,axiom,((~c1_1(a912)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.95/2.16 tff(2145,plain,
% 1.95/2.16 ((~hskp11) | (~c1_1(a912))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2144, 2143])).
% 1.95/2.16 tff(2146,plain,
% 1.95/2.16 ((~hskp11) | (~c1_1(a912))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2145, 2142])).
% 1.95/2.16 tff(2147,plain,
% 1.95/2.16 (~hskp11),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2146, 2141])).
% 1.95/2.16 tff(2148,plain,
% 1.95/2.16 (~hskp17),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1729, 2147, 46])).
% 1.95/2.16 tff(2149,plain,
% 1.95/2.16 (c1_1(a901)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[286, 152, 48, 51, 46, 47])).
% 1.95/2.16 tff(2150,plain,
% 1.95/2.16 (hskp25),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1826, 2149, 48])).
% 1.95/2.16 tff(2151,plain,
% 1.95/2.16 (~c3_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1692, 2150])).
% 1.95/2.16 tff(2152,plain,
% 1.95/2.16 (~c1_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1698, 2150])).
% 1.95/2.16 tff(2153,plain,
% 1.95/2.16 (c3_1(a907)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1495, 1479, 32, 31])).
% 1.95/2.16 tff(2154,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a907) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2155,plain,
% 1.95/2.16 (((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c1_1(a958) | c3_1(a958) | c0_1(a907) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2156,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a907) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[2155])).
% 1.95/2.16 tff(2157,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))),
% 1.95/2.16 inference(transitivity,[status(thm)],[2156, 2154])).
% 1.95/2.16 tff(2158,plain,
% 1.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(2159,plain,
% 1.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c0_1(a901) | c2_1(a901) | (~ndr1_0) | (~c1_1(a901)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 1.95/2.16 tff(2160,plain,
% 1.95/2.16 (c2_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2159, 112, 2153, 2152, 2151, 44, 51, 47, 1721, 2149, 1479])).
% 1.95/2.16 tff(2161,plain,
% 1.95/2.16 (~c0_1(a958)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1841, 2150])).
% 1.95/2.16 tff(2162,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1848, 112, 32, 31, 2161, 2151, 891, 2160])).
% 1.95/2.16 tff(2163,plain,(hskp1 | hskp17 | hskp0 | c0_1(a907) | c0_1(a901) | c2_1(a901) | c3_1(a901) | c1_1(a907) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(2164,plain,
% 1.95/2.16 (hskp1),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2163, 2148, 800, 44, 51, 47, 48, 45, 46])).
% 1.95/2.16 tff(2165,plain,
% 1.95/2.16 (~c0_1(a899)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[292, 2164])).
% 1.95/2.16 tff(2166,plain,
% 1.95/2.16 (c1_1(a899)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[308, 2164])).
% 1.95/2.16 tff(2167,plain,
% 1.95/2.16 (c2_1(a899)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[300, 2164])).
% 1.95/2.16 tff(2168,plain,
% 1.95/2.16 (c3_1(a899)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[897, 112, 2148, 800, 2167, 2165, 891])).
% 1.95/2.16 tff(2169,plain,
% 1.95/2.16 (hskp14),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[381, 2168, 2167, 2166, 2165, 50])).
% 1.95/2.16 tff(2170,plain,
% 1.95/2.16 (~c1_1(a918)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[672, 2169])).
% 1.95/2.16 tff(2171,plain,
% 1.95/2.16 (c0_1(a918)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[734, 2169])).
% 1.95/2.16 tff(2172,plain,
% 1.95/2.16 (hskp12 | (~c3_1(a899))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[340, 112, 50, 2166, 2165, 334])).
% 1.95/2.16 tff(2173,plain,
% 1.95/2.16 (hskp12),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2172, 2168])).
% 1.95/2.16 tff(2174,plain,
% 1.95/2.16 (~c3_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[347, 2173])).
% 1.95/2.16 tff(2175,plain,
% 1.95/2.16 (c0_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[355, 2173])).
% 1.95/2.16 tff(2176,plain,
% 1.95/2.16 (c3_1(a918)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[742, 2169])).
% 1.95/2.16 tff(2177,plain,
% 1.95/2.16 (~hskp20),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1021, 800, 2148])).
% 1.95/2.16 tff(2178,plain,
% 1.95/2.16 (~c1_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[409, 2173])).
% 1.95/2.16 tff(2179,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a913))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2180,plain,
% 1.95/2.16 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a913) | c1_1(a913) | c2_1(a913)) <=> (c1_1(a913) | c3_1(a913) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a913))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2181,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a913)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[2180])).
% 1.95/2.16 tff(2182,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a913))),
% 1.95/2.16 inference(transitivity,[status(thm)],[2181, 2179])).
% 1.95/2.16 tff(2183,plain,
% 1.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a913) | c1_1(a913) | c2_1(a913))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(2184,plain,
% 1.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a913)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 1.95/2.16 tff(2185,plain,
% 1.95/2.16 ((~c1_1(a901)) | c2_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2184, 112, 312, 704, 694, 51, 47, 43, 1721, 314])).
% 1.95/2.16 tff(2186,plain,
% 1.95/2.16 (c2_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2185, 132])).
% 1.95/2.16 tff(2187,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a913) | c3_1(a913) | c0_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | (~c2_1(a913)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | (~c2_1(a913)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2188,plain,
% 1.95/2.16 (((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a901) | c0_1(a901) | (~c1_1(a901))) <=> (c1_1(a913) | c3_1(a913) | c0_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | (~c2_1(a913)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2189,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a901) | c0_1(a901) | (~c1_1(a901)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a913) | c3_1(a913) | c0_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | (~c2_1(a913))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[2188])).
% 1.95/2.16 tff(2190,plain,
% 1.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a901) | c0_1(a901) | (~c1_1(a901)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | (~c2_1(a913)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[2189, 2187])).
% 1.95/2.16 tff(2191,plain,
% 1.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a901) | c0_1(a901) | (~c1_1(a901)))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(2192,plain,
% 1.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | (~c2_1(a913))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2191, 2190])).
% 1.95/2.16 tff(2193,plain,
% 1.95/2.16 ((~c1_1(a901)) | (~c2_1(a913))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2192, 112, 312, 704, 694, 51, 48, 43, 392, 314])).
% 1.95/2.16 tff(2194,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2193, 2186, 132])).
% 1.95/2.16 tff(2195,plain,((~c1_1(a901)) | (~c2_1(a899)) | c1_1(a913) | c3_1(a913) | c0_1(a901) | c3_1(a901) | c0_1(a899) | (~c3_1(a899)) | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(2196,plain,
% 1.95/2.16 (~c1_1(a901)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2195, 2167, 2178, 2174, 51, 48, 2165, 2168, 47])).
% 1.95/2.16 tff(2197,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a913) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a913) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2198,plain,
% 1.95/2.16 ((hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a901) | c2_1(a901) | c1_1(a901)) <=> (hskp20 | c3_1(a913) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2199,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a913) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a913)) | (~c2_1(a913))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[2198])).
% 1.95/2.16 tff(2200,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a901) | c2_1(a901) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a913) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a913)) | (~c2_1(a913)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[2199, 2197])).
% 1.95/2.16 tff(2201,plain,
% 1.95/2.16 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a901) | c2_1(a901) | c1_1(a901))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(2202,plain,
% 1.95/2.16 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a913) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c0_1(a913)) | (~c2_1(a913))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 1.95/2.16 tff(2203,plain,
% 1.95/2.16 (c1_1(a901) | (~c2_1(a913))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2202, 112, 1103, 695, 694, 47, 48, 1064])).
% 1.95/2.16 tff(2204,plain,
% 1.95/2.16 (~c2_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2203, 49])).
% 1.95/2.16 tff(2205,plain,
% 1.95/2.16 (hskp18),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1082, 2204, 1038, 695, 694, 1033, 754])).
% 1.95/2.16 tff(2206,plain,
% 1.95/2.16 (~c1_1(a929)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[771, 2205])).
% 1.95/2.16 tff(2207,assumption,(c3_1(a907)), introduced(assumption)).
% 1.95/2.16 tff(2208,plain,
% 1.95/2.16 (c2_1(a929)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[781, 2205])).
% 1.95/2.16 tff(2209,plain,
% 1.95/2.16 (c0_1(a929)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[789, 2205])).
% 1.95/2.16 tff(2210,plain,
% 1.95/2.16 (hskp3),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1095, 112, 2209, 2208, 2207, 2206, 44, 45, 1032])).
% 1.95/2.16 tff(2211,plain,
% 1.95/2.16 (~c3_1(a903)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1101, 2210])).
% 1.95/2.16 tff(2212,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1131, 2211, 2210, 48, 49, 1103, 47])).
% 1.95/2.16 tff(2213,plain,(c1_1(a901) | c3_1(a901) | hskp20 | c2_1(a901) | (~c3_1(a907)) | c0_1(a907) | c1_1(a907) | (~c3_1(a918)) | (~c0_1(a913)) | c3_1(a913) | (~c0_1(a918)) | c1_1(a918)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(2214,plain,
% 1.95/2.16 (~c3_1(a907)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2213, 2196, 2177, 47, 48, 44, 45, 2176, 2175, 2174, 2171, 2170])).
% 1.95/2.16 tff(2215,plain,
% 1.95/2.16 (c1_1(a901) | (~c2_1(a913))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2202, 112, 2177, 2175, 2174, 47, 48, 1064])).
% 1.95/2.16 tff(2216,plain,
% 1.95/2.16 (~c2_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2215, 2196])).
% 1.95/2.16 tff(2217,plain,
% 1.95/2.16 (hskp7 | c2_1(a913)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[701, 112, 50, 2175, 2174, 693])).
% 1.95/2.16 tff(2218,plain,
% 1.95/2.16 (hskp7),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2217, 2216])).
% 1.95/2.16 tff(2219,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[512, 2218, 2214])).
% 1.95/2.16 tff(2220,plain,(c0_1(a901) | hskp10 | c2_1(a901) | c3_1(a901) | c0_1(a907) | c1_1(a907) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(2221,plain,
% 1.95/2.16 (c0_1(a901)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2220, 50, 47, 48, 44, 45, 46])).
% 1.95/2.16 tff(2222,plain,
% 1.95/2.16 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2223,plain,
% 1.95/2.16 ((hskp31 | (~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c0_1(a901)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901))) <=> (hskp31 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(2224,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c0_1(a901)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2223])).
% 1.95/2.17 tff(2225,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c0_1(a901)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[2224, 2222])).
% 1.95/2.17 tff(2226,plain,
% 1.95/2.17 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c0_1(a901)) | c3_1(a901) | c2_1(a901) | (~c1_1(a901)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(2227,plain,
% 1.95/2.17 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | (~c1_1(a901))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 1.95/2.17 tff(2228,plain,
% 1.95/2.17 ((~c0_1(a901)) | (~c1_1(a901))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2227, 46, 112, 47, 48, 10])).
% 1.95/2.17 tff(2229,plain,
% 1.95/2.17 (~c1_1(a901)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2228, 2221])).
% 1.95/2.17 tff(2230,plain,
% 1.95/2.17 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2231,plain,
% 1.95/2.17 ((hskp10 | hskp7 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901))) <=> (hskp10 | hskp7 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2232,plain,
% 1.95/2.17 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2231])).
% 1.95/2.17 tff(2233,plain,
% 1.95/2.17 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0))),
% 1.95/2.17 inference(transitivity,[status(thm)],[2232, 2230])).
% 1.95/2.17 tff(2234,plain,
% 1.95/2.17 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(2235,plain,
% 1.95/2.17 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | (~ndr1_0)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 1.95/2.17 tff(2236,plain,
% 1.95/2.17 (hskp10 | hskp7 | (~c0_1(a901)) | c3_1(a901)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2235, 112, 47, 693])).
% 1.95/2.17 tff(2237,plain,
% 1.95/2.17 (hskp7),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2236, 2221, 50, 48])).
% 1.95/2.17 tff(2238,plain,
% 1.95/2.17 (c3_1(a907)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[512, 2237])).
% 1.95/2.17 tff(2239,plain,
% 1.95/2.17 (c3_1(a898)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[120, 60, 66, 74, 46])).
% 1.95/2.17 tff(2240,plain,
% 1.95/2.17 (hskp4),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[646, 112, 2207, 74, 44, 45, 66, 640, 2239])).
% 1.95/2.17 tff(2241,plain,
% 1.95/2.17 (~c3_1(a904)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[536, 2240])).
% 1.95/2.17 tff(2242,plain,
% 1.95/2.17 (~c1_1(a904)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[542, 2240])).
% 1.95/2.17 tff(2243,assumption,(c0_1(a901)), introduced(assumption)).
% 1.95/2.17 tff(2244,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~c0_1(a901)) | c2_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a901))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a901)) | c2_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a901))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2245,plain,
% 1.95/2.17 ((hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c1_1(a901) | (~c0_1(a901))) <=> (hskp22 | (~c0_1(a901)) | c2_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a901))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2246,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c1_1(a901) | (~c0_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~c0_1(a901)) | c2_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a901)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2245])).
% 1.95/2.17 tff(2247,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c1_1(a901) | (~c0_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a901)) | c2_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a901))),
% 1.95/2.17 inference(transitivity,[status(thm)],[2246, 2244])).
% 1.95/2.17 tff(2248,plain,
% 1.95/2.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a898) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a901) | c1_1(a901) | (~c0_1(a901)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(2249,plain,
% 1.95/2.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a901)) | c2_1(a901) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | c1_1(a901)),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 1.95/2.17 tff(2250,plain,
% 1.95/2.17 (hskp22),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2249, 112, 74, 2243, 47, 66, 1234, 49, 2239])).
% 1.95/2.17 tff(2251,plain,
% 1.95/2.17 (~c3_1(a939)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1247, 2250])).
% 1.95/2.17 tff(2252,plain,
% 1.95/2.17 (~c0_1(a939)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1253, 2250])).
% 1.95/2.17 tff(2253,plain,
% 1.95/2.17 (c2_1(a904)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[605, 2240])).
% 1.95/2.17 tff(2254,plain,
% 1.95/2.17 (c1_1(a939)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1262, 2250])).
% 1.95/2.17 tff(2255,plain,
% 1.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c0_1(a907) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c0_1(a907) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2256,plain,
% 1.95/2.17 (((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c0_1(a939) | c3_1(a939) | c0_1(a907) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2257,plain,
% 1.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c0_1(a907) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2256])).
% 1.95/2.17 tff(2258,plain,
% 1.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c0_1(a907) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[2257, 2255])).
% 1.95/2.17 tff(2259,plain,
% 1.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(2260,plain,
% 1.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c0_1(a907) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[2259, 2258])).
% 1.95/2.17 tff(2261,plain,
% 1.95/2.17 (~c2_1(a907)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2260, 112, 2254, 2207, 2253, 2252, 2251, 44, 2242, 2241, 392])).
% 1.95/2.17 tff(2262,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[664, 112, 2207, 2253, 60, 44, 2242, 2241, 66, 503, 2261, 2239])).
% 1.95/2.17 tff(2263,plain,((~hskp0) | (~c3_1(a907)) | c0_1(a907) | c1_1(a907) | (~c0_1(a901)) | c2_1(a901) | c1_1(a901) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(2264,plain,
% 1.95/2.17 (~hskp0),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2263, 2238, 44, 45, 2221, 47, 2229, 46])).
% 1.95/2.17 tff(2265,plain,
% 1.95/2.17 (hskp7),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2236, 2243, 50, 48])).
% 1.95/2.17 tff(2266,plain,
% 1.95/2.17 (c3_1(a907)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[512, 2265])).
% 1.95/2.17 tff(2267,plain,
% 1.95/2.17 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2268,plain,
% 1.95/2.17 ((hskp24 | hskp17 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907))) <=> (hskp24 | hskp17 | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2269,plain,
% 1.95/2.17 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2268])).
% 1.95/2.17 tff(2270,plain,
% 1.95/2.17 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[2269, 2267])).
% 1.95/2.17 tff(2271,plain,
% 1.95/2.17 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(2272,plain,
% 1.95/2.17 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.95/2.17 tff(2273,plain,
% 1.95/2.17 (hskp24 | hskp17 | (~c2_1(a907)) | (~c3_1(a907))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2272, 112, 45, 1169])).
% 1.95/2.17 tff(2274,plain,
% 1.95/2.17 (hskp24),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2273, 1479, 32, 2207])).
% 1.95/2.17 tff(2275,plain,
% 1.95/2.17 (~c2_1(a953)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1209, 2274])).
% 1.95/2.17 tff(2276,plain,
% 1.95/2.17 (c1_1(a953)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1196, 2274])).
% 1.95/2.17 tff(2277,plain,
% 1.95/2.17 (c3_1(a953)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1188, 2274])).
% 1.95/2.17 tff(2278,plain,
% 1.95/2.17 (c0_1(a953)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2009, 2277, 2276, 2275, 50])).
% 1.95/2.17 tff(2279,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2079, 112, 1884, 152, 2276, 2275, 42, 2278])).
% 1.95/2.17 tff(2280,plain,(hskp1 | hskp10 | hskp17 | (~c3_1(a907)) | c1_1(a907) | hskp0 | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(2281,plain,
% 1.95/2.17 (hskp1),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2280, 32, 50, 2266, 45, 31, 44])).
% 1.95/2.17 tff(2282,plain,
% 1.95/2.17 (c2_1(a899)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[300, 2281])).
% 1.95/2.17 tff(2283,plain,
% 1.95/2.17 (c1_1(a899)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[308, 2281])).
% 1.95/2.17 tff(2284,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2285,plain,
% 1.95/2.17 ((hskp14 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp14 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(2286,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[2285])).
% 1.95/2.17 tff(2287,plain,
% 1.95/2.17 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.95/2.17 inference(transitivity,[status(thm)],[2286, 2284])).
% 1.95/2.17 tff(2288,plain,
% 1.95/2.17 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a901) | c3_1(a901) | (~c0_1(a901)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(2289,plain,
% 1.95/2.17 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | (~c0_1(a901)) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[2288, 2287])).
% 1.95/2.17 tff(2290,plain,
% 1.95/2.17 (hskp14 | (~c2_1(a899)) | (~c1_1(a899))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2289, 112, 2243, 47, 48, 43, 373])).
% 1.95/2.17 tff(2291,plain,
% 1.95/2.17 (hskp14),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2290, 2283, 2282])).
% 1.95/2.17 tff(2292,plain,
% 1.95/2.17 (~c1_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[672, 2291])).
% 1.95/2.17 tff(2293,plain,
% 1.95/2.17 (c0_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[734, 2291])).
% 1.95/2.17 tff(2294,plain,
% 1.95/2.17 (c3_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[742, 2291])).
% 1.95/2.17 tff(2295,plain,
% 1.95/2.17 (hskp17 | c3_1(a899) | (~c2_1(a899))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[897, 112, 31, 43, 891])).
% 1.95/2.17 tff(2296,plain,
% 1.95/2.17 (c3_1(a899)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2295, 2282, 32])).
% 1.95/2.17 tff(2297,plain,
% 1.95/2.17 (hskp12),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[341, 2296, 2283])).
% 1.95/2.17 tff(2298,plain,
% 1.95/2.17 (c0_1(a913)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[355, 2297])).
% 1.95/2.17 tff(2299,plain,
% 1.95/2.17 (~c3_1(a913)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[347, 2297])).
% 1.95/2.17 tff(2300,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2213, 2299, 2298, 49, 47, 48, 44, 45, 2266, 1884, 2294, 2293, 2292])).
% 1.95/2.17 tff(2301,plain,(hskp17 | c1_1(a901) | c2_1(a901) | c3_1(a901) | c0_1(a907) | c1_1(a907) | hskp10 | c0_1(a899) | hskp0 | (~c0_1(a901))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(2302,plain,
% 1.95/2.17 (hskp17),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2301, 43, 47, 48, 44, 45, 50, 2229, 2264, 2221])).
% 1.95/2.17 tff(2303,plain,
% 1.95/2.17 (hskp11),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1729, 2302, 46])).
% 1.95/2.17 tff(2304,plain,
% 1.95/2.17 (~c1_1(a912)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2146, 2303])).
% 1.95/2.17 tff(2305,plain,
% 1.95/2.17 (~c2_1(a912)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1679, 2303])).
% 1.95/2.17 tff(2306,plain,
% 1.95/2.17 (hskp1),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2280, 859, 50, 2238, 45, 31, 44])).
% 1.95/2.17 tff(2307,plain,
% 1.95/2.17 (c2_1(a899)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[300, 2306])).
% 1.95/2.17 tff(2308,plain,
% 1.95/2.17 (c1_1(a899)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[308, 2306])).
% 1.95/2.17 tff(2309,plain,
% 1.95/2.17 (hskp14 | (~c2_1(a899)) | (~c1_1(a899))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2289, 112, 2221, 47, 48, 43, 373])).
% 1.95/2.17 tff(2310,plain,
% 1.95/2.17 (hskp14),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2309, 2308, 2307])).
% 1.95/2.17 tff(2311,plain,
% 1.95/2.17 (c3_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[742, 2310])).
% 1.95/2.17 tff(2312,plain,
% 1.95/2.17 (c0_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[734, 2310])).
% 1.95/2.17 tff(2313,plain,
% 1.95/2.17 (~c1_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[672, 2310])).
% 1.95/2.17 tff(2314,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1156, 2313, 2312, 2229, 47, 44, 45, 48, 802, 31, 50, 801, 813, 2311, 2308, 43, 859, 2307])).
% 1.95/2.17 tff(2315,plain,(c3_1(a912) | c2_1(a901) | c0_1(a907) | c1_1(a907) | c3_1(a901) | c2_1(a912) | hskp0 | hskp10 | c1_1(a912) | c0_1(a899) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(2316,plain,
% 1.95/2.17 (c3_1(a912)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2315, 31, 44, 45, 48, 802, 47, 50, 801, 43, 46])).
% 1.95/2.17 tff(2317,plain,
% 1.95/2.17 (~hskp17),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1470, 2316, 801, 802, 46])).
% 1.95/2.17 tff(2318,plain,
% 1.95/2.17 (hskp1),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2280, 2317, 50, 2238, 45, 31, 44])).
% 1.95/2.17 tff(2319,plain,
% 1.95/2.17 (c2_1(a899)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[300, 2318])).
% 1.95/2.17 tff(2320,plain,
% 1.95/2.17 (c1_1(a899)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[308, 2318])).
% 1.95/2.17 tff(2321,plain,
% 1.95/2.17 (hskp14),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2309, 2320, 2319])).
% 1.95/2.17 tff(2322,plain,
% 1.95/2.17 (~c1_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[672, 2321])).
% 1.95/2.17 tff(2323,plain,
% 1.95/2.17 (c0_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[734, 2321])).
% 1.95/2.17 tff(2324,plain,
% 1.95/2.17 (c3_1(a918)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[742, 2321])).
% 1.95/2.17 tff(2325,plain,
% 1.95/2.17 (~hskp20),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1021, 2317, 31])).
% 1.95/2.17 tff(2326,plain,
% 2.01/2.17 (c3_1(a899)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[898, 2319, 31, 2317])).
% 2.01/2.17 tff(2327,plain,
% 2.01/2.17 (hskp12),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[341, 2326, 2320])).
% 2.01/2.17 tff(2328,plain,
% 2.01/2.17 (c0_1(a913)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[355, 2327])).
% 2.01/2.17 tff(2329,plain,
% 2.01/2.17 (~c3_1(a913)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[347, 2327])).
% 2.01/2.17 tff(2330,plain,
% 2.01/2.17 ($false),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2213, 2329, 2328, 2229, 47, 48, 44, 45, 2238, 2325, 2324, 2323, 2322])).
% 2.01/2.17 tff(2331,plain,(hskp0 | c2_1(a901) | c3_1(a901) | c0_1(a907) | c1_1(a907) | hskp10 | c0_1(a899) | c1_1(a912) | c2_1(a912) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.01/2.17 tff(2332,plain,
% 2.01/2.17 ($false),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2331, 2305, 2304, 48, 44, 45, 50, 2264, 43, 47, 46])).
% 2.01/2.17 tff(2333,plain,(c0_1(a899) | c3_1(a901) | c0_1(a907) | c1_1(a907) | hskp10 | c2_1(a901) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.01/2.17 tff(2334,plain,
% 2.01/2.17 (c0_1(a899)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2333, 50, 44, 45, 48, 47, 46])).
% 2.01/2.17 tff(2335,plain,
% 2.01/2.17 (~hskp1),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[292, 2334])).
% 2.01/2.17 tff(2336,plain,
% 2.01/2.17 (hskp17),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2280, 2335, 50, 2238, 45, 2264, 44])).
% 2.01/2.17 tff(2337,plain,
% 2.01/2.17 (hskp11),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[1729, 2336, 46])).
% 2.01/2.17 tff(2338,plain,
% 2.01/2.17 (~c2_1(a912)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[1679, 2337])).
% 2.01/2.17 tff(2339,plain,
% 2.01/2.17 (~c1_1(a912)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2146, 2337])).
% 2.01/2.17 tff(2340,plain,
% 2.01/2.17 (~c3_1(a912)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[1390, 2337])).
% 2.01/2.17 tff(2341,plain,
% 2.01/2.17 ($false),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[858, 2340, 2339, 2336, 2338, 50, 46])).
% 2.01/2.17 tff(2342,plain,(hskp10 | hskp31 | c1_1(a907) | c0_1(a907) | c3_1(a901) | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.17 tff(2343,plain,
% 2.01/2.17 (hskp10),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2342, 48, 45, 44, 46, 47])).
% 2.01/2.17 tff(2344,plain,
% 2.01/2.17 (((~hskp10) | (~c2_1(a910))) <=> ((~hskp10) | (~c2_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2345,plain,
% 2.01/2.17 (((~c2_1(a910)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2346,axiom,((~c2_1(a910)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 2.01/2.17 tff(2347,plain,
% 2.01/2.17 ((~hskp10) | (~c2_1(a910))),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 2.01/2.17 tff(2348,plain,
% 2.01/2.17 ((~hskp10) | (~c2_1(a910))),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2347, 2344])).
% 2.01/2.17 tff(2349,plain,
% 2.01/2.17 (~c2_1(a910)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2348, 2343])).
% 2.01/2.17 tff(2350,plain,
% 2.01/2.17 (((~hskp10) | (~c0_1(a910))) <=> ((~hskp10) | (~c0_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2351,plain,
% 2.01/2.17 (((~c0_1(a910)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2352,axiom,((~c0_1(a910)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 2.01/2.17 tff(2353,plain,
% 2.01/2.17 ((~hskp10) | (~c0_1(a910))),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2352, 2351])).
% 2.01/2.17 tff(2354,plain,
% 2.01/2.17 ((~hskp10) | (~c0_1(a910))),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2353, 2350])).
% 2.01/2.17 tff(2355,plain,
% 2.01/2.17 (~c0_1(a910)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2354, 2343])).
% 2.01/2.17 tff(2356,plain,
% 2.01/2.17 (((~hskp10) | c1_1(a910)) <=> ((~hskp10) | c1_1(a910))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2357,axiom,((~hskp10) | c1_1(a910)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 2.01/2.17 tff(2358,plain,
% 2.01/2.17 ((~hskp10) | c1_1(a910)),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 2.01/2.17 tff(2359,plain,
% 2.01/2.17 ((~hskp10) | c1_1(a910)),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2358, 2356])).
% 2.01/2.17 tff(2360,plain,
% 2.01/2.17 ((~hskp10) | c1_1(a910)),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2359, 2356])).
% 2.01/2.17 tff(2361,plain,
% 2.01/2.17 ((~hskp10) | c1_1(a910)),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2360, 2356])).
% 2.01/2.17 tff(2362,plain,
% 2.01/2.17 ((~hskp10) | c1_1(a910)),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2361, 2356])).
% 2.01/2.17 tff(2363,plain,
% 2.01/2.17 (c1_1(a910)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2362, 2343])).
% 2.01/2.17 tff(2364,assumption,(~c2_1(a910)), introduced(assumption)).
% 2.01/2.17 tff(2365,assumption,(~c0_1(a910)), introduced(assumption)).
% 2.01/2.17 tff(2366,assumption,(c1_1(a910)), introduced(assumption)).
% 2.01/2.17 tff(2367,plain,
% 2.01/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a910) | c2_1(a910) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a910) | c2_1(a910) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2368,plain,
% 2.01/2.17 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901)) <=> (c0_1(a910) | c2_1(a910) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2369,plain,
% 2.01/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a910) | c2_1(a910) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910))))),
% 2.01/2.17 inference(monotonicity,[status(thm)],[2368])).
% 2.01/2.17 tff(2370,plain,
% 2.01/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a910) | c2_1(a910) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)))),
% 2.01/2.17 inference(transitivity,[status(thm)],[2369, 2367])).
% 2.01/2.17 tff(2371,plain,
% 2.01/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901))),
% 2.01/2.17 inference(quant_inst,[status(thm)],[])).
% 2.01/2.17 tff(2372,plain,
% 2.01/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a910) | c2_1(a910) | c2_1(a901) | c3_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910))),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 2.01/2.17 tff(2373,plain,
% 2.01/2.17 ((~c3_1(a899)) | (~c2_1(a899))),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2372, 112, 2366, 2365, 2364, 47, 48, 43, 1721, 49])).
% 2.01/2.17 tff(2374,plain,
% 2.01/2.17 (~c3_1(a899)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2373, 312])).
% 2.01/2.17 tff(2375,plain,
% 2.01/2.17 ($false),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2295, 2374, 312, 32])).
% 2.01/2.17 tff(2376,plain,((~c2_1(a899)) | hskp17 | hskp0 | c0_1(a899) | (~c1_1(a910)) | c0_1(a910) | c2_1(a910) | c2_1(a901) | c3_1(a901) | c1_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.17 tff(2377,plain,
% 2.01/2.17 (~c2_1(a899)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2376, 32, 31, 43, 2366, 2365, 2364, 47, 48, 49])).
% 2.01/2.17 tff(2378,plain,
% 2.01/2.17 (~hskp1),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[300, 2377])).
% 2.01/2.17 tff(2379,plain,
% 2.01/2.17 (c2_1(a907)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[1478, 2378, 45, 31])).
% 2.01/2.17 tff(2380,plain,
% 2.01/2.17 (c3_1(a907)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[1495, 2379, 32, 31])).
% 2.01/2.17 tff(2381,plain,
% 2.01/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a910) | c2_1(a910) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a910) | c2_1(a910) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2382,plain,
% 2.01/2.17 (((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901)) <=> (c0_1(a910) | c2_1(a910) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))),
% 2.01/2.17 inference(rewrite,[status(thm)],[])).
% 2.01/2.17 tff(2383,plain,
% 2.01/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a910) | c2_1(a910) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910))))),
% 2.01/2.17 inference(monotonicity,[status(thm)],[2382])).
% 2.01/2.17 tff(2384,plain,
% 2.01/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a910) | c2_1(a910) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))),
% 2.01/2.17 inference(transitivity,[status(thm)],[2383, 2381])).
% 2.01/2.17 tff(2385,plain,
% 2.01/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a901) | c1_1(a901) | c2_1(a901))),
% 2.01/2.17 inference(quant_inst,[status(thm)],[])).
% 2.01/2.17 tff(2386,plain,
% 2.01/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a910) | c2_1(a910) | c0_1(a907) | c2_1(a901) | c3_1(a901) | (~ndr1_0) | c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910))),
% 2.01/2.17 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 2.01/2.17 tff(2387,plain,
% 2.01/2.17 (c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907))),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2386, 112, 2366, 2365, 2364, 44, 47, 48, 1721])).
% 2.01/2.17 tff(2388,plain,
% 2.01/2.17 ($false),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2387, 2380, 2379, 49])).
% 2.01/2.17 tff(2389,plain,(hskp17 | c1_1(a901) | (~c1_1(a910)) | c0_1(a910) | c2_1(a910) | c0_1(a907) | c2_1(a901) | c3_1(a901) | hskp0 | c1_1(a907) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.17 tff(2390,plain,
% 2.01/2.17 (hskp17),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[2389, 43, 2363, 2355, 2349, 44, 47, 48, 31, 45, 49])).
% 2.01/2.17 tff(2391,plain,
% 2.01/2.17 (~c3_1(a928)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[828, 2390])).
% 2.01/2.17 tff(2392,plain,
% 2.01/2.17 (~c2_1(a928)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[834, 2390])).
% 2.01/2.17 tff(2393,plain,
% 2.01/2.17 (c1_1(a928)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[842, 2390])).
% 2.01/2.17 tff(2394,plain,
% 2.01/2.17 (~c0_1(a928)),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[849, 46, 112, 2393, 2392, 2391, 10])).
% 2.01/2.17 tff(2395,plain,
% 2.01/2.17 (hskp11),
% 2.01/2.17 inference(unit_resolution,[status(thm)],[1729, 2390, 46])).
% 2.01/2.18 tff(2396,plain,
% 2.01/2.18 (~c3_1(a912)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1390, 2395])).
% 2.01/2.18 tff(2397,plain,
% 2.01/2.18 (~c2_1(a912)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1679, 2395])).
% 2.01/2.18 tff(2398,plain,
% 2.01/2.18 (~c1_1(a912)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2146, 2395])).
% 2.01/2.18 tff(2399,plain,
% 2.01/2.18 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2400,plain,
% 2.01/2.18 ((hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a928) | c2_1(a928) | c0_1(a928)) <=> (hskp9 | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2401,plain,
% 2.01/2.18 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a928) | c2_1(a928) | c0_1(a928))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928)))),
% 2.01/2.18 inference(monotonicity,[status(thm)],[2400])).
% 2.01/2.18 tff(2402,plain,
% 2.01/2.18 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a928) | c2_1(a928) | c0_1(a928))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928))),
% 2.01/2.18 inference(transitivity,[status(thm)],[2401, 2399])).
% 2.01/2.18 tff(2403,plain,
% 2.01/2.18 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c3_1(a912) | c3_1(a928) | c2_1(a928) | c0_1(a928))),
% 2.01/2.18 inference(quant_inst,[status(thm)],[])).
% 2.01/2.18 tff(2404,plain,
% 2.01/2.18 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c2_1(a928) | c3_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | c0_1(a928)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 2.01/2.18 tff(2405,plain,
% 2.01/2.18 (hskp9),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2404, 112, 2392, 2391, 2398, 2397, 2396, 1310, 2394])).
% 2.01/2.18 tff(2406,plain,
% 2.01/2.18 (~c2_1(a909)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1323, 2405])).
% 2.01/2.18 tff(2407,plain,
% 2.01/2.18 (~c1_1(a909)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1329, 2405])).
% 2.01/2.18 tff(2408,plain,
% 2.01/2.18 (~c0_1(a909)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1335, 2405])).
% 2.01/2.18 tff(2409,plain,
% 2.01/2.18 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2410,plain,
% 2.01/2.18 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a909) | c1_1(a909) | c0_1(a909)) <=> (hskp1 | hskp0 | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2411,plain,
% 2.01/2.18 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a909) | c1_1(a909) | c0_1(a909))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0)))),
% 2.01/2.18 inference(monotonicity,[status(thm)],[2410])).
% 2.01/2.18 tff(2412,plain,
% 2.01/2.18 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a909) | c1_1(a909) | c0_1(a909))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0))),
% 2.01/2.18 inference(transitivity,[status(thm)],[2411, 2409])).
% 2.01/2.18 tff(2413,plain,
% 2.01/2.18 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a909) | c1_1(a909) | c0_1(a909))),
% 2.01/2.18 inference(quant_inst,[status(thm)],[])).
% 2.01/2.18 tff(2414,plain,
% 2.01/2.18 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2413, 2412])).
% 2.01/2.18 tff(2415,plain,
% 2.01/2.18 (hskp1),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2414, 112, 31, 2408, 2407, 2406, 20])).
% 2.01/2.18 tff(2416,plain,
% 2.01/2.18 (c2_1(a899)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[300, 2415])).
% 2.01/2.18 tff(2417,plain,
% 2.01/2.18 ((~c3_1(a899)) | (~c2_1(a899))),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2372, 112, 2363, 2355, 2349, 47, 48, 43, 1721, 49])).
% 2.01/2.18 tff(2418,plain,
% 2.01/2.18 (~c3_1(a899)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2417, 2416])).
% 2.01/2.18 tff(2419,plain,
% 2.01/2.18 (c1_1(a899)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[308, 2415])).
% 2.01/2.18 tff(2420,plain,
% 2.01/2.18 (hskp4),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[530, 547, 311, 504])).
% 2.01/2.18 tff(2421,plain,
% 2.01/2.18 (~c3_1(a904)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[536, 2420])).
% 2.01/2.18 tff(2422,plain,
% 2.01/2.18 (~c1_1(a904)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[542, 2420])).
% 2.01/2.18 tff(2423,assumption,(~c3_1(a928)), introduced(assumption)).
% 2.01/2.18 tff(2424,plain,
% 2.01/2.18 (hskp9),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2404, 112, 1403, 2423, 801, 802, 813, 1310, 1392])).
% 2.01/2.18 tff(2425,plain,
% 2.01/2.18 (~c2_1(a909)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1323, 2424])).
% 2.01/2.18 tff(2426,plain,
% 2.01/2.18 (~c1_1(a909)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1329, 2424])).
% 2.01/2.18 tff(2427,plain,
% 2.01/2.18 (~c0_1(a909)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1335, 2424])).
% 2.01/2.18 tff(2428,plain,
% 2.01/2.18 (c2_1(a904)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[605, 2420])).
% 2.01/2.18 tff(2429,plain,
% 2.01/2.18 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2430,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2429])).
% 2.01/2.18 tff(2431,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2432,plain,
% 2.01/2.18 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2433,plain,
% 2.01/2.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2432])).
% 2.01/2.18 tff(2434,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 2.01/2.18 tff(2435,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 2.01/2.18 tff(2436,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2435, 2431])).
% 2.01/2.18 tff(2437,plain,(
% 2.01/2.18 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.01/2.18 inference(skolemize,[status(sab)],[2436])).
% 2.01/2.18 tff(2438,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2437, 2430])).
% 2.01/2.18 tff(2439,plain,
% 2.01/2.18 (^[U: $i] : refl((hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2440,plain,
% 2.01/2.18 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2439])).
% 2.01/2.18 tff(2441,plain,
% 2.01/2.18 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2442,plain,
% 2.01/2.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp15) <=> ((hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp15))), rewrite(((hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp15) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp15) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2443,plain,
% 2.01/2.18 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp15) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2442])).
% 2.01/2.18 tff(2444,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 2.01/2.18 tff(2445,plain,
% 2.01/2.18 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 2.01/2.18 tff(2446,plain,
% 2.01/2.18 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2445, 2441])).
% 2.01/2.18 tff(2447,plain,(
% 2.01/2.18 ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.01/2.18 inference(skolemize,[status(sab)],[2446])).
% 2.01/2.18 tff(2448,plain,
% 2.01/2.18 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2447, 2440])).
% 2.01/2.18 tff(2449,assumption,(~c3_1(a904)), introduced(assumption)).
% 2.01/2.18 tff(2450,assumption,(~c1_1(a904)), introduced(assumption)).
% 2.01/2.18 tff(2451,assumption,(c2_1(a904)), introduced(assumption)).
% 2.01/2.18 tff(2452,plain,
% 2.01/2.18 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp29 | hskp15 | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2453,plain,
% 2.01/2.18 ((hskp29 | hskp15 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904))) <=> (hskp29 | hskp15 | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2454,plain,
% 2.01/2.18 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904))))),
% 2.01/2.18 inference(monotonicity,[status(thm)],[2453])).
% 2.01/2.18 tff(2455,plain,
% 2.01/2.18 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp29 | hskp15 | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)))),
% 2.01/2.18 inference(transitivity,[status(thm)],[2454, 2452])).
% 2.01/2.18 tff(2456,plain,
% 2.01/2.18 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)))),
% 2.01/2.18 inference(quant_inst,[status(thm)],[])).
% 2.01/2.18 tff(2457,plain,
% 2.01/2.18 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp29 | hskp15 | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2456, 2455])).
% 2.01/2.18 tff(2458,plain,
% 2.01/2.18 (hskp29 | hskp15),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2457, 112, 2451, 2450, 2449, 2448])).
% 2.01/2.18 tff(2459,plain,
% 2.01/2.18 (hskp15),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2458, 86])).
% 2.01/2.18 tff(2460,plain,
% 2.01/2.18 (((~hskp15) | (~c3_1(a921))) <=> ((~hskp15) | (~c3_1(a921)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2461,plain,
% 2.01/2.18 (((~c3_1(a921)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a921)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2462,axiom,((~c3_1(a921)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 2.01/2.18 tff(2463,plain,
% 2.01/2.18 ((~hskp15) | (~c3_1(a921))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 2.01/2.18 tff(2464,plain,
% 2.01/2.18 ((~hskp15) | (~c3_1(a921))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2463, 2460])).
% 2.01/2.18 tff(2465,plain,
% 2.01/2.18 (~c3_1(a921)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2464, 2459])).
% 2.01/2.18 tff(2466,plain,
% 2.01/2.18 (((~hskp15) | c1_1(a921)) <=> ((~hskp15) | c1_1(a921))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2467,axiom,((~hskp15) | c1_1(a921)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 2.01/2.18 tff(2468,plain,
% 2.01/2.18 ((~hskp15) | c1_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2467, 2466])).
% 2.01/2.18 tff(2469,plain,
% 2.01/2.18 ((~hskp15) | c1_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2468, 2466])).
% 2.01/2.18 tff(2470,plain,
% 2.01/2.18 ((~hskp15) | c1_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2469, 2466])).
% 2.01/2.18 tff(2471,plain,
% 2.01/2.18 ((~hskp15) | c1_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2470, 2466])).
% 2.01/2.18 tff(2472,plain,
% 2.01/2.18 ((~hskp15) | c1_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2471, 2466])).
% 2.01/2.18 tff(2473,plain,
% 2.01/2.18 (c1_1(a921)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2472, 2459])).
% 2.01/2.18 tff(2474,plain,
% 2.01/2.18 (((~hskp15) | c0_1(a921)) <=> ((~hskp15) | c0_1(a921))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2475,axiom,((~hskp15) | c0_1(a921)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 2.01/2.18 tff(2476,plain,
% 2.01/2.18 ((~hskp15) | c0_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2475, 2474])).
% 2.01/2.18 tff(2477,plain,
% 2.01/2.18 ((~hskp15) | c0_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2476, 2474])).
% 2.01/2.18 tff(2478,plain,
% 2.01/2.18 ((~hskp15) | c0_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2477, 2474])).
% 2.01/2.18 tff(2479,plain,
% 2.01/2.18 ((~hskp15) | c0_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2478, 2474])).
% 2.01/2.18 tff(2480,plain,
% 2.01/2.18 ((~hskp15) | c0_1(a921)),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2479, 2474])).
% 2.01/2.18 tff(2481,plain,
% 2.01/2.18 (c0_1(a921)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2480, 2459])).
% 2.01/2.18 tff(2482,plain,
% 2.01/2.18 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c2_1(a928) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a928) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2483,plain,
% 2.01/2.18 ((hskp29 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (hskp29 | c2_1(a928) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2484,plain,
% 2.01/2.18 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c2_1(a928) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | c0_1(a928) | (~c1_1(a928))))),
% 2.01/2.18 inference(monotonicity,[status(thm)],[2483])).
% 2.01/2.18 tff(2485,plain,
% 2.01/2.18 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a928) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.18 inference(transitivity,[status(thm)],[2484, 2482])).
% 2.01/2.18 tff(2486,plain,
% 2.01/2.18 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.18 inference(quant_inst,[status(thm)],[])).
% 2.01/2.18 tff(2487,plain,
% 2.01/2.18 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a928) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | c0_1(a928) | (~c1_1(a928))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 2.01/2.18 tff(2488,plain,
% 2.01/2.18 ($false),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2487, 112, 86, 1404, 2481, 2473, 1403, 2465, 2438, 1392])).
% 2.01/2.18 tff(2489,plain,(hskp29 | (~c1_1(a928)) | c2_1(a928) | c0_1(a928) | (~c2_1(a904)) | c1_1(a904) | c3_1(a904)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.18 tff(2490,plain,
% 2.01/2.18 (hskp29),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2489, 2428, 1403, 1392, 1404, 2422, 2421])).
% 2.01/2.18 tff(2491,plain,
% 2.01/2.18 (c3_1(a911)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1412, 2490])).
% 2.01/2.18 tff(2492,plain,
% 2.01/2.18 (c0_1(a911)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[1428, 2490])).
% 2.01/2.18 tff(2493,plain,
% 2.01/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a911)) | (~c0_1(a911)) | (~c2_1(a911)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a911)) | (~c0_1(a911)) | (~c2_1(a911)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2494,plain,
% 2.01/2.18 (((~ndr1_0) | (~c3_1(a911)) | (~c2_1(a911)) | (~c0_1(a911)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909)) <=> (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a911)) | (~c0_1(a911)) | (~c2_1(a911)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2495,plain,
% 2.01/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a911)) | (~c2_1(a911)) | (~c0_1(a911)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a911)) | (~c0_1(a911)) | (~c2_1(a911))))),
% 2.01/2.18 inference(monotonicity,[status(thm)],[2494])).
% 2.01/2.18 tff(2496,plain,
% 2.01/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a911)) | (~c2_1(a911)) | (~c0_1(a911)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a911)) | (~c0_1(a911)) | (~c2_1(a911)))),
% 2.01/2.18 inference(transitivity,[status(thm)],[2495, 2493])).
% 2.01/2.18 tff(2497,plain,
% 2.01/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a911)) | (~c2_1(a911)) | (~c0_1(a911)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))),
% 2.01/2.18 inference(quant_inst,[status(thm)],[])).
% 2.01/2.18 tff(2498,plain,
% 2.01/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a911)) | (~c0_1(a911)) | (~c2_1(a911))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 2.01/2.18 tff(2499,plain,
% 2.01/2.18 (~c2_1(a911)),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2498, 112, 2492, 2491, 2428, 2427, 2426, 2425, 2422, 2421, 870])).
% 2.01/2.18 tff(2500,plain,
% 2.01/2.18 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2501,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2500])).
% 2.01/2.18 tff(2502,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2503,plain,
% 2.01/2.18 (^[V: $i, U: $i] : 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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2504,plain,
% 2.01/2.18 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2503])).
% 2.01/2.18 tff(2505,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 2.01/2.18 tff(2506,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 2.01/2.18 tff(2507,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2506, 2502])).
% 2.01/2.18 tff(2508,plain,(
% 2.01/2.18 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.18 inference(skolemize,[status(sab)],[2507])).
% 2.01/2.18 tff(2509,plain,
% 2.01/2.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2508, 2501])).
% 2.01/2.18 tff(2510,plain,
% 2.01/2.18 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2511,plain,
% 2.01/2.18 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2510])).
% 2.01/2.18 tff(2512,plain,
% 2.01/2.18 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2513,plain,
% 2.01/2.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp13) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp13))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 2.01/2.18 inference(bind,[status(th)],[])).
% 2.01/2.18 tff(2514,plain,
% 2.01/2.18 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp13) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.01/2.18 inference(quant_intro,[status(thm)],[2513])).
% 2.01/2.18 tff(2515,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp12) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 2.01/2.18 tff(2516,plain,
% 2.01/2.18 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2515, 2514])).
% 2.01/2.18 tff(2517,plain,
% 2.01/2.18 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2516, 2512])).
% 2.01/2.18 tff(2518,plain,(
% 2.01/2.18 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.01/2.18 inference(skolemize,[status(sab)],[2517])).
% 2.01/2.18 tff(2519,plain,
% 2.01/2.18 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2518, 2511])).
% 2.01/2.18 tff(2520,plain,
% 2.01/2.18 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp13 | hskp12 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp13 | hskp12 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2521,plain,
% 2.01/2.18 ((hskp13 | hskp12 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c1_1(a910))) <=> (hskp13 | hskp12 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)))),
% 2.01/2.18 inference(rewrite,[status(thm)],[])).
% 2.01/2.18 tff(2522,plain,
% 2.01/2.18 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp13 | hskp12 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910))))),
% 2.01/2.18 inference(monotonicity,[status(thm)],[2521])).
% 2.01/2.18 tff(2523,plain,
% 2.01/2.18 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp13 | hskp12 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)))),
% 2.01/2.18 inference(transitivity,[status(thm)],[2522, 2520])).
% 2.01/2.18 tff(2524,plain,
% 2.01/2.18 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))),
% 2.01/2.18 inference(quant_inst,[status(thm)],[])).
% 2.01/2.18 tff(2525,plain,
% 2.01/2.18 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp13 | hskp12 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910))),
% 2.01/2.18 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 2.01/2.18 tff(2526,plain,
% 2.01/2.18 (hskp13 | hskp12),
% 2.01/2.18 inference(unit_resolution,[status(thm)],[2525, 112, 2366, 2365, 2364, 2519])).
% 2.01/2.19 tff(2527,plain,
% 2.01/2.19 (hskp13),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2526, 1170])).
% 2.01/2.19 tff(2528,plain,
% 2.01/2.19 (~c2_1(a914)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[187, 2527])).
% 2.01/2.19 tff(2529,plain,
% 2.01/2.19 (~c1_1(a914)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[193, 2527])).
% 2.01/2.19 tff(2530,plain,
% 2.01/2.19 (c3_1(a914)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[201, 2527])).
% 2.01/2.19 tff(2531,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | c1_1(a914) | c2_1(a914) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a914) | c2_1(a914) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a914)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2532,plain,
% 2.01/2.19 ((hskp12 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914))) <=> (hskp12 | c1_1(a914) | c2_1(a914) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a914)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2533,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | c1_1(a914) | c2_1(a914) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a914))))),
% 2.01/2.19 inference(monotonicity,[status(thm)],[2532])).
% 2.01/2.19 tff(2534,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a914) | c2_1(a914) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a914)))),
% 2.01/2.19 inference(transitivity,[status(thm)],[2533, 2531])).
% 2.01/2.19 tff(2535,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))),
% 2.01/2.19 inference(quant_inst,[status(thm)],[])).
% 2.01/2.19 tff(2536,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a914) | c2_1(a914) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a914))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2535, 2534])).
% 2.01/2.19 tff(2537,plain,
% 2.01/2.19 ($false),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2536, 112, 1170, 2530, 2451, 2529, 2528, 2450, 2449, 2509])).
% 2.01/2.19 tff(2538,plain,(hskp12 | (~c2_1(a904)) | c1_1(a904) | c3_1(a904) | (~c1_1(a910)) | c0_1(a910) | c2_1(a910)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.19 tff(2539,plain,
% 2.01/2.19 (hskp12),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2538, 2428, 2422, 2421, 2366, 2365, 2364])).
% 2.01/2.19 tff(2540,plain,
% 2.01/2.19 (~c3_1(a913)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[347, 2539])).
% 2.01/2.19 tff(2541,plain,
% 2.01/2.19 (~c1_1(a913)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[409, 2539])).
% 2.01/2.19 tff(2542,plain,
% 2.01/2.19 (c0_1(a913)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[355, 2539])).
% 2.01/2.19 tff(2543,plain,
% 2.01/2.19 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 2.01/2.19 inference(bind,[status(th)],[])).
% 2.01/2.19 tff(2544,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.01/2.19 inference(quant_intro,[status(thm)],[2543])).
% 2.01/2.19 tff(2545,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2546,plain,
% 2.01/2.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp21))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 2.01/2.19 inference(bind,[status(th)],[])).
% 2.01/2.19 tff(2547,plain,
% 2.01/2.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.01/2.19 inference(quant_intro,[status(thm)],[2546])).
% 2.01/2.19 tff(2548,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 2.01/2.19 tff(2549,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 2.01/2.19 tff(2550,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2549, 2545])).
% 2.01/2.19 tff(2551,plain,(
% 2.01/2.19 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.01/2.19 inference(skolemize,[status(sab)],[2550])).
% 2.01/2.19 tff(2552,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2551, 2544])).
% 2.01/2.19 tff(2553,plain,
% 2.01/2.19 ($false),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[379, 112, 313, 695, 311, 312, 694, 43, 373, 1073])).
% 2.01/2.19 tff(2554,plain,(c2_1(a913) | hskp14 | (~c0_1(a913)) | (~c1_1(a899)) | (~c2_1(a899)) | c3_1(a913) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.19 tff(2555,plain,
% 2.01/2.19 (c2_1(a913)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2554, 313, 695, 311, 312, 694, 43])).
% 2.01/2.19 tff(2556,plain,
% 2.01/2.19 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 2.01/2.19 inference(bind,[status(th)],[])).
% 2.01/2.19 tff(2557,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.01/2.19 inference(quant_intro,[status(thm)],[2556])).
% 2.01/2.19 tff(2558,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2559,plain,
% 2.01/2.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.01/2.19 inference(bind,[status(th)],[])).
% 2.01/2.19 tff(2560,plain,
% 2.01/2.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.01/2.19 inference(quant_intro,[status(thm)],[2559])).
% 2.01/2.19 tff(2561,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 2.01/2.19 tff(2562,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 2.01/2.19 tff(2563,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2562, 2558])).
% 2.01/2.19 tff(2564,plain,(
% 2.01/2.19 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.01/2.19 inference(skolemize,[status(sab)],[2563])).
% 2.01/2.19 tff(2565,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2564, 2557])).
% 2.01/2.19 tff(2566,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp15 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2567,plain,
% 2.01/2.19 ((hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp15 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2568,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913))))),
% 2.01/2.19 inference(monotonicity,[status(thm)],[2567])).
% 2.01/2.19 tff(2569,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp15 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.01/2.19 inference(transitivity,[status(thm)],[2568, 2566])).
% 2.01/2.19 tff(2570,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.01/2.19 inference(quant_inst,[status(thm)],[])).
% 2.01/2.19 tff(2571,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp15 | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a913)) | (~c2_1(a913))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 2.01/2.19 tff(2572,plain,
% 2.01/2.19 (hskp15 | (~c2_1(a913))),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2571, 112, 695, 311, 312, 694, 43, 2565])).
% 2.01/2.19 tff(2573,plain,
% 2.01/2.19 (hskp15),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2572, 2555])).
% 2.01/2.19 tff(2574,plain,
% 2.01/2.19 (c1_1(a921)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2472, 2573])).
% 2.01/2.19 tff(2575,plain,
% 2.01/2.19 (c0_1(a921)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2480, 2573])).
% 2.01/2.19 tff(2576,plain,
% 2.01/2.19 (~hskp21),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[441, 313, 312, 311, 43])).
% 2.01/2.19 tff(2577,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a921)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a921)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2578,plain,
% 2.01/2.19 ((hskp21 | (~ndr1_0) | (~c1_1(a921)) | (~c2_1(a921)) | (~c0_1(a921)) | c3_1(a912) | c2_1(a912) | c1_1(a912)) <=> (hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a921)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2579,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | (~ndr1_0) | (~c1_1(a921)) | (~c2_1(a921)) | (~c0_1(a921)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a921))))),
% 2.01/2.19 inference(monotonicity,[status(thm)],[2578])).
% 2.01/2.19 tff(2580,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | (~ndr1_0) | (~c1_1(a921)) | (~c2_1(a921)) | (~c0_1(a921)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a921)))),
% 2.01/2.19 inference(transitivity,[status(thm)],[2579, 2577])).
% 2.01/2.19 tff(2581,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | (~ndr1_0) | (~c1_1(a921)) | (~c2_1(a921)) | (~c0_1(a921)) | c3_1(a912) | c2_1(a912) | c1_1(a912))),
% 2.01/2.19 inference(quant_inst,[status(thm)],[])).
% 2.01/2.19 tff(2582,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a921))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2581, 2580])).
% 2.01/2.19 tff(2583,plain,
% 2.01/2.19 (~c2_1(a921)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2582, 112, 2576, 2575, 2574, 801, 802, 813, 2552])).
% 2.01/2.19 tff(2584,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)) | c2_1(a921) | (~c0_1(a921)) | (~c1_1(a921)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)) | c2_1(a921) | (~c0_1(a921)) | (~c1_1(a921)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2585,plain,
% 2.01/2.19 ((hskp7 | (~ndr1_0) | c2_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913))) <=> (hskp7 | c1_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)) | c2_1(a921) | (~c0_1(a921)) | (~c1_1(a921)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2586,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)) | c2_1(a921) | (~c0_1(a921)) | (~c1_1(a921))))),
% 2.01/2.19 inference(monotonicity,[status(thm)],[2585])).
% 2.01/2.19 tff(2587,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)) | c2_1(a921) | (~c0_1(a921)) | (~c1_1(a921)))),
% 2.01/2.19 inference(transitivity,[status(thm)],[2586, 2584])).
% 2.01/2.19 tff(2588,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c1_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))),
% 2.01/2.19 inference(quant_inst,[status(thm)],[])).
% 2.01/2.19 tff(2589,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)) | c2_1(a921) | (~c0_1(a921)) | (~c1_1(a921))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2588, 2587])).
% 2.01/2.19 tff(2590,plain,
% 2.01/2.19 ($false),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2589, 112, 547, 2575, 2574, 695, 704, 576, 2555, 2583])).
% 2.01/2.19 tff(2591,plain,(hskp14 | hskp7 | (~c0_1(a913)) | c1_1(a913) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~c1_1(a899)) | (~c2_1(a899)) | c3_1(a913) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.19 tff(2592,plain,
% 2.01/2.19 (hskp14),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2591, 547, 2542, 2541, 801, 802, 813, 311, 312, 2540, 43])).
% 2.01/2.19 tff(2593,plain,
% 2.01/2.19 (c3_1(a918)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[742, 2592])).
% 2.01/2.19 tff(2594,plain,
% 2.01/2.19 (c0_1(a918)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[734, 2592])).
% 2.01/2.19 tff(2595,plain,
% 2.01/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2596,plain,
% 2.01/2.19 (((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909)) <=> (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2597,plain,
% 2.01/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 2.01/2.19 inference(monotonicity,[status(thm)],[2596])).
% 2.01/2.19 tff(2598,plain,
% 2.01/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.19 inference(transitivity,[status(thm)],[2597, 2595])).
% 2.01/2.19 tff(2599,plain,
% 2.01/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a909) | c0_1(a909) | c2_1(a909))),
% 2.01/2.19 inference(quant_inst,[status(thm)],[])).
% 2.01/2.19 tff(2600,plain,
% 2.01/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a909) | c1_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2599, 2598])).
% 2.01/2.19 tff(2601,plain,
% 2.01/2.19 (~c2_1(a918)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2600, 112, 2594, 2593, 2428, 2427, 2426, 2425, 2422, 2421, 870])).
% 2.01/2.19 tff(2602,plain,
% 2.01/2.19 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 2.01/2.19 inference(bind,[status(th)],[])).
% 2.01/2.19 tff(2603,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.19 inference(quant_intro,[status(thm)],[2602])).
% 2.01/2.19 tff(2604,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2605,plain,
% 2.01/2.19 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_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(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 2.01/2.19 inference(bind,[status(th)],[])).
% 2.01/2.19 tff(2606,plain,
% 2.01/2.19 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.19 inference(quant_intro,[status(thm)],[2605])).
% 2.01/2.19 tff(2607,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 2.01/2.19 tff(2608,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 2.01/2.19 tff(2609,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2608, 2604])).
% 2.01/2.19 tff(2610,plain,(
% 2.01/2.19 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.19 inference(skolemize,[status(sab)],[2609])).
% 2.01/2.19 tff(2611,plain,
% 2.01/2.19 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2610, 2603])).
% 2.01/2.19 tff(2612,plain,
% 2.01/2.19 (~c1_1(a918)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[672, 2592])).
% 2.01/2.19 tff(2613,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2614,plain,
% 2.01/2.19 ((hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918))) <=> (hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2615,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928))))),
% 2.01/2.19 inference(monotonicity,[status(thm)],[2614])).
% 2.01/2.19 tff(2616,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928)))),
% 2.01/2.19 inference(transitivity,[status(thm)],[2615, 2613])).
% 2.01/2.19 tff(2617,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a918) | c1_1(a918) | (~c3_1(a918)))),
% 2.01/2.19 inference(quant_inst,[status(thm)],[])).
% 2.01/2.19 tff(2618,plain,
% 2.01/2.19 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c1_1(a928))),
% 2.01/2.19 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 2.01/2.19 tff(2619,plain,
% 2.01/2.19 (hskp18),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[2618, 112, 1404, 2593, 1403, 2423, 2612, 2611, 2601])).
% 2.01/2.19 tff(2620,plain,
% 2.01/2.19 (~c1_1(a929)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[771, 2619])).
% 2.01/2.19 tff(2621,plain,
% 2.01/2.19 (c2_1(a929)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[781, 2619])).
% 2.01/2.19 tff(2622,plain,
% 2.01/2.19 (c0_1(a929)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[789, 2619])).
% 2.01/2.19 tff(2623,plain,
% 2.01/2.19 (c1_1(a911)),
% 2.01/2.19 inference(unit_resolution,[status(thm)],[1420, 2490])).
% 2.01/2.19 tff(2624,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a929) | (~ndr1_0) | (~c0_1(a911)) | c2_1(a911) | (~c1_1(a911)) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | (~ndr1_0) | (~c0_1(a911)) | c2_1(a911) | (~c1_1(a911)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2625,plain,
% 2.01/2.19 ((hskp7 | (~ndr1_0) | c2_1(a911) | (~c1_1(a911)) | (~c0_1(a911)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929))) <=> (hskp7 | c1_1(a929) | (~ndr1_0) | (~c0_1(a911)) | c2_1(a911) | (~c1_1(a911)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.01/2.19 inference(rewrite,[status(thm)],[])).
% 2.01/2.19 tff(2626,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a911) | (~c1_1(a911)) | (~c0_1(a911)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a929) | (~ndr1_0) | (~c0_1(a911)) | c2_1(a911) | (~c1_1(a911)) | (~c2_1(a929)) | (~c0_1(a929))))),
% 2.01/2.19 inference(monotonicity,[status(thm)],[2625])).
% 2.01/2.19 tff(2627,plain,
% 2.01/2.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a911) | (~c1_1(a911)) | (~c0_1(a911)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | (~ndr1_0) | (~c0_1(a911)) | c2_1(a911) | (~c1_1(a911)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2626, 2624])).
% 2.01/2.20 tff(2628,plain,
% 2.01/2.20 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a911) | (~c1_1(a911)) | (~c0_1(a911)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2629,plain,
% 2.01/2.20 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | (~ndr1_0) | (~c0_1(a911)) | c2_1(a911) | (~c1_1(a911)) | (~c2_1(a929)) | (~c0_1(a929))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 2.01/2.20 tff(2630,plain,
% 2.01/2.20 ($false),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2629, 112, 547, 2492, 2623, 2622, 2621, 2620, 576, 2499])).
% 2.01/2.20 tff(2631,plain,(hskp7 | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899) | (~c1_1(a910)) | c0_1(a910) | c2_1(a910) | c3_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.20 tff(2632,plain,
% 2.01/2.20 (hskp7),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2631, 2392, 2394, 2393, 2391, 2398, 2397, 2396, 2419, 2416, 43, 2363, 2355, 2349, 2418])).
% 2.01/2.20 tff(2633,plain,
% 2.01/2.20 (c3_1(a907)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[512, 2632])).
% 2.01/2.20 tff(2634,plain,
% 2.01/2.20 (c1_1(a901) | (~c2_1(a907)) | (~c3_1(a907))),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2386, 112, 2363, 2355, 2349, 44, 47, 48, 1721])).
% 2.01/2.20 tff(2635,plain,
% 2.01/2.20 (~c2_1(a907)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2634, 2633, 49])).
% 2.01/2.20 tff(2636,plain,
% 2.01/2.20 (hskp25),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1686, 112, 2393, 2392, 2391, 30])).
% 2.01/2.20 tff(2637,plain,
% 2.01/2.20 (~c3_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1692, 2636])).
% 2.01/2.20 tff(2638,plain,
% 2.01/2.20 (~c1_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1698, 2636])).
% 2.01/2.20 tff(2639,plain,
% 2.01/2.20 (~c0_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1841, 2636])).
% 2.01/2.20 tff(2640,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2641,plain,
% 2.01/2.20 (((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | c0_1(a958)) <=> (c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2642,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | c0_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907))))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2641])).
% 2.01/2.20 tff(2643,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | c0_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2642, 2640])).
% 2.01/2.20 tff(2644,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | c0_1(a958))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2645,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 2.01/2.20 tff(2646,plain,
% 2.01/2.20 ($false),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2645, 112, 2633, 2639, 2638, 2637, 44, 45, 151, 2635])).
% 2.01/2.20 tff(2647,plain,(c0_1(a899) | c0_1(a907) | c1_1(a907) | c1_1(a901) | c2_1(a901) | c3_1(a901) | hskp0 | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.01/2.20 tff(2648,plain,
% 2.01/2.20 (c0_1(a899)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2647, 49, 45, 44, 47, 48, 31, 46])).
% 2.01/2.20 tff(2649,plain,
% 2.01/2.20 (~hskp1),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[292, 2648])).
% 2.01/2.20 tff(2650,plain,
% 2.01/2.20 (c2_1(a907)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1478, 2649, 45, 31])).
% 2.01/2.20 tff(2651,plain,
% 2.01/2.20 (~c3_1(a907)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2634, 2650, 49])).
% 2.01/2.20 tff(2652,plain,
% 2.01/2.20 (hskp17),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1495, 2651, 2650, 31])).
% 2.01/2.20 tff(2653,plain,
% 2.01/2.20 (~c3_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[828, 2652])).
% 2.01/2.20 tff(2654,plain,
% 2.01/2.20 (~c2_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[834, 2652])).
% 2.01/2.20 tff(2655,plain,
% 2.01/2.20 (c1_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[842, 2652])).
% 2.01/2.20 tff(2656,plain,
% 2.01/2.20 (~c0_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[849, 46, 112, 2655, 2654, 2653, 10])).
% 2.01/2.20 tff(2657,plain,
% 2.01/2.20 (hskp11),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1729, 2652, 46])).
% 2.01/2.20 tff(2658,plain,
% 2.01/2.20 (~c3_1(a912)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1390, 2657])).
% 2.01/2.20 tff(2659,plain,
% 2.01/2.20 (~c2_1(a912)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1679, 2657])).
% 2.01/2.20 tff(2660,plain,
% 2.01/2.20 (~c1_1(a912)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2146, 2657])).
% 2.01/2.20 tff(2661,plain,
% 2.01/2.20 (hskp9),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2404, 112, 2654, 2653, 2660, 2659, 2658, 1310, 2656])).
% 2.01/2.20 tff(2662,plain,
% 2.01/2.20 (~c2_1(a909)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1323, 2661])).
% 2.01/2.20 tff(2663,plain,
% 2.01/2.20 (~c1_1(a909)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1329, 2661])).
% 2.01/2.20 tff(2664,plain,
% 2.01/2.20 (c0_1(a901)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[286, 2649, 48, 49, 46, 47])).
% 2.01/2.20 tff(2665,plain,
% 2.01/2.20 (((~hskp2) | (~c0_1(a901))) <=> ((~hskp2) | (~c0_1(a901)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2666,plain,
% 2.01/2.20 (((~c0_1(a901)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a901)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2667,axiom,((~c0_1(a901)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 2.01/2.20 tff(2668,plain,
% 2.01/2.20 ((~hskp2) | (~c0_1(a901))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 2.01/2.20 tff(2669,plain,
% 2.01/2.20 ((~hskp2) | (~c0_1(a901))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2668, 2665])).
% 2.01/2.20 tff(2670,plain,
% 2.01/2.20 (~hskp2),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2669, 2664])).
% 2.01/2.20 tff(2671,plain,
% 2.01/2.20 (^[U: $i] : refl((hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 2.01/2.20 inference(bind,[status(th)],[])).
% 2.01/2.20 tff(2672,plain,
% 2.01/2.20 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.01/2.20 inference(quant_intro,[status(thm)],[2671])).
% 2.01/2.20 tff(2673,plain,
% 2.01/2.20 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2674,plain,
% 2.01/2.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp2) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp2))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp2) <=> (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp2) <=> (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 2.01/2.20 inference(bind,[status(th)],[])).
% 2.01/2.20 tff(2675,plain,
% 2.01/2.20 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp2) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.01/2.20 inference(quant_intro,[status(thm)],[2674])).
% 2.01/2.20 tff(2676,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 2.01/2.20 tff(2677,plain,
% 2.01/2.20 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 2.01/2.20 tff(2678,plain,
% 2.01/2.20 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2677, 2673])).
% 2.01/2.20 tff(2679,plain,(
% 2.01/2.20 ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.01/2.20 inference(skolemize,[status(sab)],[2678])).
% 2.01/2.20 tff(2680,plain,
% 2.01/2.20 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2679, 2672])).
% 2.01/2.20 tff(2681,plain,
% 2.01/2.20 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | c3_1(a907) | c0_1(a907) | c1_1(a907) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp2 | c3_1(a907) | c0_1(a907) | c1_1(a907) | (~ndr1_0))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2682,plain,
% 2.01/2.20 ((hskp28 | hskp2 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | c3_1(a907)) <=> (hskp28 | hskp2 | c3_1(a907) | c0_1(a907) | c1_1(a907) | (~ndr1_0))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2683,plain,
% 2.01/2.20 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | c3_1(a907))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | c3_1(a907) | c0_1(a907) | c1_1(a907) | (~ndr1_0)))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2682])).
% 2.01/2.20 tff(2684,plain,
% 2.01/2.20 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | c3_1(a907))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp2 | c3_1(a907) | c0_1(a907) | c1_1(a907) | (~ndr1_0))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2683, 2681])).
% 2.01/2.20 tff(2685,plain,
% 2.01/2.20 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | (~ndr1_0) | c1_1(a907) | c0_1(a907) | c3_1(a907))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2686,plain,
% 2.01/2.20 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp2 | c3_1(a907) | c0_1(a907) | c1_1(a907) | (~ndr1_0)),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 2.01/2.20 tff(2687,plain,
% 2.01/2.20 (hskp28 | hskp2 | c3_1(a907) | c1_1(a907)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2686, 112, 44, 2680])).
% 2.01/2.20 tff(2688,plain,
% 2.01/2.20 (hskp28),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2687, 2670, 2651, 45])).
% 2.01/2.20 tff(2689,plain,
% 2.01/2.20 (c0_1(a900)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[965, 2688])).
% 2.01/2.20 tff(2690,plain,
% 2.01/2.20 (c3_1(a900)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[949, 2688])).
% 2.01/2.20 tff(2691,plain,
% 2.01/2.20 (c2_1(a900)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[957, 2688])).
% 2.01/2.20 tff(2692,plain,
% 2.01/2.20 (~hskp7),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[512, 2651])).
% 2.01/2.20 tff(2693,plain,
% 2.01/2.20 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2694,plain,
% 2.01/2.20 ((hskp7 | hskp4 | (~ndr1_0) | c0_1(a928) | c3_1(a928) | (~c1_1(a928))) <=> (hskp7 | hskp4 | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2695,plain,
% 2.01/2.20 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a928) | c3_1(a928) | (~c1_1(a928)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928))))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2694])).
% 2.01/2.20 tff(2696,plain,
% 2.01/2.20 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a928) | c3_1(a928) | (~c1_1(a928)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2695, 2693])).
% 2.01/2.20 tff(2697,plain,
% 2.01/2.20 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a928) | c3_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2698,plain,
% 2.01/2.20 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c3_1(a928) | (~ndr1_0) | c0_1(a928) | (~c1_1(a928))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2697, 2696])).
% 2.01/2.20 tff(2699,plain,
% 2.01/2.20 (hskp4),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2698, 112, 2692, 2655, 2653, 523, 2656])).
% 2.01/2.20 tff(2700,plain,
% 2.01/2.20 (~c0_1(a909)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1335, 2661])).
% 2.01/2.20 tff(2701,plain,
% 2.01/2.20 ($false),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2050, 2700, 2699, 2691, 2690, 2689, 2663, 2662])).
% 2.01/2.20 tff(2702,plain,(c1_1(a901) | hskp31 | hskp0 | c0_1(a907) | c1_1(a907) | c2_1(a901) | c3_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.20 tff(2703,plain,
% 2.01/2.20 (c1_1(a901)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2702, 31, 46, 44, 45, 47, 48])).
% 2.01/2.20 tff(2704,plain,
% 2.01/2.20 (~c0_1(a901)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2228, 2703])).
% 2.01/2.20 tff(2705,plain,
% 2.01/2.20 (hskp1),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2163, 32, 31, 44, 2704, 47, 48, 45, 46])).
% 2.01/2.20 tff(2706,plain,
% 2.01/2.20 (c2_1(a899)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[300, 2705])).
% 2.01/2.20 tff(2707,plain,
% 2.01/2.20 (hskp25),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1826, 2703, 48])).
% 2.01/2.20 tff(2708,plain,
% 2.01/2.20 (~c3_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1692, 2707])).
% 2.01/2.20 tff(2709,plain,
% 2.01/2.20 (~c0_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1841, 2707])).
% 2.01/2.20 tff(2710,plain,
% 2.01/2.20 (hskp17 | (~c2_1(a958))),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1848, 112, 31, 2709, 2708, 891])).
% 2.01/2.20 tff(2711,plain,
% 2.01/2.20 (~c2_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2710, 32])).
% 2.01/2.20 tff(2712,plain,
% 2.01/2.20 (~c1_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1698, 2707])).
% 2.01/2.20 tff(2713,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a958))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2714,plain,
% 2.01/2.20 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a958))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2715,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a958)))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2714])).
% 2.01/2.20 tff(2716,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a958))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2715, 2713])).
% 2.01/2.20 tff(2717,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2718,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a958)),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 2.01/2.20 tff(2719,plain,
% 2.01/2.20 ((~c3_1(a899)) | (~c2_1(a899)) | c2_1(a958)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2718, 112, 2363, 2712, 2708, 2355, 2349, 43, 1721])).
% 2.01/2.20 tff(2720,plain,
% 2.01/2.20 (~c3_1(a899)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2719, 2706, 2711])).
% 2.01/2.20 tff(2721,plain,
% 2.01/2.20 ($false),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2295, 2720, 2706, 32])).
% 2.01/2.20 tff(2722,plain,(hskp17 | hskp0 | c0_1(a899) | c0_1(a907) | c2_1(a901) | c3_1(a901) | c1_1(a907) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.01/2.20 tff(2723,plain,
% 2.01/2.20 (hskp17),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2722, 43, 31, 44, 47, 48, 45, 46])).
% 2.01/2.20 tff(2724,plain,
% 2.01/2.20 (~c3_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[828, 2723])).
% 2.01/2.20 tff(2725,plain,
% 2.01/2.20 (~c2_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[834, 2723])).
% 2.01/2.20 tff(2726,plain,
% 2.01/2.20 (c1_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[842, 2723])).
% 2.01/2.20 tff(2727,plain,
% 2.01/2.20 (~c0_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[849, 46, 112, 2726, 2725, 2724, 10])).
% 2.01/2.20 tff(2728,plain,
% 2.01/2.20 (hskp11),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1729, 2723, 46])).
% 2.01/2.20 tff(2729,plain,
% 2.01/2.20 (~c3_1(a912)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1390, 2728])).
% 2.01/2.20 tff(2730,plain,
% 2.01/2.20 (~c2_1(a912)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1679, 2728])).
% 2.01/2.20 tff(2731,plain,
% 2.01/2.20 (~c1_1(a912)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2146, 2728])).
% 2.01/2.20 tff(2732,plain,
% 2.01/2.20 (hskp9),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2404, 112, 2725, 2724, 2731, 2730, 2729, 1310, 2727])).
% 2.01/2.20 tff(2733,plain,
% 2.01/2.20 (~c2_1(a909)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1323, 2732])).
% 2.01/2.20 tff(2734,plain,
% 2.01/2.20 (~c1_1(a909)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1329, 2732])).
% 2.01/2.20 tff(2735,plain,
% 2.01/2.20 (~c0_1(a909)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[1335, 2732])).
% 2.01/2.20 tff(2736,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2737,plain,
% 2.01/2.20 (((~ndr1_0) | c2_1(a909) | c1_1(a909) | (~c3_1(a909)) | c2_1(a909) | c0_1(a909) | (~c3_1(a909)) | c3_1(a958) | c1_1(a958) | c0_1(a958)) <=> (c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2738,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a909) | c1_1(a909) | (~c3_1(a909)) | c2_1(a909) | c0_1(a909) | (~c3_1(a909)) | c3_1(a958) | c1_1(a958) | c0_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909))))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2737])).
% 2.01/2.20 tff(2739,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a909) | c1_1(a909) | (~c3_1(a909)) | c2_1(a909) | c0_1(a909) | (~c3_1(a909)) | c3_1(a958) | c1_1(a958) | c0_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2738, 2736])).
% 2.01/2.20 tff(2740,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a909) | c1_1(a909) | (~c3_1(a909)) | c2_1(a909) | c0_1(a909) | (~c3_1(a909)) | c3_1(a958) | c1_1(a958) | c0_1(a958))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2741,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a958) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 2.01/2.20 tff(2742,plain,
% 2.01/2.20 (~c3_1(a909)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2741, 112, 2709, 2712, 2708, 2735, 2734, 2733, 151])).
% 2.01/2.20 tff(2743,plain,
% 2.01/2.20 (hskp1),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2414, 112, 31, 2735, 2734, 2733, 20])).
% 2.01/2.20 tff(2744,plain,
% 2.01/2.20 (c1_1(a899)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[308, 2743])).
% 2.01/2.20 tff(2745,plain,
% 2.01/2.20 (c2_1(a899)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[300, 2743])).
% 2.01/2.20 tff(2746,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2747,plain,
% 2.01/2.20 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912)) <=> (c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2748,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928))))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2747])).
% 2.01/2.20 tff(2749,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2748, 2746])).
% 2.01/2.20 tff(2750,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2751,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2750, 2749])).
% 2.01/2.20 tff(2752,plain,
% 2.01/2.20 ((~c3_1(a899)) | (~c2_1(a899)) | c0_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2751, 112, 2726, 2725, 2731, 2730, 2729, 43, 1721])).
% 2.01/2.20 tff(2753,plain,
% 2.01/2.20 (~c3_1(a899)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2752, 2745, 2727])).
% 2.01/2.20 tff(2754,plain,
% 2.01/2.20 (hskp7),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2631, 2753, 2726, 2745, 2724, 2725, 2730, 2729, 2731, 2727, 43, 2363, 2355, 2349, 2744])).
% 2.01/2.20 tff(2755,plain,
% 2.01/2.20 (c3_1(a907)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[512, 2754])).
% 2.01/2.20 tff(2756,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2757,plain,
% 2.01/2.20 (((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912)) <=> (c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2758,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928))))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2757])).
% 2.01/2.20 tff(2759,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)))),
% 2.01/2.20 inference(transitivity,[status(thm)],[2758, 2756])).
% 2.01/2.20 tff(2760,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a912) | c1_1(a912) | c2_1(a912))),
% 2.01/2.20 inference(quant_inst,[status(thm)],[])).
% 2.01/2.20 tff(2761,plain,
% 2.01/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928))),
% 2.01/2.20 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 2.01/2.20 tff(2762,plain,
% 2.01/2.20 ((~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2761, 112, 2726, 2725, 2731, 2730, 2729, 44, 1721])).
% 2.01/2.20 tff(2763,plain,
% 2.01/2.20 (~c2_1(a907)),
% 2.01/2.20 inference(unit_resolution,[status(thm)],[2762, 2755, 2727])).
% 2.01/2.20 tff(2764,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a909) | c1_1(a909) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | c3_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a909) | c1_1(a909) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | c3_1(a909))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2765,plain,
% 2.01/2.20 (((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a909) | c1_1(a909) | c0_1(a909)) <=> (c0_1(a909) | c1_1(a909) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | c3_1(a909))),
% 2.01/2.20 inference(rewrite,[status(thm)],[])).
% 2.01/2.20 tff(2766,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a909) | c1_1(a909) | c0_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a909) | c1_1(a909) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | c3_1(a909)))),
% 2.01/2.20 inference(monotonicity,[status(thm)],[2765])).
% 2.01/2.20 tff(2767,plain,
% 2.01/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a909) | c1_1(a909) | c0_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a909) | c1_1(a909) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | c3_1(a909))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2766, 2764])).
% 2.01/2.21 tff(2768,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c1_1(a907) | (~c3_1(a907)) | c2_1(a907) | c0_1(a907) | (~c3_1(a907)) | c3_1(a909) | c1_1(a909) | c0_1(a909))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2769,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a909) | c1_1(a909) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | c3_1(a909)),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2768, 2767])).
% 2.01/2.21 tff(2770,plain,
% 2.01/2.21 ($false),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2769, 112, 2755, 2735, 2734, 44, 45, 151, 2763, 2742])).
% 2.01/2.21 tff(2771,plain,(c0_1(a899) | c0_1(a907) | c1_1(a907) | hskp0 | hskp31 | c2_1(a901) | c3_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.21 tff(2772,plain,
% 2.01/2.21 (c0_1(a899)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2771, 31, 45, 44, 46, 47, 48])).
% 2.01/2.21 tff(2773,plain,
% 2.01/2.21 (~hskp1),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[292, 2772])).
% 2.01/2.21 tff(2774,plain,
% 2.01/2.21 (hskp17),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2163, 2773, 31, 44, 2704, 47, 48, 45, 46])).
% 2.01/2.21 tff(2775,plain,
% 2.01/2.21 (~c3_1(a928)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[828, 2774])).
% 2.01/2.21 tff(2776,plain,
% 2.01/2.21 (~c2_1(a928)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[834, 2774])).
% 2.01/2.21 tff(2777,plain,
% 2.01/2.21 (c1_1(a928)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[842, 2774])).
% 2.01/2.21 tff(2778,plain,
% 2.01/2.21 (~c0_1(a928)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[849, 46, 112, 2777, 2776, 2775, 10])).
% 2.01/2.21 tff(2779,plain,
% 2.01/2.21 (hskp11),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1729, 2774, 46])).
% 2.01/2.21 tff(2780,plain,
% 2.01/2.21 (~c3_1(a912)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1390, 2779])).
% 2.01/2.21 tff(2781,plain,
% 2.01/2.21 (~c2_1(a912)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1679, 2779])).
% 2.01/2.21 tff(2782,plain,
% 2.01/2.21 (~c1_1(a912)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2146, 2779])).
% 2.01/2.21 tff(2783,plain,
% 2.01/2.21 (hskp9),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2404, 112, 2776, 2775, 2782, 2781, 2780, 1310, 2778])).
% 2.01/2.21 tff(2784,plain,
% 2.01/2.21 (~c2_1(a909)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1323, 2783])).
% 2.01/2.21 tff(2785,plain,
% 2.01/2.21 (~c1_1(a909)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1329, 2783])).
% 2.01/2.21 tff(2786,plain,
% 2.01/2.21 (~c0_1(a909)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1335, 2783])).
% 2.01/2.21 tff(2787,plain,
% 2.01/2.21 ($false),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2414, 112, 2773, 31, 2786, 2785, 2784, 20])).
% 2.01/2.21 tff(2788,plain,(hskp0 | hskp31 | c0_1(a907) | c2_1(a901) | c3_1(a901) | c1_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.21 tff(2789,plain,
% 2.01/2.21 (hskp0),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2788, 48, 44, 47, 46, 45])).
% 2.01/2.21 tff(2790,plain,
% 2.01/2.21 (~c2_1(a898)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[65, 2789])).
% 2.01/2.21 tff(2791,plain,
% 2.01/2.21 (c1_1(a898)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[59, 2789])).
% 2.01/2.21 tff(2792,plain,
% 2.01/2.21 (c0_1(a898)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[73, 2789])).
% 2.01/2.21 tff(2793,assumption,(~c3_1(a910)), introduced(assumption)).
% 2.01/2.21 tff(2794,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)) | c3_1(a910))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2795,plain,
% 2.01/2.21 ((hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a910) | c2_1(a910) | (~c1_1(a910))) <=> (hskp31 | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2796,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a910) | c2_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)) | c3_1(a910)))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2795])).
% 2.01/2.21 tff(2797,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a910) | c2_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2796, 2794])).
% 2.01/2.21 tff(2798,plain,
% 2.01/2.21 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a910) | c2_1(a910) | (~c1_1(a910)))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2799,plain,
% 2.01/2.21 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)) | c3_1(a910)),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 2.01/2.21 tff(2800,plain,
% 2.01/2.21 ($false),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2799, 46, 112, 2366, 78, 77, 2364, 76, 10, 2793])).
% 2.01/2.21 tff(2801,plain,(c3_1(a910) | hskp31 | (~c1_1(a910)) | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a910) | c2_1(a898)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.21 tff(2802,plain,
% 2.01/2.21 (c3_1(a910)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2801, 2363, 46, 2792, 2791, 2349, 2790])).
% 2.01/2.21 tff(2803,plain,
% 2.01/2.21 (c3_1(a898)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[120, 2792, 2790, 2791, 46])).
% 2.01/2.21 tff(2804,plain,
% 2.01/2.21 (hskp5 | hskp1),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[235, 112, 2792, 2790, 229, 2803])).
% 2.01/2.21 tff(2805,plain,
% 2.01/2.21 (hskp5),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2804, 152])).
% 2.01/2.21 tff(2806,plain,
% 2.01/2.21 (~c0_1(a905)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[276, 2805])).
% 2.01/2.21 tff(2807,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2808,plain,
% 2.01/2.21 ((hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910))) <=> (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2809,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910))))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2808])).
% 2.01/2.21 tff(2810,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2809, 2807])).
% 2.01/2.21 tff(2811,plain,
% 2.01/2.21 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2812,plain,
% 2.01/2.21 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910))),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 2.01/2.21 tff(2813,plain,
% 2.01/2.21 (hskp11),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2812, 112, 2363, 2792, 2791, 2355, 2349, 1402, 2803])).
% 2.01/2.21 tff(2814,plain,
% 2.01/2.21 (~c3_1(a912)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1390, 2813])).
% 2.01/2.21 tff(2815,plain,
% 2.01/2.21 (~c2_1(a912)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[1679, 2813])).
% 2.01/2.21 tff(2816,plain,
% 2.01/2.21 (~c1_1(a912)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2146, 2813])).
% 2.01/2.21 tff(2817,plain,
% 2.01/2.21 (c3_1(a905)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[244, 2805])).
% 2.01/2.21 tff(2818,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2819,plain,
% 2.01/2.21 (((~ndr1_0) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2820,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a910))))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2819])).
% 2.01/2.21 tff(2821,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a910)))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2820, 2818])).
% 2.01/2.21 tff(2822,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a905) | (~c3_1(a905)) | (~c2_1(a905)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2823,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c2_1(a905)) | (~c1_1(a910))),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 2.01/2.21 tff(2824,plain,
% 2.01/2.21 (~c2_1(a905)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2823, 112, 2363, 2817, 2816, 2815, 2814, 2355, 2349, 2806, 1721])).
% 2.01/2.21 tff(2825,plain,
% 2.01/2.21 (hskp13 | hskp1),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[180, 112, 2791, 2790, 174, 2803])).
% 2.01/2.21 tff(2826,plain,
% 2.01/2.21 (hskp13),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2825, 152])).
% 2.01/2.21 tff(2827,plain,
% 2.01/2.21 (~c2_1(a914)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[187, 2826])).
% 2.01/2.21 tff(2828,plain,
% 2.01/2.21 (~c1_1(a914)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[193, 2826])).
% 2.01/2.21 tff(2829,plain,
% 2.01/2.21 (~c1_1(a901)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[140, 2789, 47, 48, 46])).
% 2.01/2.21 tff(2830,plain,
% 2.01/2.21 (c0_1(a901)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[286, 152, 48, 2829, 46, 47])).
% 2.01/2.21 tff(2831,plain,
% 2.01/2.21 (~c3_1(a907)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2263, 2830, 44, 45, 2789, 47, 2829, 46])).
% 2.01/2.21 tff(2832,plain,
% 2.01/2.21 (c3_1(a914)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[201, 2826])).
% 2.01/2.21 tff(2833,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c1_1(a914) | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c1_1(a914) | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2834,plain,
% 2.01/2.21 (((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a907) | c1_1(a907) | c0_1(a907)) <=> (c3_1(a907) | c1_1(a914) | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2835,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c1_1(a914) | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914)))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2834])).
% 2.01/2.21 tff(2836,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c1_1(a914) | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2835, 2833])).
% 2.01/2.21 tff(2837,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a907) | c1_1(a907) | c0_1(a907))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2838,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c1_1(a914) | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914)),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 2.01/2.21 tff(2839,plain,
% 2.01/2.21 (c0_1(a914)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2838, 112, 2832, 2831, 2828, 2827, 44, 45, 151])).
% 2.01/2.21 tff(2840,plain,
% 2.01/2.21 (c2_1(a905) | (~c0_1(a914))),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[283, 112, 2832, 2817, 2792, 2791, 2828, 2806, 2790, 271])).
% 2.01/2.21 tff(2841,plain,
% 2.01/2.21 ($false),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2840, 2839, 2824])).
% 2.01/2.21 tff(2842,plain,(hskp1 | c0_1(a907) | c1_1(a907) | c2_1(a901) | hskp31 | c3_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.21 tff(2843,plain,
% 2.01/2.21 (hskp1),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2842, 48, 45, 47, 46, 44])).
% 2.01/2.21 tff(2844,plain,
% 2.01/2.21 (~c0_1(a899)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[292, 2843])).
% 2.01/2.21 tff(2845,plain,
% 2.01/2.21 (c2_1(a899)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[300, 2843])).
% 2.01/2.21 tff(2846,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2847,plain,
% 2.01/2.21 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2848,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910))))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2847])).
% 2.01/2.21 tff(2849,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2848, 2846])).
% 2.01/2.21 tff(2850,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2851,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910))),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2850, 2849])).
% 2.01/2.21 tff(2852,plain,
% 2.01/2.21 (~c3_1(a899)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2851, 112, 2363, 2845, 2816, 2815, 2814, 2355, 2349, 2844, 1721])).
% 2.01/2.21 tff(2853,plain,
% 2.01/2.21 (c1_1(a899)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[308, 2843])).
% 2.01/2.21 tff(2854,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2855,plain,
% 2.01/2.21 ((hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910))) <=> (hskp14 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a910)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2856,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a910))))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2855])).
% 2.01/2.21 tff(2857,plain,
% 2.01/2.21 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a910)))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2856, 2854])).
% 2.01/2.21 tff(2858,plain,
% 2.01/2.21 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2859,plain,
% 2.01/2.21 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c1_1(a899)) | (~c3_1(a910))),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 2.01/2.21 tff(2860,plain,
% 2.01/2.21 (hskp14 | (~c3_1(a910))),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2859, 112, 2853, 2845, 2355, 2349, 881, 2852])).
% 2.01/2.21 tff(2861,plain,
% 2.01/2.21 (hskp14),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2860, 2802])).
% 2.01/2.21 tff(2862,plain,
% 2.01/2.21 (~c1_1(a918)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[672, 2861])).
% 2.01/2.21 tff(2863,plain,
% 2.01/2.21 (c3_1(a918)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[742, 2861])).
% 2.01/2.21 tff(2864,plain,
% 2.01/2.21 (c0_1(a918)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[734, 2861])).
% 2.01/2.21 tff(2865,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c0_1(a910) | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a910)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a910) | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a910)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2866,plain,
% 2.01/2.21 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910))) <=> (c1_1(a918) | c0_1(a910) | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a910)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2867,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c0_1(a910) | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a910)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2866])).
% 2.01/2.21 tff(2868,plain,
% 2.01/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a910) | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a910)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2867, 2865])).
% 2.01/2.21 tff(2869,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))),
% 2.01/2.21 inference(quant_inst,[status(thm)],[])).
% 2.01/2.21 tff(2870,plain,
% 2.01/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c0_1(a910) | c2_1(a910) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a910)) | (~c0_1(a918)) | (~c3_1(a918))),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 2.01/2.21 tff(2871,plain,
% 2.01/2.21 ($false),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2870, 112, 2864, 2863, 2792, 2791, 2862, 2355, 2349, 2790, 271, 2802])).
% 2.01/2.21 tff(2872,plain,(c3_1(a901) | hskp31 | c1_1(a907) | c2_1(a901) | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.21 tff(2873,plain,
% 2.01/2.21 (c3_1(a901)),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2872, 47, 45, 46, 44])).
% 2.01/2.21 tff(2874,plain,
% 2.01/2.21 (((~hskp2) | (~c3_1(a901))) <=> ((~hskp2) | (~c3_1(a901)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2875,plain,
% 2.01/2.21 (((~c3_1(a901)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a901)))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2876,axiom,((~c3_1(a901)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 2.01/2.21 tff(2877,plain,
% 2.01/2.21 ((~hskp2) | (~c3_1(a901))),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2876, 2875])).
% 2.01/2.21 tff(2878,plain,
% 2.01/2.21 ((~hskp2) | (~c3_1(a901))),
% 2.01/2.21 inference(modus_ponens,[status(thm)],[2877, 2874])).
% 2.01/2.21 tff(2879,plain,
% 2.01/2.21 (~hskp2),
% 2.01/2.21 inference(unit_resolution,[status(thm)],[2878, 2873])).
% 2.01/2.21 tff(2880,plain,
% 2.01/2.21 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | c0_1(a912))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | c0_1(a912))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2881,plain,
% 2.01/2.21 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c0_1(a912)) <=> (hskp1 | hskp0 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | c0_1(a912))),
% 2.01/2.21 inference(rewrite,[status(thm)],[])).
% 2.01/2.21 tff(2882,plain,
% 2.01/2.21 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c0_1(a912))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | c0_1(a912)))),
% 2.01/2.21 inference(monotonicity,[status(thm)],[2881])).
% 2.01/2.21 tff(2883,plain,
% 2.01/2.21 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c0_1(a912))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | c0_1(a912))),
% 2.01/2.21 inference(transitivity,[status(thm)],[2882, 2880])).
% 2.01/2.21 tff(2884,plain,
% 2.01/2.21 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a912) | c1_1(a912) | c0_1(a912))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(2885,plain,
% 2.01/2.22 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | c0_1(a912)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[2884, 2883])).
% 2.01/2.22 tff(2886,plain,
% 2.01/2.22 (hskp1 | c2_1(a912) | c0_1(a912)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2885, 112, 31, 801, 20])).
% 2.01/2.22 tff(2887,plain,
% 2.01/2.22 (c0_1(a912)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2886, 152, 802])).
% 2.01/2.22 tff(2888,assumption,(~hskp2), introduced(assumption)).
% 2.01/2.22 tff(2889,plain,
% 2.01/2.22 (c3_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1495, 32, 31, 1479])).
% 2.01/2.22 tff(2890,plain,
% 2.01/2.22 (hskp10),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2280, 32, 152, 2889, 45, 31, 44])).
% 2.01/2.22 tff(2891,plain,
% 2.01/2.22 (~c2_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2348, 2890])).
% 2.01/2.22 tff(2892,plain,
% 2.01/2.22 (~c0_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2354, 2890])).
% 2.01/2.22 tff(2893,plain,
% 2.01/2.22 (c1_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2362, 2890])).
% 2.01/2.22 tff(2894,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2895,plain,
% 2.01/2.22 (((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2896,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910))))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[2895])).
% 2.01/2.22 tff(2897,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)))),
% 2.01/2.22 inference(transitivity,[status(thm)],[2896, 2894])).
% 2.01/2.22 tff(2898,plain,
% 2.01/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a912) | c1_1(a912) | c2_1(a912))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(2899,plain,
% 2.01/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910))),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 2.01/2.22 tff(2900,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2899, 112, 2893, 2889, 801, 802, 813, 2892, 2891, 44, 1721, 1479])).
% 2.01/2.22 tff(2901,plain,(hskp17 | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a907) | hskp1 | c1_1(a907) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(2902,plain,
% 2.01/2.22 (hskp17),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2901, 813, 802, 801, 44, 152, 45, 31])).
% 2.01/2.22 tff(2903,plain,
% 2.01/2.22 (~c3_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[828, 2902])).
% 2.01/2.22 tff(2904,plain,
% 2.01/2.22 (~c2_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[834, 2902])).
% 2.01/2.22 tff(2905,plain,
% 2.01/2.22 (c1_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[842, 2902])).
% 2.01/2.22 tff(2906,plain,
% 2.01/2.22 (~c0_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[849, 46, 112, 2905, 2904, 2903, 10])).
% 2.01/2.22 tff(2907,plain,
% 2.01/2.22 (hskp9),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2404, 112, 2904, 2903, 801, 802, 813, 1310, 2906])).
% 2.01/2.22 tff(2908,plain,
% 2.01/2.22 (~c2_1(a909)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1323, 2907])).
% 2.01/2.22 tff(2909,plain,
% 2.01/2.22 (~c1_1(a909)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1329, 2907])).
% 2.01/2.22 tff(2910,plain,
% 2.01/2.22 (hskp10),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[858, 2902, 813, 802, 801, 46])).
% 2.01/2.22 tff(2911,plain,
% 2.01/2.22 (~c2_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2348, 2910])).
% 2.01/2.22 tff(2912,plain,
% 2.01/2.22 (~c0_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2354, 2910])).
% 2.01/2.22 tff(2913,plain,
% 2.01/2.22 (c1_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2362, 2910])).
% 2.01/2.22 tff(2914,plain,
% 2.01/2.22 (~c3_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2899, 112, 2913, 801, 802, 813, 2912, 2911, 44, 1721, 1479])).
% 2.01/2.22 tff(2915,plain,
% 2.01/2.22 (hskp28),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2687, 2914, 2888, 45])).
% 2.01/2.22 tff(2916,plain,
% 2.01/2.22 (c0_1(a900)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[965, 2915])).
% 2.01/2.22 tff(2917,plain,
% 2.01/2.22 (~hskp7),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[512, 2914])).
% 2.01/2.22 tff(2918,plain,
% 2.01/2.22 (hskp7 | hskp4 | c0_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2698, 112, 2905, 2903, 523])).
% 2.01/2.22 tff(2919,plain,
% 2.01/2.22 (hskp4),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2918, 2917, 2906])).
% 2.01/2.22 tff(2920,plain,
% 2.01/2.22 (~c0_1(a909)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1335, 2907])).
% 2.01/2.22 tff(2921,plain,
% 2.01/2.22 (c2_1(a900)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[957, 2915])).
% 2.01/2.22 tff(2922,plain,
% 2.01/2.22 (c3_1(a900)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[949, 2915])).
% 2.01/2.22 tff(2923,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2050, 2922, 2921, 2920, 2919, 2916, 2909, 2908])).
% 2.01/2.22 tff(2924,plain,(c3_1(a912) | hskp2 | c1_1(a907) | c0_1(a907) | c1_1(a912) | c2_1(a912) | hskp31 | hskp1 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(2925,plain,
% 2.01/2.22 (c3_1(a912)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2924, 152, 45, 44, 801, 802, 46, 2888, 31])).
% 2.01/2.22 tff(2926,plain,
% 2.01/2.22 (~hskp17),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1470, 2925, 801, 802, 46])).
% 2.01/2.22 tff(2927,plain,
% 2.01/2.22 (c3_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1495, 2926, 31, 1479])).
% 2.01/2.22 tff(2928,plain,
% 2.01/2.22 (hskp4),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1606, 2927, 2925, 2887])).
% 2.01/2.22 tff(2929,plain,
% 2.01/2.22 (~c3_1(a904)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[536, 2928])).
% 2.01/2.22 tff(2930,plain,
% 2.01/2.22 (~c1_1(a904)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[542, 2928])).
% 2.01/2.22 tff(2931,plain,
% 2.01/2.22 (hskp22),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1544, 2925, 2887])).
% 2.01/2.22 tff(2932,plain,
% 2.01/2.22 (~c3_1(a939)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1247, 2931])).
% 2.01/2.22 tff(2933,plain,
% 2.01/2.22 (~c0_1(a939)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1253, 2931])).
% 2.01/2.22 tff(2934,plain,
% 2.01/2.22 (c2_1(a904)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[605, 2928])).
% 2.01/2.22 tff(2935,plain,
% 2.01/2.22 (c1_1(a939)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1262, 2931])).
% 2.01/2.22 tff(2936,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2260, 112, 2935, 2927, 2934, 2933, 2932, 44, 2930, 2929, 392, 1479])).
% 2.01/2.22 tff(2937,plain,(hskp1 | c0_1(a907) | c2_1(a912) | c1_1(a907) | hskp0 | c1_1(a912) | hskp31 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(2938,plain,
% 2.01/2.22 (hskp1),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2937, 802, 44, 45, 31, 801, 46, 2879])).
% 2.01/2.22 tff(2939,plain,
% 2.01/2.22 (c2_1(a899)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[300, 2938])).
% 2.01/2.22 tff(2940,plain,
% 2.01/2.22 (c1_1(a899)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[308, 2938])).
% 2.01/2.22 tff(2941,plain,
% 2.01/2.22 (c3_1(a899)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[898, 32, 31, 312])).
% 2.01/2.22 tff(2942,assumption,(c3_1(a901)), introduced(assumption)).
% 2.01/2.22 tff(2943,plain,
% 2.01/2.22 (~c2_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1495, 505, 31, 32])).
% 2.01/2.22 tff(2944,plain,
% 2.01/2.22 (~hskp2),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2878, 2942])).
% 2.01/2.22 tff(2945,plain,
% 2.01/2.22 (hskp28),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2687, 505, 2944, 45])).
% 2.01/2.22 tff(2946,plain,
% 2.01/2.22 (c3_1(a900)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[949, 2945])).
% 2.01/2.22 tff(2947,plain,
% 2.01/2.22 (c2_1(a900)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[957, 2945])).
% 2.01/2.22 tff(2948,plain,
% 2.01/2.22 (c0_1(a900)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[965, 2945])).
% 2.01/2.22 tff(2949,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~c0_1(a901)) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | (~c0_1(a901)) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2950,plain,
% 2.01/2.22 ((hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a901) | (~c3_1(a901)) | (~c0_1(a901))) <=> (hskp0 | (~c0_1(a901)) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2951,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a901) | (~c3_1(a901)) | (~c0_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~c0_1(a901)) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900))))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[2950])).
% 2.01/2.22 tff(2952,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a901) | (~c3_1(a901)) | (~c0_1(a901)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | (~c0_1(a901)) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 2.01/2.22 inference(transitivity,[status(thm)],[2951, 2949])).
% 2.01/2.22 tff(2953,plain,
% 2.01/2.22 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a901) | (~c3_1(a901)) | (~c0_1(a901)))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(2954,plain,
% 2.01/2.22 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | (~c0_1(a901)) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900))),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[2953, 2952])).
% 2.01/2.22 tff(2955,plain,
% 2.01/2.22 (~c0_1(a901)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2954, 112, 31, 2948, 2947, 2946, 47, 2942, 1526])).
% 2.01/2.22 tff(2956,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a907))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2957,plain,
% 2.01/2.22 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a907) | c1_1(a907) | c2_1(a907)) <=> (c3_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a907))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2958,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a907) | c1_1(a907) | c2_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a907)))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[2957])).
% 2.01/2.22 tff(2959,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a907) | c1_1(a907) | c2_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a907))),
% 2.01/2.22 inference(transitivity,[status(thm)],[2958, 2956])).
% 2.01/2.22 tff(2960,plain,
% 2.01/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a901) | c0_1(a901) | (~c1_1(a901)) | c3_1(a907) | c1_1(a907) | c2_1(a907))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(2961,plain,
% 2.01/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a901)) | c2_1(a907)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[2960, 2959])).
% 2.01/2.22 tff(2962,plain,
% 2.01/2.22 (~c1_1(a901)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2961, 112, 505, 312, 45, 2955, 47, 43, 1721, 2941, 2943])).
% 2.01/2.22 tff(2963,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c0_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | c1_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c0_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | c1_1(a901))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2964,plain,
% 2.01/2.22 (((~ndr1_0) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c2_1(a901) | c0_1(a901) | (~c3_1(a901)) | c3_1(a907) | c1_1(a907) | c0_1(a907)) <=> (c3_1(a907) | c0_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | c1_1(a901))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2965,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c2_1(a901) | c0_1(a901) | (~c3_1(a901)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a907) | c0_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | c1_1(a901)))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[2964])).
% 2.01/2.22 tff(2966,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c2_1(a901) | c0_1(a901) | (~c3_1(a901)) | c3_1(a907) | c1_1(a907) | c0_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c0_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | c1_1(a901))),
% 2.01/2.22 inference(transitivity,[status(thm)],[2965, 2963])).
% 2.01/2.22 tff(2967,plain,
% 2.01/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c2_1(a901) | c0_1(a901) | (~c3_1(a901)) | c3_1(a907) | c1_1(a907) | c0_1(a907))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(2968,plain,
% 2.01/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a907) | c0_1(a907) | c1_1(a907) | c0_1(a901) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | c1_1(a901)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 2.01/2.22 tff(2969,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2968, 112, 505, 44, 45, 2955, 47, 2942, 151, 2962])).
% 2.01/2.22 tff(2970,plain,(c3_1(a907) | c0_1(a907) | c1_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~c2_1(a899)) | c0_1(a899) | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(2971,plain,
% 2.01/2.22 (c3_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2970, 32, 45, 47, 2942, 312, 43, 31, 44])).
% 2.01/2.22 tff(2972,plain,
% 2.01/2.22 (hskp12 | hskp10 | (~c3_1(a899)) | (~c1_1(a899))),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[340, 112, 43, 334])).
% 2.01/2.22 tff(2973,plain,
% 2.01/2.22 (hskp12),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2972, 50, 311, 314])).
% 2.01/2.22 tff(2974,plain,
% 2.01/2.22 (~c3_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[347, 2973])).
% 2.01/2.22 tff(2975,plain,
% 2.01/2.22 (c0_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[355, 2973])).
% 2.01/2.22 tff(2976,plain,
% 2.01/2.22 (~c2_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1145, 112, 1103, 2975, 2974, 801, 802, 813, 1064])).
% 2.01/2.22 tff(2977,plain,
% 2.01/2.22 (hskp14),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[381, 50, 312, 311, 43, 314])).
% 2.01/2.22 tff(2978,plain,
% 2.01/2.22 (~c1_1(a918)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[672, 2977])).
% 2.01/2.22 tff(2979,plain,
% 2.01/2.22 (c0_1(a918)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[734, 2977])).
% 2.01/2.22 tff(2980,plain,
% 2.01/2.22 (c3_1(a918)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[742, 2977])).
% 2.01/2.22 tff(2981,plain,
% 2.01/2.22 (hskp18),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1082, 2976, 2980, 2975, 2974, 2979, 2978])).
% 2.01/2.22 tff(2982,plain,
% 2.01/2.22 (~c1_1(a929)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[771, 2981])).
% 2.01/2.22 tff(2983,plain,
% 2.01/2.22 (c2_1(a929)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[781, 2981])).
% 2.01/2.22 tff(2984,plain,
% 2.01/2.22 (c0_1(a929)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[789, 2981])).
% 2.01/2.22 tff(2985,plain,
% 2.01/2.22 (hskp3),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1095, 112, 2984, 2983, 2207, 2982, 44, 45, 1032])).
% 2.01/2.22 tff(2986,plain,
% 2.01/2.22 (~c3_1(a903)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1101, 2985])).
% 2.01/2.22 tff(2987,plain,
% 2.01/2.22 (~c1_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[409, 2973])).
% 2.01/2.22 tff(2988,plain,
% 2.01/2.22 (c2_1(a903)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1119, 2985])).
% 2.01/2.22 tff(2989,plain,
% 2.01/2.22 (c0_1(a903)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1111, 2985])).
% 2.01/2.22 tff(2990,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a913) | c3_1(a913) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | c2_1(a913))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a913) | c3_1(a913) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | c2_1(a913))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2991,plain,
% 2.01/2.22 ((hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a913) | c2_1(a913) | c1_1(a913)) <=> (hskp20 | c1_1(a913) | c3_1(a913) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | c2_1(a913))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(2992,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a913) | c2_1(a913) | c1_1(a913))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a913) | c3_1(a913) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | c2_1(a913)))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[2991])).
% 2.01/2.22 tff(2993,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a913) | c2_1(a913) | c1_1(a913))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a913) | c3_1(a913) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | c2_1(a913))),
% 2.01/2.22 inference(transitivity,[status(thm)],[2992, 2990])).
% 2.01/2.22 tff(2994,plain,
% 2.01/2.22 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c3_1(a913) | c2_1(a913) | c1_1(a913))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(2995,plain,
% 2.01/2.22 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a913) | c3_1(a913) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | c2_1(a913)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 2.01/2.22 tff(2996,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2995, 112, 1103, 2989, 2988, 2987, 2974, 2986, 1064, 2976])).
% 2.01/2.22 tff(2997,plain,(hskp10 | hskp20 | (~c3_1(a907)) | c0_1(a907) | c1_1(a907) | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~c2_1(a899)) | (~c1_1(a899)) | c0_1(a899) | (~c3_1(a899))), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(2998,plain,
% 2.01/2.22 (hskp10),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2997, 1884, 2971, 44, 45, 801, 802, 813, 312, 311, 43, 2941])).
% 2.01/2.22 tff(2999,plain,
% 2.01/2.22 (~c2_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2348, 2998])).
% 2.01/2.22 tff(3000,plain,
% 2.01/2.22 (~c0_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2354, 2998])).
% 2.01/2.22 tff(3001,plain,
% 2.01/2.22 (c1_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2362, 2998])).
% 2.01/2.22 tff(3002,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2851, 112, 3001, 312, 801, 802, 813, 3000, 2999, 43, 1721, 2941])).
% 2.01/2.22 tff(3003,plain,(hskp17 | (~c2_1(a899)) | c1_1(a912) | c2_1(a912) | c3_1(a912) | c0_1(a899) | c0_1(a907) | c1_1(a907) | (~c1_1(a899)) | c2_1(a901) | (~c3_1(a901)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(3004,plain,
% 2.01/2.22 (hskp17),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3003, 813, 801, 802, 2939, 43, 44, 45, 2940, 47, 2873, 31])).
% 2.01/2.22 tff(3005,plain,
% 2.01/2.22 (~c3_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[828, 3004])).
% 2.01/2.22 tff(3006,plain,
% 2.01/2.22 (~c2_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[834, 3004])).
% 2.01/2.22 tff(3007,plain,
% 2.01/2.22 (c1_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[842, 3004])).
% 2.01/2.22 tff(3008,plain,
% 2.01/2.22 (~c0_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[849, 46, 112, 3007, 3006, 3005, 10])).
% 2.01/2.22 tff(3009,plain,
% 2.01/2.22 (hskp10),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[858, 3004, 813, 802, 801, 46])).
% 2.01/2.22 tff(3010,plain,
% 2.01/2.22 (~c2_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2348, 3009])).
% 2.01/2.22 tff(3011,plain,
% 2.01/2.22 (~c0_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2354, 3009])).
% 2.01/2.22 tff(3012,plain,
% 2.01/2.22 (c1_1(a910)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2362, 3009])).
% 2.01/2.22 tff(3013,plain,
% 2.01/2.22 (~c3_1(a899)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2851, 112, 3012, 2939, 801, 802, 813, 3011, 3010, 43, 1721])).
% 2.01/2.22 tff(3014,plain,
% 2.01/2.22 (hskp7),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2631, 3013, 2939, 3005, 3007, 3006, 802, 813, 801, 3008, 43, 3012, 3011, 3010, 2940])).
% 2.01/2.22 tff(3015,plain,
% 2.01/2.22 (c3_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[512, 3014])).
% 2.01/2.22 tff(3016,plain,
% 2.01/2.22 ((~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2761, 112, 3007, 3006, 801, 802, 813, 44, 1721])).
% 2.01/2.22 tff(3017,plain,
% 2.01/2.22 (~c2_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3016, 3015, 3008])).
% 2.01/2.22 tff(3018,plain,
% 2.01/2.22 (hskp25),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1686, 112, 3007, 3006, 3005, 30])).
% 2.01/2.22 tff(3019,plain,
% 2.01/2.22 (~c3_1(a958)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1692, 3018])).
% 2.01/2.22 tff(3020,plain,
% 2.01/2.22 (~c1_1(a958)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1698, 3018])).
% 2.01/2.22 tff(3021,plain,
% 2.01/2.22 (~c0_1(a958)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1841, 3018])).
% 2.01/2.22 tff(3022,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2645, 112, 3015, 3021, 3020, 3019, 44, 45, 151, 3017])).
% 2.01/2.22 tff(3023,plain,(c3_1(a912) | c0_1(a907) | c1_1(a907) | c1_1(a912) | c2_1(a912) | c0_1(a899) | hskp31 | c2_1(a901) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(3024,plain,
% 2.01/2.22 (c3_1(a912)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3023, 802, 45, 801, 44, 43, 46, 47, 31])).
% 2.01/2.22 tff(3025,plain,
% 2.01/2.22 (~hskp17),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1470, 3024, 801, 802, 46])).
% 2.01/2.22 tff(3026,plain,
% 2.01/2.22 (c3_1(a907)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2970, 3025, 45, 47, 2873, 2939, 43, 31, 44])).
% 2.01/2.22 tff(3027,plain,
% 2.01/2.22 (hskp14),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[381, 50, 312, 311, 43, 2941])).
% 2.01/2.22 tff(3028,plain,
% 2.01/2.22 (~c1_1(a918)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[672, 3027])).
% 2.01/2.22 tff(3029,plain,
% 2.01/2.22 (c0_1(a918)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[734, 3027])).
% 2.01/2.22 tff(3030,plain,
% 2.01/2.22 (hskp12),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2972, 50, 311, 2941])).
% 2.01/2.22 tff(3031,plain,
% 2.01/2.22 (c0_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[355, 3030])).
% 2.01/2.22 tff(3032,plain,
% 2.01/2.22 (c3_1(a918)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[742, 3027])).
% 2.01/2.22 tff(3033,plain,
% 2.01/2.22 (~c3_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[347, 3030])).
% 2.01/2.22 tff(3034,plain,
% 2.01/2.22 (~c1_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[409, 3030])).
% 2.01/2.22 tff(3035,plain,
% 2.01/2.22 (hskp18),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1082, 1073, 1038, 695, 694, 1033, 754])).
% 2.01/2.22 tff(3036,plain,
% 2.01/2.22 (~c1_1(a929)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[771, 3035])).
% 2.01/2.22 tff(3037,plain,
% 2.01/2.22 (c2_1(a929)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[781, 3035])).
% 2.01/2.22 tff(3038,plain,
% 2.01/2.22 (c0_1(a929)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[789, 3035])).
% 2.01/2.22 tff(3039,plain,
% 2.01/2.22 (hskp3),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1095, 112, 3038, 3037, 2207, 3036, 44, 45, 1032])).
% 2.01/2.22 tff(3040,plain,
% 2.01/2.22 (~c3_1(a903)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1101, 3039])).
% 2.01/2.22 tff(3041,plain,
% 2.01/2.22 (c2_1(a903)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1119, 3039])).
% 2.01/2.22 tff(3042,plain,
% 2.01/2.22 (c0_1(a903)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1111, 3039])).
% 2.01/2.22 tff(3043,plain,
% 2.01/2.22 ($false),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[2995, 112, 1103, 3042, 3041, 704, 694, 3040, 1064, 1073])).
% 2.01/2.22 tff(3044,plain,(c2_1(a913) | hskp20 | c1_1(a913) | c3_1(a913) | (~c3_1(a907)) | c0_1(a907) | c1_1(a907) | (~c3_1(a918)) | (~c0_1(a913)) | (~c0_1(a918)) | c1_1(a918)), inference(lemma,lemma(discharge,[]))).
% 2.01/2.22 tff(3045,plain,
% 2.01/2.22 (c2_1(a913)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3044, 3034, 1884, 3033, 2207, 44, 45, 3032, 3031, 3029, 3028])).
% 2.01/2.22 tff(3046,plain,
% 2.01/2.22 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | c3_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | c3_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3047,plain,
% 2.01/2.22 ((hskp16 | hskp10 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913))) <=> (hskp16 | hskp10 | c3_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3048,plain,
% 2.01/2.22 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | c3_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913))))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[3047])).
% 2.01/2.22 tff(3049,plain,
% 2.01/2.22 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | c3_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.01/2.22 inference(transitivity,[status(thm)],[3048, 3046])).
% 2.01/2.22 tff(3050,plain,
% 2.01/2.22 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(3051,plain,
% 2.01/2.22 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | c3_1(a913) | (~ndr1_0) | (~c0_1(a913)) | (~c2_1(a913))),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 2.01/2.22 tff(3052,plain,
% 2.01/2.22 (hskp16 | (~c2_1(a913))),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3051, 112, 50, 3031, 3033, 1906])).
% 2.01/2.22 tff(3053,plain,
% 2.01/2.22 (hskp16),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3052, 3045])).
% 2.01/2.22 tff(3054,plain,
% 2.01/2.22 (~c3_1(a923)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1919, 3053])).
% 2.01/2.22 tff(3055,plain,
% 2.01/2.22 (c2_1(a923)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1927, 3053])).
% 2.01/2.22 tff(3056,plain,
% 2.01/2.22 (c0_1(a923)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1934, 112, 32, 31, 3055, 3054, 891])).
% 2.01/2.22 tff(3057,plain,
% 2.01/2.22 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 2.01/2.22 inference(bind,[status(th)],[])).
% 2.01/2.22 tff(3058,plain,
% 2.01/2.22 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.01/2.22 inference(quant_intro,[status(thm)],[3057])).
% 2.01/2.22 tff(3059,plain,
% 2.01/2.22 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3060,plain,
% 2.01/2.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 2.01/2.22 inference(bind,[status(th)],[])).
% 2.01/2.22 tff(3061,plain,
% 2.01/2.22 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.01/2.22 inference(quant_intro,[status(thm)],[3060])).
% 2.01/2.22 tff(3062,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 2.01/2.22 tff(3063,plain,
% 2.01/2.22 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 2.01/2.22 tff(3064,plain,
% 2.01/2.22 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3063, 3059])).
% 2.01/2.22 tff(3065,plain,(
% 2.01/2.22 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.01/2.22 inference(skolemize,[status(sab)],[3064])).
% 2.01/2.22 tff(3066,plain,
% 2.01/2.22 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3065, 3058])).
% 2.01/2.22 tff(3067,plain,
% 2.01/2.22 (((~hskp16) | c1_1(a923)) <=> ((~hskp16) | c1_1(a923))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3068,axiom,((~hskp16) | c1_1(a923)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 2.01/2.22 tff(3069,plain,
% 2.01/2.22 ((~hskp16) | c1_1(a923)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3068, 3067])).
% 2.01/2.22 tff(3070,plain,
% 2.01/2.22 ((~hskp16) | c1_1(a923)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3069, 3067])).
% 2.01/2.22 tff(3071,plain,
% 2.01/2.22 ((~hskp16) | c1_1(a923)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3070, 3067])).
% 2.01/2.22 tff(3072,plain,
% 2.01/2.22 ((~hskp16) | c1_1(a923)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3071, 3067])).
% 2.01/2.22 tff(3073,plain,
% 2.01/2.22 ((~hskp16) | c1_1(a923)),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3072, 3067])).
% 2.01/2.22 tff(3074,plain,
% 2.01/2.22 (c1_1(a923)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3073, 3053])).
% 2.01/2.22 tff(3075,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c1_1(a923)) | (~c2_1(a923)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c1_1(a923)) | (~c2_1(a923)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3076,plain,
% 2.01/2.22 ((hskp9 | (~ndr1_0) | (~c1_1(a923)) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923))) <=> (hskp9 | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c1_1(a923)) | (~c2_1(a923)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3077,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a923)) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c1_1(a923)) | (~c2_1(a923))))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[3076])).
% 2.01/2.22 tff(3078,plain,
% 2.01/2.22 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a923)) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c1_1(a923)) | (~c2_1(a923)))),
% 2.01/2.22 inference(transitivity,[status(thm)],[3077, 3075])).
% 2.01/2.22 tff(3079,plain,
% 2.01/2.22 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a923)) | (~c2_1(a923)) | (~c0_1(a923)) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)))),
% 2.01/2.22 inference(quant_inst,[status(thm)],[])).
% 2.01/2.22 tff(3080,plain,
% 2.01/2.22 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a923) | (~ndr1_0) | (~c0_1(a923)) | (~c1_1(a923)) | (~c2_1(a923))),
% 2.01/2.22 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 2.01/2.22 tff(3081,plain,
% 2.01/2.22 (hskp9),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[3080, 112, 3074, 3055, 3054, 3066, 3056])).
% 2.01/2.22 tff(3082,plain,
% 2.01/2.22 (~c2_1(a909)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1323, 3081])).
% 2.01/2.22 tff(3083,plain,
% 2.01/2.22 (~c1_1(a909)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1329, 3081])).
% 2.01/2.22 tff(3084,plain,
% 2.01/2.22 (~c0_1(a909)),
% 2.01/2.22 inference(unit_resolution,[status(thm)],[1335, 3081])).
% 2.01/2.22 tff(3085,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c2_1(a913)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c2_1(a913)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3086,plain,
% 2.01/2.22 (((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c1_1(a909) | c0_1(a909) | c2_1(a909)) <=> (c1_1(a913) | c3_1(a913) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c2_1(a913)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.22 inference(rewrite,[status(thm)],[])).
% 2.01/2.22 tff(3087,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c2_1(a913)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 2.01/2.22 inference(monotonicity,[status(thm)],[3086])).
% 2.01/2.22 tff(3088,plain,
% 2.01/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c2_1(a913)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3087, 3085])).
% 2.01/2.23 tff(3089,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a918)) | (~c2_1(a918)) | (~c0_1(a918)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c1_1(a909) | c0_1(a909) | c2_1(a909))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3090,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c2_1(a913)) | (~c2_1(a918)) | (~c0_1(a918)) | (~c3_1(a918))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3089, 3088])).
% 2.01/2.23 tff(3091,plain,
% 2.01/2.23 (~c2_1(a918)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3090, 112, 3029, 3032, 3034, 3033, 3084, 3083, 3082, 870, 3045])).
% 2.01/2.23 tff(3092,plain,
% 2.01/2.23 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3093,plain,
% 2.01/2.23 ((hskp4 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907))) <=> (hskp4 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3094,plain,
% 2.01/2.23 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918))))),
% 2.01/2.23 inference(monotonicity,[status(thm)],[3093])).
% 2.01/2.23 tff(3095,plain,
% 2.01/2.23 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3094, 3092])).
% 2.01/2.23 tff(3096,plain,
% 2.01/2.23 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3097,plain,
% 2.01/2.23 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | c2_1(a918) | (~c0_1(a918)) | (~c3_1(a918))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 2.01/2.23 tff(3098,plain,
% 2.01/2.23 (hskp4),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3097, 112, 3029, 3032, 2207, 44, 45, 640, 3091])).
% 2.01/2.23 tff(3099,plain,
% 2.01/2.23 (~c3_1(a904)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[536, 3098])).
% 2.01/2.23 tff(3100,plain,
% 2.01/2.23 (~c1_1(a904)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[542, 3098])).
% 2.01/2.23 tff(3101,plain,
% 2.01/2.23 (hskp22),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[1780, 112, 3029, 3032, 3028, 1234, 3091])).
% 2.01/2.23 tff(3102,plain,
% 2.01/2.23 (~c3_1(a939)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[1247, 3101])).
% 2.01/2.23 tff(3103,plain,
% 2.01/2.23 (~c0_1(a939)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[1253, 3101])).
% 2.01/2.23 tff(3104,plain,
% 2.01/2.23 (c2_1(a904)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[605, 3098])).
% 2.01/2.23 tff(3105,plain,
% 2.01/2.23 (c1_1(a939)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[1262, 3101])).
% 2.01/2.23 tff(3106,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)) | (~c1_1(a939)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3107,plain,
% 2.01/2.23 (((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)) | (~c1_1(a939)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3108,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)) | (~c1_1(a939))))),
% 2.01/2.23 inference(monotonicity,[status(thm)],[3107])).
% 2.01/2.23 tff(3109,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)) | (~c1_1(a939)))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3108, 3106])).
% 2.01/2.23 tff(3110,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3111,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)) | (~c1_1(a939))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3110, 3109])).
% 2.01/2.23 tff(3112,plain,
% 2.01/2.23 ($false),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3111, 112, 3105, 3104, 312, 3103, 3102, 3100, 3099, 43, 392, 2941])).
% 2.01/2.23 tff(3113,plain,(hskp10 | (~c2_1(a899)) | c0_1(a899) | (~c3_1(a907)) | c0_1(a907) | c1_1(a907) | hskp17 | hskp0 | (~c1_1(a899))), inference(lemma,lemma(discharge,[]))).
% 2.01/2.23 tff(3114,plain,
% 2.01/2.23 (hskp10),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3113, 2939, 43, 3026, 44, 45, 3025, 31, 2940])).
% 2.01/2.23 tff(3115,plain,
% 2.01/2.23 (~c2_1(a910)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[2348, 3114])).
% 2.01/2.23 tff(3116,plain,
% 2.01/2.23 (~c0_1(a910)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[2354, 3114])).
% 2.01/2.23 tff(3117,plain,
% 2.01/2.23 (c1_1(a910)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[2362, 3114])).
% 2.01/2.23 tff(3118,plain,
% 2.01/2.23 (c3_1(a899)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[898, 3025, 31, 2939])).
% 2.01/2.23 tff(3119,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c3_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3120,plain,
% 2.01/2.23 (((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899))) <=> (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3121,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c3_1(a910)))),
% 2.01/2.23 inference(monotonicity,[status(thm)],[3120])).
% 2.01/2.23 tff(3122,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3121, 3119])).
% 2.01/2.23 tff(3123,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3124,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c3_1(a910)),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3123, 3122])).
% 2.01/2.23 tff(3125,plain,
% 2.01/2.23 (c3_1(a910)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3124, 112, 3117, 2939, 801, 802, 3024, 3115, 43, 1384, 3118])).
% 2.01/2.23 tff(3126,plain,
% 2.01/2.23 (c3_1(a910)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3124, 112, 2366, 312, 801, 802, 1385, 2364, 43, 1384, 2941])).
% 2.01/2.23 tff(3127,assumption,(~c0_1(a913)), introduced(assumption)).
% 2.01/2.23 tff(3128,plain,
% 2.01/2.23 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3129,plain,
% 2.01/2.23 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a913) | c3_1(a913) | (~c2_1(a913))) <=> (hskp17 | hskp0 | c0_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3130,plain,
% 2.01/2.23 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a913) | c3_1(a913) | (~c2_1(a913)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c0_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913))))),
% 2.01/2.23 inference(monotonicity,[status(thm)],[3129])).
% 2.01/2.23 tff(3131,plain,
% 2.01/2.23 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a913) | c3_1(a913) | (~c2_1(a913)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3130, 3128])).
% 2.01/2.23 tff(3132,plain,
% 2.01/2.23 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a913) | c3_1(a913) | (~c2_1(a913)))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3133,plain,
% 2.01/2.23 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c0_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3132, 3131])).
% 2.01/2.23 tff(3134,plain,
% 2.01/2.23 (c0_1(a913) | (~c2_1(a913))),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3133, 112, 32, 31, 694, 891])).
% 2.01/2.23 tff(3135,plain,
% 2.01/2.23 (~c2_1(a913)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3134, 3127])).
% 2.01/2.23 tff(3136,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a913) | c1_1(a913) | c3_1(a913) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a913) | c1_1(a913) | c3_1(a913) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3137,plain,
% 2.01/2.23 (((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | c0_1(a913)) <=> (c0_1(a913) | c1_1(a913) | c3_1(a913) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3138,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | c0_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a913) | c1_1(a913) | c3_1(a913) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910))))),
% 2.01/2.23 inference(monotonicity,[status(thm)],[3137])).
% 2.01/2.23 tff(3139,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | c0_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a913) | c1_1(a913) | c3_1(a913) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3138, 3136])).
% 2.01/2.23 tff(3140,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | c0_1(a913))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3141,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a913) | c1_1(a913) | c3_1(a913) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 2.01/2.23 tff(3142,plain,
% 2.01/2.23 (c0_1(a913) | c1_1(a913)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3141, 112, 694, 801, 802, 1385, 2365, 2364, 151, 3126])).
% 2.01/2.23 tff(3143,plain,
% 2.01/2.23 (c1_1(a913)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3142, 3127])).
% 2.01/2.23 tff(3144,plain,
% 2.01/2.23 (~hskp12),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[355, 3127])).
% 2.01/2.23 tff(3145,plain,
% 2.01/2.23 (hskp13),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[2526, 3144])).
% 2.01/2.23 tff(3146,plain,
% 2.01/2.23 (~c2_1(a914)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[187, 3145])).
% 2.01/2.23 tff(3147,plain,
% 2.01/2.23 (~c1_1(a914)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[193, 3145])).
% 2.01/2.23 tff(3148,plain,
% 2.01/2.23 (c3_1(a914)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[201, 3145])).
% 2.01/2.23 tff(3149,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a914) | c2_1(a914) | (~c1_1(a913)) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a913) | (~c3_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a914) | c2_1(a914) | (~c1_1(a913)) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a913) | (~c3_1(a914)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3150,plain,
% 2.01/2.23 (((~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c1_1(a913)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899))) <=> (c1_1(a914) | c2_1(a914) | (~c1_1(a913)) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a913) | (~c3_1(a914)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3151,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c1_1(a913)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a914) | c2_1(a914) | (~c1_1(a913)) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a913) | (~c3_1(a914))))),
% 2.01/2.23 inference(monotonicity,[status(thm)],[3150])).
% 2.01/2.23 tff(3152,plain,
% 2.01/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c1_1(a913)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a914) | c2_1(a914) | (~c1_1(a913)) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a913) | (~c3_1(a914)))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3151, 3149])).
% 2.01/2.23 tff(3153,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a913) | c3_1(a913) | (~c1_1(a913)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3154,plain,
% 2.01/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a914) | c2_1(a914) | (~c1_1(a913)) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a913) | (~c3_1(a914))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 2.01/2.23 tff(3155,plain,
% 2.01/2.23 ($false),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3154, 112, 3148, 312, 3147, 3146, 3143, 694, 43, 1384, 2941, 3135])).
% 2.01/2.23 tff(3156,plain,(c0_1(a913) | (~c2_1(a899)) | c3_1(a913) | c0_1(a899) | (~c1_1(a910)) | c0_1(a910) | c2_1(a910) | hskp17 | hskp0 | c1_1(a912) | c2_1(a912) | (~c3_1(a912))), inference(lemma,lemma(discharge,[]))).
% 2.01/2.23 tff(3157,plain,
% 2.01/2.23 (c0_1(a913)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3156, 694, 312, 43, 2366, 2365, 2364, 32, 31, 801, 802, 1385])).
% 2.01/2.23 tff(3158,assumption,(c1_1(a913)), introduced(assumption)).
% 2.01/2.23 tff(3159,assumption,(c3_1(a910)), introduced(assumption)).
% 2.01/2.23 tff(3160,plain,
% 2.01/2.23 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.01/2.23 inference(bind,[status(th)],[])).
% 2.01/2.23 tff(3161,plain,
% 2.01/2.23 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.01/2.23 inference(quant_intro,[status(thm)],[3160])).
% 2.01/2.23 tff(3162,plain,
% 2.01/2.23 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3163,plain,
% 2.01/2.23 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.01/2.23 inference(bind,[status(th)],[])).
% 2.01/2.23 tff(3164,plain,
% 2.01/2.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.01/2.23 inference(quant_intro,[status(thm)],[3163])).
% 2.01/2.23 tff(3165,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 2.01/2.23 tff(3166,plain,
% 2.01/2.23 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 2.01/2.23 tff(3167,plain,
% 2.01/2.23 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3166, 3162])).
% 2.01/2.23 tff(3168,plain,(
% 2.01/2.23 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.01/2.23 inference(skolemize,[status(sab)],[3167])).
% 2.01/2.23 tff(3169,plain,
% 2.01/2.23 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3168, 3161])).
% 2.01/2.23 tff(3170,plain,
% 2.01/2.23 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~c1_1(a913)) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | (~c1_1(a913)) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)) | (~c0_1(a913)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3171,plain,
% 2.01/2.23 ((hskp4 | (~ndr1_0) | c3_1(a913) | (~c1_1(a913)) | (~c0_1(a913)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910))) <=> (hskp4 | (~c1_1(a913)) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)) | (~c0_1(a913)))),
% 2.01/2.23 inference(rewrite,[status(thm)],[])).
% 2.01/2.23 tff(3172,plain,
% 2.01/2.23 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a913) | (~c1_1(a913)) | (~c0_1(a913)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~c1_1(a913)) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)) | (~c0_1(a913))))),
% 2.01/2.23 inference(monotonicity,[status(thm)],[3171])).
% 2.01/2.23 tff(3173,plain,
% 2.01/2.23 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a913) | (~c1_1(a913)) | (~c0_1(a913)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | (~c1_1(a913)) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)) | (~c0_1(a913)))),
% 2.01/2.23 inference(transitivity,[status(thm)],[3172, 3170])).
% 2.01/2.23 tff(3174,plain,
% 2.01/2.23 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a913) | (~c1_1(a913)) | (~c0_1(a913)) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))),
% 2.01/2.23 inference(quant_inst,[status(thm)],[])).
% 2.01/2.23 tff(3175,plain,
% 2.01/2.23 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | (~c1_1(a913)) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)) | (~c0_1(a913))),
% 2.01/2.23 inference(modus_ponens,[status(thm)],[3174, 3173])).
% 2.01/2.23 tff(3176,plain,
% 2.01/2.23 (hskp4 | (~c1_1(a913)) | (~c0_1(a913))),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3175, 112, 694, 2365, 2364, 3169, 3159])).
% 2.01/2.23 tff(3177,plain,
% 2.01/2.23 (hskp4),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[3176, 3158, 695])).
% 2.01/2.23 tff(3178,plain,
% 2.01/2.23 (~c3_1(a904)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[536, 3177])).
% 2.01/2.23 tff(3179,plain,
% 2.01/2.23 (~hskp12),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[409, 3158])).
% 2.01/2.23 tff(3180,plain,
% 2.01/2.23 (c2_1(a904)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[605, 3177])).
% 2.01/2.23 tff(3181,plain,
% 2.01/2.23 (~c1_1(a904)),
% 2.01/2.23 inference(unit_resolution,[status(thm)],[542, 3177])).
% 2.01/2.24 tff(3182,plain,
% 2.01/2.24 ($false),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[2538, 3181, 3180, 3179, 3178, 2366, 2365, 2364])).
% 2.01/2.24 tff(3183,plain,((~c1_1(a913)) | (~c1_1(a910)) | c0_1(a910) | c2_1(a910) | (~c0_1(a913)) | c3_1(a913) | (~c3_1(a910))), inference(lemma,lemma(discharge,[]))).
% 2.01/2.24 tff(3184,plain,
% 2.01/2.24 (~c1_1(a913)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3183, 3157, 2365, 2364, 2366, 694, 3126])).
% 2.01/2.24 tff(3185,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a913)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a913)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3186,plain,
% 2.01/2.24 (((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910))) <=> (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a913)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3187,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a913))))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3186])).
% 2.01/2.24 tff(3188,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a913)))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3187, 3185])).
% 2.01/2.24 tff(3189,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3190,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a913))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 2.01/2.24 tff(3191,plain,
% 2.01/2.24 (c1_1(a913) | (~c2_1(a913))),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3190, 112, 2366, 694, 2365, 2364, 503, 3126])).
% 2.01/2.24 tff(3192,plain,
% 2.01/2.24 (~c2_1(a913)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3191, 3184])).
% 2.01/2.24 tff(3193,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a913))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3194,plain,
% 2.01/2.24 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913)) <=> (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a913))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3195,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a913)))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3194])).
% 2.01/2.24 tff(3196,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a913))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3195, 3193])).
% 2.01/2.24 tff(3197,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3198,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | c2_1(a913)),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3197, 3196])).
% 2.01/2.24 tff(3199,plain,
% 2.01/2.24 (c1_1(a913) | c2_1(a913)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3198, 112, 2366, 312, 694, 2365, 2364, 43, 1721, 2941])).
% 2.01/2.24 tff(3200,plain,
% 2.01/2.24 ($false),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3199, 3192, 3184])).
% 2.01/2.24 tff(3201,plain,(c3_1(a913) | (~c1_1(a910)) | (~c2_1(a899)) | c0_1(a910) | c2_1(a910) | c0_1(a899) | hskp17 | hskp0 | c1_1(a912) | c2_1(a912) | (~c3_1(a912))), inference(lemma,lemma(discharge,[]))).
% 2.01/2.24 tff(3202,plain,
% 2.01/2.24 (c3_1(a913)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3201, 3117, 2939, 3116, 3115, 43, 3025, 31, 801, 802, 3024])).
% 2.01/2.24 tff(3203,plain,
% 2.01/2.24 (~hskp12),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[347, 3202])).
% 2.01/2.24 tff(3204,plain,
% 2.01/2.24 (((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))) <=> ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp6 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3205,plain,
% 2.01/2.24 ((hskp12 | hskp6 | (~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910))) <=> (hskp12 | hskp6 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3206,plain,
% 2.01/2.24 (((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | (~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)))) <=> ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910))))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3205])).
% 2.01/2.24 tff(3207,plain,
% 2.01/2.24 (((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | (~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)))) <=> ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp6 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3206, 3204])).
% 2.01/2.24 tff(3208,plain,
% 2.01/2.24 ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp6 | (~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3209,plain,
% 2.01/2.24 ((~![U: $i] : (hskp12 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp6 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 2.01/2.24 tff(3210,plain,
% 2.01/2.24 (hskp12 | hskp6 | (~c3_1(a910))),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3209, 112, 3117, 3115, 463])).
% 2.01/2.24 tff(3211,plain,
% 2.01/2.24 (hskp6),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3210, 3203, 3125])).
% 2.01/2.24 tff(3212,plain,
% 2.01/2.24 (~c1_1(a906)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[492, 3211])).
% 2.01/2.24 tff(3213,plain,
% 2.01/2.24 (c3_1(a906)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[478, 3211])).
% 2.01/2.24 tff(3214,plain,
% 2.01/2.24 (c2_1(a906)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[486, 3211])).
% 2.01/2.24 tff(3215,plain,
% 2.01/2.24 (hskp24),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1180, 112, 3025, 3214, 3213, 3212, 1169])).
% 2.01/2.24 tff(3216,plain,
% 2.01/2.24 (c3_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1188, 3215])).
% 2.01/2.24 tff(3217,plain,
% 2.01/2.24 (c1_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1196, 3215])).
% 2.01/2.24 tff(3218,plain,
% 2.01/2.24 (~hskp11),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1390, 3024])).
% 2.01/2.24 tff(3219,plain,
% 2.01/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3220,plain,
% 2.01/2.24 ((hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910))) <=> (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3221,plain,
% 2.01/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3220])).
% 2.01/2.24 tff(3222,plain,
% 2.01/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3221, 3219])).
% 2.01/2.24 tff(3223,plain,
% 2.01/2.24 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3224,plain,
% 2.01/2.24 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3223, 3222])).
% 2.01/2.24 tff(3225,plain,
% 2.01/2.24 (~c0_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3224, 112, 3218, 3217, 3216, 3117, 3116, 3115, 1402])).
% 2.01/2.24 tff(3226,plain,
% 2.01/2.24 (~c2_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1209, 3215])).
% 2.01/2.24 tff(3227,assumption,(hskp25), introduced(assumption)).
% 2.01/2.24 tff(3228,plain,
% 2.01/2.24 (~c3_1(a958)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1692, 3227])).
% 2.01/2.24 tff(3229,plain,
% 2.01/2.24 (~c0_1(a958)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1841, 3227])).
% 2.01/2.24 tff(3230,plain,
% 2.01/2.24 (~c2_1(a958)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1848, 112, 32, 31, 3229, 3228, 891])).
% 2.01/2.24 tff(3231,plain,
% 2.01/2.24 (~c1_1(a958)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1698, 3227])).
% 2.01/2.24 tff(3232,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c2_1(a953) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a953)) | c0_1(a953) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a953) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a953)) | c0_1(a953) | c2_1(a958))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3233,plain,
% 2.01/2.24 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c1_1(a958) | c3_1(a958) | c2_1(a953) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a953)) | c0_1(a953) | c2_1(a958))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3234,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c2_1(a953) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a953)) | c0_1(a953) | c2_1(a958)))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3233])).
% 2.01/2.24 tff(3235,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a953) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a953)) | c0_1(a953) | c2_1(a958))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3234, 3232])).
% 2.01/2.24 tff(3236,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3237,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a953) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c1_1(a953)) | c0_1(a953) | c2_1(a958)),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3236, 3235])).
% 2.01/2.24 tff(3238,plain,
% 2.01/2.24 ($false),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3237, 112, 1280, 312, 3231, 3228, 1279, 43, 1721, 2941, 1989, 3230])).
% 2.01/2.24 tff(3239,plain,((~hskp25) | (~c1_1(a953)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a899) | c0_1(a953) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.01/2.24 tff(3240,plain,
% 2.01/2.24 (~hskp25),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3239, 3217, 2939, 3226, 43, 3225, 3025, 31])).
% 2.01/2.24 tff(3241,plain,
% 2.01/2.24 ((hskp25 | hskp21 | hskp0) <=> (hskp25 | hskp21 | hskp0)),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3242,plain,
% 2.01/2.24 (((hskp0 | hskp21) | hskp25) <=> (hskp25 | hskp21 | hskp0)),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3243,axiom,((hskp0 | hskp21) | hskp25), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 2.01/2.24 tff(3244,plain,
% 2.01/2.24 (hskp25 | hskp21 | hskp0),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 2.01/2.24 tff(3245,plain,
% 2.01/2.24 (hskp25 | hskp21 | hskp0),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3244, 3241])).
% 2.01/2.24 tff(3246,plain,
% 2.01/2.24 (hskp25 | hskp21 | hskp0),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3245, 3241])).
% 2.01/2.24 tff(3247,plain,
% 2.01/2.24 (hskp25 | hskp21 | hskp0),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3246, 3241])).
% 2.01/2.24 tff(3248,plain,
% 2.01/2.24 (hskp25 | hskp21 | hskp0),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3247, 3241])).
% 2.01/2.24 tff(3249,plain,
% 2.01/2.24 (hskp21),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3248, 3240, 31])).
% 2.01/2.24 tff(3250,plain,
% 2.01/2.24 (hskp14),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[441, 3249, 2939, 2940, 43])).
% 2.01/2.24 tff(3251,plain,
% 2.01/2.24 (~c1_1(a918)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[672, 3250])).
% 2.01/2.24 tff(3252,plain,
% 2.01/2.24 (hskp18),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[765, 3251, 3249, 2940, 2939, 43])).
% 2.01/2.24 tff(3253,plain,
% 2.01/2.24 (~c1_1(a929)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[771, 3252])).
% 2.01/2.24 tff(3254,plain,
% 2.01/2.24 (~c3_1(a938)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[416, 3249])).
% 2.01/2.24 tff(3255,plain,
% 2.01/2.24 (~c2_1(a938)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[422, 3249])).
% 2.01/2.24 tff(3256,plain,
% 2.01/2.24 (c2_1(a929)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[781, 3252])).
% 2.01/2.24 tff(3257,plain,
% 2.01/2.24 (c0_1(a929)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[789, 3252])).
% 2.01/2.24 tff(3258,plain,
% 2.01/2.24 (c0_1(a938)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[430, 3249])).
% 2.01/2.24 tff(3259,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a953) | c2_1(a938) | c3_1(a938) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)) | (~c1_1(a953)) | (~c3_1(a953)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a953) | c2_1(a938) | c3_1(a938) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3260,plain,
% 2.01/2.24 (((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929))) <=> (c2_1(a953) | c2_1(a938) | c3_1(a938) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3261,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a953) | c2_1(a938) | c3_1(a938) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)) | (~c1_1(a953)) | (~c3_1(a953))))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3260])).
% 2.01/2.24 tff(3262,plain,
% 2.01/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a953) | c2_1(a938) | c3_1(a938) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3261, 3259])).
% 2.01/2.24 tff(3263,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3264,plain,
% 2.01/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a953) | c2_1(a938) | c3_1(a938) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)) | (~c1_1(a953)) | (~c3_1(a953))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3263, 3262])).
% 2.01/2.24 tff(3265,plain,
% 2.01/2.24 ($false),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3264, 112, 3217, 3216, 3258, 3257, 3256, 3226, 3255, 3254, 3253, 131])).
% 2.01/2.24 tff(3266,plain,(c2_1(a912) | c0_1(a899) | hskp0 | c1_1(a912) | c0_1(a907) | c1_1(a907) | c2_1(a901) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.01/2.24 tff(3267,plain,
% 2.01/2.24 (c2_1(a912)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3266, 801, 31, 43, 44, 45, 47, 46])).
% 2.01/2.24 tff(3268,plain,
% 2.01/2.24 (~hskp11),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1679, 3267])).
% 2.01/2.24 tff(3269,plain,
% 2.01/2.24 (~hskp17),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1729, 3268, 46])).
% 2.01/2.24 tff(3270,assumption,(~c2_1(a899)), introduced(assumption)).
% 2.01/2.24 tff(3271,plain,
% 2.01/2.24 (~hskp1),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[300, 3270])).
% 2.01/2.24 tff(3272,plain,
% 2.01/2.24 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a899) | c2_1(a899) | c0_1(a899) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a899) | c2_1(a899) | c0_1(a899) | (~ndr1_0))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3273,plain,
% 2.01/2.24 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a899) | c1_1(a899) | c0_1(a899)) <=> (hskp1 | hskp0 | c1_1(a899) | c2_1(a899) | c0_1(a899) | (~ndr1_0))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3274,plain,
% 2.01/2.24 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a899) | c1_1(a899) | c0_1(a899))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a899) | c2_1(a899) | c0_1(a899) | (~ndr1_0)))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3273])).
% 2.01/2.24 tff(3275,plain,
% 2.01/2.24 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a899) | c1_1(a899) | c0_1(a899))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a899) | c2_1(a899) | c0_1(a899) | (~ndr1_0))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3274, 3272])).
% 2.01/2.24 tff(3276,plain,
% 2.01/2.24 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a899) | c1_1(a899) | c0_1(a899))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3277,plain,
% 2.01/2.24 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a899) | c2_1(a899) | c0_1(a899) | (~ndr1_0)),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3276, 3275])).
% 2.01/2.24 tff(3278,plain,
% 2.01/2.24 (hskp1 | hskp0 | c1_1(a899) | c2_1(a899)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3277, 112, 43, 20])).
% 2.01/2.24 tff(3279,plain,
% 2.01/2.24 (c1_1(a899)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3278, 3270, 31, 3271])).
% 2.01/2.24 tff(3280,plain,
% 2.01/2.24 (c2_1(a907)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1478, 3271, 45, 31])).
% 2.01/2.24 tff(3281,plain,
% 2.01/2.24 (c3_1(a907)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1495, 3280, 31, 32])).
% 2.01/2.24 tff(3282,plain,
% 2.01/2.24 (hskp24),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[2273, 3280, 32, 3281])).
% 2.01/2.24 tff(3283,plain,
% 2.01/2.24 (c3_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1188, 3282])).
% 2.01/2.24 tff(3284,plain,
% 2.01/2.24 (c1_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1196, 3282])).
% 2.01/2.24 tff(3285,plain,
% 2.01/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3286,plain,
% 2.01/2.24 ((hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899))) <=> (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3287,plain,
% 2.01/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3286])).
% 2.01/2.24 tff(3288,plain,
% 2.01/2.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3287, 3285])).
% 2.01/2.24 tff(3289,plain,
% 2.01/2.24 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3290,plain,
% 2.01/2.24 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c1_1(a953)) | (~c3_1(a953)) | (~c0_1(a953))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3289, 3288])).
% 2.01/2.24 tff(3291,plain,
% 2.01/2.24 (~c0_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3290, 112, 1430, 3284, 3283, 3279, 3270, 43, 1402])).
% 2.01/2.24 tff(3292,plain,
% 2.01/2.24 (^[U: $i] : refl((hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 2.01/2.24 inference(bind,[status(th)],[])).
% 2.01/2.24 tff(3293,plain,
% 2.01/2.24 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.01/2.24 inference(quant_intro,[status(thm)],[3292])).
% 2.01/2.24 tff(3294,plain,
% 2.01/2.24 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3295,plain,
% 2.01/2.24 (^[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)) | 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)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp1))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp1) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 2.01/2.24 inference(bind,[status(th)],[])).
% 2.01/2.24 tff(3296,plain,
% 2.01/2.24 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.01/2.24 inference(quant_intro,[status(thm)],[3295])).
% 2.01/2.24 tff(3297,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 2.01/2.24 tff(3298,plain,
% 2.01/2.24 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3297, 3296])).
% 2.01/2.24 tff(3299,plain,
% 2.01/2.24 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3298, 3294])).
% 2.01/2.24 tff(3300,plain,(
% 2.01/2.24 ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.01/2.24 inference(skolemize,[status(sab)],[3299])).
% 2.01/2.24 tff(3301,plain,
% 2.01/2.24 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3300, 3293])).
% 2.01/2.24 tff(3302,plain,
% 2.01/2.24 (~c2_1(a953)),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[1209, 3282])).
% 2.01/2.24 tff(3303,plain,
% 2.01/2.24 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c3_1(a953)) | c0_1(a953))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c3_1(a953)) | c0_1(a953))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3304,plain,
% 2.01/2.24 ((hskp30 | hskp1 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c3_1(a953))) <=> (hskp30 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c3_1(a953)) | c0_1(a953))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3305,plain,
% 2.01/2.24 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c3_1(a953)))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c3_1(a953)) | c0_1(a953)))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[3304])).
% 2.01/2.24 tff(3306,plain,
% 2.01/2.24 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c3_1(a953)))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c3_1(a953)) | c0_1(a953))),
% 2.01/2.24 inference(transitivity,[status(thm)],[3305, 3303])).
% 2.01/2.24 tff(3307,plain,
% 2.01/2.24 ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a953) | c0_1(a953) | (~c3_1(a953)))),
% 2.01/2.24 inference(quant_inst,[status(thm)],[])).
% 2.01/2.24 tff(3308,plain,
% 2.01/2.24 ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c3_1(a953)) | c0_1(a953)),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3307, 3306])).
% 2.01/2.24 tff(3309,plain,
% 2.01/2.24 (hskp30),
% 2.01/2.24 inference(unit_resolution,[status(thm)],[3308, 112, 3271, 3283, 3302, 3301, 3291])).
% 2.01/2.24 tff(3310,plain,
% 2.01/2.24 (((~hskp30) | c1_1(a919)) <=> ((~hskp30) | c1_1(a919))),
% 2.01/2.24 inference(rewrite,[status(thm)],[])).
% 2.01/2.24 tff(3311,axiom,((~hskp30) | c1_1(a919)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 2.01/2.24 tff(3312,plain,
% 2.01/2.24 ((~hskp30) | c1_1(a919)),
% 2.01/2.24 inference(modus_ponens,[status(thm)],[3311, 3310])).
% 2.01/2.25 tff(3313,plain,
% 2.01/2.25 ((~hskp30) | c1_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3312, 3310])).
% 2.01/2.25 tff(3314,plain,
% 2.01/2.25 ((~hskp30) | c1_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3313, 3310])).
% 2.01/2.25 tff(3315,plain,
% 2.01/2.25 ((~hskp30) | c1_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3314, 3310])).
% 2.01/2.25 tff(3316,plain,
% 2.01/2.25 ((~hskp30) | c1_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3315, 3310])).
% 2.01/2.25 tff(3317,plain,
% 2.01/2.25 (c1_1(a919)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3316, 3309])).
% 2.01/2.25 tff(3318,plain,
% 2.01/2.25 (((~hskp30) | c0_1(a919)) <=> ((~hskp30) | c0_1(a919))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3319,axiom,((~hskp30) | c0_1(a919)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 2.01/2.25 tff(3320,plain,
% 2.01/2.25 ((~hskp30) | c0_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3319, 3318])).
% 2.01/2.25 tff(3321,plain,
% 2.01/2.25 ((~hskp30) | c0_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3320, 3318])).
% 2.01/2.25 tff(3322,plain,
% 2.01/2.25 ((~hskp30) | c0_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3321, 3318])).
% 2.01/2.25 tff(3323,plain,
% 2.01/2.25 ((~hskp30) | c0_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3322, 3318])).
% 2.01/2.25 tff(3324,plain,
% 2.01/2.25 ((~hskp30) | c0_1(a919)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3323, 3318])).
% 2.01/2.25 tff(3325,plain,
% 2.01/2.25 (c0_1(a919)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3324, 3309])).
% 2.01/2.25 tff(3326,plain,
% 2.01/2.25 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c3_1(a919)) | (~c1_1(a919)) | (~c0_1(a919)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c3_1(a919)) | (~c1_1(a919)) | (~c0_1(a919)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3327,plain,
% 2.01/2.25 ((hskp11 | (~ndr1_0) | (~c1_1(a919)) | (~c3_1(a919)) | (~c0_1(a919)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899))) <=> (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c3_1(a919)) | (~c1_1(a919)) | (~c0_1(a919)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3328,plain,
% 2.01/2.25 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a919)) | (~c3_1(a919)) | (~c0_1(a919)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c3_1(a919)) | (~c1_1(a919)) | (~c0_1(a919))))),
% 2.01/2.25 inference(monotonicity,[status(thm)],[3327])).
% 2.01/2.25 tff(3329,plain,
% 2.01/2.25 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a919)) | (~c3_1(a919)) | (~c0_1(a919)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c3_1(a919)) | (~c1_1(a919)) | (~c0_1(a919)))),
% 2.01/2.25 inference(transitivity,[status(thm)],[3328, 3326])).
% 2.01/2.25 tff(3330,plain,
% 2.01/2.25 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a919)) | (~c3_1(a919)) | (~c0_1(a919)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))),
% 2.01/2.25 inference(quant_inst,[status(thm)],[])).
% 2.01/2.25 tff(3331,plain,
% 2.01/2.25 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c3_1(a919)) | (~c1_1(a919)) | (~c0_1(a919))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3330, 3329])).
% 2.01/2.25 tff(3332,plain,
% 2.01/2.25 (~c3_1(a919)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3331, 112, 1430, 3325, 3317, 3279, 3270, 43, 1402])).
% 2.01/2.25 tff(3333,plain,
% 2.01/2.25 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 2.01/2.25 inference(bind,[status(th)],[])).
% 2.01/2.25 tff(3334,plain,
% 2.01/2.25 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.01/2.25 inference(quant_intro,[status(thm)],[3333])).
% 2.01/2.25 tff(3335,plain,
% 2.01/2.25 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3336,plain,
% 2.01/2.25 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 2.01/2.25 inference(bind,[status(th)],[])).
% 2.01/2.25 tff(3337,plain,
% 2.01/2.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.01/2.25 inference(quant_intro,[status(thm)],[3336])).
% 2.01/2.25 tff(3338,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 2.01/2.25 tff(3339,plain,
% 2.01/2.25 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3338, 3337])).
% 2.01/2.25 tff(3340,plain,
% 2.01/2.25 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3339, 3335])).
% 2.01/2.25 tff(3341,plain,(
% 2.01/2.25 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.01/2.25 inference(skolemize,[status(sab)],[3340])).
% 2.01/2.25 tff(3342,plain,
% 2.01/2.25 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3341, 3334])).
% 2.01/2.25 tff(3343,plain,
% 2.01/2.25 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a919)) | c3_1(a919) | (~c0_1(a919)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a919)) | c3_1(a919) | (~c0_1(a919)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3344,plain,
% 2.01/2.25 ((hskp1 | (~ndr1_0) | c3_1(a919) | (~c1_1(a919)) | (~c0_1(a919)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907))) <=> (hskp1 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a919)) | c3_1(a919) | (~c0_1(a919)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3345,plain,
% 2.01/2.25 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a919) | (~c1_1(a919)) | (~c0_1(a919)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a919)) | c3_1(a919) | (~c0_1(a919))))),
% 2.01/2.25 inference(monotonicity,[status(thm)],[3344])).
% 2.01/2.25 tff(3346,plain,
% 2.01/2.25 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a919) | (~c1_1(a919)) | (~c0_1(a919)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a919)) | c3_1(a919) | (~c0_1(a919)))),
% 2.01/2.25 inference(transitivity,[status(thm)],[3345, 3343])).
% 2.01/2.25 tff(3347,plain,
% 2.01/2.25 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a919) | (~c1_1(a919)) | (~c0_1(a919)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907)))),
% 2.01/2.25 inference(quant_inst,[status(thm)],[])).
% 2.01/2.25 tff(3348,plain,
% 2.01/2.25 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a919)) | c3_1(a919) | (~c0_1(a919))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 2.01/2.25 tff(3349,plain,
% 2.01/2.25 ($false),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3348, 112, 3271, 3325, 3317, 44, 45, 3342, 3280, 3332])).
% 2.01/2.25 tff(3350,plain,(c2_1(a899) | c0_1(a907) | c1_1(a907) | hskp11 | c0_1(a899) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.01/2.25 tff(3351,plain,
% 2.01/2.25 (c2_1(a899)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3350, 3268, 45, 44, 43, 3269, 31])).
% 2.01/2.25 tff(3352,plain,
% 2.01/2.25 (c3_1(a907)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[2970, 3351, 45, 47, 2873, 3269, 43, 31, 44])).
% 2.01/2.25 tff(3353,plain,
% 2.01/2.25 (hskp1),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[2280, 50, 32, 2207, 45, 31, 44])).
% 2.01/2.25 tff(3354,plain,
% 2.01/2.25 (~c1_1(a899)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3113, 50, 43, 312, 44, 45, 32, 31, 2207])).
% 2.01/2.25 tff(3355,plain,
% 2.01/2.25 ($false),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[308, 3354, 3353])).
% 2.01/2.25 tff(3356,plain,(hskp10 | c0_1(a899) | (~c2_1(a899)) | c0_1(a907) | c1_1(a907) | hskp17 | hskp0 | (~c3_1(a907))), inference(lemma,lemma(discharge,[]))).
% 2.01/2.25 tff(3357,plain,
% 2.01/2.25 (hskp10),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3356, 3351, 43, 44, 45, 3269, 31, 3352])).
% 2.01/2.25 tff(3358,plain,
% 2.01/2.25 (~c2_1(a910)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[2348, 3357])).
% 2.01/2.25 tff(3359,plain,
% 2.01/2.25 (~c0_1(a910)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[2354, 3357])).
% 2.01/2.25 tff(3360,plain,
% 2.01/2.25 (c1_1(a910)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[2362, 3357])).
% 2.01/2.25 tff(3361,plain,
% 2.01/2.25 (c3_1(a899)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[898, 3351, 31, 3269])).
% 2.01/2.25 tff(3362,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3363,plain,
% 2.01/2.25 (((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910))) <=> (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3364,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910))))),
% 2.01/2.25 inference(monotonicity,[status(thm)],[3363])).
% 2.01/2.25 tff(3365,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.01/2.25 inference(transitivity,[status(thm)],[3364, 3362])).
% 2.01/2.25 tff(3366,plain,
% 2.01/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))),
% 2.01/2.25 inference(quant_inst,[status(thm)],[])).
% 2.01/2.25 tff(3367,plain,
% 2.01/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3366, 3365])).
% 2.01/2.25 tff(3368,plain,
% 2.01/2.25 (~c3_1(a910)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3367, 112, 2366, 801, 1731, 813, 2365, 2364, 503])).
% 2.01/2.25 tff(3369,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a910) | c2_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)) | c3_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a910) | c2_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3370,plain,
% 2.01/2.25 (((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899))) <=> (c2_1(a910) | c2_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3371,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a910) | c2_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)) | c3_1(a910)))),
% 2.01/2.25 inference(monotonicity,[status(thm)],[3370])).
% 2.01/2.25 tff(3372,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a910) | c2_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.25 inference(transitivity,[status(thm)],[3371, 3369])).
% 2.01/2.25 tff(3373,plain,
% 2.01/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)) | c2_1(a901) | c1_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))),
% 2.01/2.25 inference(quant_inst,[status(thm)],[])).
% 2.01/2.25 tff(3374,plain,
% 2.01/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a910) | c2_1(a901) | (~c3_1(a901)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a901) | (~c1_1(a910)) | c3_1(a910)),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3373, 3372])).
% 2.01/2.25 tff(3375,plain,
% 2.01/2.25 (c1_1(a901) | c3_1(a910)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3374, 112, 2366, 312, 2364, 47, 2942, 43, 1384, 314])).
% 2.01/2.25 tff(3376,plain,
% 2.01/2.25 (c1_1(a901)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3375, 3368])).
% 2.01/2.25 tff(3377,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a907) | (~c3_1(a907)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3378,plain,
% 2.01/2.25 (((~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c3_1(a901)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907))) <=> (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a907) | (~c3_1(a907)))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3379,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c3_1(a901)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a907) | (~c3_1(a907))))),
% 2.01/2.25 inference(monotonicity,[status(thm)],[3378])).
% 2.01/2.25 tff(3380,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c3_1(a901)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a907) | (~c3_1(a907)))),
% 2.01/2.25 inference(transitivity,[status(thm)],[3379, 3377])).
% 2.01/2.25 tff(3381,plain,
% 2.01/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a901) | (~c1_1(a901)) | (~c3_1(a901)) | c3_1(a912) | c1_1(a912) | (~c2_1(a912)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))),
% 2.01/2.25 inference(quant_inst,[status(thm)],[])).
% 2.01/2.25 tff(3382,plain,
% 2.01/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~ndr1_0) | (~c1_1(a901)) | c2_1(a907) | (~c3_1(a907))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 2.01/2.25 tff(3383,plain,
% 2.01/2.25 ((~c1_1(a901)) | c2_1(a907)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3382, 112, 2207, 801, 1731, 813, 44, 47, 2942, 503])).
% 2.01/2.25 tff(3384,plain,
% 2.01/2.25 (c2_1(a907)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[3383, 3376])).
% 2.01/2.25 tff(3385,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c3_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3386,plain,
% 2.01/2.25 (((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a910) | c0_1(a910) | (~c1_1(a910))) <=> (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.25 inference(rewrite,[status(thm)],[])).
% 2.01/2.25 tff(3387,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c3_1(a910)))),
% 2.01/2.25 inference(monotonicity,[status(thm)],[3386])).
% 2.01/2.25 tff(3388,plain,
% 2.01/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c3_1(a910))),
% 2.01/2.25 inference(transitivity,[status(thm)],[3387, 3385])).
% 2.01/2.25 tff(3389,plain,
% 2.01/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a912) | c3_1(a912) | (~c2_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a910) | c0_1(a910) | (~c1_1(a910)))),
% 2.09/2.25 inference(quant_inst,[status(thm)],[])).
% 2.09/2.25 tff(3390,plain,
% 2.09/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a912) | (~c2_1(a912)) | c3_1(a912) | c0_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c3_1(a910)),
% 2.09/2.25 inference(modus_ponens,[status(thm)],[3389, 3388])).
% 2.09/2.25 tff(3391,plain,
% 2.09/2.25 ($false),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[3390, 112, 2366, 2207, 801, 1731, 813, 2365, 44, 392, 3384, 3368])).
% 2.09/2.25 tff(3392,plain,(c3_1(a912) | (~c1_1(a910)) | (~c3_1(a907)) | c1_1(a912) | (~c2_1(a912)) | c0_1(a910) | c0_1(a907) | c2_1(a901) | (~c3_1(a901)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a899) | (~c3_1(a899))), inference(lemma,lemma(discharge,[]))).
% 2.09/2.25 tff(3393,plain,
% 2.09/2.25 (c3_1(a912)),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[3392, 3360, 3352, 801, 3267, 3359, 44, 47, 2873, 3351, 3358, 43, 3361])).
% 2.09/2.25 tff(3394,plain,
% 2.09/2.25 (hskp24),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[1984, 3393, 3267, 3269])).
% 2.09/2.25 tff(3395,plain,
% 2.09/2.25 (c3_1(a953)),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[1188, 3394])).
% 2.09/2.25 tff(3396,plain,
% 2.09/2.25 (c1_1(a953)),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[1196, 3394])).
% 2.09/2.25 tff(3397,plain,
% 2.09/2.25 (~c0_1(a953)),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[3224, 112, 3268, 3396, 3395, 3360, 3359, 3358, 1402])).
% 2.09/2.25 tff(3398,plain,
% 2.09/2.25 (~c2_1(a953)),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[1209, 3394])).
% 2.09/2.25 tff(3399,plain,
% 2.09/2.25 (~hskp25),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[3239, 3397, 3351, 3398, 43, 3396, 3269, 31])).
% 2.09/2.25 tff(3400,plain,
% 2.09/2.25 (hskp21),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[3248, 3399, 31])).
% 2.09/2.25 tff(3401,plain,
% 2.09/2.25 (~c3_1(a938)),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[416, 3400])).
% 2.09/2.25 tff(3402,plain,
% 2.09/2.25 (~c2_1(a938)),
% 2.09/2.25 inference(unit_resolution,[status(thm)],[422, 3400])).
% 2.09/2.25 tff(3403,plain,
% 2.09/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a953) | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a953) | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953))),
% 2.09/2.25 inference(rewrite,[status(thm)],[])).
% 2.09/2.25 tff(3404,plain,
% 2.09/2.25 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938)) <=> (c2_1(a953) | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953))),
% 2.09/2.25 inference(rewrite,[status(thm)],[])).
% 2.09/2.25 tff(3405,plain,
% 2.09/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a953) | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953)))),
% 2.09/2.25 inference(monotonicity,[status(thm)],[3404])).
% 2.09/2.25 tff(3406,plain,
% 2.09/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a953) | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3405, 3403])).
% 2.09/2.26 tff(3407,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3408,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a953) | c2_1(a938) | c3_1(a938) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953)),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 2.09/2.26 tff(3409,plain,
% 2.09/2.26 (c1_1(a938)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3408, 112, 3396, 3351, 3398, 3402, 3401, 43, 1721, 3361, 3397])).
% 2.09/2.26 tff(3410,plain,
% 2.09/2.26 (c0_1(a938)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[430, 3400])).
% 2.09/2.26 tff(3411,plain,
% 2.09/2.26 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a938) | c3_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a938) | c3_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3412,plain,
% 2.09/2.26 ((hskp31 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c3_1(a938) | c2_1(a938) | (~c1_1(a938))) <=> (hskp31 | c2_1(a938) | c3_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3413,plain,
% 2.09/2.26 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c3_1(a938) | c2_1(a938) | (~c1_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a938) | c3_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3412])).
% 2.09/2.26 tff(3414,plain,
% 2.09/2.26 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c3_1(a938) | c2_1(a938) | (~c1_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a938) | c3_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3413, 3411])).
% 2.09/2.26 tff(3415,plain,
% 2.09/2.26 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c3_1(a938) | c2_1(a938) | (~c1_1(a938)))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3416,plain,
% 2.09/2.26 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a938) | c3_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 2.09/2.26 tff(3417,plain,
% 2.09/2.26 ($false),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3416, 46, 112, 3410, 3402, 3401, 10, 3409])).
% 2.09/2.26 tff(3418,plain,(c1_1(a912) | hskp31 | c0_1(a899) | hskp0 | c0_1(a907) | c2_1(a901) | c1_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.26 tff(3419,plain,
% 2.09/2.26 (c1_1(a912)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3418, 31, 43, 46, 44, 47, 45])).
% 2.09/2.26 tff(3420,plain,
% 2.09/2.26 (~hskp11),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[2146, 3419])).
% 2.09/2.26 tff(3421,plain,
% 2.09/2.26 (~hskp17),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[1729, 3420, 46])).
% 2.09/2.26 tff(3422,plain,
% 2.09/2.26 (c2_1(a899)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3350, 3420, 45, 44, 43, 3421, 31])).
% 2.09/2.26 tff(3423,plain,
% 2.09/2.26 (c3_1(a907)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[2970, 3422, 45, 47, 2873, 3421, 43, 31, 44])).
% 2.09/2.26 tff(3424,plain,
% 2.09/2.26 (hskp10),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3356, 3422, 43, 44, 45, 3421, 31, 3423])).
% 2.09/2.26 tff(3425,plain,
% 2.09/2.26 (~c2_1(a910)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[2348, 3424])).
% 2.09/2.26 tff(3426,plain,
% 2.09/2.26 (~c0_1(a910)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[2354, 3424])).
% 2.09/2.26 tff(3427,plain,
% 2.09/2.26 (c1_1(a910)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[2362, 3424])).
% 2.09/2.26 tff(3428,plain,
% 2.09/2.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | (~c1_1(a910)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3429,plain,
% 2.09/2.26 ((hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910))) <=> (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | (~c1_1(a910)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3430,plain,
% 2.09/2.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | (~c1_1(a910))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3429])).
% 2.09/2.26 tff(3431,plain,
% 2.09/2.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | (~c1_1(a910)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3430, 3428])).
% 2.09/2.26 tff(3432,plain,
% 2.09/2.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a911)) | (~c3_1(a911)) | (~c0_1(a911)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3433,plain,
% 2.09/2.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a911)) | (~c0_1(a911)) | (~c1_1(a911)) | (~c1_1(a910))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3432, 3431])).
% 2.09/2.26 tff(3434,plain,
% 2.09/2.26 ($false),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3433, 112, 1430, 1429, 1421, 1413, 2366, 2365, 2364, 1402])).
% 2.09/2.26 tff(3435,plain,((~hskp29) | hskp11 | (~c1_1(a910)) | c0_1(a910) | c2_1(a910)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.26 tff(3436,plain,
% 2.09/2.26 (~hskp29),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3435, 3420, 3427, 3426, 3425])).
% 2.09/2.26 tff(3437,plain,
% 2.09/2.26 (hskp27),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[108, 3436, 46])).
% 2.09/2.26 tff(3438,plain,
% 2.09/2.26 (~c0_1(a978)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[1445, 3437])).
% 2.09/2.26 tff(3439,plain,
% 2.09/2.26 (c3_1(a978)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[1453, 3437])).
% 2.09/2.26 tff(3440,plain,
% 2.09/2.26 (c2_1(a978)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[1461, 3437])).
% 2.09/2.26 tff(3441,assumption,(~c1_1(a899)), introduced(assumption)).
% 2.09/2.26 tff(3442,plain,
% 2.09/2.26 (c3_1(a899)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[898, 312, 31, 32])).
% 2.09/2.26 tff(3443,plain,
% 2.09/2.26 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3444,plain,
% 2.09/2.26 ((hskp24 | hskp17 | (~ndr1_0) | c1_1(a899) | (~c3_1(a899)) | (~c2_1(a899))) <=> (hskp24 | hskp17 | c1_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3445,plain,
% 2.09/2.26 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | c1_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3444])).
% 2.09/2.26 tff(3446,plain,
% 2.09/2.26 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3445, 3443])).
% 2.09/2.26 tff(3447,plain,
% 2.09/2.26 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c1_1(a899) | (~c3_1(a899)) | (~c2_1(a899)))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3448,plain,
% 2.09/2.26 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp17 | c1_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3447, 3446])).
% 2.09/2.26 tff(3449,plain,
% 2.09/2.26 (hskp24 | c1_1(a899)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3448, 112, 32, 312, 1169, 3442])).
% 2.09/2.26 tff(3450,plain,
% 2.09/2.26 (hskp24),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3449, 3441])).
% 2.09/2.26 tff(3451,plain,
% 2.09/2.26 (~c2_1(a953)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[1209, 3450])).
% 2.09/2.26 tff(3452,plain,
% 2.09/2.26 (c1_1(a953)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[1196, 3450])).
% 2.09/2.26 tff(3453,plain,
% 2.09/2.26 (~hskp1),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[308, 3441])).
% 2.09/2.26 tff(3454,plain,
% 2.09/2.26 (~c0_1(a953)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[2079, 112, 1884, 3453, 3452, 3451, 42])).
% 2.09/2.26 tff(3455,plain,
% 2.09/2.26 (~hskp25),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3239, 3454, 312, 3451, 43, 3452, 32, 31])).
% 2.09/2.26 tff(3456,plain,
% 2.09/2.26 (hskp21),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3248, 3455, 31])).
% 2.09/2.26 tff(3457,plain,
% 2.09/2.26 (~c2_1(a938)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[422, 3456])).
% 2.09/2.26 tff(3458,plain,
% 2.09/2.26 (c0_1(a938)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[430, 3456])).
% 2.09/2.26 tff(3459,plain,
% 2.09/2.26 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3460,plain,
% 2.09/2.26 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938))) <=> (hskp20 | hskp1 | c2_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3461,plain,
% 2.09/2.26 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3460])).
% 2.09/2.26 tff(3462,plain,
% 2.09/2.26 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3461, 3459])).
% 2.09/2.26 tff(3463,plain,
% 2.09/2.26 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3464,plain,
% 2.09/2.26 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a938) | (~ndr1_0) | (~c0_1(a938)) | (~c1_1(a938))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3463, 3462])).
% 2.09/2.26 tff(3465,plain,
% 2.09/2.26 (~c1_1(a938)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3464, 112, 1884, 3453, 3458, 3457, 42])).
% 2.09/2.26 tff(3466,plain,
% 2.09/2.26 (~c3_1(a938)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[416, 3456])).
% 2.09/2.26 tff(3467,assumption,(~c0_1(a978)), introduced(assumption)).
% 2.09/2.26 tff(3468,assumption,(c3_1(a978)), introduced(assumption)).
% 2.09/2.26 tff(3469,assumption,(c2_1(a978)), introduced(assumption)).
% 2.09/2.26 tff(3470,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c2_1(a953) | c2_1(a938) | c3_1(a938) | (~ndr1_0) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c2_1(a953) | c2_1(a938) | c3_1(a938) | (~ndr1_0) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3471,plain,
% 2.09/2.26 (((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938)) <=> (c0_1(a978) | c2_1(a953) | c2_1(a938) | c3_1(a938) | (~ndr1_0) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3472,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c2_1(a953) | c2_1(a938) | c3_1(a938) | (~ndr1_0) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3471])).
% 2.09/2.26 tff(3473,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c2_1(a953) | c2_1(a938) | c3_1(a938) | (~ndr1_0) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3472, 3470])).
% 2.09/2.26 tff(3474,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a953) | c0_1(a953) | (~c1_1(a953)) | c3_1(a938) | c1_1(a938) | c2_1(a938))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3475,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c2_1(a953) | c2_1(a938) | c3_1(a938) | (~ndr1_0) | c1_1(a938) | (~c1_1(a953)) | c0_1(a953) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3474, 3473])).
% 2.09/2.26 tff(3476,plain,
% 2.09/2.26 ($false),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3475, 112, 3469, 3468, 3452, 3467, 3451, 3457, 3466, 1721, 3465, 3454])).
% 2.09/2.26 tff(3477,plain,(c1_1(a899) | (~c2_1(a978)) | (~c3_1(a978)) | c0_1(a978) | hskp0 | (~c2_1(a899)) | c0_1(a899) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.09/2.26 tff(3478,plain,
% 2.09/2.26 (c1_1(a899)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3477, 3440, 3439, 3438, 31, 3422, 43, 3421])).
% 2.09/2.26 tff(3479,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3480,plain,
% 2.09/2.26 (((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c0_1(a978) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3481,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3480])).
% 2.09/2.26 tff(3482,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3481, 3479])).
% 2.09/2.26 tff(3483,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3484,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c2_1(a958) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3483, 3482])).
% 2.09/2.26 tff(3485,plain,
% 2.09/2.26 ($false),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3484, 112, 3469, 3468, 2366, 3467, 3231, 3228, 2365, 2364, 1721, 3230])).
% 2.09/2.26 tff(3486,plain,((~hskp25) | (~c2_1(a978)) | (~c3_1(a978)) | (~c1_1(a910)) | c0_1(a978) | c0_1(a910) | c2_1(a910) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.09/2.26 tff(3487,plain,
% 2.09/2.26 (~hskp25),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3486, 3440, 3439, 3427, 3438, 3426, 3425, 3421, 31])).
% 2.09/2.26 tff(3488,plain,
% 2.09/2.26 (hskp21),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3248, 3487, 31])).
% 2.09/2.26 tff(3489,plain,
% 2.09/2.26 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c3_1(a910))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c3_1(a910))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3490,plain,
% 2.09/2.26 ((hskp25 | (~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910))) <=> (hskp25 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c3_1(a910))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3491,plain,
% 2.09/2.26 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c3_1(a910)))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3490])).
% 2.09/2.26 tff(3492,plain,
% 2.09/2.26 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c3_1(a910))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3491, 3489])).
% 2.09/2.26 tff(3493,plain,
% 2.09/2.26 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c1_1(a910)))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3494,plain,
% 2.09/2.26 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c3_1(a910)),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 2.09/2.26 tff(3495,plain,
% 2.09/2.26 (hskp25 | c3_1(a910)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3494, 112, 3427, 3425, 30])).
% 2.09/2.26 tff(3496,plain,
% 2.09/2.26 (c3_1(a910)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3495, 3487])).
% 2.09/2.26 tff(3497,plain,
% 2.09/2.26 (hskp14),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[441, 411, 312, 311, 43])).
% 2.09/2.26 tff(3498,plain,
% 2.09/2.26 (~c1_1(a918)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[672, 3497])).
% 2.09/2.26 tff(3499,plain,
% 2.09/2.26 (hskp18),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[765, 3498, 411, 311, 312, 43])).
% 2.09/2.26 tff(3500,plain,
% 2.09/2.26 (~c1_1(a929)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[771, 3499])).
% 2.09/2.26 tff(3501,plain,
% 2.09/2.26 (c2_1(a929)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[781, 3499])).
% 2.09/2.26 tff(3502,plain,
% 2.09/2.26 (c0_1(a929)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[789, 3499])).
% 2.09/2.26 tff(3503,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3504,plain,
% 2.09/2.26 (((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929))) <=> (c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3505,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3504])).
% 2.09/2.26 tff(3506,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3505, 3503])).
% 2.09/2.26 tff(3507,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a938) | c2_1(a938) | (~c0_1(a938)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3508,plain,
% 2.09/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a929) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c3_1(a910)) | (~c2_1(a929)) | (~c0_1(a929)) | (~c0_1(a938))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 2.09/2.26 tff(3509,plain,
% 2.09/2.26 ($false),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3508, 112, 431, 3502, 3501, 2366, 423, 417, 3500, 2364, 131, 3159])).
% 2.09/2.26 tff(3510,plain,((~hskp21) | (~c1_1(a910)) | c2_1(a910) | (~c3_1(a910)) | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.26 tff(3511,plain,
% 2.09/2.26 ($false),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3510, 3496, 3488, 3425, 3427, 3478, 3422, 43])).
% 2.09/2.26 tff(3512,plain,(hskp0 | c0_1(a899) | hskp31 | c0_1(a907) | c1_1(a907) | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.26 tff(3513,plain,
% 2.09/2.26 (hskp0),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3512, 43, 46, 44, 45, 47])).
% 2.09/2.26 tff(3514,plain,
% 2.09/2.26 (c1_1(a898)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[59, 3513])).
% 2.09/2.26 tff(3515,plain,
% 2.09/2.26 (c0_1(a898)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[73, 3513])).
% 2.09/2.26 tff(3516,plain,
% 2.09/2.26 (~c2_1(a898)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[65, 3513])).
% 2.09/2.26 tff(3517,plain,
% 2.09/2.26 (c3_1(a898)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[120, 3516, 3515, 3514, 46])).
% 2.09/2.26 tff(3518,plain,
% 2.09/2.26 (hskp13 | hskp1),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[180, 112, 77, 76, 174, 310])).
% 2.09/2.26 tff(3519,plain,
% 2.09/2.26 (hskp13),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3518, 152])).
% 2.09/2.26 tff(3520,plain,
% 2.09/2.26 (~c2_1(a914)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[187, 3519])).
% 2.09/2.26 tff(3521,plain,
% 2.09/2.26 (hskp5 | hskp1),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[235, 112, 78, 76, 229, 310])).
% 2.09/2.26 tff(3522,plain,
% 2.09/2.26 (hskp5),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3521, 152])).
% 2.09/2.26 tff(3523,plain,
% 2.09/2.26 (c1_1(a905)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[252, 3522])).
% 2.09/2.26 tff(3524,plain,
% 2.09/2.26 (~c0_1(a905)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[276, 3522])).
% 2.09/2.26 tff(3525,plain,
% 2.09/2.26 (~c1_1(a914)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[193, 3519])).
% 2.09/2.26 tff(3526,plain,
% 2.09/2.26 (c3_1(a905)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[244, 3522])).
% 2.09/2.26 tff(3527,plain,
% 2.09/2.26 (c3_1(a914)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[201, 3519])).
% 2.09/2.26 tff(3528,assumption,(c0_1(a914)), introduced(assumption)).
% 2.09/2.26 tff(3529,assumption,(~c2_1(a914)), introduced(assumption)).
% 2.09/2.26 tff(3530,assumption,(~c1_1(a914)), introduced(assumption)).
% 2.09/2.26 tff(3531,assumption,(c3_1(a905)), introduced(assumption)).
% 2.09/2.26 tff(3532,assumption,(c1_1(a905)), introduced(assumption)).
% 2.09/2.26 tff(3533,plain,
% 2.09/2.26 ((~c2_1(a905)) | (~c0_1(a914))),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[259, 112, 152, 3532, 3531, 3530, 3529, 219])).
% 2.09/2.26 tff(3534,plain,
% 2.09/2.26 (~c2_1(a905)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3533, 3528])).
% 2.09/2.26 tff(3535,assumption,(~c0_1(a905)), introduced(assumption)).
% 2.09/2.26 tff(3536,assumption,(c3_1(a914)), introduced(assumption)).
% 2.09/2.26 tff(3537,plain,
% 2.09/2.26 (c2_1(a905) | (~c0_1(a914))),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[283, 112, 3536, 3531, 78, 77, 3530, 3535, 76, 271])).
% 2.09/2.26 tff(3538,plain,
% 2.09/2.26 ($false),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3537, 3534, 3528])).
% 2.09/2.26 tff(3539,plain,((~c0_1(a914)) | (~c3_1(a914)) | (~c3_1(a905)) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a914) | c0_1(a905) | c2_1(a898) | hskp1 | (~c1_1(a905)) | c2_1(a914)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.26 tff(3540,plain,
% 2.09/2.26 (~c0_1(a914)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3539, 3527, 3526, 78, 77, 3525, 3524, 76, 152, 3523, 3520])).
% 2.09/2.26 tff(3541,plain,
% 2.09/2.26 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3542,plain,
% 2.09/2.26 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898))) <=> (hskp20 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3543,plain,
% 2.09/2.26 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898))))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3542])).
% 2.09/2.26 tff(3544,plain,
% 2.09/2.26 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)))),
% 2.09/2.26 inference(transitivity,[status(thm)],[3543, 3541])).
% 2.09/2.26 tff(3545,plain,
% 2.09/2.26 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)))),
% 2.09/2.26 inference(quant_inst,[status(thm)],[])).
% 2.09/2.26 tff(3546,plain,
% 2.09/2.26 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898))),
% 2.09/2.26 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 2.09/2.26 tff(3547,plain,
% 2.09/2.26 (hskp20 | hskp1),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3546, 112, 78, 77, 76, 42])).
% 2.09/2.26 tff(3548,plain,
% 2.09/2.26 (hskp20),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[3547, 152])).
% 2.09/2.26 tff(3549,plain,
% 2.09/2.26 (~c3_1(a937)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[998, 3548])).
% 2.09/2.26 tff(3550,plain,
% 2.09/2.26 (~c0_1(a937)),
% 2.09/2.26 inference(unit_resolution,[status(thm)],[1004, 3548])).
% 2.09/2.26 tff(3551,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a937) | c3_1(a937) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | c1_1(a937))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a937) | c3_1(a937) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | c1_1(a937))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3552,plain,
% 2.09/2.26 (((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a937) | c1_1(a937) | c0_1(a937)) <=> (c0_1(a937) | c3_1(a937) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | c1_1(a937))),
% 2.09/2.26 inference(rewrite,[status(thm)],[])).
% 2.09/2.26 tff(3553,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a937) | c1_1(a937) | c0_1(a937))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a937) | c3_1(a937) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | c1_1(a937)))),
% 2.09/2.26 inference(monotonicity,[status(thm)],[3552])).
% 2.09/2.26 tff(3554,plain,
% 2.09/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a937) | c1_1(a937) | c0_1(a937))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a937) | c3_1(a937) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | c1_1(a937))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3553, 3551])).
% 2.09/2.27 tff(3555,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)) | c3_1(a937) | c1_1(a937) | c0_1(a937))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3556,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a937) | c3_1(a937) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | c1_1(a937)),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3555, 3554])).
% 2.09/2.27 tff(3557,plain,
% 2.09/2.27 (c0_1(a914) | c1_1(a937)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3556, 112, 3527, 3550, 3549, 3525, 3520, 151])).
% 2.09/2.27 tff(3558,plain,
% 2.09/2.27 (c1_1(a937)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3557, 3540])).
% 2.09/2.27 tff(3559,plain,
% 2.09/2.27 (c2_1(a937)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1012, 3548])).
% 2.09/2.27 tff(3560,plain,
% 2.09/2.27 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c3_1(a937) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | (~c1_1(a937)) | (~c2_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c3_1(a937) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | (~c1_1(a937)) | (~c2_1(a937)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3561,plain,
% 2.09/2.27 ((hskp14 | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c2_1(a937)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914))) <=> (hskp14 | c3_1(a937) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | (~c1_1(a937)) | (~c2_1(a937)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3562,plain,
% 2.09/2.27 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c2_1(a937)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c3_1(a937) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | (~c1_1(a937)) | (~c2_1(a937))))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3561])).
% 2.09/2.27 tff(3563,plain,
% 2.09/2.27 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c2_1(a937)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c3_1(a937) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | (~c1_1(a937)) | (~c2_1(a937)))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3562, 3560])).
% 2.09/2.27 tff(3564,plain,
% 2.09/2.27 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c2_1(a937)) | c2_1(a914) | c0_1(a914) | (~c3_1(a914)))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3565,plain,
% 2.09/2.27 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c3_1(a937) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c0_1(a914) | (~c1_1(a937)) | (~c2_1(a937))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3564, 3563])).
% 2.09/2.27 tff(3566,plain,
% 2.09/2.27 (hskp14 | c0_1(a914) | (~c1_1(a937))),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3565, 112, 3559, 3527, 3549, 3520, 881])).
% 2.09/2.27 tff(3567,plain,
% 2.09/2.27 (hskp14),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3566, 3558, 3540])).
% 2.09/2.27 tff(3568,plain,
% 2.09/2.27 (~c1_1(a918)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[672, 3567])).
% 2.09/2.27 tff(3569,plain,
% 2.09/2.27 (c3_1(a918)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[742, 3567])).
% 2.09/2.27 tff(3570,plain,
% 2.09/2.27 (c0_1(a918)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[734, 3567])).
% 2.09/2.27 tff(3571,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c2_1(a914) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a914)) | c0_1(a914) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c2_1(a914) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a914)) | c0_1(a914) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3572,plain,
% 2.09/2.27 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a914) | c2_1(a914) | (~c3_1(a914))) <=> (c1_1(a918) | c2_1(a914) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a914)) | c0_1(a914) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3573,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a914) | c2_1(a914) | (~c3_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a918) | c2_1(a914) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a914)) | c0_1(a914) | (~c0_1(a918)) | (~c3_1(a918))))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3572])).
% 2.09/2.27 tff(3574,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a914) | c2_1(a914) | (~c3_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c2_1(a914) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a914)) | c0_1(a914) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3573, 3571])).
% 2.09/2.27 tff(3575,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a914) | c2_1(a914) | (~c3_1(a914)))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3576,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a918) | c2_1(a914) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c3_1(a914)) | c0_1(a914) | (~c0_1(a918)) | (~c3_1(a918))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3575, 3574])).
% 2.09/2.27 tff(3577,plain,
% 2.09/2.27 ($false),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3576, 112, 3570, 3569, 3527, 78, 77, 3568, 3520, 76, 271, 3540])).
% 2.09/2.27 tff(3578,plain,(hskp1 | (~c0_1(a898)) | (~c1_1(a898)) | c2_1(a898) | (~c3_1(a898))), inference(lemma,lemma(discharge,[]))).
% 2.09/2.27 tff(3579,plain,
% 2.09/2.27 (hskp1),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3578, 3515, 3514, 3516, 3517])).
% 2.09/2.27 tff(3580,plain,
% 2.09/2.27 (c2_1(a899)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[300, 3579])).
% 2.09/2.27 tff(3581,plain,
% 2.09/2.27 (c1_1(a899)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[308, 3579])).
% 2.09/2.27 tff(3582,plain,
% 2.09/2.27 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 2.09/2.27 inference(bind,[status(th)],[])).
% 2.09/2.27 tff(3583,plain,
% 2.09/2.27 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/2.27 inference(quant_intro,[status(thm)],[3582])).
% 2.09/2.27 tff(3584,plain,
% 2.09/2.27 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3585,plain,
% 2.09/2.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp9) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.09/2.27 inference(bind,[status(th)],[])).
% 2.09/2.27 tff(3586,plain,
% 2.09/2.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/2.27 inference(quant_intro,[status(thm)],[3585])).
% 2.09/2.27 tff(3587,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 2.09/2.27 tff(3588,plain,
% 2.09/2.27 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 2.09/2.27 tff(3589,plain,
% 2.09/2.27 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3588, 3584])).
% 2.09/2.27 tff(3590,plain,(
% 2.09/2.27 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/2.27 inference(skolemize,[status(sab)],[3589])).
% 2.09/2.27 tff(3591,plain,
% 2.09/2.27 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3590, 3583])).
% 2.09/2.27 tff(3592,plain,
% 2.09/2.27 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a899) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a899) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3593,plain,
% 2.09/2.27 ((hskp9 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp9 | c0_1(a899) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3594,plain,
% 2.09/2.27 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a899) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a899)) | (~c1_1(a899))))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3593])).
% 2.09/2.27 tff(3595,plain,
% 2.09/2.27 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a899) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3594, 3592])).
% 2.09/2.27 tff(3596,plain,
% 2.09/2.27 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a898)) | (~c3_1(a898)) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3597,plain,
% 2.09/2.27 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a899) | (~ndr1_0) | (~c3_1(a898)) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a899)) | (~c1_1(a899))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3596, 3595])).
% 2.09/2.27 tff(3598,plain,
% 2.09/2.27 (hskp9 | (~c2_1(a899)) | (~c1_1(a899))),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3597, 112, 3515, 3514, 43, 3591, 3517])).
% 2.09/2.27 tff(3599,plain,
% 2.09/2.27 (hskp9),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3598, 3581, 3580])).
% 2.09/2.27 tff(3600,plain,
% 2.09/2.27 (~c2_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1323, 3599])).
% 2.09/2.27 tff(3601,plain,
% 2.09/2.27 (~c1_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1329, 3599])).
% 2.09/2.27 tff(3602,plain,
% 2.09/2.27 (c3_1(a898)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[120, 76, 78, 77, 46])).
% 2.09/2.27 tff(3603,plain,
% 2.09/2.27 (hskp1),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3578, 78, 77, 76, 3602])).
% 2.09/2.27 tff(3604,plain,
% 2.09/2.27 (c1_1(a899)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[308, 3603])).
% 2.09/2.27 tff(3605,plain,
% 2.09/2.27 (c2_1(a899)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[300, 3603])).
% 2.09/2.27 tff(3606,plain,
% 2.09/2.27 (hskp9 | (~c2_1(a899)) | (~c1_1(a899))),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3597, 112, 78, 77, 43, 3591, 3602])).
% 2.09/2.27 tff(3607,plain,
% 2.09/2.27 (hskp9),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3606, 3604, 3605])).
% 2.09/2.27 tff(3608,plain,
% 2.09/2.27 (~c2_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1323, 3607])).
% 2.09/2.27 tff(3609,plain,
% 2.09/2.27 (~c1_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1329, 3607])).
% 2.09/2.27 tff(3610,plain,
% 2.09/2.27 (hskp28),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2687, 505, 2888, 45])).
% 2.09/2.27 tff(3611,plain,
% 2.09/2.27 (c0_1(a900)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[965, 3610])).
% 2.09/2.27 tff(3612,plain,
% 2.09/2.27 (c3_1(a900)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[949, 3610])).
% 2.09/2.27 tff(3613,plain,
% 2.09/2.27 (~c0_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1335, 3607])).
% 2.09/2.27 tff(3614,plain,
% 2.09/2.27 (c2_1(a900)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[957, 3610])).
% 2.09/2.27 tff(3615,plain,
% 2.09/2.27 (~hskp4),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2050, 3614, 3613, 3612, 3611, 3609, 3608])).
% 2.09/2.27 tff(3616,plain,
% 2.09/2.27 (hskp10),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[715, 3615, 77, 76, 3602, 3604, 43, 44, 45, 78])).
% 2.09/2.27 tff(3617,plain,
% 2.09/2.27 (~c2_1(a910)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2348, 3616])).
% 2.09/2.27 tff(3618,plain,
% 2.09/2.27 (c1_1(a910)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2362, 3616])).
% 2.09/2.27 tff(3619,plain,
% 2.09/2.27 (c3_1(a910)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2801, 3618, 78, 76, 77, 3617, 46])).
% 2.09/2.27 tff(3620,plain,
% 2.09/2.27 (~c0_1(a910)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2354, 3616])).
% 2.09/2.27 tff(3621,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a910)) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3622,plain,
% 2.09/2.27 (((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a907) | c1_1(a907) | (~c2_1(a907)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910))) <=> (c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3623,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a907) | c1_1(a907) | (~c2_1(a907)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a910)) | (~c3_1(a910))))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3622])).
% 2.09/2.27 tff(3624,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a907) | c1_1(a907) | (~c2_1(a907)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3623, 3621])).
% 2.09/2.27 tff(3625,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a907) | c1_1(a907) | (~c2_1(a907)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3626,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c1_1(a910)) | (~c3_1(a910))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3625, 3624])).
% 2.09/2.27 tff(3627,plain,
% 2.09/2.27 (~c2_1(a907)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3626, 112, 3618, 505, 3620, 3617, 45, 503, 3619])).
% 2.09/2.27 tff(3628,plain,
% 2.09/2.27 (c3_1(a899)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[530, 3615, 3604, 513])).
% 2.09/2.27 tff(3629,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | (~c1_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | (~c1_1(a910)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3630,plain,
% 2.09/2.27 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a907) | c1_1(a907) | c2_1(a907)) <=> (c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | (~c1_1(a910)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3631,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a907) | c1_1(a907) | c2_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | (~c1_1(a910))))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3630])).
% 2.09/2.27 tff(3632,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a907) | c1_1(a907) | c2_1(a907))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | (~c1_1(a910)))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3631, 3629])).
% 2.09/2.27 tff(3633,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a907) | c1_1(a907) | c2_1(a907))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3634,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a907) | c0_1(a910) | c2_1(a910) | c1_1(a907) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | (~c1_1(a910))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 2.09/2.27 tff(3635,plain,
% 2.09/2.27 ($false),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3634, 112, 3618, 505, 3605, 3620, 3617, 45, 43, 1721, 3628, 3627])).
% 2.09/2.27 tff(3636,plain,(c3_1(a907) | c1_1(a907) | c0_1(a899) | (~c0_1(a898)) | c2_1(a898) | (~c1_1(a898)) | hskp31 | c0_1(a907) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.09/2.27 tff(3637,plain,
% 2.09/2.27 (c3_1(a907)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3636, 43, 45, 3515, 3516, 3514, 46, 44, 2879])).
% 2.09/2.27 tff(3638,plain,
% 2.09/2.27 (hskp4 | (~c3_1(a907))),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[646, 112, 3515, 44, 45, 3516, 640, 3517])).
% 2.09/2.27 tff(3639,plain,
% 2.09/2.27 (hskp4),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3638, 3637])).
% 2.09/2.27 tff(3640,plain,
% 2.09/2.27 (~c3_1(a904)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[536, 3639])).
% 2.09/2.27 tff(3641,plain,
% 2.09/2.27 (~c1_1(a904)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[542, 3639])).
% 2.09/2.27 tff(3642,plain,
% 2.09/2.27 (~c0_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1335, 3599])).
% 2.09/2.27 tff(3643,plain,
% 2.09/2.27 (c2_1(a904)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[605, 3639])).
% 2.09/2.27 tff(3644,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | (~c3_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | (~c3_1(a909)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3645,plain,
% 2.09/2.27 (((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909))) <=> (c0_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | (~c3_1(a909)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3646,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | (~c3_1(a909))))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3645])).
% 2.09/2.27 tff(3647,plain,
% 2.09/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | (~c3_1(a909)))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3646, 3644])).
% 2.09/2.27 tff(3648,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c3_1(a898)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909)))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3649,plain,
% 2.09/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a909) | c2_1(a909) | c1_1(a904) | c3_1(a904) | c2_1(a898) | (~ndr1_0) | (~c3_1(a898)) | (~c1_1(a898)) | (~c2_1(a904)) | (~c3_1(a909))),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3648, 3647])).
% 2.09/2.27 tff(3650,plain,
% 2.09/2.27 (~c3_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3649, 112, 3643, 3514, 3642, 3600, 3641, 3640, 3516, 503, 3517])).
% 2.09/2.27 tff(3651,plain,
% 2.09/2.27 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | c0_1(a909) | c1_1(a909) | (~ndr1_0) | c3_1(a909))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp2 | c0_1(a909) | c1_1(a909) | (~ndr1_0) | c3_1(a909))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3652,plain,
% 2.09/2.27 ((hskp28 | hskp2 | (~ndr1_0) | c1_1(a909) | c0_1(a909) | c3_1(a909)) <=> (hskp28 | hskp2 | c0_1(a909) | c1_1(a909) | (~ndr1_0) | c3_1(a909))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3653,plain,
% 2.09/2.27 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | (~ndr1_0) | c1_1(a909) | c0_1(a909) | c3_1(a909))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | c0_1(a909) | c1_1(a909) | (~ndr1_0) | c3_1(a909)))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3652])).
% 2.09/2.27 tff(3654,plain,
% 2.09/2.27 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | (~ndr1_0) | c1_1(a909) | c0_1(a909) | c3_1(a909))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp2 | c0_1(a909) | c1_1(a909) | (~ndr1_0) | c3_1(a909))),
% 2.09/2.27 inference(transitivity,[status(thm)],[3653, 3651])).
% 2.09/2.27 tff(3655,plain,
% 2.09/2.27 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp2 | (~ndr1_0) | c1_1(a909) | c0_1(a909) | c3_1(a909))),
% 2.09/2.27 inference(quant_inst,[status(thm)],[])).
% 2.09/2.27 tff(3656,plain,
% 2.09/2.27 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp2 | c0_1(a909) | c1_1(a909) | (~ndr1_0) | c3_1(a909)),
% 2.09/2.27 inference(modus_ponens,[status(thm)],[3655, 3654])).
% 2.09/2.27 tff(3657,plain,
% 2.09/2.27 (hskp28 | c3_1(a909)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3656, 112, 2879, 3642, 3601, 2680])).
% 2.09/2.27 tff(3658,plain,
% 2.09/2.27 (hskp28),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3657, 3650])).
% 2.09/2.27 tff(3659,plain,
% 2.09/2.27 (c0_1(a900)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[965, 3658])).
% 2.09/2.27 tff(3660,plain,
% 2.09/2.27 (c2_1(a900)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[957, 3658])).
% 2.09/2.27 tff(3661,plain,
% 2.09/2.27 (c3_1(a900)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[949, 3658])).
% 2.09/2.27 tff(3662,plain,
% 2.09/2.27 ($false),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2050, 3661, 3660, 3642, 3639, 3659, 3601, 3600])).
% 2.09/2.27 tff(3663,plain,(c0_1(a899) | c0_1(a907) | c1_1(a907) | hskp31 | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.27 tff(3664,plain,
% 2.09/2.27 (c0_1(a899)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3663, 47, 45, 46, 44])).
% 2.09/2.27 tff(3665,plain,
% 2.09/2.27 (~hskp1),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[292, 3664])).
% 2.09/2.27 tff(3666,plain,
% 2.09/2.27 (~c3_1(a898)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3578, 60, 152, 66, 74])).
% 2.09/2.27 tff(3667,plain,
% 2.09/2.27 ($false),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[120, 3666, 66, 74, 60, 46])).
% 2.09/2.27 tff(3668,plain,((~hskp0) | hskp31 | hskp1), inference(lemma,lemma(discharge,[]))).
% 2.09/2.27 tff(3669,plain,
% 2.09/2.27 (~hskp0),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[3668, 3665, 46])).
% 2.09/2.27 tff(3670,plain,
% 2.09/2.27 (c2_1(a907)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1478, 31, 45, 152])).
% 2.09/2.27 tff(3671,plain,
% 2.09/2.27 (c3_1(a907)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1495, 32, 31, 3670])).
% 2.09/2.27 tff(3672,plain,
% 2.09/2.27 (hskp24),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[2273, 3671, 3670, 32])).
% 2.09/2.27 tff(3673,plain,
% 2.09/2.27 (~c2_1(a953)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1209, 3672])).
% 2.09/2.27 tff(3674,plain,
% 2.09/2.27 (c3_1(a953)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1188, 3672])).
% 2.09/2.27 tff(3675,plain,
% 2.09/2.27 (c1_1(a953)),
% 2.09/2.27 inference(unit_resolution,[status(thm)],[1196, 3672])).
% 2.09/2.27 tff(3676,plain,
% 2.09/2.27 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3677,plain,
% 2.09/2.27 ((hskp13 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953))) <=> (hskp13 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.09/2.27 inference(rewrite,[status(thm)],[])).
% 2.09/2.27 tff(3678,plain,
% 2.09/2.27 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953))))),
% 2.09/2.27 inference(monotonicity,[status(thm)],[3677])).
% 2.09/2.27 tff(3679,plain,
% 2.09/2.27 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3678, 3676])).
% 2.09/2.28 tff(3680,plain,
% 2.09/2.28 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3681,plain,
% 2.09/2.28 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | c2_1(a953) | (~ndr1_0) | (~c1_1(a953)) | (~c3_1(a953))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3680, 3679])).
% 2.09/2.28 tff(3682,plain,
% 2.09/2.28 (hskp13),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3681, 112, 152, 3675, 3674, 3673, 174])).
% 2.09/2.28 tff(3683,plain,
% 2.09/2.28 (~c2_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[187, 3682])).
% 2.09/2.28 tff(3684,plain,
% 2.09/2.28 (~c1_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[193, 3682])).
% 2.09/2.28 tff(3685,plain,
% 2.09/2.28 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | c0_1(a914))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | c0_1(a914))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3686,plain,
% 2.09/2.28 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | c0_1(a914)) <=> (hskp1 | hskp0 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | c0_1(a914))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3687,plain,
% 2.09/2.28 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | c0_1(a914))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | c0_1(a914)))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3686])).
% 2.09/2.28 tff(3688,plain,
% 2.09/2.28 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | c0_1(a914))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | c0_1(a914))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3687, 3685])).
% 2.09/2.28 tff(3689,plain,
% 2.09/2.28 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | c0_1(a914))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3690,plain,
% 2.09/2.28 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | c0_1(a914)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3689, 3688])).
% 2.09/2.28 tff(3691,plain,
% 2.09/2.28 (c0_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3690, 112, 152, 31, 3684, 3683, 20])).
% 2.09/2.28 tff(3692,plain,
% 2.09/2.28 (c3_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[201, 3682])).
% 2.09/2.28 tff(3693,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3694,plain,
% 2.09/2.28 ((hskp4 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907))) <=> (hskp4 | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3695,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a914)) | (~c0_1(a914))))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3694])).
% 2.09/2.28 tff(3696,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3695, 3693])).
% 2.09/2.28 tff(3697,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c0_1(a907) | c1_1(a907) | (~c3_1(a907)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3698,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a914) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c3_1(a914)) | (~c0_1(a914))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 2.09/2.28 tff(3699,plain,
% 2.09/2.28 (hskp4),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3698, 112, 3692, 3671, 3683, 44, 45, 640, 3691])).
% 2.09/2.28 tff(3700,plain,
% 2.09/2.28 (~c3_1(a904)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[536, 3699])).
% 2.09/2.28 tff(3701,plain,
% 2.09/2.28 (~c1_1(a904)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[542, 3699])).
% 2.09/2.28 tff(3702,plain,
% 2.09/2.28 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3703,plain,
% 2.09/2.28 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp5 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3704,plain,
% 2.09/2.28 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3703])).
% 2.09/2.28 tff(3705,plain,
% 2.09/2.28 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3704, 3702])).
% 2.09/2.28 tff(3706,plain,
% 2.09/2.28 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3707,plain,
% 2.09/2.28 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3706, 3705])).
% 2.09/2.28 tff(3708,plain,
% 2.09/2.28 (hskp5 | (~c0_1(a914))),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3707, 112, 152, 3692, 3683, 229])).
% 2.09/2.28 tff(3709,plain,
% 2.09/2.28 (hskp5),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3708, 3691])).
% 2.09/2.28 tff(3710,plain,
% 2.09/2.28 (~c0_1(a905)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[276, 3709])).
% 2.09/2.28 tff(3711,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3712,plain,
% 2.09/2.28 ((hskp22 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914))) <=> (hskp22 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3713,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3712])).
% 2.09/2.28 tff(3714,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3713, 3711])).
% 2.09/2.28 tff(3715,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3716,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 2.09/2.28 tff(3717,plain,
% 2.09/2.28 (hskp22),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3716, 112, 3692, 3684, 3683, 1234, 3691])).
% 2.09/2.28 tff(3718,plain,
% 2.09/2.28 (~c3_1(a939)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1247, 3717])).
% 2.09/2.28 tff(3719,plain,
% 2.09/2.28 (~c0_1(a939)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1253, 3717])).
% 2.09/2.28 tff(3720,plain,
% 2.09/2.28 (c2_1(a904)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[605, 3699])).
% 2.09/2.28 tff(3721,plain,
% 2.09/2.28 (c3_1(a905)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[244, 3709])).
% 2.09/2.28 tff(3722,plain,
% 2.09/2.28 (c1_1(a939)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1262, 3717])).
% 2.09/2.28 tff(3723,plain,
% 2.09/2.28 (~c2_1(a905)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1671, 112, 3722, 3721, 3720, 3719, 3718, 3710, 3701, 3700, 392])).
% 2.09/2.28 tff(3724,plain,
% 2.09/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a953) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | c2_1(a905) | (~c1_1(a953)) | (~c3_1(a953)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | c2_1(a905) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3725,plain,
% 2.09/2.28 (((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905))) <=> (c2_1(a953) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | c2_1(a905) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3726,plain,
% 2.09/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a953) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | c2_1(a905) | (~c1_1(a953)) | (~c3_1(a953))))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3725])).
% 2.09/2.28 tff(3727,plain,
% 2.09/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | c2_1(a905) | (~c1_1(a953)) | (~c3_1(a953)))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3726, 3724])).
% 2.09/2.28 tff(3728,plain,
% 2.09/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a905) | c2_1(a905) | (~c3_1(a905)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3729,plain,
% 2.09/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a953) | c0_1(a905) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c3_1(a905)) | c2_1(a905) | (~c1_1(a953)) | (~c3_1(a953))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3728, 3727])).
% 2.09/2.28 tff(3730,plain,
% 2.09/2.28 ($false),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3729, 112, 3675, 3674, 3721, 3720, 3673, 3710, 3701, 3700, 503, 3723])).
% 2.09/2.28 tff(3731,plain,(hskp17 | hskp1 | c0_1(a907) | c1_1(a907) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.09/2.28 tff(3732,plain,
% 2.09/2.28 (hskp17),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3731, 3665, 44, 45, 3669])).
% 2.09/2.28 tff(3733,plain,
% 2.09/2.28 (hskp11),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1729, 3732, 46])).
% 2.09/2.28 tff(3734,plain,
% 2.09/2.28 (~c1_1(a912)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2146, 3733])).
% 2.09/2.28 tff(3735,plain,
% 2.09/2.28 (~c2_1(a912)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1679, 3733])).
% 2.09/2.28 tff(3736,plain,
% 2.09/2.28 ($false),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2937, 3735, 3734, 44, 45, 3665, 3669, 46, 2879])).
% 2.09/2.28 tff(3737,plain,(c2_1(a901) | c0_1(a907) | c1_1(a907) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.09/2.28 tff(3738,plain,
% 2.09/2.28 (c2_1(a901)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3737, 45, 44, 46])).
% 2.09/2.28 tff(3739,plain,
% 2.09/2.28 (((~hskp2) | (~c2_1(a901))) <=> ((~hskp2) | (~c2_1(a901)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3740,plain,
% 2.09/2.28 (((~c2_1(a901)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a901)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3741,axiom,((~c2_1(a901)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 2.09/2.28 tff(3742,plain,
% 2.09/2.28 ((~hskp2) | (~c2_1(a901))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3741, 3740])).
% 2.09/2.28 tff(3743,plain,
% 2.09/2.28 ((~hskp2) | (~c2_1(a901))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3742, 3739])).
% 2.09/2.28 tff(3744,plain,
% 2.09/2.28 (~hskp2),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3743, 3738])).
% 2.09/2.28 tff(3745,plain,
% 2.09/2.28 (^[U: $i] : refl((hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 2.09/2.28 inference(bind,[status(th)],[])).
% 2.09/2.28 tff(3746,plain,
% 2.09/2.28 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.09/2.28 inference(quant_intro,[status(thm)],[3745])).
% 2.09/2.28 tff(3747,plain,
% 2.09/2.28 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3748,plain,
% 2.09/2.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp2) <=> ((hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp2) <=> (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.09/2.28 inference(bind,[status(th)],[])).
% 2.09/2.28 tff(3749,plain,
% 2.09/2.28 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp2) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.09/2.28 inference(quant_intro,[status(thm)],[3748])).
% 2.09/2.28 tff(3750,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 2.09/2.28 tff(3751,plain,
% 2.09/2.28 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 2.09/2.28 tff(3752,plain,
% 2.09/2.28 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3751, 3747])).
% 2.09/2.28 tff(3753,plain,(
% 2.09/2.28 ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.09/2.28 inference(skolemize,[status(sab)],[3752])).
% 2.09/2.28 tff(3754,plain,
% 2.09/2.28 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3753, 3746])).
% 2.09/2.28 tff(3755,plain,
% 2.09/2.28 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3756,plain,
% 2.09/2.28 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3757,plain,
% 2.09/2.28 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3756, 3755])).
% 2.09/2.28 tff(3758,plain,
% 2.09/2.28 (hskp13),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3757, 112, 2888, 3611, 3614, 3612, 3754])).
% 2.09/2.28 tff(3759,plain,
% 2.09/2.28 (~c2_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[187, 3758])).
% 2.09/2.28 tff(3760,plain,
% 2.09/2.28 (~c1_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[193, 3758])).
% 2.09/2.28 tff(3761,plain,
% 2.09/2.28 (c3_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[201, 3758])).
% 2.09/2.28 tff(3762,plain,
% 2.09/2.28 (c0_1(a914)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2838, 112, 3761, 505, 3760, 3759, 44, 45, 151])).
% 2.09/2.28 tff(3763,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a914) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a914) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3764,plain,
% 2.09/2.28 ((hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp0 | c2_1(a914) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3765,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a914) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a914)) | (~c0_1(a914))))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3764])).
% 2.09/2.28 tff(3766,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a914) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3765, 3763])).
% 2.09/2.28 tff(3767,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3768,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a914) | (~ndr1_0) | (~c3_1(a900)) | (~c2_1(a900)) | (~c0_1(a900)) | (~c3_1(a914)) | (~c0_1(a914))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 2.09/2.28 tff(3769,plain,
% 2.09/2.28 ($false),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3768, 112, 31, 3611, 3614, 3612, 3761, 3759, 1526, 3762])).
% 2.09/2.28 tff(3770,plain,(c3_1(a907) | hskp0 | c0_1(a907) | c1_1(a907) | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.09/2.28 tff(3771,plain,
% 2.09/2.28 (c3_1(a907)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3770, 31, 44, 45, 3744])).
% 2.09/2.28 tff(3772,plain,
% 2.09/2.28 (hskp1),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3731, 32, 44, 45, 31])).
% 2.09/2.28 tff(3773,plain,
% 2.09/2.28 (c2_1(a899)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[300, 3772])).
% 2.09/2.28 tff(3774,plain,
% 2.09/2.28 (c1_1(a899)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[308, 3772])).
% 2.09/2.28 tff(3775,plain,
% 2.09/2.28 (hskp10),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3113, 3774, 31, 2207, 44, 45, 43, 32, 3773])).
% 2.09/2.28 tff(3776,plain,
% 2.09/2.28 (c1_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2362, 3775])).
% 2.09/2.28 tff(3777,plain,
% 2.09/2.28 (~c2_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2348, 3775])).
% 2.09/2.28 tff(3778,assumption,(~hskp25), introduced(assumption)).
% 2.09/2.28 tff(3779,plain,
% 2.09/2.28 (hskp21),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3248, 3778, 31])).
% 2.09/2.28 tff(3780,plain,
% 2.09/2.28 (hskp25 | c3_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3494, 112, 2366, 2364, 30])).
% 2.09/2.28 tff(3781,plain,
% 2.09/2.28 (c3_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3780, 3778])).
% 2.09/2.28 tff(3782,plain,
% 2.09/2.28 ($false),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3510, 3781, 3779, 43, 2364, 311, 312, 2366])).
% 2.09/2.28 tff(3783,plain,(hskp25 | c0_1(a899) | c2_1(a910) | (~c1_1(a899)) | (~c2_1(a899)) | (~c1_1(a910)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.09/2.28 tff(3784,plain,
% 2.09/2.28 (hskp25),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3783, 3777, 43, 3774, 3773, 3776, 31])).
% 2.09/2.28 tff(3785,plain,
% 2.09/2.28 (~c3_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1692, 3784])).
% 2.09/2.28 tff(3786,plain,
% 2.09/2.28 (~c0_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1841, 3784])).
% 2.09/2.28 tff(3787,plain,
% 2.09/2.28 (~c2_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1848, 112, 32, 31, 3786, 3785, 891])).
% 2.09/2.28 tff(3788,plain,
% 2.09/2.28 (c3_1(a899)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2295, 3773, 32])).
% 2.09/2.28 tff(3789,plain,
% 2.09/2.28 (~c0_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2354, 3775])).
% 2.09/2.28 tff(3790,plain,
% 2.09/2.28 (~c1_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1698, 3784])).
% 2.09/2.28 tff(3791,plain,
% 2.09/2.28 ($false),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2718, 112, 3776, 3773, 3790, 3785, 3789, 3777, 43, 1721, 3788, 3787])).
% 2.09/2.28 tff(3792,plain,(hskp17 | c0_1(a899) | hskp0 | (~c3_1(a907)) | c0_1(a907) | c1_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.28 tff(3793,plain,
% 2.09/2.28 (hskp17),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3792, 43, 31, 3771, 44, 45])).
% 2.09/2.28 tff(3794,plain,
% 2.09/2.28 (hskp11),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1729, 3793, 46])).
% 2.09/2.28 tff(3795,plain,
% 2.09/2.28 (~c1_1(a912)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2146, 3794])).
% 2.09/2.28 tff(3796,plain,
% 2.09/2.28 (~c2_1(a912)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1679, 3794])).
% 2.09/2.28 tff(3797,plain,
% 2.09/2.28 (~c3_1(a912)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1390, 3794])).
% 2.09/2.28 tff(3798,plain,
% 2.09/2.28 (hskp10),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[858, 3797, 3793, 3796, 3795, 46])).
% 2.09/2.28 tff(3799,plain,
% 2.09/2.28 (~c2_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2348, 3798])).
% 2.09/2.28 tff(3800,plain,
% 2.09/2.28 (~c0_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2354, 3798])).
% 2.09/2.28 tff(3801,plain,
% 2.09/2.28 (c1_1(a910)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2362, 3798])).
% 2.09/2.28 tff(3802,plain,
% 2.09/2.28 (~c2_1(a907)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2899, 112, 3801, 3771, 3795, 3796, 3797, 3800, 3799, 44, 1721])).
% 2.09/2.28 tff(3803,plain,
% 2.09/2.28 (hskp1),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2937, 3796, 44, 45, 3795, 31, 46, 3744])).
% 2.09/2.28 tff(3804,plain,
% 2.09/2.28 (c2_1(a899)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[300, 3803])).
% 2.09/2.28 tff(3805,plain,
% 2.09/2.28 (c1_1(a899)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[308, 3803])).
% 2.09/2.28 tff(3806,plain,
% 2.09/2.28 (hskp25),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3783, 3799, 43, 3805, 3804, 3801, 31])).
% 2.09/2.28 tff(3807,plain,
% 2.09/2.28 (~c3_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1692, 3806])).
% 2.09/2.28 tff(3808,plain,
% 2.09/2.28 (~c1_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1698, 3806])).
% 2.09/2.28 tff(3809,plain,
% 2.09/2.28 (~c0_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1841, 3806])).
% 2.09/2.28 tff(3810,plain,
% 2.09/2.28 ($false),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2645, 112, 3771, 3809, 3808, 3807, 44, 45, 151, 3802])).
% 2.09/2.28 tff(3811,plain,(c0_1(a899) | c0_1(a907) | c1_1(a907) | hskp0 | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.09/2.28 tff(3812,plain,
% 2.09/2.28 (c0_1(a899)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3811, 31, 45, 44, 46])).
% 2.09/2.28 tff(3813,plain,
% 2.09/2.28 (~hskp1),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[292, 3812])).
% 2.09/2.28 tff(3814,plain,
% 2.09/2.28 (hskp17),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3731, 3813, 44, 45, 31])).
% 2.09/2.28 tff(3815,plain,
% 2.09/2.28 (hskp11),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1729, 3814, 46])).
% 2.09/2.28 tff(3816,plain,
% 2.09/2.28 (~c1_1(a912)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2146, 3815])).
% 2.09/2.28 tff(3817,plain,
% 2.09/2.28 (~c2_1(a912)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1679, 3815])).
% 2.09/2.28 tff(3818,plain,
% 2.09/2.28 ($false),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[2937, 3817, 3816, 44, 45, 3813, 31, 46, 3744])).
% 2.09/2.28 tff(3819,plain,(hskp0 | c0_1(a907) | c1_1(a907) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.09/2.28 tff(3820,plain,
% 2.09/2.28 (hskp31),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3819, 45, 31, 44])).
% 2.09/2.28 tff(3821,plain,
% 2.09/2.28 (((~hskp31) | c1_1(a957)) <=> ((~hskp31) | c1_1(a957))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3822,axiom,((~hskp31) | c1_1(a957)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 2.09/2.28 tff(3823,plain,
% 2.09/2.28 ((~hskp31) | c1_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3822, 3821])).
% 2.09/2.28 tff(3824,plain,
% 2.09/2.28 ((~hskp31) | c1_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3823, 3821])).
% 2.09/2.28 tff(3825,plain,
% 2.09/2.28 ((~hskp31) | c1_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3824, 3821])).
% 2.09/2.28 tff(3826,plain,
% 2.09/2.28 ((~hskp31) | c1_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3825, 3821])).
% 2.09/2.28 tff(3827,plain,
% 2.09/2.28 ((~hskp31) | c1_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3826, 3821])).
% 2.09/2.28 tff(3828,plain,
% 2.09/2.28 (c1_1(a957)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3827, 3820])).
% 2.09/2.28 tff(3829,plain,
% 2.09/2.28 (((~hskp31) | c3_1(a957)) <=> ((~hskp31) | c3_1(a957))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3830,axiom,((~hskp31) | c3_1(a957)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 2.09/2.28 tff(3831,plain,
% 2.09/2.28 ((~hskp31) | c3_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3830, 3829])).
% 2.09/2.28 tff(3832,plain,
% 2.09/2.28 ((~hskp31) | c3_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3831, 3829])).
% 2.09/2.28 tff(3833,plain,
% 2.09/2.28 ((~hskp31) | c3_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3832, 3829])).
% 2.09/2.28 tff(3834,plain,
% 2.09/2.28 ((~hskp31) | c3_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3833, 3829])).
% 2.09/2.28 tff(3835,plain,
% 2.09/2.28 ((~hskp31) | c3_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3834, 3829])).
% 2.09/2.28 tff(3836,plain,
% 2.09/2.28 (c3_1(a957)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3835, 3820])).
% 2.09/2.28 tff(3837,plain,
% 2.09/2.28 (((~hskp31) | c2_1(a957)) <=> ((~hskp31) | c2_1(a957))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3838,axiom,((~hskp31) | c2_1(a957)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 2.09/2.28 tff(3839,plain,
% 2.09/2.28 ((~hskp31) | c2_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3838, 3837])).
% 2.09/2.28 tff(3840,plain,
% 2.09/2.28 ((~hskp31) | c2_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3839, 3837])).
% 2.09/2.28 tff(3841,plain,
% 2.09/2.28 ((~hskp31) | c2_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3840, 3837])).
% 2.09/2.28 tff(3842,plain,
% 2.09/2.28 ((~hskp31) | c2_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3841, 3837])).
% 2.09/2.28 tff(3843,plain,
% 2.09/2.28 ((~hskp31) | c2_1(a957)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3842, 3837])).
% 2.09/2.28 tff(3844,plain,
% 2.09/2.28 (c2_1(a957)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3843, 3820])).
% 2.09/2.28 tff(3845,plain,
% 2.09/2.28 (hskp17),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3731, 3271, 44, 45, 31])).
% 2.09/2.28 tff(3846,plain,
% 2.09/2.28 (~c3_1(a928)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[828, 3845])).
% 2.09/2.28 tff(3847,plain,
% 2.09/2.28 (~c2_1(a928)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[834, 3845])).
% 2.09/2.28 tff(3848,plain,
% 2.09/2.28 (c1_1(a928)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[842, 3845])).
% 2.09/2.28 tff(3849,plain,
% 2.09/2.28 (hskp25),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1686, 112, 3848, 3847, 3846, 30])).
% 2.09/2.28 tff(3850,plain,
% 2.09/2.28 (~c1_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1698, 3849])).
% 2.09/2.28 tff(3851,plain,
% 2.09/2.28 (~c0_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1841, 3849])).
% 2.09/2.28 tff(3852,plain,
% 2.09/2.28 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c2_1(a958))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c2_1(a958))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3853,plain,
% 2.09/2.28 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a958) | c1_1(a958) | c0_1(a958)) <=> (hskp1 | hskp0 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c2_1(a958))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3854,plain,
% 2.09/2.28 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a958) | c1_1(a958) | c0_1(a958))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c2_1(a958)))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3853])).
% 2.09/2.28 tff(3855,plain,
% 2.09/2.28 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a958) | c1_1(a958) | c0_1(a958))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c2_1(a958))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3854, 3852])).
% 2.09/2.28 tff(3856,plain,
% 2.09/2.28 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a958) | c1_1(a958) | c0_1(a958))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3857,plain,
% 2.09/2.28 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c2_1(a958)),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3856, 3855])).
% 2.09/2.28 tff(3858,plain,
% 2.09/2.28 (c2_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3857, 112, 3271, 31, 3851, 3850, 20])).
% 2.09/2.28 tff(3859,plain,
% 2.09/2.28 (hskp1 | c1_1(a907) | c2_1(a907)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1477, 112, 31, 44, 20])).
% 2.09/2.28 tff(3860,plain,
% 2.09/2.28 (c2_1(a907)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3859, 3271, 45])).
% 2.09/2.28 tff(3861,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a928) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a928)) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a928) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3862,plain,
% 2.09/2.28 ((hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907))) <=> (hskp1 | c3_1(a928) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3863,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a928) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a928)) | (~c1_1(a928))))),
% 2.09/2.28 inference(monotonicity,[status(thm)],[3862])).
% 2.09/2.28 tff(3864,plain,
% 2.09/2.28 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a928) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.09/2.28 inference(transitivity,[status(thm)],[3863, 3861])).
% 2.09/2.28 tff(3865,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a907) | c1_1(a907) | (~c2_1(a907)))),
% 2.09/2.28 inference(quant_inst,[status(thm)],[])).
% 2.09/2.28 tff(3866,plain,
% 2.09/2.28 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a928) | c0_1(a907) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a928)) | (~c1_1(a928))),
% 2.09/2.28 inference(modus_ponens,[status(thm)],[3865, 3864])).
% 2.09/2.28 tff(3867,plain,
% 2.09/2.28 (~c0_1(a928)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[3866, 112, 3271, 3848, 3846, 44, 45, 3342, 3860])).
% 2.09/2.28 tff(3868,plain,
% 2.09/2.28 (~c3_1(a958)),
% 2.09/2.28 inference(unit_resolution,[status(thm)],[1692, 3849])).
% 2.09/2.28 tff(3869,assumption,(~c0_1(a957)), introduced(assumption)).
% 2.09/2.28 tff(3870,assumption,(~c3_1(a958)), introduced(assumption)).
% 2.09/2.28 tff(3871,assumption,(~c1_1(a958)), introduced(assumption)).
% 2.09/2.28 tff(3872,assumption,(c3_1(a957)), introduced(assumption)).
% 2.09/2.28 tff(3873,assumption,(c2_1(a957)), introduced(assumption)).
% 2.09/2.28 tff(3874,plain,
% 2.09/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.09/2.28 inference(rewrite,[status(thm)],[])).
% 2.09/2.28 tff(3875,plain,
% 2.09/2.28 (((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3876,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958))))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3875])).
% 2.09/2.29 tff(3877,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3876, 3874])).
% 2.09/2.29 tff(3878,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3879,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c3_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | (~c2_1(a958))),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3878, 3877])).
% 2.09/2.29 tff(3880,plain,
% 2.09/2.29 (~c2_1(a958)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3879, 432, 3873, 3872, 1404, 3871, 3870, 2423, 392, 3869, 1392])).
% 2.09/2.29 tff(3881,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3882,plain,
% 2.09/2.29 (((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3883,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958)))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3882])).
% 2.09/2.29 tff(3884,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3883, 3881])).
% 2.09/2.29 tff(3885,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3886,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958)),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 2.09/2.29 tff(3887,plain,
% 2.09/2.29 ($false),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3886, 432, 3873, 3872, 1404, 3871, 3870, 1403, 1721, 3869, 1392, 3880])).
% 2.09/2.29 tff(3888,plain,(c0_1(a957) | (~ndr1_0) | (~c2_1(a957)) | (~c3_1(a957)) | (~c1_1(a928)) | c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a928) | c3_1(a928)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.29 tff(3889,plain,
% 2.09/2.29 (c0_1(a957) | (~c2_1(a957)) | (~c3_1(a957)) | (~c1_1(a928)) | c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a928) | c3_1(a928)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3888, 112])).
% 2.09/2.29 tff(3890,plain,
% 2.09/2.29 (c0_1(a957)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3889, 3850, 3844, 3836, 3848, 3846, 3868, 3847, 3867])).
% 2.09/2.29 tff(3891,plain,
% 2.09/2.29 (hskp1 | c1_1(a899) | c2_1(a899)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3277, 112, 31, 43, 20])).
% 2.09/2.29 tff(3892,plain,
% 2.09/2.29 (c1_1(a899)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3891, 3271, 3270])).
% 2.09/2.29 tff(3893,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3894,plain,
% 2.09/2.29 ((hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899))) <=> (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3895,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957))))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3894])).
% 2.09/2.29 tff(3896,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3895, 3893])).
% 2.09/2.29 tff(3897,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3898,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a899) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957))),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3897, 3896])).
% 2.09/2.29 tff(3899,plain,
% 2.09/2.29 (hskp11 | (~c0_1(a957))),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3898, 112, 3828, 3836, 3892, 3270, 43, 1402])).
% 2.09/2.29 tff(3900,plain,
% 2.09/2.29 (hskp11),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3899, 3890])).
% 2.09/2.29 tff(3901,plain,
% 2.09/2.29 (~c2_1(a912)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1679, 3900])).
% 2.09/2.29 tff(3902,plain,
% 2.09/2.29 (~c1_1(a912)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2146, 3900])).
% 2.09/2.29 tff(3903,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c0_1(a912) | (~c2_1(a958)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c0_1(a912) | (~c2_1(a958)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3904,plain,
% 2.09/2.29 (((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c0_1(a912) | (~c2_1(a958)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3905,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c0_1(a912) | (~c2_1(a958))))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3904])).
% 2.09/2.29 tff(3906,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c0_1(a912) | (~c2_1(a958)))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3905, 3903])).
% 2.09/2.29 tff(3907,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3908,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c0_1(a912) | (~c2_1(a958))),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3907, 3906])).
% 2.09/2.29 tff(3909,plain,
% 2.09/2.29 (c0_1(a912)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3908, 112, 3844, 3836, 3850, 3868, 3902, 3901, 870, 3890, 3858])).
% 2.09/2.29 tff(3910,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a912)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3911,plain,
% 2.09/2.29 ((hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912))) <=> (hskp1 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a912)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3912,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a912))))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3911])).
% 2.09/2.29 tff(3913,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a912)))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3912, 3910])).
% 2.09/2.29 tff(3914,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3915,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a912) | c2_1(a912) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a912))),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3914, 3913])).
% 2.09/2.29 tff(3916,plain,
% 2.09/2.29 ($false),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3915, 112, 3271, 3828, 3844, 3836, 3902, 3901, 219, 3909])).
% 2.09/2.29 tff(3917,plain,(c2_1(a899) | hskp0 | c0_1(a899) | c0_1(a907) | c1_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.29 tff(3918,plain,
% 2.09/2.29 (c2_1(a899)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3917, 45, 43, 44, 31])).
% 2.09/2.29 tff(3919,plain,
% 2.09/2.29 (c3_1(a899)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2295, 32, 3918])).
% 2.09/2.29 tff(3920,plain,
% 2.09/2.29 (~c3_1(a907)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3792, 32, 31, 43, 44, 45])).
% 2.09/2.29 tff(3921,plain,
% 2.09/2.29 (hskp2),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3770, 3920, 44, 31, 45])).
% 2.09/2.29 tff(3922,plain,
% 2.09/2.29 (~c2_1(a901)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3743, 3921])).
% 2.09/2.29 tff(3923,plain,
% 2.09/2.29 (hskp17 | c3_1(a907) | (~c2_1(a907))),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1494, 112, 31, 44, 891])).
% 2.09/2.29 tff(3924,plain,
% 2.09/2.29 (~c2_1(a907)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3923, 3920, 32])).
% 2.09/2.29 tff(3925,plain,
% 2.09/2.29 (~c0_1(a901)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2669, 3921])).
% 2.09/2.29 tff(3926,plain,
% 2.09/2.29 (~c1_1(a901)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2961, 112, 3920, 3918, 45, 3925, 3922, 43, 1721, 3919, 3924])).
% 2.09/2.29 tff(3927,plain,
% 2.09/2.29 (~c3_1(a901)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2878, 3921])).
% 2.09/2.29 tff(3928,assumption,(hskp10), introduced(assumption)).
% 2.09/2.29 tff(3929,plain,
% 2.09/2.29 (~c2_1(a910)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2348, 3928])).
% 2.09/2.29 tff(3930,plain,
% 2.09/2.29 (c1_1(a910)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2362, 3928])).
% 2.09/2.29 tff(3931,plain,
% 2.09/2.29 (~c0_1(a910)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2354, 3928])).
% 2.09/2.29 tff(3932,plain,
% 2.09/2.29 ($false),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2376, 3931, 3930, 31, 43, 312, 48, 49, 47, 3929, 32])).
% 2.09/2.29 tff(3933,plain,((~hskp10) | hskp0 | c0_1(a899) | (~c2_1(a899)) | c3_1(a901) | c1_1(a901) | c2_1(a901) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.09/2.29 tff(3934,plain,
% 2.09/2.29 (~hskp10),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3933, 3927, 43, 3918, 31, 3926, 3922, 32])).
% 2.09/2.29 tff(3935,plain,
% 2.09/2.29 (hskp12),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2972, 3934, 3774, 3919])).
% 2.09/2.29 tff(3936,plain,
% 2.09/2.29 (~c3_1(a913)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[347, 3935])).
% 2.09/2.29 tff(3937,plain,
% 2.09/2.29 (c0_1(a913)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[355, 3935])).
% 2.09/2.29 tff(3938,plain,
% 2.09/2.29 (~hskp7),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[512, 3920])).
% 2.09/2.29 tff(3939,plain,
% 2.09/2.29 (c2_1(a913)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[701, 112, 3934, 3938, 3937, 3936, 693])).
% 2.09/2.29 tff(3940,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a907) | c3_1(a913) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a907) | c3_1(a913) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3941,plain,
% 2.09/2.29 ((hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a907) | c2_1(a907) | c1_1(a907)) <=> (hskp20 | c3_1(a907) | c3_1(a913) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3942,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a907) | c2_1(a907) | c1_1(a907))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c3_1(a907) | c3_1(a913) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c0_1(a913)) | (~c2_1(a913))))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3941])).
% 2.09/2.29 tff(3943,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a907) | c2_1(a907) | c1_1(a907))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a907) | c3_1(a913) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3942, 3940])).
% 2.09/2.29 tff(3944,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c3_1(a907) | c2_1(a907) | c1_1(a907))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3945,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c3_1(a907) | c3_1(a913) | c1_1(a907) | (~ndr1_0) | c2_1(a907) | (~c0_1(a913)) | (~c2_1(a913))),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3944, 3943])).
% 2.09/2.29 tff(3946,plain,
% 2.09/2.29 ($false),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3945, 112, 1884, 3937, 3920, 3936, 45, 1064, 3924, 3939])).
% 2.09/2.29 tff(3947,plain,(hskp17 | c1_1(a907) | c0_1(a899) | hskp0 | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.09/2.29 tff(3948,plain,
% 2.09/2.29 (hskp17),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3947, 45, 43, 31, 44])).
% 2.09/2.29 tff(3949,plain,
% 2.09/2.29 (~c3_1(a928)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[828, 3948])).
% 2.09/2.29 tff(3950,plain,
% 2.09/2.29 (~c2_1(a928)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[834, 3948])).
% 2.09/2.29 tff(3951,plain,
% 2.09/2.29 (c1_1(a928)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[842, 3948])).
% 2.09/2.29 tff(3952,plain,
% 2.09/2.29 (hskp25),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1686, 112, 1404, 1403, 2423, 30])).
% 2.09/2.29 tff(3953,plain,
% 2.09/2.29 (~c1_1(a958)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1698, 3952])).
% 2.09/2.29 tff(3954,plain,
% 2.09/2.29 (~c3_1(a958)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1692, 3952])).
% 2.09/2.29 tff(3955,plain,
% 2.09/2.29 (c0_1(a957)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3889, 1392, 3873, 3872, 1404, 2423, 3954, 1403, 3953])).
% 2.09/2.29 tff(3956,assumption,(c1_1(a957)), introduced(assumption)).
% 2.09/2.29 tff(3957,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a928) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a928) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3958,plain,
% 2.09/2.29 ((hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (hskp11 | c2_1(a928) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3959,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a928) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928))))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3958])).
% 2.09/2.29 tff(3960,plain,
% 2.09/2.29 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a928) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928)))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3959, 3957])).
% 2.09/2.29 tff(3961,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3962,plain,
% 2.09/2.29 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a928) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)) | c0_1(a928) | (~c1_1(a928))),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 2.09/2.29 tff(3963,plain,
% 2.09/2.29 (hskp11 | (~c0_1(a957)) | c0_1(a928)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3962, 112, 3956, 3872, 1404, 1403, 1402])).
% 2.09/2.29 tff(3964,plain,
% 2.09/2.29 (hskp11),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3963, 3955, 1392])).
% 2.09/2.29 tff(3965,plain,
% 2.09/2.29 (~c3_1(a912)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1390, 3964])).
% 2.09/2.29 tff(3966,plain,
% 2.09/2.29 (~c2_1(a912)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1679, 3964])).
% 2.09/2.29 tff(3967,plain,
% 2.09/2.29 (~c1_1(a912)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2146, 3964])).
% 2.09/2.29 tff(3968,plain,
% 2.09/2.29 (hskp9),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2404, 112, 1403, 2423, 3967, 3966, 3965, 1310, 1392])).
% 2.09/2.29 tff(3969,plain,
% 2.09/2.29 (~c2_1(a909)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1323, 3968])).
% 2.09/2.29 tff(3970,plain,
% 2.09/2.29 (~c1_1(a909)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1329, 3968])).
% 2.09/2.29 tff(3971,plain,
% 2.09/2.29 (~c0_1(a909)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[1335, 3968])).
% 2.09/2.29 tff(3972,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c2_1(a958)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c2_1(a958)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3973,plain,
% 2.09/2.29 (((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a909) | c0_1(a909) | c2_1(a909)) <=> (c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c2_1(a958)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.09/2.29 tff(3974,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c2_1(a958))))),
% 2.09/2.29 inference(monotonicity,[status(thm)],[3973])).
% 2.09/2.29 tff(3975,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c2_1(a958)))),
% 2.09/2.29 inference(transitivity,[status(thm)],[3974, 3972])).
% 2.09/2.29 tff(3976,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c1_1(a909) | c0_1(a909) | c2_1(a909))),
% 2.09/2.29 inference(quant_inst,[status(thm)],[])).
% 2.09/2.29 tff(3977,plain,
% 2.09/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c2_1(a958))),
% 2.09/2.29 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 2.09/2.29 tff(3978,plain,
% 2.09/2.29 (~c2_1(a958)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[3977, 112, 3873, 3872, 3953, 3954, 3971, 3970, 3969, 870, 3955])).
% 2.09/2.29 tff(3979,plain,
% 2.09/2.29 (hskp10),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[856, 112, 1404, 1403, 3967, 3966, 3965, 812, 1392])).
% 2.09/2.29 tff(3980,plain,
% 2.09/2.29 (c1_1(a910)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2362, 3979])).
% 2.09/2.29 tff(3981,plain,
% 2.09/2.29 (~c2_1(a910)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2348, 3979])).
% 2.09/2.29 tff(3982,plain,
% 2.09/2.29 (~c0_1(a910)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2354, 3979])).
% 2.09/2.29 tff(3983,plain,
% 2.09/2.29 (~c3_1(a899)),
% 2.09/2.29 inference(unit_resolution,[status(thm)],[2751, 112, 1404, 312, 1403, 3967, 3966, 3965, 43, 1721, 1392])).
% 2.09/2.29 tff(3984,plain,
% 2.09/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a899) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a899) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)))),
% 2.09/2.29 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(3985,plain,
% 2.13/2.30 (((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a899) | c1_1(a899) | (~c2_1(a899)) | c1_1(a909) | c0_1(a909) | c2_1(a909)) <=> (c1_1(a899) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(3986,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a899) | c1_1(a899) | (~c2_1(a899)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a899) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[3985])).
% 2.13/2.30 tff(3987,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a899) | c1_1(a899) | (~c2_1(a899)) | c1_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a899) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[3986, 3984])).
% 2.13/2.30 tff(3988,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a899) | c1_1(a899) | (~c2_1(a899)) | c1_1(a909) | c0_1(a909) | c2_1(a909))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(3989,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a899) | c0_1(a909) | c1_1(a909) | c2_1(a909) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[3988, 3987])).
% 2.13/2.30 tff(3990,plain,
% 2.13/2.30 (c1_1(a899)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3989, 112, 3873, 3872, 312, 3971, 3970, 3969, 870, 3983, 3955])).
% 2.13/2.30 tff(3991,plain,
% 2.13/2.30 (hskp7),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2631, 3990, 312, 2423, 1404, 1403, 1392, 3965, 3967, 3966, 43, 3983, 3982, 3981, 3980])).
% 2.13/2.30 tff(3992,plain,
% 2.13/2.30 (c3_1(a907)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[512, 3991])).
% 2.13/2.30 tff(3993,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(3994,plain,
% 2.13/2.30 (((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(3995,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[3994])).
% 2.13/2.30 tff(3996,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958))),
% 2.13/2.30 inference(transitivity,[status(thm)],[3995, 3993])).
% 2.13/2.30 tff(3997,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(3998,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c2_1(a928) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | (~c1_1(a928)) | c2_1(a958)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[3997, 3996])).
% 2.13/2.30 tff(3999,plain,
% 2.13/2.30 ((~c2_1(a907)) | (~c3_1(a907)) | c0_1(a928) | c2_1(a958)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3998, 112, 1404, 3953, 3954, 1403, 44, 1721])).
% 2.13/2.30 tff(4000,plain,
% 2.13/2.30 (~c2_1(a907)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3999, 3992, 1392, 3978])).
% 2.13/2.30 tff(4001,plain,
% 2.13/2.30 (~c0_1(a958)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1841, 3952])).
% 2.13/2.30 tff(4002,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2645, 112, 3992, 4001, 3953, 3954, 44, 45, 151, 4000])).
% 2.13/2.30 tff(4003,plain,(c0_1(a928) | c0_1(a907) | c1_1(a907) | (~c1_1(a928)) | c2_1(a928) | (~c2_1(a899)) | c3_1(a928) | c0_1(a899) | (~c2_1(a957)) | (~c3_1(a957)) | (~c1_1(a957))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(4004,plain,
% 2.13/2.30 (c0_1(a928)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4003, 45, 44, 3951, 3950, 3918, 3949, 43, 3844, 3836, 3828])).
% 2.13/2.30 tff(4005,assumption,(c0_1(a928)), introduced(assumption)).
% 2.13/2.30 tff(4006,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a899) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c0_1(a928)) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a899) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4007,plain,
% 2.13/2.30 ((hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a899) | c1_1(a899) | (~c2_1(a899))) <=> (hskp1 | c1_1(a899) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4008,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a899) | c1_1(a899) | (~c2_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a899) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c0_1(a928)) | (~c1_1(a928))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[4007])).
% 2.13/2.30 tff(4009,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a899) | c1_1(a899) | (~c2_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a899) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[4008, 4006])).
% 2.13/2.30 tff(4010,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a899) | c1_1(a899) | (~c2_1(a899)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(4011,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a899) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c0_1(a928)) | (~c1_1(a928))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4010, 4009])).
% 2.13/2.30 tff(4012,plain,
% 2.13/2.30 (hskp1 | c1_1(a899) | (~c0_1(a928))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4011, 112, 1404, 312, 2423, 43, 3342])).
% 2.13/2.30 tff(4013,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4012, 3453, 3441, 4005])).
% 2.13/2.30 tff(4014,plain,(c1_1(a899) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a899)) | c3_1(a928) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(4015,plain,
% 2.13/2.30 (c1_1(a899)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4014, 4004, 3951, 3918, 3949, 43])).
% 2.13/2.30 tff(4016,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c2_1(a928) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a928) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4017,plain,
% 2.13/2.30 ((hskp14 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp14 | c2_1(a928) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4018,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c2_1(a928) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a928))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[4017])).
% 2.13/2.30 tff(4019,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a928) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a928)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[4018, 4016])).
% 2.13/2.30 tff(4020,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(4021,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c2_1(a928) | c3_1(a928) | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a928))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4020, 4019])).
% 2.13/2.30 tff(4022,plain,
% 2.13/2.30 (hskp14 | (~c1_1(a899)) | (~c0_1(a928))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4021, 112, 3918, 3950, 3949, 43, 373])).
% 2.13/2.30 tff(4023,plain,
% 2.13/2.30 (hskp14),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4022, 4015, 4004])).
% 2.13/2.30 tff(4024,plain,
% 2.13/2.30 (~c1_1(a918)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[672, 4023])).
% 2.13/2.30 tff(4025,plain,
% 2.13/2.30 (hskp14 | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a928))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4021, 432, 1403, 2423, 43, 373])).
% 2.13/2.30 tff(4026,plain,
% 2.13/2.30 (hskp14),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4025, 4005, 312, 311])).
% 2.13/2.30 tff(4027,plain,
% 2.13/2.30 (c0_1(a918)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[734, 4026])).
% 2.13/2.30 tff(4028,plain,
% 2.13/2.30 (c3_1(a918)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[742, 4026])).
% 2.13/2.30 tff(4029,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4030,plain,
% 2.13/2.30 ((hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918))) <=> (hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4031,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[4030])).
% 2.13/2.30 tff(4032,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[4031, 4029])).
% 2.13/2.30 tff(4033,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(4034,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~ndr1_0) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4033, 4032])).
% 2.13/2.30 tff(4035,plain,
% 2.13/2.30 ((~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4034, 432, 755, 1403, 2423, 754, 753])).
% 2.13/2.30 tff(4036,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4035, 4028, 4027, 4005])).
% 2.13/2.30 tff(4037,plain,((~c0_1(a928)) | (~ndr1_0) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~c2_1(a899)) | (~c1_1(a899)) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(4038,plain,
% 2.13/2.30 ((~c0_1(a928)) | hskp18 | c2_1(a928) | c3_1(a928) | c1_1(a918) | (~c2_1(a899)) | (~c1_1(a899)) | c0_1(a899)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4037, 112])).
% 2.13/2.30 tff(4039,plain,
% 2.13/2.30 (hskp18),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4038, 4024, 43, 3950, 3949, 4004, 3918, 4015])).
% 2.13/2.30 tff(4040,plain,
% 2.13/2.30 (~c1_1(a929)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[771, 4039])).
% 2.13/2.30 tff(4041,plain,
% 2.13/2.30 (c2_1(a929)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[781, 4039])).
% 2.13/2.30 tff(4042,plain,
% 2.13/2.30 (c0_1(a929)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[789, 4039])).
% 2.13/2.30 tff(4043,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a929) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4044,plain,
% 2.13/2.30 ((hskp7 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929))) <=> (hskp7 | c1_1(a929) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4045,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a929) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a929)) | (~c0_1(a929))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[4044])).
% 2.13/2.30 tff(4046,plain,
% 2.13/2.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[4045, 4043])).
% 2.13/2.30 tff(4047,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(4048,plain,
% 2.13/2.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a929)) | (~c0_1(a929))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4047, 4046])).
% 2.13/2.30 tff(4049,plain,
% 2.13/2.30 (hskp7),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4048, 112, 4042, 4041, 3951, 4040, 3950, 576, 4004])).
% 2.13/2.30 tff(4050,plain,
% 2.13/2.30 (c3_1(a907)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[512, 4049])).
% 2.13/2.30 tff(4051,plain,
% 2.13/2.30 (c3_1(a918)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[742, 4023])).
% 2.13/2.30 tff(4052,plain,
% 2.13/2.30 (c0_1(a918)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[734, 4023])).
% 2.13/2.30 tff(4053,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a928) | c1_1(a918) | c0_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a928) | c1_1(a918) | c0_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4054,plain,
% 2.13/2.30 (((~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907))) <=> (c2_1(a928) | c1_1(a918) | c0_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4055,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a928) | c1_1(a918) | c0_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)) | (~c1_1(a928))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[4054])).
% 2.13/2.30 tff(4056,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a928) | c1_1(a918) | c0_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)) | (~c1_1(a928)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[4055, 4053])).
% 2.13/2.30 tff(4057,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(4058,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a928) | c1_1(a918) | c0_1(a907) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a928)) | (~c1_1(a928))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4057, 4056])).
% 2.13/2.30 tff(4059,plain,
% 2.13/2.30 (c2_1(a907) | (~c3_1(a907))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4058, 112, 3951, 4052, 4051, 3950, 4024, 44, 271, 4004])).
% 2.13/2.30 tff(4060,plain,
% 2.13/2.30 (c2_1(a907)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4059, 4050])).
% 2.13/2.30 tff(4061,plain,
% 2.13/2.30 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 2.13/2.30 inference(bind,[status(th)],[])).
% 2.13/2.30 tff(4062,plain,
% 2.13/2.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 2.13/2.30 inference(quant_intro,[status(thm)],[4061])).
% 2.13/2.30 tff(4063,plain,
% 2.13/2.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4064,plain,
% 2.13/2.30 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 2.13/2.30 inference(bind,[status(th)],[])).
% 2.13/2.30 tff(4065,plain,
% 2.13/2.30 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 2.13/2.30 inference(quant_intro,[status(thm)],[4064])).
% 2.13/2.30 tff(4066,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 2.13/2.30 tff(4067,plain,
% 2.13/2.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4066, 4065])).
% 2.13/2.30 tff(4068,plain,
% 2.13/2.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4067, 4063])).
% 2.13/2.30 tff(4069,plain,(
% 2.13/2.30 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 2.13/2.30 inference(skolemize,[status(sab)],[4068])).
% 2.13/2.30 tff(4070,plain,
% 2.13/2.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4069, 4062])).
% 2.13/2.30 tff(4071,plain,
% 2.13/2.30 (hskp3 | (~c3_1(a907))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1095, 112, 4042, 4041, 4040, 44, 45, 1032])).
% 2.13/2.30 tff(4072,plain,
% 2.13/2.30 (hskp3),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4071, 4050])).
% 2.13/2.30 tff(4073,plain,
% 2.13/2.30 (~c3_1(a903)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1101, 4072])).
% 2.13/2.30 tff(4074,plain,
% 2.13/2.30 (hskp25),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1686, 112, 3951, 3950, 3949, 30])).
% 2.13/2.30 tff(4075,plain,
% 2.13/2.30 (~c3_1(a958)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1692, 4074])).
% 2.13/2.30 tff(4076,plain,
% 2.13/2.30 (~c0_1(a958)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1841, 4074])).
% 2.13/2.30 tff(4077,plain,
% 2.13/2.30 (c2_1(a903)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1119, 4072])).
% 2.13/2.30 tff(4078,plain,
% 2.13/2.30 (c0_1(a903)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1111, 4072])).
% 2.13/2.30 tff(4079,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a958) | c3_1(a958) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a958) | c3_1(a958) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4080,plain,
% 2.13/2.30 (((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a958) | c0_1(a958) | c2_1(a958)) <=> (c0_1(a958) | c3_1(a958) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(4081,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a958) | c0_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a958) | c3_1(a958) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[4080])).
% 2.13/2.30 tff(4082,plain,
% 2.13/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a958) | c0_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a958) | c3_1(a958) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958))),
% 2.13/2.30 inference(transitivity,[status(thm)],[4081, 4079])).
% 2.13/2.30 tff(4083,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a958) | c0_1(a958) | c2_1(a958))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(4084,plain,
% 2.13/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a958) | c3_1(a958) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a958)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 2.13/2.31 tff(4085,plain,
% 2.13/2.31 (c2_1(a958)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4084, 112, 4050, 4078, 4077, 4076, 4075, 45, 4073, 4070, 4060])).
% 2.13/2.31 tff(4086,plain,
% 2.13/2.31 (~c1_1(a958)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1698, 4074])).
% 2.13/2.31 tff(4087,assumption,(c2_1(a958)), introduced(assumption)).
% 2.13/2.31 tff(4088,assumption,(c2_1(a907)), introduced(assumption)).
% 2.13/2.31 tff(4089,assumption,(hskp22), introduced(assumption)).
% 2.13/2.31 tff(4090,plain,
% 2.13/2.31 (~c3_1(a939)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1247, 4089])).
% 2.13/2.31 tff(4091,plain,
% 2.13/2.31 (~c0_1(a939)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1253, 4089])).
% 2.13/2.31 tff(4092,plain,
% 2.13/2.31 (c1_1(a939)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1262, 4089])).
% 2.13/2.31 tff(4093,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c0_1(a939) | c3_1(a939) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)) | (~c2_1(a958)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a939) | c3_1(a939) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)) | (~c2_1(a958)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4094,plain,
% 2.13/2.31 (((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c1_1(a958) | c3_1(a958) | c0_1(a939) | c3_1(a939) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)) | (~c2_1(a958)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4095,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c0_1(a939) | c3_1(a939) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)) | (~c2_1(a958))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[4094])).
% 2.13/2.31 tff(4096,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a939) | c3_1(a939) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)) | (~c2_1(a958)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[4095, 4093])).
% 2.13/2.31 tff(4097,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(4098,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a939) | c3_1(a939) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a939)) | (~c2_1(a958))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4097, 4096])).
% 2.13/2.31 tff(4099,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4098, 112, 4092, 2207, 3871, 3870, 4091, 4090, 44, 392, 4088, 4087])).
% 2.13/2.31 tff(4100,plain,((~hskp22) | (~c3_1(a907)) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c2_1(a907)) | (~c2_1(a958))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(4101,plain,
% 2.13/2.31 (~hskp22),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4100, 4050, 4086, 4075, 44, 4060, 4085])).
% 2.13/2.31 tff(4102,plain,
% 2.13/2.31 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.13/2.31 inference(bind,[status(th)],[])).
% 2.13/2.31 tff(4103,plain,
% 2.13/2.31 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.13/2.31 inference(quant_intro,[status(thm)],[4102])).
% 2.13/2.31 tff(4104,plain,
% 2.13/2.31 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4105,plain,
% 2.13/2.31 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.13/2.31 inference(bind,[status(th)],[])).
% 2.13/2.31 tff(4106,plain,
% 2.13/2.31 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.13/2.31 inference(quant_intro,[status(thm)],[4105])).
% 2.13/2.31 tff(4107,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 2.13/2.31 tff(4108,plain,
% 2.13/2.31 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 2.13/2.31 tff(4109,plain,
% 2.13/2.31 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4108, 4104])).
% 2.13/2.31 tff(4110,plain,(
% 2.13/2.31 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.13/2.31 inference(skolemize,[status(sab)],[4109])).
% 2.13/2.31 tff(4111,plain,
% 2.13/2.31 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4110, 4103])).
% 2.13/2.31 tff(4112,plain,
% 2.13/2.31 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4113,plain,
% 2.13/2.31 ((hskp21 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958))) <=> (hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4114,plain,
% 2.13/2.31 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[4113])).
% 2.13/2.31 tff(4115,plain,
% 2.13/2.31 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[4114, 4112])).
% 2.13/2.31 tff(4116,plain,
% 2.13/2.31 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(4117,plain,
% 2.13/2.31 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4116, 4115])).
% 2.13/2.31 tff(4118,plain,
% 2.13/2.31 (hskp21 | (~c0_1(a928)) | (~c2_1(a958))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4117, 112, 3951, 4086, 4075, 3950, 402])).
% 2.13/2.31 tff(4119,plain,
% 2.13/2.31 (hskp21),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4118, 4085, 4004])).
% 2.13/2.31 tff(4120,plain,
% 2.13/2.31 (~c2_1(a938)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[422, 4119])).
% 2.13/2.31 tff(4121,plain,
% 2.13/2.31 (c0_1(a938)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[430, 4119])).
% 2.13/2.31 tff(4122,plain,
% 2.13/2.31 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a938) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a938)) | c1_1(a938))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a938) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a938)) | c1_1(a938))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4123,plain,
% 2.13/2.31 ((hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a938) | c1_1(a938) | (~c0_1(a938))) <=> (hskp22 | c2_1(a938) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a938)) | c1_1(a938))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4124,plain,
% 2.13/2.31 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a938) | c1_1(a938) | (~c0_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a938) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a938)) | c1_1(a938)))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[4123])).
% 2.13/2.31 tff(4125,plain,
% 2.13/2.31 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a938) | c1_1(a938) | (~c0_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a938) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a938)) | c1_1(a938))),
% 2.13/2.31 inference(transitivity,[status(thm)],[4124, 4122])).
% 2.13/2.31 tff(4126,plain,
% 2.13/2.31 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a938) | c1_1(a938) | (~c0_1(a938)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(4127,plain,
% 2.13/2.31 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a938) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a938)) | c1_1(a938)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4126, 4125])).
% 2.13/2.31 tff(4128,plain,
% 2.13/2.31 (hskp22 | c1_1(a938)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4127, 112, 4121, 4050, 4120, 45, 4111, 4060])).
% 2.13/2.31 tff(4129,plain,
% 2.13/2.31 (c1_1(a938)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4128, 4101])).
% 2.13/2.31 tff(4130,plain,
% 2.13/2.31 (~c3_1(a938)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[416, 4119])).
% 2.13/2.31 tff(4131,assumption,(hskp16), introduced(assumption)).
% 2.13/2.31 tff(4132,plain,
% 2.13/2.31 (~c3_1(a923)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1919, 4131])).
% 2.13/2.31 tff(4133,plain,
% 2.13/2.31 (c1_1(a923)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3073, 4131])).
% 2.13/2.31 tff(4134,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c3_1(a923) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a923) | (~c1_1(a923)) | (~c2_1(a958)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c3_1(a923) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a923) | (~c1_1(a923)) | (~c2_1(a958)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4135,plain,
% 2.13/2.31 (((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a923) | c0_1(a923) | (~c1_1(a923))) <=> (c1_1(a958) | c3_1(a958) | c3_1(a923) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a923) | (~c1_1(a923)) | (~c2_1(a958)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4136,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a923) | c0_1(a923) | (~c1_1(a923)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c3_1(a923) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a923) | (~c1_1(a923)) | (~c2_1(a958))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[4135])).
% 2.13/2.31 tff(4137,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a923) | c0_1(a923) | (~c1_1(a923)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c3_1(a923) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a923) | (~c1_1(a923)) | (~c2_1(a958)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[4136, 4134])).
% 2.13/2.31 tff(4138,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a923) | c0_1(a923) | (~c1_1(a923)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(4139,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c3_1(a923) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a923) | (~c1_1(a923)) | (~c2_1(a958))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4138, 4137])).
% 2.13/2.31 tff(4140,plain,
% 2.13/2.31 (c0_1(a923)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4139, 112, 4133, 2207, 3871, 3870, 4132, 44, 392, 4088, 4087])).
% 2.13/2.31 tff(4141,plain,
% 2.13/2.31 (~hskp22),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4100, 2207, 3871, 3870, 44, 4088, 4087])).
% 2.13/2.31 tff(4142,assumption,(~c2_1(a938)), introduced(assumption)).
% 2.13/2.31 tff(4143,assumption,(c0_1(a938)), introduced(assumption)).
% 2.13/2.31 tff(4144,plain,
% 2.13/2.31 (hskp22 | c1_1(a938)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4127, 112, 4143, 2207, 4142, 45, 4111, 4088])).
% 2.13/2.31 tff(4145,plain,
% 2.13/2.31 (c1_1(a938)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4144, 4141])).
% 2.13/2.31 tff(4146,plain,
% 2.13/2.31 (c2_1(a923)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1927, 4131])).
% 2.13/2.31 tff(4147,plain,
% 2.13/2.31 (hskp9 | (~c0_1(a923))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3080, 112, 4133, 4146, 4132, 3066])).
% 2.13/2.31 tff(4148,plain,
% 2.13/2.31 (hskp9),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4147, 4140])).
% 2.13/2.31 tff(4149,plain,
% 2.13/2.31 (~c2_1(a909)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1323, 4148])).
% 2.13/2.31 tff(4150,plain,
% 2.13/2.31 (~c0_1(a909)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1335, 4148])).
% 2.13/2.31 tff(4151,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a938) | c1_1(a918) | c0_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)) | (~c1_1(a938)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a938) | c1_1(a918) | c0_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4152,plain,
% 2.13/2.31 (((~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909))) <=> (c2_1(a938) | c1_1(a918) | c0_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4153,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a938) | c1_1(a918) | c0_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)) | (~c1_1(a938))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[4152])).
% 2.13/2.31 tff(4154,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a938) | c1_1(a918) | c0_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[4153, 4151])).
% 2.13/2.31 tff(4155,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)) | c0_1(a909) | c2_1(a909) | (~c3_1(a909)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(4156,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a938) | c1_1(a918) | c0_1(a909) | c2_1(a909) | (~ndr1_0) | (~c3_1(a909)) | (~c0_1(a918)) | (~c3_1(a918)) | (~c0_1(a938)) | (~c1_1(a938))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4155, 4154])).
% 2.13/2.31 tff(4157,plain,
% 2.13/2.31 (~c3_1(a909)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4156, 112, 4143, 1033, 1038, 4142, 754, 4150, 4149, 271, 4145])).
% 2.13/2.31 tff(4158,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a923) | c0_1(a909) | c2_1(a909) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c3_1(a909) | (~c0_1(a923)) | (~c2_1(a923)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a923) | c0_1(a909) | c2_1(a909) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c3_1(a909) | (~c0_1(a923)) | (~c2_1(a923)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4159,plain,
% 2.13/2.31 (((~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a909) | c0_1(a909) | c2_1(a909)) <=> (c3_1(a923) | c0_1(a909) | c2_1(a909) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c3_1(a909) | (~c0_1(a923)) | (~c2_1(a923)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4160,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a923) | c0_1(a909) | c2_1(a909) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c3_1(a909) | (~c0_1(a923)) | (~c2_1(a923))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[4159])).
% 2.13/2.31 tff(4161,plain,
% 2.13/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a909) | c0_1(a909) | c2_1(a909))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a923) | c0_1(a909) | c2_1(a909) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c3_1(a909) | (~c0_1(a923)) | (~c2_1(a923)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[4160, 4158])).
% 2.13/2.31 tff(4162,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a923) | (~c2_1(a923)) | (~c0_1(a923)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a909) | c0_1(a909) | c2_1(a909))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(4163,plain,
% 2.13/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a923) | c0_1(a909) | c2_1(a909) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c3_1(a909) | (~c0_1(a923)) | (~c2_1(a923))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4162, 4161])).
% 2.13/2.31 tff(4164,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4163, 112, 4146, 2207, 4132, 4150, 4149, 45, 4070, 4088, 4157, 4140])).
% 2.13/2.31 tff(4165,plain,((~hskp16) | (~c3_1(a907)) | c1_1(a907) | (~c2_1(a907)) | (~c0_1(a938)) | (~c0_1(a918)) | (~c3_1(a918)) | c2_1(a938) | c1_1(a918) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c2_1(a958))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(4166,plain,
% 2.13/2.31 (~hskp16),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4165, 4050, 45, 4060, 4121, 4052, 4051, 4120, 4024, 4086, 4075, 44, 4085])).
% 2.13/2.31 tff(4167,plain,
% 2.13/2.31 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4168,plain,
% 2.13/2.31 ((hskp16 | hskp10 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903))) <=> (hskp16 | hskp10 | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(4169,plain,
% 2.13/2.31 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[4168])).
% 2.13/2.31 tff(4170,plain,
% 2.13/2.31 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[4169, 4167])).
% 2.13/2.31 tff(4171,plain,
% 2.13/2.31 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp10 | (~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(4172,plain,
% 2.13/2.31 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp10 | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[4171, 4170])).
% 2.13/2.31 tff(4173,plain,
% 2.13/2.31 (hskp16 | hskp10),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4172, 112, 4078, 4077, 4073, 1906])).
% 2.13/2.31 tff(4174,plain,
% 2.13/2.31 (hskp10),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4173, 4166])).
% 2.13/2.31 tff(4175,plain,
% 2.13/2.31 (~c2_1(a910)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2348, 4174])).
% 2.13/2.31 tff(4176,plain,
% 2.13/2.31 (c1_1(a910)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2362, 4174])).
% 2.13/2.31 tff(4177,plain,
% 2.13/2.31 (~c0_1(a910)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2354, 4174])).
% 2.13/2.31 tff(4178,plain,
% 2.13/2.31 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c0_1(a938)) | (~c1_1(a938)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4179,plain,
% 2.13/2.32 ((hskp29 | (~ndr1_0) | c3_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910))) <=> (hskp29 | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4180,plain,
% 2.13/2.32 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c0_1(a938)) | (~c1_1(a938))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4179])).
% 2.13/2.32 tff(4181,plain,
% 2.13/2.32 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c0_1(a938)) | (~c1_1(a938)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4180, 4178])).
% 2.13/2.32 tff(4182,plain,
% 2.13/2.32 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a938) | (~c1_1(a938)) | (~c0_1(a938)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4183,plain,
% 2.13/2.32 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | (~c0_1(a938)) | (~c1_1(a938))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 2.13/2.32 tff(4184,plain,
% 2.13/2.32 (hskp29),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4183, 112, 4121, 4176, 4130, 4177, 4175, 2438, 4129])).
% 2.13/2.32 tff(4185,plain,
% 2.13/2.32 (hskp11),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[3435, 4184, 4177, 4176, 4175])).
% 2.13/2.32 tff(4186,plain,
% 2.13/2.32 (~c1_1(a912)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2146, 4185])).
% 2.13/2.32 tff(4187,plain,
% 2.13/2.32 (~c2_1(a912)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1679, 4185])).
% 2.13/2.32 tff(4188,assumption,(~hskp22), introduced(assumption)).
% 2.13/2.32 tff(4189,plain,
% 2.13/2.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a912) | c2_1(a912) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4190,plain,
% 2.13/2.32 ((hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912))) <=> (hskp22 | c1_1(a912) | c2_1(a912) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4191,plain,
% 2.13/2.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a912) | c2_1(a912) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4190])).
% 2.13/2.32 tff(4192,plain,
% 2.13/2.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4191, 4189])).
% 2.13/2.32 tff(4193,plain,
% 2.13/2.32 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4194,plain,
% 2.13/2.32 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a912) | c2_1(a912) | c1_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4193, 4192])).
% 2.13/2.32 tff(4195,plain,
% 2.13/2.32 (~c0_1(a912)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4194, 112, 4188, 2207, 801, 802, 45, 4111, 4088])).
% 2.13/2.32 tff(4196,assumption,(c1_1(a938)), introduced(assumption)).
% 2.13/2.32 tff(4197,assumption,(~c3_1(a938)), introduced(assumption)).
% 2.13/2.32 tff(4198,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a938) | c3_1(a938) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a938)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a938)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4199,plain,
% 2.13/2.32 (((~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c1_1(a938)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907))) <=> (c2_1(a938) | c3_1(a938) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a938)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4200,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c1_1(a938)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a938) | c3_1(a938) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a938))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4199])).
% 2.13/2.32 tff(4201,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c1_1(a938)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a938)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4200, 4198])).
% 2.13/2.32 tff(4202,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a938) | c3_1(a938) | (~c1_1(a938)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4203,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a938) | c3_1(a938) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a938))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 2.13/2.32 tff(4204,plain,
% 2.13/2.32 (~c3_1(a912)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4203, 112, 2207, 4142, 4197, 801, 802, 44, 1384, 4088, 4196])).
% 2.13/2.32 tff(4205,assumption,(c2_1(a903)), introduced(assumption)).
% 2.13/2.32 tff(4206,assumption,(c0_1(a903)), introduced(assumption)).
% 2.13/2.32 tff(4207,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a912) | c3_1(a912) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c3_1(a912) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a912))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4208,plain,
% 2.13/2.32 (((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c2_1(a912) | c3_1(a912) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a912))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4209,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a912) | c3_1(a912) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a912)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4208])).
% 2.13/2.32 tff(4210,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c3_1(a912) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a912))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4209, 4207])).
% 2.13/2.32 tff(4211,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a903) | (~c2_1(a903)) | (~c0_1(a903)) | c1_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a912) | c0_1(a912) | c2_1(a912))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4212,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c3_1(a912) | c1_1(a907) | c3_1(a903) | (~ndr1_0) | (~c2_1(a903)) | (~c0_1(a903)) | (~c2_1(a907)) | (~c3_1(a907)) | c0_1(a912)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 2.13/2.32 tff(4213,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4212, 112, 2207, 4206, 4205, 802, 4204, 45, 1121, 4070, 4088, 4195])).
% 2.13/2.32 tff(4214,plain,(c2_1(a912) | (~c3_1(a907)) | (~c0_1(a903)) | (~c2_1(a903)) | c1_1(a907) | c3_1(a903) | (~c2_1(a907)) | hskp22 | c1_1(a912) | c2_1(a938) | c3_1(a938) | c0_1(a907) | (~c1_1(a938))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(4215,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4214, 4187, 4186, 4078, 4077, 45, 4073, 4060, 4101, 4050, 4120, 4130, 44, 4129])).
% 2.13/2.32 tff(4216,plain,(c1_1(a907) | c0_1(a907) | c0_1(a899) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(4217,plain,
% 2.13/2.32 (c1_1(a907)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4216, 44, 43, 31])).
% 2.13/2.32 tff(4218,plain,
% 2.13/2.32 (((~hskp7) | (~c1_1(a907))) <=> ((~hskp7) | (~c1_1(a907)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4219,plain,
% 2.13/2.32 (((~c1_1(a907)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a907)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4220,axiom,((~c1_1(a907)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 2.13/2.32 tff(4221,plain,
% 2.13/2.32 ((~hskp7) | (~c1_1(a907))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4220, 4219])).
% 2.13/2.32 tff(4222,plain,
% 2.13/2.32 ((~hskp7) | (~c1_1(a907))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4221, 4218])).
% 2.13/2.32 tff(4223,plain,
% 2.13/2.32 (~hskp7),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4222, 4217])).
% 2.13/2.32 tff(4224,assumption,(hskp9), introduced(assumption)).
% 2.13/2.32 tff(4225,plain,
% 2.13/2.32 (~c2_1(a909)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1323, 4224])).
% 2.13/2.32 tff(4226,plain,
% 2.13/2.32 (~c1_1(a909)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1329, 4224])).
% 2.13/2.32 tff(4227,plain,
% 2.13/2.32 (~c0_1(a909)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1335, 4224])).
% 2.13/2.32 tff(4228,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2414, 112, 152, 31, 4227, 4226, 4225, 20])).
% 2.13/2.32 tff(4229,plain,((~hskp9) | hskp1 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(4230,plain,
% 2.13/2.32 (~hskp9),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4229, 3271, 31])).
% 2.13/2.32 tff(4231,plain,
% 2.13/2.32 ((hskp12 | hskp9 | hskp0) <=> (hskp12 | hskp9 | hskp0)),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4232,plain,
% 2.13/2.32 (((hskp0 | hskp12) | hskp9) <=> (hskp12 | hskp9 | hskp0)),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4233,axiom,((hskp0 | hskp12) | hskp9), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 2.13/2.32 tff(4234,plain,
% 2.13/2.32 (hskp12 | hskp9 | hskp0),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 2.13/2.32 tff(4235,plain,
% 2.13/2.32 (hskp12 | hskp9 | hskp0),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4234, 4231])).
% 2.13/2.32 tff(4236,plain,
% 2.13/2.32 (hskp12 | hskp9 | hskp0),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4235, 4231])).
% 2.13/2.32 tff(4237,plain,
% 2.13/2.32 (hskp12 | hskp9 | hskp0),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4236, 4231])).
% 2.13/2.32 tff(4238,plain,
% 2.13/2.32 (hskp12 | hskp9 | hskp0),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4237, 4231])).
% 2.13/2.32 tff(4239,plain,
% 2.13/2.32 (hskp12),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4238, 4230, 31])).
% 2.13/2.32 tff(4240,plain,
% 2.13/2.32 (~c3_1(a913)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[347, 4239])).
% 2.13/2.32 tff(4241,plain,
% 2.13/2.32 (~c1_1(a913)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[409, 4239])).
% 2.13/2.32 tff(4242,plain,
% 2.13/2.32 ((hskp27 | hskp9 | hskp7) <=> (hskp27 | hskp9 | hskp7)),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4243,plain,
% 2.13/2.32 (((hskp27 | hskp7) | hskp9) <=> (hskp27 | hskp9 | hskp7)),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4244,axiom,((hskp27 | hskp7) | hskp9), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 2.13/2.32 tff(4245,plain,
% 2.13/2.32 (hskp27 | hskp9 | hskp7),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4244, 4243])).
% 2.13/2.32 tff(4246,plain,
% 2.13/2.32 (hskp27 | hskp9 | hskp7),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4245, 4242])).
% 2.13/2.32 tff(4247,plain,
% 2.13/2.32 (hskp27 | hskp9 | hskp7),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4246, 4242])).
% 2.13/2.32 tff(4248,plain,
% 2.13/2.32 (hskp27 | hskp9 | hskp7),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4247, 4242])).
% 2.13/2.32 tff(4249,plain,
% 2.13/2.32 (hskp27 | hskp9 | hskp7),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4248, 4242])).
% 2.13/2.32 tff(4250,plain,
% 2.13/2.32 (hskp27),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4249, 4230, 547])).
% 2.13/2.32 tff(4251,plain,
% 2.13/2.32 (~c0_1(a978)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1445, 4250])).
% 2.13/2.32 tff(4252,plain,
% 2.13/2.32 (c3_1(a978)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1453, 4250])).
% 2.13/2.32 tff(4253,plain,
% 2.13/2.32 (c2_1(a978)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1461, 4250])).
% 2.13/2.32 tff(4254,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a899) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | c2_1(a913) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a899) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | c2_1(a913) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4255,plain,
% 2.13/2.32 (((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)) | c3_1(a913) | c1_1(a913) | c2_1(a913)) <=> (c2_1(a899) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | c2_1(a913) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4256,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a899) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | c2_1(a913) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4255])).
% 2.13/2.32 tff(4257,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a899) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | c2_1(a913) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4256, 4254])).
% 2.13/2.32 tff(4258,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a899) | c0_1(a899) | (~c1_1(a899)) | c3_1(a913) | c1_1(a913) | c2_1(a913))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4259,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a899) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c1_1(a899)) | c2_1(a913) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4258, 4257])).
% 2.13/2.32 tff(4260,plain,
% 2.13/2.32 (c2_1(a913)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4259, 112, 4253, 4252, 3892, 3270, 4251, 4241, 4240, 43, 1721])).
% 2.13/2.32 tff(4261,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a899) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c2_1(a913)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a899) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c2_1(a913)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4262,plain,
% 2.13/2.32 (((~ndr1_0) | c2_1(a899) | (~c1_1(a899)) | (~c3_1(a899)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a899) | c2_1(a899) | (~c3_1(a899))) <=> (c2_1(a899) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c2_1(a913)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4263,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a899) | (~c1_1(a899)) | (~c3_1(a899)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a899) | c2_1(a899) | (~c3_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a899) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c2_1(a913))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4262])).
% 2.13/2.32 tff(4264,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a899) | (~c1_1(a899)) | (~c3_1(a899)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a899) | c2_1(a899) | (~c3_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a899) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c2_1(a913)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4263, 4261])).
% 2.13/2.32 tff(4265,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a899) | (~c1_1(a899)) | (~c3_1(a899)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a899) | c2_1(a899) | (~c3_1(a899)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4266,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a899) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c1_1(a899)) | (~c2_1(a913))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4265, 4264])).
% 2.13/2.32 tff(4267,plain,
% 2.13/2.32 (~c3_1(a899)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4266, 112, 3892, 3270, 4241, 4240, 43, 503, 4260])).
% 2.13/2.32 tff(4268,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a913)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a913)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4269,plain,
% 2.13/2.32 (((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899))) <=> (c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a913)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4270,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a913)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4269])).
% 2.13/2.32 tff(4271,plain,
% 2.13/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a913)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4270, 4268])).
% 2.13/2.32 tff(4272,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4273,plain,
% 2.13/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a913)) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4272, 4271])).
% 2.13/2.32 tff(4274,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4273, 112, 4253, 4252, 3892, 4251, 4241, 4240, 43, 392, 4267, 4260])).
% 2.13/2.32 tff(4275,plain,(c2_1(a899) | c0_1(a899) | hskp7 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(4276,plain,
% 2.13/2.32 (c2_1(a899)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4275, 4223, 43, 31])).
% 2.13/2.32 tff(4277,assumption,(c1_1(a907)), introduced(assumption)).
% 2.13/2.32 tff(4278,plain,
% 2.13/2.32 (~hskp7),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4222, 4277])).
% 2.13/2.32 tff(4279,plain,
% 2.13/2.32 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4280,plain,
% 2.13/2.32 ((hskp7 | hskp4 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c1_1(a907))) <=> (hskp7 | hskp4 | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4281,plain,
% 2.13/2.32 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4280])).
% 2.13/2.32 tff(4282,plain,
% 2.13/2.32 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4281, 4279])).
% 2.13/2.32 tff(4283,plain,
% 2.13/2.32 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c0_1(a907) | c3_1(a907) | (~c1_1(a907)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4284,plain,
% 2.13/2.32 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp4 | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4283, 4282])).
% 2.13/2.32 tff(4285,plain,
% 2.13/2.32 (hskp7 | hskp4 | c3_1(a907) | (~c1_1(a907))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4284, 112, 44, 523])).
% 2.13/2.32 tff(4286,plain,
% 2.13/2.32 (hskp4),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4285, 505, 4277, 4278])).
% 2.13/2.32 tff(4287,plain,
% 2.13/2.32 (~c3_1(a904)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[536, 4286])).
% 2.13/2.32 tff(4288,plain,
% 2.13/2.32 (c2_1(a904)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[605, 4286])).
% 2.13/2.32 tff(4289,plain,
% 2.13/2.32 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a904))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a904))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4290,plain,
% 2.13/2.32 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a904) | c3_1(a904) | (~c2_1(a904))) <=> (hskp17 | hskp0 | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a904))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4291,plain,
% 2.13/2.32 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a904) | c3_1(a904) | (~c2_1(a904)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a904)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4290])).
% 2.13/2.32 tff(4292,plain,
% 2.13/2.32 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a904) | c3_1(a904) | (~c2_1(a904)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a904))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4291, 4289])).
% 2.13/2.32 tff(4293,plain,
% 2.13/2.32 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a904) | c3_1(a904) | (~c2_1(a904)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4294,plain,
% 2.13/2.32 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp0 | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | c0_1(a904)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4293, 4292])).
% 2.13/2.32 tff(4295,plain,
% 2.13/2.32 (c0_1(a904)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4294, 112, 32, 31, 4288, 4287, 891])).
% 2.13/2.32 tff(4296,plain,
% 2.13/2.32 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c3_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c3_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4297,plain,
% 2.13/2.32 ((hskp25 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907))) <=> (hskp25 | c3_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4298,plain,
% 2.13/2.32 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c3_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[4297])).
% 2.13/2.32 tff(4299,plain,
% 2.13/2.32 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c3_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907))),
% 2.13/2.32 inference(transitivity,[status(thm)],[4298, 4296])).
% 2.13/2.32 tff(4300,plain,
% 2.13/2.32 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(4301,plain,
% 2.13/2.32 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c3_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 2.13/2.32 tff(4302,plain,
% 2.13/2.32 (hskp25 | c3_1(a907) | c2_1(a907)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4301, 112, 4277, 30])).
% 2.13/2.32 tff(4303,plain,
% 2.13/2.32 (hskp25),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4302, 505, 2943])).
% 2.13/2.32 tff(4304,plain,
% 2.13/2.32 (~c3_1(a958)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1692, 4303])).
% 2.13/2.32 tff(4305,plain,
% 2.13/2.32 (~c1_1(a958)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1698, 4303])).
% 2.13/2.32 tff(4306,plain,
% 2.13/2.32 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a904)) | c2_1(a958))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a904)) | c2_1(a958))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4307,plain,
% 2.13/2.32 ((hskp20 | (~ndr1_0) | c3_1(a904) | (~c2_1(a904)) | (~c0_1(a904)) | c3_1(a958) | c2_1(a958) | c1_1(a958)) <=> (hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a904)) | c2_1(a958))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(4308,plain,
% 2.13/2.32 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a904) | (~c2_1(a904)) | (~c0_1(a904)) | c3_1(a958) | c2_1(a958) | c1_1(a958))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a904)) | c2_1(a958)))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4307])).
% 2.13/2.33 tff(4309,plain,
% 2.13/2.33 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a904) | (~c2_1(a904)) | (~c0_1(a904)) | c3_1(a958) | c2_1(a958) | c1_1(a958))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a904)) | c2_1(a958))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4308, 4306])).
% 2.13/2.33 tff(4310,plain,
% 2.13/2.33 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp20 | (~ndr1_0) | c3_1(a904) | (~c2_1(a904)) | (~c0_1(a904)) | c3_1(a958) | c2_1(a958) | c1_1(a958))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4311,plain,
% 2.13/2.33 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp20 | c1_1(a958) | c3_1(a958) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a904)) | c2_1(a958)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4310, 4309])).
% 2.13/2.33 tff(4312,plain,
% 2.13/2.33 (c2_1(a958)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4311, 112, 1884, 4288, 4305, 4304, 4287, 1064, 4295])).
% 2.13/2.33 tff(4313,plain,
% 2.13/2.33 (~c0_1(a958)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1841, 4303])).
% 2.13/2.33 tff(4314,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1848, 112, 32, 31, 4313, 4304, 891, 4312])).
% 2.13/2.33 tff(4315,plain,(c3_1(a907) | hskp17 | hskp0 | (~c1_1(a907)) | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4316,plain,
% 2.13/2.33 (hskp17),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4315, 505, 31, 4217, 44])).
% 2.13/2.33 tff(4317,plain,
% 2.13/2.33 (~c3_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[828, 4316])).
% 2.13/2.33 tff(4318,plain,
% 2.13/2.33 (c1_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[842, 4316])).
% 2.13/2.33 tff(4319,plain,
% 2.13/2.33 (hskp4),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4285, 505, 4217, 4223])).
% 2.13/2.33 tff(4320,plain,
% 2.13/2.33 (~c3_1(a904)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[536, 4319])).
% 2.13/2.33 tff(4321,plain,
% 2.13/2.33 (~c1_1(a904)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[542, 4319])).
% 2.13/2.33 tff(4322,plain,
% 2.13/2.33 (c2_1(a904)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[605, 4319])).
% 2.13/2.33 tff(4323,plain,
% 2.13/2.33 (~c2_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[834, 4316])).
% 2.13/2.33 tff(4324,plain,
% 2.13/2.33 (~c0_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4014, 3441, 1404, 312, 2423, 43])).
% 2.13/2.33 tff(4325,plain,
% 2.13/2.33 (hskp29),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2489, 4324, 1403, 2451, 1404, 2450, 2449])).
% 2.13/2.33 tff(4326,plain,
% 2.13/2.33 (hskp11),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1438, 4325, 1404, 1403, 4324])).
% 2.13/2.33 tff(4327,plain,
% 2.13/2.33 (~c3_1(a912)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1390, 4326])).
% 2.13/2.33 tff(4328,plain,
% 2.13/2.33 (~c2_1(a912)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1679, 4326])).
% 2.13/2.33 tff(4329,plain,
% 2.13/2.33 (~c1_1(a912)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2146, 4326])).
% 2.13/2.33 tff(4330,plain,
% 2.13/2.33 (~hskp9),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4229, 3453, 31])).
% 2.13/2.33 tff(4331,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2404, 112, 4330, 1403, 2423, 4329, 4328, 4327, 1310, 4324])).
% 2.13/2.33 tff(4332,plain,(c1_1(a899) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | (~c2_1(a904)) | c1_1(a904) | c3_1(a904) | hskp0 | (~c2_1(a899)) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4333,plain,
% 2.13/2.33 (c1_1(a899)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4332, 4323, 4317, 4318, 4322, 4321, 4320, 31, 4276, 43])).
% 2.13/2.33 tff(4334,plain,
% 2.13/2.33 (hskp14 | (~c1_1(a899)) | (~c0_1(a928))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4021, 112, 312, 1403, 2423, 43, 373])).
% 2.13/2.33 tff(4335,plain,
% 2.13/2.33 (hskp14),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4334, 4005, 311])).
% 2.13/2.33 tff(4336,plain,
% 2.13/2.33 (~c1_1(a918)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[672, 4335])).
% 2.13/2.33 tff(4337,plain,
% 2.13/2.33 (hskp18),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4038, 4336, 43, 1403, 2423, 4005, 312, 311])).
% 2.13/2.33 tff(4338,plain,
% 2.13/2.33 (~c1_1(a929)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[771, 4337])).
% 2.13/2.33 tff(4339,plain,
% 2.13/2.33 (c2_1(a929)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[781, 4337])).
% 2.13/2.33 tff(4340,plain,
% 2.13/2.33 (c0_1(a929)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[789, 4337])).
% 2.13/2.33 tff(4341,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4048, 112, 547, 4340, 4339, 1404, 4338, 1403, 576, 4005])).
% 2.13/2.33 tff(4342,plain,((~c0_1(a928)) | hskp7 | (~c1_1(a928)) | c2_1(a928) | c0_1(a899) | c3_1(a928) | (~c2_1(a899)) | (~c1_1(a899))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4343,plain,
% 2.13/2.33 (~c0_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4342, 4318, 4223, 4323, 43, 4317, 4276, 4333])).
% 2.13/2.33 tff(4344,plain,
% 2.13/2.33 (hskp29),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2489, 4343, 4323, 4322, 4318, 4321, 4320])).
% 2.13/2.33 tff(4345,plain,
% 2.13/2.33 (hskp11),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1438, 4344, 4318, 4323, 4343])).
% 2.13/2.33 tff(4346,plain,
% 2.13/2.33 (~c2_1(a912)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1679, 4345])).
% 2.13/2.33 tff(4347,plain,
% 2.13/2.33 (~c1_1(a912)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2146, 4345])).
% 2.13/2.33 tff(4348,plain,
% 2.13/2.33 (~c3_1(a912)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1390, 4345])).
% 2.13/2.33 tff(4349,plain,
% 2.13/2.33 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4350,plain,
% 2.13/2.33 ((hskp10 | hskp7 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928))) <=> (hskp10 | hskp7 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4351,plain,
% 2.13/2.33 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4350])).
% 2.13/2.33 tff(4352,plain,
% 2.13/2.33 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4351, 4349])).
% 2.13/2.33 tff(4353,plain,
% 2.13/2.33 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c0_1(a928)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4354,plain,
% 2.13/2.33 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a928) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4353, 4352])).
% 2.13/2.33 tff(4355,plain,
% 2.13/2.33 (hskp10 | (~c0_1(a928))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4354, 112, 547, 1403, 2423, 693])).
% 2.13/2.33 tff(4356,plain,
% 2.13/2.33 (~c0_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4355, 50])).
% 2.13/2.33 tff(4357,plain,
% 2.13/2.33 (hskp10 | c0_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[856, 112, 1404, 1403, 801, 802, 813, 812])).
% 2.13/2.33 tff(4358,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4357, 4356, 50])).
% 2.13/2.33 tff(4359,plain,(hskp10 | (~c1_1(a928)) | c2_1(a928) | c1_1(a912) | c2_1(a912) | c3_1(a912) | hskp7 | c3_1(a928)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4360,plain,
% 2.13/2.33 (hskp10),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4359, 4348, 4323, 4347, 4346, 4318, 4223, 4317])).
% 2.13/2.33 tff(4361,plain,
% 2.13/2.33 (~c0_1(a910)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2354, 4360])).
% 2.13/2.33 tff(4362,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4363,plain,
% 2.13/2.33 (((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a907) | c0_1(a907) | (~c1_1(a907))) <=> (c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4364,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a907) | c0_1(a907) | (~c1_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4363])).
% 2.13/2.33 tff(4365,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a907) | c0_1(a907) | (~c1_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4364, 4362])).
% 2.13/2.33 tff(4366,plain,
% 2.13/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a904) | c3_1(a904) | (~c2_1(a904)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a907) | c0_1(a907) | (~c1_1(a907)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4367,plain,
% 2.13/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a907) | c0_1(a907) | (~c1_1(a907)) | c1_1(a904) | c3_1(a904) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a904))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4366, 4365])).
% 2.13/2.33 tff(4368,plain,
% 2.13/2.33 (~c3_1(a899)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4367, 112, 505, 4322, 4276, 44, 4217, 4321, 4320, 43, 392])).
% 2.13/2.33 tff(4369,plain,
% 2.13/2.33 (c1_1(a910)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2362, 4360])).
% 2.13/2.33 tff(4370,plain,
% 2.13/2.33 (~c2_1(a910)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2348, 4360])).
% 2.13/2.33 tff(4371,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2631, 4370, 4369, 4223, 4276, 4318, 4323, 4317, 4333, 4343, 4346, 43, 4368, 4347, 4348, 4361])).
% 2.13/2.33 tff(4372,plain,(c3_1(a907) | c0_1(a899) | hskp0 | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4373,plain,
% 2.13/2.33 (c3_1(a907)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4372, 44, 31, 43])).
% 2.13/2.33 tff(4374,plain,
% 2.13/2.33 (hskp27),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4249, 4330, 547])).
% 2.13/2.33 tff(4375,plain,
% 2.13/2.33 (c2_1(a978)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1461, 4374])).
% 2.13/2.33 tff(4376,plain,
% 2.13/2.33 (c2_1(a899)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4275, 547, 43, 31])).
% 2.13/2.33 tff(4377,plain,
% 2.13/2.33 (~c0_1(a978)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1445, 4374])).
% 2.13/2.33 tff(4378,plain,
% 2.13/2.33 (c3_1(a978)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1453, 4374])).
% 2.13/2.33 tff(4379,plain,
% 2.13/2.33 (hskp17),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3477, 4378, 3441, 4377, 31, 4376, 43, 4375])).
% 2.13/2.33 tff(4380,plain,
% 2.13/2.33 (~c3_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[828, 4379])).
% 2.13/2.33 tff(4381,plain,
% 2.13/2.33 (c1_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[842, 4379])).
% 2.13/2.33 tff(4382,plain,
% 2.13/2.33 (~c0_1(a928)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4014, 4381, 3441, 4376, 4380, 43])).
% 2.13/2.33 tff(4383,plain,
% 2.13/2.33 (hskp12),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4238, 4330, 31])).
% 2.13/2.33 tff(4384,plain,
% 2.13/2.33 (c0_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[355, 4383])).
% 2.13/2.33 tff(4385,plain,
% 2.13/2.33 (hskp31),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1729, 4379, 1430])).
% 2.13/2.33 tff(4386,plain,
% 2.13/2.33 (c3_1(a957)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3835, 4385])).
% 2.13/2.33 tff(4387,plain,
% 2.13/2.33 (c2_1(a957)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3843, 4385])).
% 2.13/2.33 tff(4388,plain,
% 2.13/2.33 (~c1_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[409, 4383])).
% 2.13/2.33 tff(4389,plain,
% 2.13/2.33 (c1_1(a957)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3827, 4385])).
% 2.13/2.33 tff(4390,plain,
% 2.13/2.33 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a913) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a913) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a913) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a913) | (~c0_1(a913)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4391,plain,
% 2.13/2.33 ((hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a913) | c1_1(a913) | (~c0_1(a913))) <=> (hskp1 | c1_1(a913) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a913) | (~c0_1(a913)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4392,plain,
% 2.13/2.33 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a913) | c1_1(a913) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a913) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a913) | (~c0_1(a913))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4391])).
% 2.13/2.33 tff(4393,plain,
% 2.13/2.33 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a913) | c1_1(a913) | (~c0_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a913) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a913) | (~c0_1(a913)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4392, 4390])).
% 2.13/2.33 tff(4394,plain,
% 2.13/2.33 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a913) | c1_1(a913) | (~c0_1(a913)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4395,plain,
% 2.13/2.33 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a913) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a913) | (~c0_1(a913))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4394, 4393])).
% 2.13/2.33 tff(4396,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4395, 432, 152, 3956, 3873, 3872, 695, 704, 219, 1073])).
% 2.13/2.33 tff(4397,plain,(c2_1(a913) | (~ndr1_0) | hskp1 | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a913)) | c1_1(a913)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4398,plain,
% 2.13/2.33 (c2_1(a913) | hskp1 | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a913)) | c1_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4397, 112])).
% 2.13/2.33 tff(4399,plain,
% 2.13/2.33 (c2_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4398, 4389, 3453, 4388, 4387, 4386, 4384])).
% 2.13/2.33 tff(4400,plain,
% 2.13/2.33 (~c3_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[347, 4383])).
% 2.13/2.33 tff(4401,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c3_1(a928) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c3_1(a928) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4402,plain,
% 2.13/2.33 (((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (c0_1(a978) | c3_1(a928) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4403,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a978) | c3_1(a928) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4402])).
% 2.13/2.33 tff(4404,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c3_1(a928) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4403, 4401])).
% 2.13/2.33 tff(4405,plain,
% 2.13/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4406,plain,
% 2.13/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a978) | c3_1(a928) | c1_1(a913) | c3_1(a913) | (~ndr1_0) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4405, 4404])).
% 2.13/2.33 tff(4407,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4406, 112, 4375, 4378, 4381, 4377, 4380, 4388, 4400, 392, 4399, 4382])).
% 2.13/2.33 tff(4408,plain,(c1_1(a899) | c0_1(a899) | hskp11 | hskp0 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4409,plain,
% 2.13/2.33 (c1_1(a899)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4408, 1430, 43, 31, 4223])).
% 2.13/2.33 tff(4410,plain,
% 2.13/2.33 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c3_1(a907)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4411,plain,
% 2.13/2.33 ((hskp12 | hskp10 | (~ndr1_0) | c0_1(a907) | (~c1_1(a907)) | (~c3_1(a907))) <=> (hskp12 | hskp10 | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c3_1(a907)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4412,plain,
% 2.13/2.33 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a907) | (~c1_1(a907)) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c3_1(a907))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4411])).
% 2.13/2.33 tff(4413,plain,
% 2.13/2.33 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a907) | (~c1_1(a907)) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c3_1(a907)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4412, 4410])).
% 2.13/2.33 tff(4414,plain,
% 2.13/2.33 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | c0_1(a907) | (~c1_1(a907)) | (~c3_1(a907)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4415,plain,
% 2.13/2.33 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp12 | hskp10 | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c3_1(a907))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4414, 4413])).
% 2.13/2.33 tff(4416,plain,
% 2.13/2.33 (hskp12 | hskp10 | (~c1_1(a907)) | (~c3_1(a907))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4415, 112, 44, 334])).
% 2.13/2.33 tff(4417,plain,
% 2.13/2.33 (hskp12),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4416, 50, 4277, 2207])).
% 2.13/2.33 tff(4418,plain,
% 2.13/2.33 (~c3_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[347, 4417])).
% 2.13/2.33 tff(4419,plain,
% 2.13/2.33 (c0_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[355, 4417])).
% 2.13/2.33 tff(4420,plain,
% 2.13/2.33 (c2_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[701, 112, 50, 4278, 4419, 4418, 693])).
% 2.13/2.33 tff(4421,assumption,(~c2_1(a907)), introduced(assumption)).
% 2.13/2.33 tff(4422,plain,
% 2.13/2.33 (~c1_1(a913)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[409, 4417])).
% 2.13/2.33 tff(4423,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a913) | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a913)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a913)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4424,plain,
% 2.13/2.33 (((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907))) <=> (c1_1(a913) | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a913)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4425,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a913) | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a913))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4424])).
% 2.13/2.33 tff(4426,plain,
% 2.13/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a913)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4425, 4423])).
% 2.13/2.33 tff(4427,plain,
% 2.13/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a913) | c1_1(a913) | (~c2_1(a913)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4428,plain,
% 2.13/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a913))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4427, 4426])).
% 2.13/2.33 tff(4429,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4428, 112, 2207, 4422, 4418, 44, 4277, 503, 4421, 4420])).
% 2.13/2.33 tff(4430,plain,(hskp10 | (~c3_1(a907)) | c0_1(a907) | (~c1_1(a907)) | c2_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(4431,plain,
% 2.13/2.33 (c2_1(a907)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4430, 50, 44, 4277, 2207])).
% 2.13/2.33 tff(4432,plain,
% 2.13/2.33 (^[U: $i] : refl((hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 2.13/2.33 inference(bind,[status(th)],[])).
% 2.13/2.33 tff(4433,plain,
% 2.13/2.33 (![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.13/2.33 inference(quant_intro,[status(thm)],[4432])).
% 2.13/2.33 tff(4434,plain,
% 2.13/2.33 (![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4435,plain,
% 2.13/2.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp17) <=> ((hskp26 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp26 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp17) <=> (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.13/2.33 inference(bind,[status(th)],[])).
% 2.13/2.33 tff(4436,plain,
% 2.13/2.33 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp17) <=> ![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.13/2.33 inference(quant_intro,[status(thm)],[4435])).
% 2.13/2.33 tff(4437,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 2.13/2.33 tff(4438,plain,
% 2.13/2.33 (![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4437, 4436])).
% 2.13/2.33 tff(4439,plain,
% 2.13/2.33 (![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4438, 4434])).
% 2.13/2.33 tff(4440,plain,(
% 2.13/2.33 ![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.13/2.33 inference(skolemize,[status(sab)],[4439])).
% 2.13/2.33 tff(4441,plain,
% 2.13/2.33 (![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4440, 4433])).
% 2.13/2.33 tff(4442,plain,
% 2.13/2.33 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a913)) | (~c2_1(a913)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp15 | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4443,plain,
% 2.13/2.33 ((hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a907) | (~c2_1(a907)) | (~c1_1(a907))) <=> (hskp15 | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(4444,plain,
% 2.13/2.33 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a907) | (~c2_1(a907)) | (~c1_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a913)) | (~c2_1(a913))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[4443])).
% 2.13/2.33 tff(4445,plain,
% 2.13/2.33 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a907) | (~c2_1(a907)) | (~c1_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp15 | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a913)) | (~c2_1(a913)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[4444, 4442])).
% 2.13/2.33 tff(4446,plain,
% 2.13/2.33 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a913) | (~c2_1(a913)) | (~c0_1(a913)) | c0_1(a907) | (~c2_1(a907)) | (~c1_1(a907)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(4447,plain,
% 2.13/2.33 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp15 | c3_1(a913) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c0_1(a913)) | (~c2_1(a913))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[4446, 4445])).
% 2.13/2.33 tff(4448,plain,
% 2.13/2.33 (hskp15),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4447, 112, 4419, 4418, 44, 4277, 2565, 4088, 4420])).
% 2.13/2.33 tff(4449,plain,
% 2.13/2.33 (~c3_1(a921)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2464, 4448])).
% 2.13/2.33 tff(4450,plain,
% 2.13/2.33 (c1_1(a921)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2472, 4448])).
% 2.13/2.33 tff(4451,plain,
% 2.13/2.33 (c0_1(a921)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2480, 4448])).
% 2.13/2.33 tff(4452,plain,
% 2.13/2.33 (((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)))) <=> ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp17 | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(4453,plain,
% 2.13/2.34 ((hskp26 | hskp17 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921))) <=> (hskp26 | hskp17 | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(4454,plain,
% 2.13/2.34 (((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)))) <=> ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[4453])).
% 2.13/2.34 tff(4455,plain,
% 2.13/2.34 (((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)))) <=> ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp17 | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)))),
% 2.13/2.34 inference(transitivity,[status(thm)],[4454, 4452])).
% 2.13/2.34 tff(4456,plain,
% 2.13/2.34 ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(4457,plain,
% 2.13/2.34 ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp17 | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[4456, 4455])).
% 2.13/2.34 tff(4458,plain,
% 2.13/2.34 (hskp26),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[4457, 112, 32, 4451, 4450, 4449, 4441])).
% 2.13/2.34 tff(4459,plain,
% 2.13/2.34 (((~hskp26) | (~c2_1(a969))) <=> ((~hskp26) | (~c2_1(a969)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(4460,plain,
% 2.13/2.34 (((~c2_1(a969)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a969)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4461,axiom,((~c2_1(a969)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 2.18/2.34 tff(4462,plain,
% 2.18/2.34 ((~hskp26) | (~c2_1(a969))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4461, 4460])).
% 2.18/2.34 tff(4463,plain,
% 2.18/2.34 ((~hskp26) | (~c2_1(a969))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4462, 4459])).
% 2.18/2.34 tff(4464,plain,
% 2.18/2.34 (~c2_1(a969)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4463, 4458])).
% 2.18/2.34 tff(4465,plain,
% 2.18/2.34 (((~hskp26) | c0_1(a969)) <=> ((~hskp26) | c0_1(a969))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4466,axiom,((~hskp26) | c0_1(a969)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 2.18/2.34 tff(4467,plain,
% 2.18/2.34 ((~hskp26) | c0_1(a969)),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4466, 4465])).
% 2.18/2.34 tff(4468,plain,
% 2.18/2.34 ((~hskp26) | c0_1(a969)),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4467, 4465])).
% 2.18/2.34 tff(4469,plain,
% 2.18/2.34 ((~hskp26) | c0_1(a969)),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4468, 4465])).
% 2.18/2.34 tff(4470,plain,
% 2.18/2.34 ((~hskp26) | c0_1(a969)),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4469, 4465])).
% 2.18/2.34 tff(4471,plain,
% 2.18/2.34 ((~hskp26) | c0_1(a969)),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4470, 4465])).
% 2.18/2.34 tff(4472,plain,
% 2.18/2.34 (c0_1(a969)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4471, 4458])).
% 2.18/2.34 tff(4473,plain,
% 2.18/2.34 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c2_1(a969) | (~ndr1_0) | c3_1(a969) | (~c0_1(a969)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a969) | (~ndr1_0) | c3_1(a969) | (~c0_1(a969)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4474,plain,
% 2.18/2.34 ((hskp10 | hskp7 | (~ndr1_0) | c2_1(a969) | c3_1(a969) | (~c0_1(a969))) <=> (hskp10 | hskp7 | c2_1(a969) | (~ndr1_0) | c3_1(a969) | (~c0_1(a969)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4475,plain,
% 2.18/2.34 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a969) | c3_1(a969) | (~c0_1(a969)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c2_1(a969) | (~ndr1_0) | c3_1(a969) | (~c0_1(a969))))),
% 2.18/2.34 inference(monotonicity,[status(thm)],[4474])).
% 2.18/2.34 tff(4476,plain,
% 2.18/2.34 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a969) | c3_1(a969) | (~c0_1(a969)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a969) | (~ndr1_0) | c3_1(a969) | (~c0_1(a969)))),
% 2.18/2.34 inference(transitivity,[status(thm)],[4475, 4473])).
% 2.18/2.34 tff(4477,plain,
% 2.18/2.34 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a969) | c3_1(a969) | (~c0_1(a969)))),
% 2.18/2.34 inference(quant_inst,[status(thm)],[])).
% 2.18/2.34 tff(4478,plain,
% 2.18/2.34 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a969) | (~ndr1_0) | c3_1(a969) | (~c0_1(a969))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4477, 4476])).
% 2.18/2.34 tff(4479,plain,
% 2.18/2.34 (c3_1(a969)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4478, 112, 50, 4278, 4472, 4464, 693])).
% 2.18/2.34 tff(4480,plain,
% 2.18/2.34 (((~hskp26) | (~c1_1(a969))) <=> ((~hskp26) | (~c1_1(a969)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4481,plain,
% 2.18/2.34 (((~c1_1(a969)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a969)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4482,axiom,((~c1_1(a969)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 2.18/2.34 tff(4483,plain,
% 2.18/2.34 ((~hskp26) | (~c1_1(a969))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4482, 4481])).
% 2.18/2.34 tff(4484,plain,
% 2.18/2.34 ((~hskp26) | (~c1_1(a969))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4483, 4480])).
% 2.18/2.34 tff(4485,plain,
% 2.18/2.34 (~c1_1(a969)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4484, 4458])).
% 2.18/2.34 tff(4486,plain,
% 2.18/2.34 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c3_1(a969)) | (~c0_1(a969)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c3_1(a969)) | (~c0_1(a969)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4487,plain,
% 2.18/2.34 ((hskp22 | (~ndr1_0) | c2_1(a969) | (~c3_1(a969)) | (~c0_1(a969)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969))) <=> (hskp22 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c3_1(a969)) | (~c0_1(a969)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4488,plain,
% 2.18/2.34 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a969) | (~c3_1(a969)) | (~c0_1(a969)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c3_1(a969)) | (~c0_1(a969))))),
% 2.18/2.34 inference(monotonicity,[status(thm)],[4487])).
% 2.18/2.34 tff(4489,plain,
% 2.18/2.34 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a969) | (~c3_1(a969)) | (~c0_1(a969)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c3_1(a969)) | (~c0_1(a969)))),
% 2.18/2.34 inference(transitivity,[status(thm)],[4488, 4486])).
% 2.18/2.34 tff(4490,plain,
% 2.18/2.34 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a969) | (~c3_1(a969)) | (~c0_1(a969)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969)))),
% 2.18/2.34 inference(quant_inst,[status(thm)],[])).
% 2.18/2.34 tff(4491,plain,
% 2.18/2.34 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c3_1(a969)) | (~c0_1(a969))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4490, 4489])).
% 2.18/2.34 tff(4492,plain,
% 2.18/2.34 (hskp22),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4491, 112, 4472, 4485, 4464, 1234, 4479])).
% 2.18/2.34 tff(4493,plain,
% 2.18/2.34 (~c3_1(a939)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1247, 4492])).
% 2.18/2.34 tff(4494,plain,
% 2.18/2.34 (~c0_1(a939)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1253, 4492])).
% 2.18/2.34 tff(4495,plain,
% 2.18/2.34 (c1_1(a939)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1262, 4492])).
% 2.18/2.34 tff(4496,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | (~c1_1(a939)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4497,plain,
% 2.18/2.34 (((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | (~c1_1(a939)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4498,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | (~c1_1(a939))))),
% 2.18/2.34 inference(monotonicity,[status(thm)],[4497])).
% 2.18/2.34 tff(4499,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | (~c1_1(a939)))),
% 2.18/2.34 inference(transitivity,[status(thm)],[4498, 4496])).
% 2.18/2.34 tff(4500,plain,
% 2.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 2.18/2.34 inference(quant_inst,[status(thm)],[])).
% 2.18/2.34 tff(4501,plain,
% 2.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | (~c1_1(a939))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4500, 4499])).
% 2.18/2.34 tff(4502,plain,
% 2.18/2.34 ($false),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4501, 112, 4495, 2207, 4494, 4493, 4422, 4418, 44, 392, 4088, 4420])).
% 2.18/2.34 tff(4503,plain,(hskp10 | (~c3_1(a907)) | c0_1(a907) | (~c2_1(a907)) | hskp17 | (~c1_1(a907))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.34 tff(4504,plain,
% 2.18/2.34 (hskp17),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4503, 4431, 44, 2207, 50, 4277])).
% 2.18/2.34 tff(4505,plain,
% 2.18/2.34 (~c2_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[834, 4504])).
% 2.18/2.34 tff(4506,plain,
% 2.18/2.34 (~c3_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[828, 4504])).
% 2.18/2.34 tff(4507,plain,
% 2.18/2.34 (c1_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[842, 4504])).
% 2.18/2.34 tff(4508,plain,
% 2.18/2.34 (~c0_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4342, 4507, 4278, 311, 43, 4506, 312, 4505])).
% 2.18/2.34 tff(4509,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a913) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a913) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4510,plain,
% 2.18/2.34 (((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a913) | c1_1(a913) | c2_1(a913)) <=> (c2_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a913) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4511,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a913) | c0_1(a928) | (~c1_1(a928))))),
% 2.18/2.34 inference(monotonicity,[status(thm)],[4510])).
% 2.18/2.34 tff(4512,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a913) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.34 inference(transitivity,[status(thm)],[4511, 4509])).
% 2.18/2.34 tff(4513,plain,
% 2.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a928) | c0_1(a928) | (~c1_1(a928)) | c3_1(a913) | c1_1(a913) | c2_1(a913))),
% 2.18/2.34 inference(quant_inst,[status(thm)],[])).
% 2.18/2.34 tff(4514,plain,
% 2.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | c2_1(a913) | c0_1(a928) | (~c1_1(a928))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4513, 4512])).
% 2.18/2.34 tff(4515,plain,
% 2.18/2.34 (c2_1(a913)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4514, 112, 4507, 2207, 4505, 4422, 4418, 44, 1721, 4431, 4508])).
% 2.18/2.34 tff(4516,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4517,plain,
% 2.18/2.34 (((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (c3_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4518,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928))))),
% 2.18/2.34 inference(monotonicity,[status(thm)],[4517])).
% 2.18/2.34 tff(4519,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.34 inference(transitivity,[status(thm)],[4518, 4516])).
% 2.18/2.34 tff(4520,plain,
% 2.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.34 inference(quant_inst,[status(thm)],[])).
% 2.18/2.34 tff(4521,plain,
% 2.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a928) | c1_1(a913) | c3_1(a913) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c2_1(a913)) | c0_1(a928) | (~c1_1(a928))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4520, 4519])).
% 2.18/2.34 tff(4522,plain,
% 2.18/2.34 ($false),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4521, 112, 4507, 2207, 4506, 4422, 4418, 44, 392, 4431, 4515, 4508])).
% 2.18/2.34 tff(4523,plain,(hskp10 | (~c3_1(a907)) | c0_1(a907) | (~c1_1(a899)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a907))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.34 tff(4524,plain,
% 2.18/2.34 (hskp10),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4523, 4409, 44, 4373, 43, 4276, 4217])).
% 2.18/2.34 tff(4525,plain,
% 2.18/2.34 (~c2_1(a910)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2348, 4524])).
% 2.18/2.34 tff(4526,plain,
% 2.18/2.34 (c1_1(a910)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2362, 4524])).
% 2.18/2.34 tff(4527,plain,
% 2.18/2.34 (hskp25),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[3783, 4526, 43, 4409, 4276, 4525, 31])).
% 2.18/2.34 tff(4528,plain,
% 2.18/2.34 (~c0_1(a958)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1841, 4527])).
% 2.18/2.34 tff(4529,plain,
% 2.18/2.34 (~c0_1(a910)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2354, 4524])).
% 2.18/2.34 tff(4530,plain,
% 2.18/2.34 (~c3_1(a958)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1692, 4527])).
% 2.18/2.34 tff(4531,plain,
% 2.18/2.34 (~c1_1(a958)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1698, 4527])).
% 2.18/2.34 tff(4532,plain,
% 2.18/2.34 (c3_1(a899)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2295, 32, 312])).
% 2.18/2.34 tff(4533,assumption,(~c0_1(a958)), introduced(assumption)).
% 2.18/2.34 tff(4534,plain,
% 2.18/2.34 (hskp17 | (~c2_1(a958))),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1848, 112, 31, 4533, 3870, 891])).
% 2.18/2.34 tff(4535,plain,
% 2.18/2.34 (~c2_1(a958)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4534, 32])).
% 2.18/2.34 tff(4536,plain,
% 2.18/2.34 ((~c3_1(a899)) | c2_1(a958)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2718, 112, 2366, 312, 3871, 3870, 2365, 2364, 43, 1721])).
% 2.18/2.34 tff(4537,plain,
% 2.18/2.34 ($false),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4536, 4535, 4532])).
% 2.18/2.34 tff(4538,plain,(hskp17 | (~c1_1(a910)) | (~c2_1(a899)) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a899) | hskp0 | c0_1(a958)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.34 tff(4539,plain,
% 2.18/2.34 (hskp17),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4538, 4526, 4276, 4531, 4530, 4529, 4525, 43, 31, 4528])).
% 2.18/2.34 tff(4540,plain,
% 2.18/2.34 (~c2_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[834, 4539])).
% 2.18/2.34 tff(4541,plain,
% 2.18/2.34 (~c3_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[828, 4539])).
% 2.18/2.34 tff(4542,plain,
% 2.18/2.34 (c1_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[842, 4539])).
% 2.18/2.34 tff(4543,plain,
% 2.18/2.34 (~c0_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4342, 4542, 4223, 4409, 43, 4541, 4276, 4540])).
% 2.18/2.34 tff(4544,plain,
% 2.18/2.34 (hskp31),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1729, 4539, 1430])).
% 2.18/2.34 tff(4545,plain,
% 2.18/2.34 (c2_1(a957)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[3843, 4544])).
% 2.18/2.34 tff(4546,plain,
% 2.18/2.34 (c3_1(a957)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[3835, 4544])).
% 2.18/2.34 tff(4547,plain,
% 2.18/2.34 (c0_1(a957)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[3889, 4543, 4530, 4546, 4542, 4541, 4545, 4540, 4531])).
% 2.18/2.34 tff(4548,plain,
% 2.18/2.34 (c1_1(a957)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[3827, 4544])).
% 2.18/2.34 tff(4549,plain,
% 2.18/2.34 ($false),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[3962, 112, 1430, 4548, 4546, 4542, 4540, 1402, 4547, 4543])).
% 2.18/2.34 tff(4550,plain,(hskp11 | c0_1(a899) | hskp0 | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.34 tff(4551,plain,
% 2.18/2.34 (hskp11),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4550, 44, 31, 43])).
% 2.18/2.34 tff(4552,plain,
% 2.18/2.34 (~c1_1(a912)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2146, 4551])).
% 2.18/2.34 tff(4553,plain,
% 2.18/2.34 (~c2_1(a912)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1679, 4551])).
% 2.18/2.34 tff(4554,plain,
% 2.18/2.34 (c3_1(a899)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2295, 32, 4276])).
% 2.18/2.34 tff(4555,plain,
% 2.18/2.34 ($false),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1145, 112, 1103, 4419, 4418, 801, 802, 813, 1064, 4420])).
% 2.18/2.34 tff(4556,plain,(hskp10 | hskp20 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~c1_1(a907)) | (~c3_1(a907)) | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.34 tff(4557,plain,
% 2.18/2.34 (hskp10),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4556, 813, 801, 802, 1103, 4277, 2207, 44])).
% 2.18/2.34 tff(4558,plain,
% 2.18/2.34 (~c2_1(a910)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2348, 4557])).
% 2.18/2.34 tff(4559,plain,
% 2.18/2.34 (c1_1(a910)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2362, 4557])).
% 2.18/2.34 tff(4560,plain,
% 2.18/2.34 (~c0_1(a910)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2354, 4557])).
% 2.18/2.34 tff(4561,plain,
% 2.18/2.34 ($false),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2851, 112, 2366, 312, 801, 802, 813, 2365, 2364, 43, 1721, 314])).
% 2.18/2.34 tff(4562,plain,(c3_1(a912) | (~c1_1(a910)) | (~c2_1(a899)) | c1_1(a912) | c2_1(a912) | c0_1(a910) | c2_1(a910) | c0_1(a899) | (~c3_1(a899))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.34 tff(4563,plain,
% 2.18/2.34 ($false),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4562, 4560, 4559, 314, 801, 802, 813, 4558, 43, 312])).
% 2.18/2.34 tff(4564,plain,(c3_1(a912) | (~c3_1(a899)) | c1_1(a912) | c2_1(a912) | c0_1(a899) | (~c2_1(a899)) | hskp20 | (~c1_1(a907)) | (~c3_1(a907)) | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.34 tff(4565,plain,
% 2.18/2.34 (c3_1(a912)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4564, 4554, 801, 802, 43, 4276, 1884, 4217, 4373, 44])).
% 2.18/2.34 tff(4566,plain,
% 2.18/2.34 (c0_1(a912)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[2886, 3453, 802])).
% 2.18/2.34 tff(4567,plain,
% 2.18/2.34 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a912) | c2_1(a912) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a912) | c2_1(a912) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4568,plain,
% 2.18/2.34 ((hskp1 | (~ndr1_0) | (~c1_1(a907)) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912))) <=> (hskp1 | c1_1(a912) | c2_1(a912) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4569,plain,
% 2.18/2.34 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a907)) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a912) | c2_1(a912) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912))))),
% 2.18/2.34 inference(monotonicity,[status(thm)],[4568])).
% 2.18/2.34 tff(4570,plain,
% 2.18/2.34 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a907)) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a912) | c2_1(a912) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912)))),
% 2.18/2.34 inference(transitivity,[status(thm)],[4569, 4567])).
% 2.18/2.34 tff(4571,plain,
% 2.18/2.34 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a907)) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a912) | c1_1(a912) | (~c0_1(a912)))),
% 2.18/2.34 inference(quant_inst,[status(thm)],[])).
% 2.18/2.34 tff(4572,plain,
% 2.18/2.34 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a912) | c2_1(a912) | (~c1_1(a907)) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c0_1(a912))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4571, 4570])).
% 2.18/2.34 tff(4573,plain,
% 2.18/2.34 (hskp1 | (~c2_1(a907)) | (~c0_1(a912))),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4572, 112, 2207, 801, 802, 4277, 219])).
% 2.18/2.34 tff(4574,plain,
% 2.18/2.34 (~c2_1(a907)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4573, 3453, 4566])).
% 2.18/2.34 tff(4575,plain,
% 2.18/2.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4576,plain,
% 2.18/2.34 ((hskp13 | hskp1 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907))) <=> (hskp13 | hskp1 | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))),
% 2.18/2.34 inference(rewrite,[status(thm)],[])).
% 2.18/2.34 tff(4577,plain,
% 2.18/2.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907))))),
% 2.18/2.34 inference(monotonicity,[status(thm)],[4576])).
% 2.18/2.34 tff(4578,plain,
% 2.18/2.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)))),
% 2.18/2.34 inference(transitivity,[status(thm)],[4577, 4575])).
% 2.18/2.34 tff(4579,plain,
% 2.18/2.34 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)))),
% 2.18/2.34 inference(quant_inst,[status(thm)],[])).
% 2.18/2.34 tff(4580,plain,
% 2.18/2.34 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp1 | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907))),
% 2.18/2.34 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 2.18/2.34 tff(4581,plain,
% 2.18/2.34 (hskp13 | hskp1 | c2_1(a907) | (~c3_1(a907))),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4580, 112, 4277, 174])).
% 2.18/2.34 tff(4582,plain,
% 2.18/2.34 (hskp13),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4581, 4574, 2207, 3453])).
% 2.18/2.34 tff(4583,plain,
% 2.18/2.34 (~c2_1(a914)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[187, 4582])).
% 2.18/2.34 tff(4584,plain,
% 2.18/2.34 (~c1_1(a914)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[193, 4582])).
% 2.18/2.34 tff(4585,plain,
% 2.18/2.34 (hskp27),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4249, 4330, 4278])).
% 2.18/2.34 tff(4586,plain,
% 2.18/2.34 (c2_1(a978)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1461, 4585])).
% 2.18/2.34 tff(4587,plain,
% 2.18/2.34 (c2_1(a899)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[4275, 4278, 43, 31])).
% 2.18/2.34 tff(4588,plain,
% 2.18/2.34 (~c0_1(a978)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1445, 4585])).
% 2.18/2.34 tff(4589,plain,
% 2.18/2.34 (c3_1(a978)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[1453, 4585])).
% 2.18/2.34 tff(4590,plain,
% 2.18/2.34 (hskp17),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[3477, 4589, 3441, 4588, 31, 4587, 43, 4586])).
% 2.18/2.34 tff(4591,plain,
% 2.18/2.34 (~c3_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[828, 4590])).
% 2.18/2.34 tff(4592,plain,
% 2.18/2.34 (~c2_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[834, 4590])).
% 2.18/2.34 tff(4593,plain,
% 2.18/2.34 (c3_1(a914)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[201, 4582])).
% 2.18/2.34 tff(4594,plain,
% 2.18/2.34 (c1_1(a928)),
% 2.18/2.34 inference(unit_resolution,[status(thm)],[842, 4590])).
% 2.18/2.34 tff(4595,plain,
% 2.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4596,plain,
% 2.18/2.35 (((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978))) <=> (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4597,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.18/2.35 inference(monotonicity,[status(thm)],[4596])).
% 2.18/2.35 tff(4598,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(transitivity,[status(thm)],[4597, 4595])).
% 2.18/2.35 tff(4599,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a928) | c3_1(a928) | (~c1_1(a928)) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(quant_inst,[status(thm)],[])).
% 2.18/2.35 tff(4600,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a978) | c2_1(a928) | c3_1(a928) | c1_1(a914) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4599, 4598])).
% 2.18/2.35 tff(4601,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4600, 112, 4586, 4589, 4594, 4593, 4588, 4592, 4591, 4584, 4583, 1384])).
% 2.18/2.35 tff(4602,plain,(c1_1(a899) | hskp0 | c0_1(a899) | (~c3_1(a907)) | (~c1_1(a907)) | c1_1(a912) | c2_1(a912)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4603,plain,
% 2.18/2.35 (c1_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4602, 802, 43, 4373, 4217, 801, 31])).
% 2.18/2.35 tff(4604,plain,
% 2.18/2.35 (hskp10),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4430, 4421, 44, 4217, 4373])).
% 2.18/2.35 tff(4605,plain,
% 2.18/2.35 (~c2_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2348, 4604])).
% 2.18/2.35 tff(4606,plain,
% 2.18/2.35 (c1_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2362, 4604])).
% 2.18/2.35 tff(4607,plain,
% 2.18/2.35 (hskp25),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3783, 4606, 43, 311, 4276, 4605, 31])).
% 2.18/2.35 tff(4608,plain,
% 2.18/2.35 (~c3_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1692, 4607])).
% 2.18/2.35 tff(4609,plain,
% 2.18/2.35 (~c1_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1698, 4607])).
% 2.18/2.35 tff(4610,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a958)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a958)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4611,plain,
% 2.18/2.35 (((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907))) <=> (c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a958)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4612,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a958))))),
% 2.18/2.35 inference(monotonicity,[status(thm)],[4611])).
% 2.18/2.35 tff(4613,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a958)))),
% 2.18/2.35 inference(transitivity,[status(thm)],[4612, 4610])).
% 2.18/2.35 tff(4614,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c3_1(a907)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)) | c0_1(a907) | c2_1(a907) | (~c3_1(a907)))),
% 2.18/2.35 inference(quant_inst,[status(thm)],[])).
% 2.18/2.35 tff(4615,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c2_1(a958))),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4614, 4613])).
% 2.18/2.35 tff(4616,plain,
% 2.18/2.35 (~c2_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4615, 112, 4373, 4609, 4608, 44, 4217, 503, 4421])).
% 2.18/2.35 tff(4617,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c2_1(a958))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4618,plain,
% 2.18/2.35 (((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c0_1(a907) | (~c1_1(a907)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c2_1(a958))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4619,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c0_1(a907) | (~c1_1(a907)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c2_1(a958)))),
% 2.18/2.35 inference(monotonicity,[status(thm)],[4618])).
% 2.18/2.35 tff(4620,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c0_1(a907) | (~c1_1(a907)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c2_1(a958))),
% 2.18/2.35 inference(transitivity,[status(thm)],[4619, 4617])).
% 2.18/2.35 tff(4621,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c0_1(a907) | (~c1_1(a907)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 2.18/2.35 inference(quant_inst,[status(thm)],[])).
% 2.18/2.35 tff(4622,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a907) | (~c1_1(a907)) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | c2_1(a907) | c2_1(a958)),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 2.18/2.35 tff(4623,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4622, 112, 4276, 4609, 4608, 44, 4217, 43, 1721, 314, 4421, 4616])).
% 2.18/2.35 tff(4624,plain,(c2_1(a907) | c0_1(a907) | c0_1(a899) | (~c3_1(a899)) | (~c1_1(a899)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4625,plain,
% 2.18/2.35 (c2_1(a907)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4624, 4554, 43, 44, 4603, 31])).
% 2.18/2.35 tff(4626,plain,
% 2.18/2.35 (hskp10),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4503, 4625, 44, 4373, 32, 4217])).
% 2.18/2.35 tff(4627,plain,
% 2.18/2.35 (~c2_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2348, 4626])).
% 2.18/2.35 tff(4628,plain,
% 2.18/2.35 (c1_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2362, 4626])).
% 2.18/2.35 tff(4629,plain,
% 2.18/2.35 (hskp25),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3783, 4628, 43, 4603, 4276, 4627, 31])).
% 2.18/2.35 tff(4630,plain,
% 2.18/2.35 (~c3_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1692, 4629])).
% 2.18/2.35 tff(4631,plain,
% 2.18/2.35 (~c1_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1698, 4629])).
% 2.18/2.35 tff(4632,plain,
% 2.18/2.35 (~c0_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2354, 4626])).
% 2.18/2.35 tff(4633,plain,
% 2.18/2.35 (c3_1(a913)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3201, 4627, 31, 43, 4276, 32, 4565, 4632, 801, 4628, 802])).
% 2.18/2.35 tff(4634,plain,
% 2.18/2.35 (~hskp12),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[347, 4633])).
% 2.18/2.35 tff(4635,plain,
% 2.18/2.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c2_1(a958)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4636,plain,
% 2.18/2.35 ((hskp12 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912))) <=> (hskp12 | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c2_1(a958)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4637,plain,
% 2.18/2.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c2_1(a958))))),
% 2.18/2.35 inference(monotonicity,[status(thm)],[4636])).
% 2.18/2.35 tff(4638,plain,
% 2.18/2.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c2_1(a958)))),
% 2.18/2.35 inference(transitivity,[status(thm)],[4637, 4635])).
% 2.18/2.35 tff(4639,plain,
% 2.18/2.35 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c2_1(a912) | c1_1(a912) | (~c3_1(a912)))),
% 2.18/2.35 inference(quant_inst,[status(thm)],[])).
% 2.18/2.35 tff(4640,plain,
% 2.18/2.35 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp12 | c1_1(a958) | c3_1(a958) | c1_1(a912) | c2_1(a912) | (~c3_1(a912)) | (~ndr1_0) | (~c2_1(a958))),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4639, 4638])).
% 2.18/2.35 tff(4641,plain,
% 2.18/2.35 (~c2_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4640, 112, 4634, 4631, 4630, 801, 802, 4565, 2509])).
% 2.18/2.35 tff(4642,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c2_1(a958))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4643,plain,
% 2.18/2.35 (((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958)) <=> (c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c2_1(a958))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4644,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c2_1(a958)))),
% 2.18/2.35 inference(monotonicity,[status(thm)],[4643])).
% 2.18/2.35 tff(4645,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c2_1(a958))),
% 2.18/2.35 inference(transitivity,[status(thm)],[4644, 4642])).
% 2.18/2.35 tff(4646,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a958) | c1_1(a958) | c2_1(a958))),
% 2.18/2.35 inference(quant_inst,[status(thm)],[])).
% 2.18/2.35 tff(4647,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a958) | c3_1(a958) | c0_1(a910) | c2_1(a910) | c0_1(a907) | (~ndr1_0) | (~c2_1(a907)) | (~c3_1(a907)) | (~c1_1(a910)) | c2_1(a958)),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4646, 4645])).
% 2.18/2.35 tff(4648,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4647, 112, 4628, 4373, 4631, 4630, 4632, 4627, 44, 1721, 4625, 4641])).
% 2.18/2.35 tff(4649,plain,(hskp17 | c0_1(a907) | c1_1(a912) | c2_1(a912) | hskp0 | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4650,plain,
% 2.18/2.35 (hskp17),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4649, 802, 801, 44, 31, 43])).
% 2.18/2.35 tff(4651,plain,
% 2.18/2.35 (~c3_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[828, 4650])).
% 2.18/2.35 tff(4652,plain,
% 2.18/2.35 (~c2_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[834, 4650])).
% 2.18/2.35 tff(4653,plain,
% 2.18/2.35 (c1_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[842, 4650])).
% 2.18/2.35 tff(4654,plain,
% 2.18/2.35 (~c0_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4342, 4653, 4223, 4603, 43, 4651, 4276, 4652])).
% 2.18/2.35 tff(4655,plain,
% 2.18/2.35 (hskp4),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2698, 112, 4223, 4653, 4651, 523, 4654])).
% 2.18/2.35 tff(4656,plain,
% 2.18/2.35 (~c3_1(a904)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[536, 4655])).
% 2.18/2.35 tff(4657,plain,
% 2.18/2.35 (~c1_1(a904)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[542, 4655])).
% 2.18/2.35 tff(4658,plain,
% 2.18/2.35 (c2_1(a904)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[605, 4655])).
% 2.18/2.35 tff(4659,plain,
% 2.18/2.35 (hskp29),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2489, 4658, 4652, 4654, 4653, 4657, 4656])).
% 2.18/2.35 tff(4660,plain,
% 2.18/2.35 (hskp11),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1438, 4659, 4653, 4652, 4654])).
% 2.18/2.35 tff(4661,plain,
% 2.18/2.35 (~c3_1(a912)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1390, 4660])).
% 2.18/2.35 tff(4662,plain,
% 2.18/2.35 (hskp10),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4359, 4661, 4653, 801, 802, 4652, 4223, 4651])).
% 2.18/2.35 tff(4663,plain,
% 2.18/2.35 (~c0_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2354, 4662])).
% 2.18/2.35 tff(4664,plain,
% 2.18/2.35 (c1_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2362, 4662])).
% 2.18/2.35 tff(4665,plain,
% 2.18/2.35 (~c2_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2348, 4662])).
% 2.18/2.35 tff(4666,plain,
% 2.18/2.35 (~c3_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4562, 4663, 4661, 801, 802, 4664, 4665, 43, 4276])).
% 2.18/2.35 tff(4667,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2631, 4666, 4665, 4223, 4276, 4653, 4652, 4651, 4603, 4654, 802, 43, 4664, 801, 4661, 4663])).
% 2.18/2.35 tff(4668,plain,(c2_1(a912) | c0_1(a899) | c1_1(a912) | c0_1(a907) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4669,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4668, 4553, 4552, 43, 44, 31])).
% 2.18/2.35 tff(4670,plain,(c0_1(a907) | c0_1(a899) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4671,plain,
% 2.18/2.35 (c0_1(a907)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4670, 43, 31])).
% 2.18/2.35 tff(4672,plain,
% 2.18/2.35 (((~hskp7) | (~c0_1(a907))) <=> ((~hskp7) | (~c0_1(a907)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4673,plain,
% 2.18/2.35 (((~c0_1(a907)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a907)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4674,axiom,((~c0_1(a907)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 2.18/2.35 tff(4675,plain,
% 2.18/2.35 ((~hskp7) | (~c0_1(a907))),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 2.18/2.35 tff(4676,plain,
% 2.18/2.35 ((~hskp7) | (~c0_1(a907))),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4675, 4672])).
% 2.18/2.35 tff(4677,plain,
% 2.18/2.35 (~hskp7),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4676, 4671])).
% 2.18/2.35 tff(4678,plain,
% 2.18/2.35 (hskp27),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4249, 4330, 4677])).
% 2.18/2.35 tff(4679,plain,
% 2.18/2.35 (c2_1(a978)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1461, 4678])).
% 2.18/2.35 tff(4680,plain,
% 2.18/2.35 (c2_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4275, 4677, 43, 31])).
% 2.18/2.35 tff(4681,plain,
% 2.18/2.35 (~c0_1(a978)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1445, 4678])).
% 2.18/2.35 tff(4682,plain,
% 2.18/2.35 (c3_1(a978)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1453, 4678])).
% 2.18/2.35 tff(4683,plain,
% 2.18/2.35 (hskp17),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3477, 4682, 3441, 4681, 31, 4680, 43, 4679])).
% 2.18/2.35 tff(4684,plain,
% 2.18/2.35 (~c3_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[828, 4683])).
% 2.18/2.35 tff(4685,plain,
% 2.18/2.35 (c1_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[842, 4683])).
% 2.18/2.35 tff(4686,plain,
% 2.18/2.35 (~c0_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4014, 4685, 3441, 4680, 4684, 43])).
% 2.18/2.35 tff(4687,plain,
% 2.18/2.35 (~c2_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[834, 4683])).
% 2.18/2.35 tff(4688,plain,
% 2.18/2.35 (hskp11),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4408, 3441, 43, 31, 4677])).
% 2.18/2.35 tff(4689,plain,
% 2.18/2.35 (~c3_1(a912)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1390, 4688])).
% 2.18/2.35 tff(4690,plain,
% 2.18/2.35 (~c1_1(a912)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2146, 4688])).
% 2.18/2.35 tff(4691,plain,
% 2.18/2.35 (~c2_1(a912)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1679, 4688])).
% 2.18/2.35 tff(4692,plain,
% 2.18/2.35 (hskp10),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4359, 4685, 4691, 4690, 4689, 4687, 4677, 4684])).
% 2.18/2.35 tff(4693,plain,
% 2.18/2.35 (~c2_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2348, 4692])).
% 2.18/2.35 tff(4694,plain,
% 2.18/2.35 (c1_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2362, 4692])).
% 2.18/2.35 tff(4695,plain,
% 2.18/2.35 (~c0_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2354, 4692])).
% 2.18/2.35 tff(4696,plain,
% 2.18/2.35 (~c3_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4562, 4695, 4691, 4690, 4689, 4694, 4693, 43, 4680])).
% 2.18/2.35 tff(4697,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a899) | c0_1(a978) | c3_1(a928) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a899) | c0_1(a978) | c3_1(a928) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4698,plain,
% 2.18/2.35 (((~ndr1_0) | c1_1(a899) | c3_1(a899) | (~c2_1(a899)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928))) <=> (c1_1(a899) | c0_1(a978) | c3_1(a928) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4699,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a899) | c3_1(a899) | (~c2_1(a899)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a899) | c0_1(a978) | c3_1(a928) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.18/2.35 inference(monotonicity,[status(thm)],[4698])).
% 2.18/2.35 tff(4700,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a899) | c3_1(a899) | (~c2_1(a899)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a899) | c0_1(a978) | c3_1(a928) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(transitivity,[status(thm)],[4699, 4697])).
% 2.18/2.35 tff(4701,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a899) | c3_1(a899) | (~c2_1(a899)) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c3_1(a928) | c0_1(a928) | (~c1_1(a928)))),
% 2.18/2.35 inference(quant_inst,[status(thm)],[])).
% 2.18/2.35 tff(4702,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a899) | c0_1(a978) | c3_1(a928) | (~ndr1_0) | c3_1(a899) | (~c2_1(a899)) | c0_1(a928) | (~c1_1(a928)) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4701, 4700])).
% 2.18/2.35 tff(4703,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4702, 112, 4679, 4682, 4685, 3441, 4680, 4681, 4684, 392, 4696, 4686])).
% 2.18/2.35 tff(4704,plain,(c1_1(a899) | c0_1(a899) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4705,plain,
% 2.18/2.35 (c1_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4704, 43, 31])).
% 2.18/2.35 tff(4706,plain,
% 2.18/2.35 (~c0_1(a928)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4342, 843, 547, 311, 43, 829, 312, 835])).
% 2.18/2.35 tff(4707,plain,
% 2.18/2.35 (hskp4),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2698, 112, 547, 843, 829, 523, 4706])).
% 2.18/2.35 tff(4708,plain,
% 2.18/2.35 (~c3_1(a904)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[536, 4707])).
% 2.18/2.35 tff(4709,plain,
% 2.18/2.35 (c2_1(a904)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[605, 4707])).
% 2.18/2.35 tff(4710,plain,
% 2.18/2.35 (~c1_1(a904)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[542, 4707])).
% 2.18/2.35 tff(4711,plain,
% 2.18/2.35 (hskp29),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2489, 4710, 835, 4706, 843, 4709, 4708])).
% 2.18/2.35 tff(4712,plain,
% 2.18/2.35 (hskp11),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1438, 4711, 4706, 835, 843])).
% 2.18/2.35 tff(4713,plain,
% 2.18/2.35 (~c2_1(a912)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1679, 4712])).
% 2.18/2.35 tff(4714,plain,
% 2.18/2.35 (~c1_1(a912)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2146, 4712])).
% 2.18/2.35 tff(4715,plain,
% 2.18/2.35 (~c3_1(a912)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1390, 4712])).
% 2.18/2.35 tff(4716,plain,
% 2.18/2.35 (hskp10),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4359, 4715, 843, 4714, 4713, 835, 547, 829])).
% 2.18/2.35 tff(4717,plain,
% 2.18/2.35 (~c0_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2354, 4716])).
% 2.18/2.35 tff(4718,plain,
% 2.18/2.35 (c1_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2362, 4716])).
% 2.18/2.35 tff(4719,plain,
% 2.18/2.35 (~c2_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2348, 4716])).
% 2.18/2.35 tff(4720,plain,
% 2.18/2.35 (~c3_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4562, 4717, 4713, 4714, 4715, 4718, 4719, 43, 312])).
% 2.18/2.35 tff(4721,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2631, 4720, 4719, 547, 312, 311, 835, 829, 4713, 4706, 843, 43, 4718, 4714, 4715, 4717])).
% 2.18/2.35 tff(4722,plain,((~hskp17) | hskp7 | (~c2_1(a899)) | (~c1_1(a899)) | c0_1(a899)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4723,plain,
% 2.18/2.35 (~hskp17),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4722, 4677, 4680, 4705, 43])).
% 2.18/2.35 tff(4724,plain,
% 2.18/2.35 (c3_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2295, 4723, 4680])).
% 2.18/2.35 tff(4725,plain,
% 2.18/2.35 (c2_1(a913)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[701, 112, 50, 547, 2975, 2974, 693])).
% 2.18/2.35 tff(4726,plain,
% 2.18/2.35 (hskp15),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2571, 112, 2975, 311, 312, 2974, 43, 2565, 4725])).
% 2.18/2.35 tff(4727,plain,
% 2.18/2.35 (~c3_1(a921)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2464, 4726])).
% 2.18/2.35 tff(4728,plain,
% 2.18/2.35 (c1_1(a921)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2472, 4726])).
% 2.18/2.35 tff(4729,plain,
% 2.18/2.35 (c0_1(a921)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2480, 4726])).
% 2.18/2.35 tff(4730,plain,
% 2.18/2.35 (~hskp17),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4722, 547, 312, 311, 43])).
% 2.18/2.35 tff(4731,plain,
% 2.18/2.35 (hskp26),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4457, 112, 4730, 4729, 4728, 4727, 4441])).
% 2.18/2.35 tff(4732,plain,
% 2.18/2.35 (~c2_1(a969)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4463, 4731])).
% 2.18/2.35 tff(4733,plain,
% 2.18/2.35 (c0_1(a969)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4471, 4731])).
% 2.18/2.35 tff(4734,plain,
% 2.18/2.35 (c3_1(a969)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4478, 112, 50, 547, 4733, 4732, 693])).
% 2.18/2.35 tff(4735,plain,
% 2.18/2.35 (~c1_1(a969)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4484, 4731])).
% 2.18/2.35 tff(4736,plain,
% 2.18/2.35 (hskp22),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4491, 112, 4733, 4735, 4732, 1234, 4734])).
% 2.18/2.35 tff(4737,plain,
% 2.18/2.35 (~c3_1(a939)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1247, 4736])).
% 2.18/2.35 tff(4738,plain,
% 2.18/2.35 (~c0_1(a939)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1253, 4736])).
% 2.18/2.35 tff(4739,plain,
% 2.18/2.35 (c1_1(a939)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1262, 4736])).
% 2.18/2.35 tff(4740,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a913)) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a913)) | (~c1_1(a939)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4741,plain,
% 2.18/2.35 (((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939))) <=> (c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a913)) | (~c1_1(a939)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4742,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a913)) | (~c1_1(a939))))),
% 2.18/2.35 inference(monotonicity,[status(thm)],[4741])).
% 2.18/2.35 tff(4743,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a913)) | (~c1_1(a939)))),
% 2.18/2.35 inference(transitivity,[status(thm)],[4742, 4740])).
% 2.18/2.35 tff(4744,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a913) | c3_1(a913) | (~c2_1(a913)) | c0_1(a899) | (~c3_1(a899)) | (~c2_1(a899)) | c3_1(a939) | c0_1(a939) | (~c1_1(a939)))),
% 2.18/2.35 inference(quant_inst,[status(thm)],[])).
% 2.18/2.35 tff(4745,plain,
% 2.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a939) | c3_1(a939) | c1_1(a913) | c3_1(a913) | c0_1(a899) | (~ndr1_0) | (~c3_1(a899)) | (~c2_1(a899)) | (~c2_1(a913)) | (~c1_1(a939))),
% 2.18/2.35 inference(modus_ponens,[status(thm)],[4744, 4743])).
% 2.18/2.35 tff(4746,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4745, 112, 4739, 312, 4738, 4737, 2987, 2974, 43, 392, 314, 4725])).
% 2.18/2.35 tff(4747,plain,(hskp10 | (~c2_1(a899)) | c0_1(a899) | (~c3_1(a899)) | hskp7 | (~c1_1(a899))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4748,plain,
% 2.18/2.35 (hskp10),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4747, 4680, 43, 4724, 4677, 4705])).
% 2.18/2.35 tff(4749,plain,
% 2.18/2.35 (~c2_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2348, 4748])).
% 2.18/2.35 tff(4750,plain,
% 2.18/2.35 (c1_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2362, 4748])).
% 2.18/2.35 tff(4751,plain,
% 2.18/2.35 (hskp25),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3783, 4750, 43, 4705, 4680, 4749, 31])).
% 2.18/2.35 tff(4752,plain,
% 2.18/2.35 (~c0_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1841, 4751])).
% 2.18/2.35 tff(4753,plain,
% 2.18/2.35 (~c0_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2354, 4748])).
% 2.18/2.35 tff(4754,plain,
% 2.18/2.35 (~c1_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1698, 4751])).
% 2.18/2.35 tff(4755,plain,
% 2.18/2.35 (~c3_1(a958)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1692, 4751])).
% 2.18/2.35 tff(4756,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4538, 4755, 4754, 4680, 4723, 4750, 4753, 4749, 43, 31, 4752])).
% 2.18/2.35 tff(4757,plain,(c0_1(a899) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4758,plain,
% 2.18/2.35 (c0_1(a899)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4757, 31])).
% 2.18/2.35 tff(4759,plain,
% 2.18/2.35 (~hskp1),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[292, 4758])).
% 2.18/2.35 tff(4760,plain,
% 2.18/2.35 (c1_1(a907)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3731, 44, 32, 4759, 31])).
% 2.18/2.35 tff(4761,plain,
% 2.18/2.35 (c3_1(a907)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4315, 4760, 31, 32, 44])).
% 2.18/2.35 tff(4762,plain,
% 2.18/2.35 ($false),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4503, 4431, 50, 44, 2207, 32, 4277])).
% 2.18/2.35 tff(4763,plain,(hskp10 | c0_1(a907) | (~c3_1(a907)) | hskp17 | (~c1_1(a907))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.35 tff(4764,plain,
% 2.18/2.35 (hskp10),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4763, 44, 4761, 32, 4760])).
% 2.18/2.35 tff(4765,plain,
% 2.18/2.35 (~c0_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2354, 4764])).
% 2.18/2.35 tff(4766,plain,
% 2.18/2.35 (~c2_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2348, 4764])).
% 2.18/2.35 tff(4767,plain,
% 2.18/2.35 (~hskp9),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4229, 4759, 31])).
% 2.18/2.35 tff(4768,plain,
% 2.18/2.35 (~hskp7),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4222, 4760])).
% 2.18/2.35 tff(4769,plain,
% 2.18/2.35 (hskp27),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[4249, 4768, 4767])).
% 2.18/2.35 tff(4770,plain,
% 2.18/2.35 (c3_1(a978)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1453, 4769])).
% 2.18/2.35 tff(4771,plain,
% 2.18/2.35 (~c0_1(a978)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1445, 4769])).
% 2.18/2.35 tff(4772,plain,
% 2.18/2.35 (c2_1(a978)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[1461, 4769])).
% 2.18/2.35 tff(4773,plain,
% 2.18/2.35 (c1_1(a910)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[2362, 4764])).
% 2.18/2.35 tff(4774,plain,
% 2.18/2.35 (~hskp25),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3486, 4773, 32, 4772, 4771, 4770, 4766, 4765, 31])).
% 2.18/2.35 tff(4775,plain,
% 2.18/2.35 (hskp21),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3248, 4774, 31])).
% 2.18/2.35 tff(4776,plain,
% 2.18/2.35 (~c2_1(a938)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[422, 4775])).
% 2.18/2.35 tff(4777,plain,
% 2.18/2.35 (c0_1(a938)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[430, 4775])).
% 2.18/2.35 tff(4778,plain,
% 2.18/2.35 (~c1_1(a938)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[3464, 112, 1884, 4759, 4777, 4776, 42])).
% 2.18/2.35 tff(4779,plain,
% 2.18/2.35 (~c3_1(a938)),
% 2.18/2.35 inference(unit_resolution,[status(thm)],[416, 4775])).
% 2.18/2.35 tff(4780,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c2_1(a938) | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c1_1(a938) | (~c3_1(a978)) | (~c2_1(a978)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c2_1(a938) | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c1_1(a938) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4781,plain,
% 2.18/2.35 (((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a938) | c1_1(a938) | c2_1(a938)) <=> (c0_1(a978) | c2_1(a938) | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c1_1(a938) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.35 inference(rewrite,[status(thm)],[])).
% 2.18/2.35 tff(4782,plain,
% 2.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a938) | c1_1(a938) | c2_1(a938))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a978) | c2_1(a938) | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c1_1(a938) | (~c3_1(a978)) | (~c2_1(a978))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4781])).
% 2.18/2.36 tff(4783,plain,
% 2.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a938) | c1_1(a938) | c2_1(a938))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c2_1(a938) | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c1_1(a938) | (~c3_1(a978)) | (~c2_1(a978)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4782, 4780])).
% 2.18/2.36 tff(4784,plain,
% 2.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a978) | (~c3_1(a978)) | (~c2_1(a978)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a938) | c1_1(a938) | c2_1(a938))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4785,plain,
% 2.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a978) | c2_1(a938) | c3_1(a938) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c1_1(a910)) | c1_1(a938) | (~c3_1(a978)) | (~c2_1(a978))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4784, 4783])).
% 2.18/2.36 tff(4786,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4785, 112, 4772, 4770, 4773, 4771, 4776, 4779, 4765, 4766, 1721, 4778])).
% 2.18/2.36 tff(4787,plain,(c0_1(a907) | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4788,plain,
% 2.18/2.36 (c0_1(a907)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4787, 32, 31])).
% 2.18/2.36 tff(4789,plain,
% 2.18/2.36 (~hskp7),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4676, 4788])).
% 2.18/2.36 tff(4790,plain,
% 2.18/2.36 (hskp12),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4238, 4767, 31])).
% 2.18/2.36 tff(4791,plain,
% 2.18/2.36 (~c3_1(a913)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[347, 4790])).
% 2.18/2.36 tff(4792,plain,
% 2.18/2.36 (c0_1(a913)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[355, 4790])).
% 2.18/2.36 tff(4793,plain,
% 2.18/2.36 (c0_1(a923)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1934, 112, 32, 31, 4146, 4132, 891])).
% 2.18/2.36 tff(4794,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3080, 112, 4767, 4133, 4146, 4132, 3066, 4793])).
% 2.18/2.36 tff(4795,plain,((~hskp16) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4796,plain,
% 2.18/2.36 (~hskp16),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4795, 32, 31])).
% 2.18/2.36 tff(4797,assumption,(~hskp16), introduced(assumption)).
% 2.18/2.36 tff(4798,plain,
% 2.18/2.36 (hskp10 | hskp7 | c2_1(a913)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[701, 112, 695, 694, 693])).
% 2.18/2.36 tff(4799,plain,
% 2.18/2.36 (c2_1(a913)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4798, 50, 547])).
% 2.18/2.36 tff(4800,plain,
% 2.18/2.36 (hskp16 | hskp10 | (~c2_1(a913))),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3051, 112, 695, 694, 1906])).
% 2.18/2.36 tff(4801,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4800, 4799, 50, 4797])).
% 2.18/2.36 tff(4802,plain,(hskp10 | hskp16 | (~c0_1(a913)) | c3_1(a913) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4803,plain,
% 2.18/2.36 (hskp10),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4802, 4796, 4792, 4791, 4789])).
% 2.18/2.36 tff(4804,plain,
% 2.18/2.36 (~c2_1(a910)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2348, 4803])).
% 2.18/2.36 tff(4805,plain,
% 2.18/2.36 (c1_1(a910)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2362, 4803])).
% 2.18/2.36 tff(4806,plain,
% 2.18/2.36 (~c0_1(a910)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2354, 4803])).
% 2.18/2.36 tff(4807,plain,
% 2.18/2.36 (hskp27),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4249, 4789, 4767])).
% 2.18/2.36 tff(4808,plain,
% 2.18/2.36 (c3_1(a978)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1453, 4807])).
% 2.18/2.36 tff(4809,plain,
% 2.18/2.36 (~c0_1(a978)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1445, 4807])).
% 2.18/2.36 tff(4810,plain,
% 2.18/2.36 (c2_1(a978)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1461, 4807])).
% 2.18/2.36 tff(4811,plain,
% 2.18/2.36 (~hskp25),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3486, 4805, 32, 4810, 4809, 4808, 4804, 4806, 31])).
% 2.18/2.36 tff(4812,plain,
% 2.18/2.36 (c3_1(a910)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3494, 112, 4811, 4805, 4804, 30])).
% 2.18/2.36 tff(4813,plain,
% 2.18/2.36 (^[U: $i] : refl((hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 2.18/2.36 inference(bind,[status(th)],[])).
% 2.18/2.36 tff(4814,plain,
% 2.18/2.36 (![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.18/2.36 inference(quant_intro,[status(thm)],[4813])).
% 2.18/2.36 tff(4815,plain,
% 2.18/2.36 (![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4816,plain,
% 2.18/2.36 (^[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)) | 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)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp9) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp9))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp9) <=> (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp9) <=> (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 2.18/2.36 inference(bind,[status(th)],[])).
% 2.18/2.36 tff(4817,plain,
% 2.18/2.36 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp9) <=> ![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.18/2.36 inference(quant_intro,[status(thm)],[4816])).
% 2.18/2.36 tff(4818,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 2.18/2.36 tff(4819,plain,
% 2.18/2.36 (![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4818, 4817])).
% 2.18/2.36 tff(4820,plain,
% 2.18/2.36 (![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4819, 4815])).
% 2.18/2.36 tff(4821,plain,(
% 2.18/2.36 ![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.18/2.36 inference(skolemize,[status(sab)],[4820])).
% 2.18/2.36 tff(4822,plain,
% 2.18/2.36 (![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4821, 4814])).
% 2.18/2.36 tff(4823,plain,
% 2.18/2.36 (((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp9 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))) <=> ((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp9 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4824,plain,
% 2.18/2.36 ((hskp16 | hskp9 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c3_1(a910))) <=> (hskp16 | hskp9 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4825,plain,
% 2.18/2.36 (((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp9 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))) <=> ((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp9 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4824])).
% 2.18/2.36 tff(4826,plain,
% 2.18/2.36 (((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp9 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))) <=> ((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp9 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4825, 4823])).
% 2.18/2.36 tff(4827,plain,
% 2.18/2.36 ((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp9 | (~ndr1_0) | c2_1(a910) | c0_1(a910) | (~c3_1(a910)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4828,plain,
% 2.18/2.36 ((~![U: $i] : (hskp16 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp9 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c3_1(a910))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4827, 4826])).
% 2.18/2.36 tff(4829,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4828, 112, 4796, 4767, 4806, 4804, 4822, 4812])).
% 2.18/2.36 tff(4830,plain,(hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4831,plain,
% 2.18/2.36 (hskp17),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4830, 31])).
% 2.18/2.36 tff(4832,plain,
% 2.18/2.36 (~c3_1(a928)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[828, 4831])).
% 2.18/2.36 tff(4833,plain,
% 2.18/2.36 (~c2_1(a928)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[834, 4831])).
% 2.18/2.36 tff(4834,plain,
% 2.18/2.36 (c1_1(a928)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[842, 4831])).
% 2.18/2.36 tff(4835,plain,
% 2.18/2.36 (hskp25),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1686, 112, 4834, 4833, 4832, 30])).
% 2.18/2.36 tff(4836,plain,
% 2.18/2.36 (~c1_1(a958)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1698, 4835])).
% 2.18/2.36 tff(4837,plain,
% 2.18/2.36 (~c0_1(a958)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1841, 4835])).
% 2.18/2.36 tff(4838,plain,
% 2.18/2.36 (c2_1(a958)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3857, 112, 4759, 31, 4837, 4836, 20])).
% 2.18/2.36 tff(4839,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4840,plain,
% 2.18/2.36 ((hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958))) <=> (hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4841,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4840])).
% 2.18/2.36 tff(4842,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4841, 4839])).
% 2.18/2.36 tff(4843,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a928) | (~c1_1(a928)) | (~c0_1(a928)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4844,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a928) | (~ndr1_0) | (~c0_1(a928)) | (~c1_1(a928)) | (~c2_1(a958))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4843, 4842])).
% 2.18/2.36 tff(4845,plain,
% 2.18/2.36 ((~c0_1(a928)) | (~c2_1(a958))),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4844, 112, 4759, 4834, 4837, 4836, 4832, 3342])).
% 2.18/2.36 tff(4846,plain,
% 2.18/2.36 (~c0_1(a928)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4845, 4838])).
% 2.18/2.36 tff(4847,assumption,(hskp15), introduced(assumption)).
% 2.18/2.36 tff(4848,plain,
% 2.18/2.36 (~c3_1(a921)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2464, 4847])).
% 2.18/2.36 tff(4849,plain,
% 2.18/2.36 (c1_1(a921)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2472, 4847])).
% 2.18/2.36 tff(4850,plain,
% 2.18/2.36 (c0_1(a921)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2480, 4847])).
% 2.18/2.36 tff(4851,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a958)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4852,plain,
% 2.18/2.36 ((hskp1 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958))) <=> (hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a958)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4853,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a958))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4852])).
% 2.18/2.36 tff(4854,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a958)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4853, 4851])).
% 2.18/2.36 tff(4855,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a921) | (~c1_1(a921)) | (~c0_1(a921)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4856,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | c3_1(a921) | (~ndr1_0) | (~c0_1(a921)) | (~c1_1(a921)) | (~c2_1(a958))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4855, 4854])).
% 2.18/2.36 tff(4857,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4856, 112, 152, 4850, 4849, 4533, 3871, 4848, 3342, 4087])).
% 2.18/2.36 tff(4858,plain,((~hskp15) | hskp1 | c0_1(a958) | c1_1(a958) | (~c2_1(a958))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4859,plain,
% 2.18/2.36 (~hskp15),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4858, 4759, 4837, 4836, 4838])).
% 2.18/2.36 tff(4860,plain,
% 2.18/2.36 (~c3_1(a958)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1692, 4835])).
% 2.18/2.36 tff(4861,plain,
% 2.18/2.36 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | c1_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp29 | hskp15 | c1_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4862,plain,
% 2.18/2.36 ((hskp29 | hskp15 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958))) <=> (hskp29 | hskp15 | c1_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4863,plain,
% 2.18/2.36 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | c1_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4862])).
% 2.18/2.36 tff(4864,plain,
% 2.18/2.36 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp29 | hskp15 | c1_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4863, 4861])).
% 2.18/2.36 tff(4865,plain,
% 2.18/2.36 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4866,plain,
% 2.18/2.36 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp29 | hskp15 | c1_1(a958) | c3_1(a958) | (~ndr1_0) | (~c2_1(a958))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4865, 4864])).
% 2.18/2.36 tff(4867,plain,
% 2.18/2.36 (hskp29 | hskp15),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4866, 112, 4836, 4860, 2448, 4838])).
% 2.18/2.36 tff(4868,plain,
% 2.18/2.36 (hskp29),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4867, 4859])).
% 2.18/2.36 tff(4869,plain,
% 2.18/2.36 (hskp11),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1438, 4868, 4846, 4833, 4834])).
% 2.18/2.36 tff(4870,plain,
% 2.18/2.36 (~c3_1(a912)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1390, 4869])).
% 2.18/2.36 tff(4871,plain,
% 2.18/2.36 (~c2_1(a912)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1679, 4869])).
% 2.18/2.36 tff(4872,plain,
% 2.18/2.36 (~c1_1(a912)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2146, 4869])).
% 2.18/2.36 tff(4873,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[2404, 112, 4767, 4833, 4832, 4872, 4871, 4870, 1310, 4846])).
% 2.18/2.36 tff(4874,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4875,plain,
% 2.18/2.36 (~c2_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[65, 4874])).
% 2.18/2.36 tff(4876,plain,
% 2.18/2.36 (c0_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[73, 4874])).
% 2.18/2.36 tff(4877,plain,
% 2.18/2.36 (c1_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[59, 4874])).
% 2.18/2.36 tff(4878,plain,
% 2.18/2.36 (hskp1 | (~c3_1(a898))),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3578, 4877, 4875, 4876])).
% 2.18/2.36 tff(4879,plain,
% 2.18/2.36 (~c3_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4878, 152])).
% 2.18/2.36 tff(4880,plain,
% 2.18/2.36 (((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))) <=> ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4881,plain,
% 2.18/2.36 ((hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898))) <=> (hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4882,plain,
% 2.18/2.36 (((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4881])).
% 2.18/2.36 tff(4883,plain,
% 2.18/2.36 (((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4882, 4880])).
% 2.18/2.36 tff(4884,plain,
% 2.18/2.36 ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4885,plain,
% 2.18/2.36 ((~![U: $i] : (hskp26 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp17 | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4884, 4883])).
% 2.18/2.36 tff(4886,plain,
% 2.18/2.36 (hskp26 | hskp17 | c3_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4885, 112, 4876, 4877, 4441])).
% 2.18/2.36 tff(4887,plain,
% 2.18/2.36 (hskp26),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4886, 4879, 32])).
% 2.18/2.36 tff(4888,plain,
% 2.18/2.36 (~c2_1(a969)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4463, 4887])).
% 2.18/2.36 tff(4889,plain,
% 2.18/2.36 (~c1_1(a969)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4484, 4887])).
% 2.18/2.36 tff(4890,plain,
% 2.18/2.36 (c0_1(a969)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4471, 4887])).
% 2.18/2.36 tff(4891,plain,
% 2.18/2.36 (hskp31 | hskp1),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3668, 4874])).
% 2.18/2.36 tff(4892,plain,
% 2.18/2.36 (hskp31),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4891, 152])).
% 2.18/2.36 tff(4893,plain,
% 2.18/2.36 (c3_1(a957)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3835, 4892])).
% 2.18/2.36 tff(4894,plain,
% 2.18/2.36 (c2_1(a957)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3843, 4892])).
% 2.18/2.36 tff(4895,plain,
% 2.18/2.36 (c1_1(a957)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[3827, 4892])).
% 2.18/2.36 tff(4896,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a969)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a969)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4897,plain,
% 2.18/2.36 ((hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969))) <=> (hskp1 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a969)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4898,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a969))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4897])).
% 2.18/2.36 tff(4899,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a969)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4898, 4896])).
% 2.18/2.36 tff(4900,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a969) | c1_1(a969) | (~c0_1(a969)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4901,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a969) | c2_1(a969) | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | (~c0_1(a969))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4900, 4899])).
% 2.18/2.36 tff(4902,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4901, 112, 152, 4895, 4894, 4893, 4890, 4889, 4888, 219])).
% 2.18/2.36 tff(4903,plain,(hskp1 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4904,plain,
% 2.18/2.36 (hskp1),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4903, 32])).
% 2.18/2.36 tff(4905,plain,
% 2.18/2.36 (c2_1(a899)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[300, 4904])).
% 2.18/2.36 tff(4906,plain,
% 2.18/2.36 (~c0_1(a899)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[292, 4904])).
% 2.18/2.36 tff(4907,plain,
% 2.18/2.36 (c1_1(a899)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[308, 4904])).
% 2.18/2.36 tff(4908,plain,
% 2.18/2.36 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4909,plain,
% 2.18/2.36 ((hskp10 | hskp7 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898))) <=> (hskp10 | hskp7 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4910,plain,
% 2.18/2.36 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4909])).
% 2.18/2.36 tff(4911,plain,
% 2.18/2.36 (((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)))) <=> ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4910, 4908])).
% 2.18/2.36 tff(4912,plain,
% 2.18/2.36 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp10 | hskp7 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4913,plain,
% 2.18/2.36 ((~![U: $i] : (hskp10 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp10 | hskp7 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4912, 4911])).
% 2.18/2.36 tff(4914,plain,
% 2.18/2.36 (hskp10 | hskp7 | c3_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4913, 112, 4876, 4875, 693])).
% 2.18/2.36 tff(4915,plain,
% 2.18/2.36 (c3_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4914, 547, 50])).
% 2.18/2.36 tff(4916,plain,
% 2.18/2.36 (~c3_1(a899)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4747, 547, 43, 312, 50, 311])).
% 2.18/2.36 tff(4917,plain,
% 2.18/2.36 (hskp4),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[677, 4916, 547])).
% 2.18/2.36 tff(4918,plain,
% 2.18/2.36 (~c3_1(a904)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[536, 4917])).
% 2.18/2.36 tff(4919,plain,
% 2.18/2.36 (~c1_1(a904)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[542, 4917])).
% 2.18/2.36 tff(4920,plain,
% 2.18/2.36 (c2_1(a904)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[605, 4917])).
% 2.18/2.36 tff(4921,plain,
% 2.18/2.36 (hskp21),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[725, 112, 4920, 4876, 4877, 4919, 4918, 4875, 402])).
% 2.18/2.36 tff(4922,plain,
% 2.18/2.36 (hskp14),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[441, 4921, 312, 311, 43])).
% 2.18/2.36 tff(4923,plain,
% 2.18/2.36 (~c1_1(a918)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[672, 4922])).
% 2.18/2.36 tff(4924,plain,
% 2.18/2.36 (hskp18),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[765, 4923, 4921, 311, 312, 43])).
% 2.18/2.36 tff(4925,plain,
% 2.18/2.36 (~c1_1(a929)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[771, 4924])).
% 2.18/2.36 tff(4926,plain,
% 2.18/2.36 (~c3_1(a938)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[416, 4921])).
% 2.18/2.36 tff(4927,plain,
% 2.18/2.36 (~c2_1(a938)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[422, 4921])).
% 2.18/2.36 tff(4928,plain,
% 2.18/2.36 (c2_1(a929)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[781, 4924])).
% 2.18/2.36 tff(4929,plain,
% 2.18/2.36 (c0_1(a929)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[789, 4924])).
% 2.18/2.36 tff(4930,plain,
% 2.18/2.36 (c0_1(a938)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[430, 4921])).
% 2.18/2.36 tff(4931,plain,
% 2.18/2.36 ($false),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[797, 112, 4930, 4929, 4928, 4877, 4927, 4926, 4925, 4875, 131, 4915])).
% 2.18/2.36 tff(4932,plain,(hskp7 | (~c1_1(a899)) | (~c2_1(a899)) | c0_1(a899) | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.18/2.36 tff(4933,plain,
% 2.18/2.36 (hskp7),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4932, 50, 4905, 4906, 4907])).
% 2.18/2.36 tff(4934,plain,
% 2.18/2.36 (~c0_1(a907)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4676, 4933])).
% 2.18/2.36 tff(4935,plain,
% 2.18/2.36 (~c1_1(a907)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4222, 4933])).
% 2.18/2.36 tff(4936,plain,
% 2.18/2.36 (c3_1(a907)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[512, 4933])).
% 2.18/2.36 tff(4937,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c0_1(a899) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c0_1(a899) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4938,plain,
% 2.18/2.36 ((hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp14 | c0_1(a899) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.18/2.36 inference(rewrite,[status(thm)],[])).
% 2.18/2.36 tff(4939,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c0_1(a899) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c2_1(a899)) | (~c1_1(a899))))),
% 2.18/2.36 inference(monotonicity,[status(thm)],[4938])).
% 2.18/2.36 tff(4940,plain,
% 2.18/2.36 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c0_1(a899) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.18/2.36 inference(transitivity,[status(thm)],[4939, 4937])).
% 2.18/2.36 tff(4941,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.18/2.36 inference(quant_inst,[status(thm)],[])).
% 2.18/2.36 tff(4942,plain,
% 2.18/2.36 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c0_1(a899) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c2_1(a899)) | (~c1_1(a899))),
% 2.18/2.36 inference(modus_ponens,[status(thm)],[4941, 4940])).
% 2.18/2.36 tff(4943,plain,
% 2.18/2.36 (hskp14 | c3_1(a898)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4942, 112, 4907, 4905, 4876, 4906, 4875, 373])).
% 2.18/2.36 tff(4944,plain,
% 2.18/2.36 (hskp14),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4943, 75])).
% 2.18/2.36 tff(4945,plain,
% 2.18/2.36 (~c1_1(a918)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[672, 4944])).
% 2.18/2.36 tff(4946,plain,
% 2.18/2.36 (c3_1(a918)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[742, 4944])).
% 2.18/2.36 tff(4947,plain,
% 2.18/2.36 (c0_1(a918)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[734, 4944])).
% 2.18/2.36 tff(4948,plain,
% 2.18/2.36 (c2_1(a907)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[1343, 112, 4947, 4946, 2207, 4876, 4877, 4945, 44, 4875, 271])).
% 2.18/2.36 tff(4949,plain,
% 2.18/2.36 (hskp26),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4886, 75, 32])).
% 2.18/2.36 tff(4950,plain,
% 2.18/2.36 (~c2_1(a969)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4463, 4949])).
% 2.18/2.36 tff(4951,plain,
% 2.18/2.36 (~c1_1(a969)),
% 2.18/2.36 inference(unit_resolution,[status(thm)],[4484, 4949])).
% 2.18/2.36 tff(4952,plain,
% 2.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a969) | c2_1(a969) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c3_1(a969)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a969) | c2_1(a969) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c3_1(a969)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(4953,plain,
% 2.18/2.37 (((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907))) <=> (c1_1(a969) | c2_1(a969) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c3_1(a969)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(4954,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a969) | c2_1(a969) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c3_1(a969))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[4953])).
% 2.18/2.37 tff(4955,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a969) | c2_1(a969) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c3_1(a969)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[4954, 4952])).
% 2.18/2.37 tff(4956,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a907) | (~c3_1(a907)) | (~c2_1(a907)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(4957,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a969) | c2_1(a969) | c0_1(a907) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a907)) | (~c3_1(a907)) | (~c3_1(a969))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[4956, 4955])).
% 2.18/2.37 tff(4958,plain,
% 2.18/2.37 (~c3_1(a969)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4957, 112, 2207, 4877, 4951, 4950, 44, 4875, 1384, 4948, 75])).
% 2.18/2.37 tff(4959,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c1_1(a918) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c0_1(a918)) | (~c3_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c1_1(a918) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(4960,plain,
% 2.18/2.37 ((hskp18 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918))) <=> (hskp18 | c1_1(a918) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(4961,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c1_1(a918) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c0_1(a918)) | (~c3_1(a918))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[4960])).
% 2.18/2.37 tff(4962,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c1_1(a918) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c0_1(a918)) | (~c3_1(a918)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[4961, 4959])).
% 2.18/2.37 tff(4963,plain,
% 2.18/2.37 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c1_1(a918) | (~c3_1(a918)) | (~c0_1(a918)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(4964,plain,
% 2.18/2.37 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c1_1(a918) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c0_1(a918)) | (~c3_1(a918))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[4963, 4962])).
% 2.18/2.37 tff(4965,plain,
% 2.18/2.37 (hskp18),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4964, 112, 4947, 4946, 4876, 4945, 4875, 753, 75])).
% 2.18/2.37 tff(4966,plain,
% 2.18/2.37 (~c1_1(a929)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[771, 4965])).
% 2.18/2.37 tff(4967,plain,
% 2.18/2.37 (hskp24 | (~c2_1(a907))),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2272, 112, 32, 2207, 45, 1169])).
% 2.18/2.37 tff(4968,plain,
% 2.18/2.37 (hskp24),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4967, 4948])).
% 2.18/2.37 tff(4969,plain,
% 2.18/2.37 (~c2_1(a953)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1209, 4968])).
% 2.18/2.37 tff(4970,plain,
% 2.18/2.37 (c2_1(a929)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[781, 4965])).
% 2.18/2.37 tff(4971,plain,
% 2.18/2.37 (c0_1(a929)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[789, 4965])).
% 2.18/2.37 tff(4972,plain,
% 2.18/2.37 (c3_1(a953)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1188, 4968])).
% 2.18/2.37 tff(4973,plain,
% 2.18/2.37 (c1_1(a953)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1196, 4968])).
% 2.18/2.37 tff(4974,plain,
% 2.18/2.37 (c0_1(a969)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4471, 4949])).
% 2.18/2.37 tff(4975,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a969) | c2_1(a953) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | (~c0_1(a969)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a969) | c2_1(a953) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | (~c0_1(a969)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(4976,plain,
% 2.18/2.37 (((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | c2_1(a969) | (~c0_1(a969)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929))) <=> (c2_1(a969) | c2_1(a953) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | (~c0_1(a969)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(4977,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | c2_1(a969) | (~c0_1(a969)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a969) | c2_1(a953) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | (~c0_1(a969))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[4976])).
% 2.18/2.37 tff(4978,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | c2_1(a969) | (~c0_1(a969)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a969) | c2_1(a953) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | (~c0_1(a969)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[4977, 4975])).
% 2.18/2.37 tff(4979,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a953) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | c2_1(a969) | (~c0_1(a969)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(4980,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a969) | c2_1(a953) | c1_1(a929) | (~ndr1_0) | (~c2_1(a929)) | (~c0_1(a929)) | (~c1_1(a953)) | (~c3_1(a953)) | c3_1(a969) | (~c0_1(a969))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[4979, 4978])).
% 2.18/2.37 tff(4981,plain,
% 2.18/2.37 ($false),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4980, 112, 4974, 4973, 4972, 4971, 4970, 4950, 4969, 4966, 131, 4958])).
% 2.18/2.37 tff(4982,plain,(c3_1(a898) | hskp17 | (~c3_1(a907)) | c1_1(a907) | c0_1(a907)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.37 tff(4983,plain,
% 2.18/2.37 (c3_1(a898)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4982, 4936, 32, 4935, 4934])).
% 2.18/2.37 tff(4984,plain,
% 2.18/2.37 (hskp9 | (~c3_1(a898))),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[3597, 112, 4907, 4905, 4876, 4877, 4906, 3591])).
% 2.18/2.37 tff(4985,plain,
% 2.18/2.37 (hskp9),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4984, 4983])).
% 2.18/2.37 tff(4986,plain,
% 2.18/2.37 (~c2_1(a909)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1323, 4985])).
% 2.18/2.37 tff(4987,plain,
% 2.18/2.37 (~c1_1(a909)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1329, 4985])).
% 2.18/2.37 tff(4988,plain,
% 2.18/2.37 (hskp4 | hskp10 | (~c1_1(a899)) | c0_1(a899) | c0_1(a907) | c1_1(a907) | (~c3_1(a898))),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[715, 4877, 4875, 4876])).
% 2.18/2.37 tff(4989,plain,
% 2.18/2.37 (hskp4),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4988, 4983, 50, 4907, 4906, 4934, 4935])).
% 2.18/2.37 tff(4990,plain,
% 2.18/2.37 (~c3_1(a904)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[536, 4989])).
% 2.18/2.37 tff(4991,plain,
% 2.18/2.37 (~c1_1(a904)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[542, 4989])).
% 2.18/2.37 tff(4992,plain,
% 2.18/2.37 (c2_1(a904)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[605, 4989])).
% 2.18/2.37 tff(4993,plain,
% 2.18/2.37 (c2_1(a907)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[664, 112, 4936, 4992, 4877, 4934, 4991, 4990, 4875, 503, 4983])).
% 2.18/2.37 tff(4994,plain,
% 2.18/2.37 (hskp28 | (~c3_1(a898)) | (~c2_1(a907))),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1351, 112, 4936, 4876, 4877, 4935, 935])).
% 2.18/2.37 tff(4995,plain,
% 2.18/2.37 (hskp28),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4994, 4993, 4983])).
% 2.18/2.37 tff(4996,plain,
% 2.18/2.37 (c0_1(a900)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[965, 4995])).
% 2.18/2.37 tff(4997,plain,
% 2.18/2.37 (~c0_1(a909)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1335, 4985])).
% 2.18/2.37 tff(4998,plain,
% 2.18/2.37 (c2_1(a900)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[957, 4995])).
% 2.18/2.37 tff(4999,plain,
% 2.18/2.37 (c3_1(a900)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[949, 4995])).
% 2.18/2.37 tff(5000,plain,
% 2.18/2.37 ($false),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2050, 4999, 4998, 4989, 4997, 4996, 4987, 4986])).
% 2.18/2.37 tff(5001,plain,(hskp10 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.18/2.37 tff(5002,plain,
% 2.18/2.37 (hskp10),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5001, 32])).
% 2.18/2.37 tff(5003,plain,
% 2.18/2.37 (~c2_1(a910)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2348, 5002])).
% 2.18/2.37 tff(5004,plain,
% 2.18/2.37 (c1_1(a910)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2362, 5002])).
% 2.18/2.37 tff(5005,plain,
% 2.18/2.37 (~c0_1(a910)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2354, 5002])).
% 2.18/2.37 tff(5006,plain,
% 2.18/2.37 (hskp11 | (~c3_1(a898))),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2812, 112, 2366, 4876, 4877, 2365, 2364, 1402])).
% 2.18/2.37 tff(5007,plain,
% 2.18/2.37 (~c3_1(a898)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5006, 1430])).
% 2.18/2.37 tff(5008,plain,
% 2.18/2.37 (~hskp29),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[3435, 1430, 2365, 2366, 2364])).
% 2.18/2.37 tff(5009,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5010,plain,
% 2.18/2.37 ((hskp29 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910))) <=> (hskp29 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5011,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[5010])).
% 2.18/2.37 tff(5012,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[5011, 5009])).
% 2.18/2.37 tff(5013,plain,
% 2.18/2.37 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(5014,plain,
% 2.18/2.37 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a910) | c2_1(a910) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a910))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[5013, 5012])).
% 2.18/2.37 tff(5015,plain,
% 2.18/2.37 ($false),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5014, 112, 5008, 2366, 4876, 4877, 2365, 2364, 2438, 5007])).
% 2.18/2.37 tff(5016,plain,(hskp11 | (~c1_1(a910)) | c0_1(a910) | c2_1(a910)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.37 tff(5017,plain,
% 2.18/2.37 (hskp11),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5016, 5004, 5005, 5003])).
% 2.18/2.37 tff(5018,assumption,(hskp11), introduced(assumption)).
% 2.18/2.37 tff(5019,plain,
% 2.18/2.37 (~c3_1(a912)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1390, 5018])).
% 2.18/2.37 tff(5020,plain,
% 2.18/2.37 (~c1_1(a912)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2146, 5018])).
% 2.18/2.37 tff(5021,plain,
% 2.18/2.37 (~c2_1(a912)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1679, 5018])).
% 2.18/2.37 tff(5022,plain,
% 2.18/2.37 ($false),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4562, 5021, 5020, 2365, 314, 5019, 2366, 2364, 43, 312])).
% 2.18/2.37 tff(5023,plain,((~hskp11) | c0_1(a910) | (~c3_1(a899)) | (~c1_1(a910)) | c2_1(a910) | c0_1(a899) | (~c2_1(a899))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.37 tff(5024,plain,
% 2.18/2.37 (~c3_1(a899)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5023, 5017, 5005, 5004, 5003, 4906, 4905])).
% 2.18/2.37 tff(5025,plain,
% 2.18/2.37 (hskp7 | hskp4 | c3_1(a899)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[529, 112, 4907, 4906, 523])).
% 2.18/2.37 tff(5026,plain,
% 2.18/2.37 (hskp4),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5025, 504, 547])).
% 2.18/2.37 tff(5027,plain,
% 2.18/2.37 (~c1_1(a904)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[542, 5026])).
% 2.18/2.37 tff(5028,plain,
% 2.18/2.37 (~c3_1(a904)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[536, 5026])).
% 2.18/2.37 tff(5029,plain,
% 2.18/2.37 (c2_1(a904)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[605, 5026])).
% 2.18/2.37 tff(5030,plain,
% 2.18/2.37 (hskp12),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2538, 5029, 5004, 5028, 5027, 5005, 5003])).
% 2.18/2.37 tff(5031,plain,
% 2.18/2.37 (~c1_1(a913)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[409, 5030])).
% 2.18/2.37 tff(5032,plain,
% 2.18/2.37 (~c3_1(a913)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[347, 5030])).
% 2.18/2.37 tff(5033,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a910) | c2_1(a910) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a910)) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a910) | c2_1(a910) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5034,plain,
% 2.18/2.37 (((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910))) <=> (c0_1(a910) | c2_1(a910) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5035,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a910) | c2_1(a910) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a910)) | (~c3_1(a910))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[5034])).
% 2.18/2.37 tff(5036,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a910) | c2_1(a910) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a910)) | (~c3_1(a910)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[5035, 5033])).
% 2.18/2.37 tff(5037,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a910) | (~c1_1(a910)) | (~c3_1(a910)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c0_1(a910) | c2_1(a910) | (~c3_1(a910)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(5038,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a910) | c2_1(a910) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c1_1(a910)) | (~c3_1(a910))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[5037, 5036])).
% 2.18/2.37 tff(5039,plain,
% 2.18/2.37 (~c3_1(a910)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5038, 112, 5004, 5029, 5005, 5003, 5027, 5028, 503])).
% 2.18/2.37 tff(5040,plain,
% 2.18/2.37 (c3_1(a910) | hskp31 | (~c1_1(a910)) | c2_1(a910)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[2801, 4876, 4875, 4877])).
% 2.18/2.37 tff(5041,plain,
% 2.18/2.37 (hskp31),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5040, 5039, 5003, 5004])).
% 2.18/2.37 tff(5042,plain,
% 2.18/2.37 (c2_1(a957)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[3843, 5041])).
% 2.18/2.37 tff(5043,plain,
% 2.18/2.37 (c0_1(a913)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[355, 5030])).
% 2.18/2.37 tff(5044,plain,
% 2.18/2.37 (~c2_1(a913)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[710, 112, 547, 5043, 4876, 4877, 5031, 4875, 576])).
% 2.18/2.37 tff(5045,plain,
% 2.18/2.37 (c3_1(a957)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[3835, 5041])).
% 2.18/2.37 tff(5046,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c1_1(a910)) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c1_1(a910)) | c2_1(a913))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5047,plain,
% 2.18/2.37 (((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913)) <=> (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c1_1(a910)) | c2_1(a913))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5048,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c1_1(a910)) | c2_1(a913)))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[5047])).
% 2.18/2.37 tff(5049,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c1_1(a910)) | c2_1(a913))),
% 2.18/2.37 inference(transitivity,[status(thm)],[5048, 5046])).
% 2.18/2.37 tff(5050,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c2_1(a910) | c0_1(a910) | (~c1_1(a910)) | c3_1(a913) | c1_1(a913) | c2_1(a913))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(5051,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~ndr1_0) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c1_1(a910)) | c2_1(a913)),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[5050, 5049])).
% 2.18/2.37 tff(5052,plain,
% 2.18/2.37 ($false),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5051, 432, 3873, 3872, 2366, 704, 694, 2365, 2364, 1721, 3869, 1073])).
% 2.18/2.37 tff(5053,plain,(c0_1(a957) | (~ndr1_0) | (~c2_1(a957)) | (~c3_1(a957)) | (~c1_1(a910)) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c2_1(a913)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.37 tff(5054,plain,
% 2.18/2.37 (c0_1(a957) | (~c2_1(a957)) | (~c3_1(a957)) | (~c1_1(a910)) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | c2_1(a913)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5053, 112])).
% 2.18/2.37 tff(5055,plain,
% 2.18/2.37 (c0_1(a957)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5054, 5045, 5004, 5044, 5042, 5005, 5032, 5031, 5003])).
% 2.18/2.37 tff(5056,plain,
% 2.18/2.37 (c1_1(a957)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[3827, 5041])).
% 2.18/2.37 tff(5057,assumption,(~hskp9), introduced(assumption)).
% 2.18/2.37 tff(5058,plain,
% 2.18/2.37 (~c3_1(a898)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4984, 5057])).
% 2.18/2.37 tff(5059,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5060,plain,
% 2.18/2.37 ((hskp9 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899))) <=> (hskp9 | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5061,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[5060])).
% 2.18/2.37 tff(5062,plain,
% 2.18/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[5061, 5059])).
% 2.18/2.37 tff(5063,plain,
% 2.18/2.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c1_1(a957)) | (~c3_1(a957)) | (~c0_1(a957)) | c0_1(a899) | (~c2_1(a899)) | (~c1_1(a899)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(5064,plain,
% 2.18/2.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp9 | c0_1(a899) | (~ndr1_0) | (~c2_1(a899)) | (~c1_1(a899)) | (~c0_1(a957)) | (~c1_1(a957)) | (~c3_1(a957))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[5063, 5062])).
% 2.18/2.37 tff(5065,plain,
% 2.18/2.37 (hskp9 | (~c0_1(a957))),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5064, 112, 3956, 3872, 4907, 4905, 4906, 3591])).
% 2.18/2.37 tff(5066,plain,
% 2.18/2.37 (~c0_1(a957)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5065, 5057])).
% 2.18/2.37 tff(5067,plain,
% 2.18/2.37 (hskp26),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4886, 5058, 32])).
% 2.18/2.37 tff(5068,plain,
% 2.18/2.37 (~c2_1(a969)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4463, 5067])).
% 2.18/2.37 tff(5069,plain,
% 2.18/2.37 (~c1_1(a969)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[4484, 5067])).
% 2.18/2.37 tff(5070,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a969) | c2_1(a969) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c3_1(a969)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a969) | c2_1(a969) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c3_1(a969)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5071,plain,
% 2.18/2.37 (((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957))) <=> (c1_1(a969) | c2_1(a969) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c3_1(a969)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5072,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a969) | c2_1(a969) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c3_1(a969))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[5071])).
% 2.18/2.37 tff(5073,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a969) | c2_1(a969) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c3_1(a969)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[5072, 5070])).
% 2.18/2.37 tff(5074,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)) | c2_1(a969) | c1_1(a969) | (~c3_1(a969)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(5075,plain,
% 2.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a969) | c2_1(a969) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c3_1(a969))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[5074, 5073])).
% 2.18/2.37 tff(5076,plain,
% 2.18/2.37 (~c3_1(a969)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5075, 112, 3873, 3872, 4877, 5069, 5068, 4875, 1384, 5066, 5058])).
% 2.18/2.37 tff(5077,plain,
% 2.18/2.37 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5078,plain,
% 2.18/2.37 ((hskp25 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898))) <=> (hskp25 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)))),
% 2.18/2.37 inference(rewrite,[status(thm)],[])).
% 2.18/2.37 tff(5079,plain,
% 2.18/2.37 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898))))),
% 2.18/2.37 inference(monotonicity,[status(thm)],[5078])).
% 2.18/2.37 tff(5080,plain,
% 2.18/2.37 (((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)))),
% 2.18/2.37 inference(transitivity,[status(thm)],[5079, 5077])).
% 2.18/2.37 tff(5081,plain,
% 2.18/2.37 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c1_1(a898)))),
% 2.18/2.37 inference(quant_inst,[status(thm)],[])).
% 2.18/2.37 tff(5082,plain,
% 2.18/2.37 ((~![U: $i] : (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c1_1(a898))),
% 2.18/2.37 inference(modus_ponens,[status(thm)],[5081, 5080])).
% 2.18/2.37 tff(5083,plain,
% 2.18/2.37 (hskp25 | c3_1(a898)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5082, 112, 4877, 4875, 30])).
% 2.18/2.37 tff(5084,plain,
% 2.18/2.37 (hskp25),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[5083, 5058])).
% 2.18/2.37 tff(5085,plain,
% 2.18/2.37 (~c3_1(a958)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1692, 5084])).
% 2.18/2.37 tff(5086,plain,
% 2.18/2.37 (~c1_1(a958)),
% 2.18/2.37 inference(unit_resolution,[status(thm)],[1698, 5084])).
% 2.18/2.37 tff(5087,plain,
% 2.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a958)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a958)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5088,plain,
% 2.18/2.38 (((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899))) <=> (c1_1(a958) | c3_1(a958) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a958)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5089,plain,
% 2.18/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a958) | c3_1(a958) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a958))))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5088])).
% 2.18/2.38 tff(5090,plain,
% 2.18/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a958)))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5089, 5087])).
% 2.18/2.38 tff(5091,plain,
% 2.18/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a958) | c3_1(a958) | (~c2_1(a958)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a957)) | c3_1(a899) | c0_1(a899) | (~c1_1(a899)))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5092,plain,
% 2.18/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a958) | c3_1(a958) | c0_1(a899) | (~ndr1_0) | c3_1(a899) | (~c1_1(a899)) | (~c2_1(a957)) | c0_1(a957) | (~c3_1(a957)) | (~c2_1(a958))),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5091, 5090])).
% 2.18/2.38 tff(5093,plain,
% 2.18/2.38 (~c2_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5092, 112, 3873, 3872, 4907, 5086, 5085, 4906, 392, 504, 5066])).
% 2.18/2.38 tff(5094,plain,
% 2.18/2.38 (~c0_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1841, 5084])).
% 2.18/2.38 tff(5095,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c1_1(a969) | c2_1(a969) | c0_1(a958) | c3_1(a958) | (~ndr1_0) | c2_1(a958) | c3_1(a969))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c1_1(a969) | c2_1(a969) | c0_1(a958) | c3_1(a958) | (~ndr1_0) | c2_1(a958) | c3_1(a969))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5096,plain,
% 2.18/2.38 ((hskp9 | (~ndr1_0) | c2_1(a969) | c1_1(a969) | c3_1(a969) | c3_1(a958) | c2_1(a958) | c0_1(a958)) <=> (hskp9 | c1_1(a969) | c2_1(a969) | c0_1(a958) | c3_1(a958) | (~ndr1_0) | c2_1(a958) | c3_1(a969))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5097,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a969) | c1_1(a969) | c3_1(a969) | c3_1(a958) | c2_1(a958) | c0_1(a958))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c1_1(a969) | c2_1(a969) | c0_1(a958) | c3_1(a958) | (~ndr1_0) | c2_1(a958) | c3_1(a969)))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5096])).
% 2.18/2.38 tff(5098,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a969) | c1_1(a969) | c3_1(a969) | c3_1(a958) | c2_1(a958) | c0_1(a958))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c1_1(a969) | c2_1(a969) | c0_1(a958) | c3_1(a958) | (~ndr1_0) | c2_1(a958) | c3_1(a969))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5097, 5095])).
% 2.18/2.38 tff(5099,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a969) | c1_1(a969) | c3_1(a969) | c3_1(a958) | c2_1(a958) | c0_1(a958))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5100,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c1_1(a969) | c2_1(a969) | c0_1(a958) | c3_1(a958) | (~ndr1_0) | c2_1(a958) | c3_1(a969)),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5099, 5098])).
% 2.18/2.38 tff(5101,plain,
% 2.18/2.38 ($false),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5100, 112, 5057, 5069, 5068, 5094, 5085, 1310, 5093, 5076])).
% 2.18/2.38 tff(5102,plain,(hskp9 | (~c2_1(a957)) | (~c3_1(a957)) | c3_1(a899) | hskp17 | (~c1_1(a957))), inference(lemma,lemma(discharge,[]))).
% 2.18/2.38 tff(5103,plain,
% 2.18/2.38 (hskp9),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5102, 5045, 504, 5042, 32, 5056])).
% 2.18/2.38 tff(5104,plain,
% 2.18/2.38 (~c2_1(a909)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1323, 5103])).
% 2.18/2.38 tff(5105,plain,
% 2.18/2.38 (~c1_1(a909)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1329, 5103])).
% 2.18/2.38 tff(5106,plain,
% 2.18/2.38 (~c0_1(a909)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1335, 5103])).
% 2.18/2.38 tff(5107,plain,
% 2.18/2.38 (hskp25 | c3_1(a910)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3494, 112, 5004, 5003, 30])).
% 2.18/2.38 tff(5108,plain,
% 2.18/2.38 (hskp25),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5107, 5039])).
% 2.18/2.38 tff(5109,plain,
% 2.18/2.38 (~c3_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1692, 5108])).
% 2.18/2.38 tff(5110,plain,
% 2.18/2.38 (~c1_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1698, 5108])).
% 2.18/2.38 tff(5111,plain,
% 2.18/2.38 (~c2_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3977, 112, 5042, 5045, 5110, 5109, 5106, 5105, 5104, 870, 5055])).
% 2.18/2.38 tff(5112,plain,
% 2.18/2.38 (~c0_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1841, 5108])).
% 2.18/2.38 tff(5113,plain,
% 2.18/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a958) | c1_1(a958) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a958) | c1_1(a958) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a958))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5114,plain,
% 2.18/2.38 (((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a958) | c0_1(a958) | c2_1(a958)) <=> (c0_1(a958) | c1_1(a958) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a958))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5115,plain,
% 2.18/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a958) | c0_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a958) | c1_1(a958) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a958)))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5114])).
% 2.18/2.38 tff(5116,plain,
% 2.18/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a958) | c0_1(a958) | c2_1(a958))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a958) | c1_1(a958) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a958))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5115, 5113])).
% 2.18/2.38 tff(5117,plain,
% 2.18/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a904) | c1_1(a904) | (~c2_1(a904)) | c1_1(a958) | c0_1(a958) | c2_1(a958))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5118,plain,
% 2.18/2.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a958) | c1_1(a958) | c1_1(a904) | c3_1(a904) | (~ndr1_0) | (~c2_1(a904)) | (~c0_1(a957)) | (~c2_1(a957)) | (~c3_1(a957)) | c2_1(a958)),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5117, 5116])).
% 2.18/2.38 tff(5119,plain,
% 2.18/2.38 ($false),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5118, 112, 5042, 5045, 5029, 5112, 5110, 5027, 5028, 870, 5055, 5111])).
% 2.18/2.38 tff(5120,plain,(c3_1(a899) | hskp17 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.18/2.38 tff(5121,plain,
% 2.18/2.38 (hskp7),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5120, 5024, 32])).
% 2.18/2.38 tff(5122,plain,
% 2.18/2.38 (~c0_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4676, 5121])).
% 2.18/2.38 tff(5123,plain,
% 2.18/2.38 (~c3_1(a912)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1390, 5017])).
% 2.18/2.38 tff(5124,plain,
% 2.18/2.38 (~c2_1(a912)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1679, 5017])).
% 2.18/2.38 tff(5125,plain,
% 2.18/2.38 (~c1_1(a912)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[2146, 5017])).
% 2.18/2.38 tff(5126,plain,
% 2.18/2.38 (c3_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[512, 5121])).
% 2.18/2.38 tff(5127,plain,
% 2.18/2.38 (~c2_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[2899, 112, 5004, 5126, 5125, 5124, 5123, 5005, 5003, 5122, 1721])).
% 2.18/2.38 tff(5128,plain,
% 2.18/2.38 (~c1_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4222, 5121])).
% 2.18/2.38 tff(5129,plain,
% 2.18/2.38 (hskp0),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3819, 45, 44, 46])).
% 2.18/2.38 tff(5130,plain,
% 2.18/2.38 (c1_1(a898)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[59, 5129])).
% 2.18/2.38 tff(5131,plain,
% 2.18/2.38 (c0_1(a898)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[73, 5129])).
% 2.18/2.38 tff(5132,plain,
% 2.18/2.38 (~c2_1(a898)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[65, 5129])).
% 2.18/2.38 tff(5133,plain,
% 2.18/2.38 (c3_1(a898)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[120, 5132, 5131, 5130, 46])).
% 2.18/2.38 tff(5134,plain,
% 2.18/2.38 (hskp1),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3668, 5129, 46])).
% 2.18/2.38 tff(5135,plain,
% 2.18/2.38 (~c0_1(a899)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[292, 5134])).
% 2.18/2.38 tff(5136,plain,
% 2.18/2.38 (c2_1(a899)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[300, 5134])).
% 2.18/2.38 tff(5137,plain,
% 2.18/2.38 (c1_1(a899)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[308, 5134])).
% 2.18/2.38 tff(5138,plain,
% 2.18/2.38 (hskp9),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3597, 112, 5137, 5136, 5131, 5130, 5135, 3591, 5133])).
% 2.18/2.38 tff(5139,plain,
% 2.18/2.38 (~c2_1(a909)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1323, 5138])).
% 2.18/2.38 tff(5140,plain,
% 2.18/2.38 (~c1_1(a909)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1329, 5138])).
% 2.18/2.38 tff(5141,plain,
% 2.18/2.38 (c3_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3636, 5135, 45, 5131, 5132, 5130, 46, 44, 3744])).
% 2.18/2.38 tff(5142,plain,
% 2.18/2.38 (hskp4),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[646, 112, 5141, 5131, 44, 45, 5132, 640, 5133])).
% 2.18/2.38 tff(5143,plain,
% 2.18/2.38 (~c3_1(a904)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[536, 5142])).
% 2.18/2.38 tff(5144,plain,
% 2.18/2.38 (~c1_1(a904)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[542, 5142])).
% 2.18/2.38 tff(5145,plain,
% 2.18/2.38 (~c0_1(a909)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1335, 5138])).
% 2.18/2.38 tff(5146,plain,
% 2.18/2.38 (c2_1(a904)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[605, 5142])).
% 2.18/2.38 tff(5147,plain,
% 2.18/2.38 (~c3_1(a909)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3649, 112, 5146, 5130, 5145, 5139, 5144, 5143, 5132, 503, 5133])).
% 2.18/2.38 tff(5148,plain,
% 2.18/2.38 (hskp28),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3656, 112, 3744, 5145, 5140, 2680, 5147])).
% 2.18/2.38 tff(5149,plain,
% 2.18/2.38 (c0_1(a900)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[965, 5148])).
% 2.18/2.38 tff(5150,plain,
% 2.18/2.38 (c2_1(a900)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[957, 5148])).
% 2.18/2.38 tff(5151,plain,
% 2.18/2.38 (c3_1(a900)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[949, 5148])).
% 2.18/2.38 tff(5152,plain,
% 2.18/2.38 ($false),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[2050, 5151, 5150, 5142, 5145, 5149, 5140, 5139])).
% 2.18/2.38 tff(5153,plain,(c1_1(a907) | c0_1(a907) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.18/2.38 tff(5154,plain,
% 2.18/2.38 (hskp31),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5153, 5128, 5122])).
% 2.18/2.38 tff(5155,plain,
% 2.18/2.38 (c1_1(a957)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3827, 5154])).
% 2.18/2.38 tff(5156,plain,
% 2.18/2.38 (c2_1(a957)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3843, 5154])).
% 2.18/2.38 tff(5157,plain,
% 2.18/2.38 (c3_1(a898)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4982, 5128, 32, 5126, 5122])).
% 2.18/2.38 tff(5158,plain,
% 2.18/2.38 (hskp4),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[646, 112, 5126, 4876, 5122, 5128, 4875, 640, 5157])).
% 2.18/2.38 tff(5159,plain,
% 2.18/2.38 (~c1_1(a904)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[542, 5158])).
% 2.18/2.38 tff(5160,plain,
% 2.18/2.38 (~c3_1(a904)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[536, 5158])).
% 2.18/2.38 tff(5161,plain,
% 2.18/2.38 (c2_1(a904)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[605, 5158])).
% 2.18/2.38 tff(5162,plain,
% 2.18/2.38 (hskp12),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[2538, 5161, 5004, 5160, 5159, 5005, 5003])).
% 2.18/2.38 tff(5163,plain,
% 2.18/2.38 (~c3_1(a913)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[347, 5162])).
% 2.18/2.38 tff(5164,plain,
% 2.18/2.38 (c3_1(a957)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3835, 5154])).
% 2.18/2.38 tff(5165,plain,
% 2.18/2.38 (~c1_1(a913)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[409, 5162])).
% 2.18/2.38 tff(5166,assumption,(~hskp21), introduced(assumption)).
% 2.18/2.38 tff(5167,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c2_1(a957)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c2_1(a957)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5168,plain,
% 2.18/2.38 ((hskp21 | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a912) | c2_1(a912) | c1_1(a912)) <=> (hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c2_1(a957)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5169,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c2_1(a957))))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5168])).
% 2.18/2.38 tff(5170,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a912) | c2_1(a912) | c1_1(a912))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c2_1(a957)))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5169, 5167])).
% 2.18/2.38 tff(5171,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp21 | (~ndr1_0) | (~c1_1(a957)) | (~c2_1(a957)) | (~c0_1(a957)) | c3_1(a912) | c2_1(a912) | c1_1(a912))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5172,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp21 | c1_1(a912) | c2_1(a912) | c3_1(a912) | (~ndr1_0) | (~c0_1(a957)) | (~c1_1(a957)) | (~c2_1(a957))),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5171, 5170])).
% 2.18/2.38 tff(5173,plain,
% 2.18/2.38 (hskp21 | c1_1(a912) | c2_1(a912) | (~c0_1(a957))),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5172, 432, 3956, 3873, 813, 2552])).
% 2.18/2.38 tff(5174,plain,
% 2.18/2.38 (~c0_1(a957)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5173, 5166, 802, 801])).
% 2.18/2.38 tff(5175,plain,
% 2.18/2.38 (hskp21 | c1_1(a913) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a913))),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[448, 432, 694, 76, 402])).
% 2.18/2.38 tff(5176,plain,
% 2.18/2.38 (~c2_1(a913)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5175, 5166, 77, 704, 78])).
% 2.18/2.38 tff(5177,plain,
% 2.18/2.38 ($false),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5053, 5176, 5174, 3873, 3872, 432, 704, 694, 2365, 2364, 2366])).
% 2.18/2.38 tff(5178,plain,(hskp21 | (~c2_1(a957)) | (~c3_1(a957)) | (~ndr1_0) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~c1_1(a910)) | (~c1_1(a898)) | (~c0_1(a898)) | c2_1(a898) | c2_1(a912) | c1_1(a912) | (~c1_1(a957)) | c3_1(a912)), inference(lemma,lemma(discharge,[]))).
% 2.18/2.38 tff(5179,plain,
% 2.18/2.38 (hskp21 | (~c2_1(a957)) | (~c3_1(a957)) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~c1_1(a910)) | (~c1_1(a898)) | (~c0_1(a898)) | c2_1(a898) | c2_1(a912) | c1_1(a912) | (~c1_1(a957)) | c3_1(a912)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5178, 112])).
% 2.18/2.38 tff(5180,plain,
% 2.18/2.38 (hskp21 | (~c2_1(a957)) | (~c3_1(a957)) | c1_1(a913) | c3_1(a913) | c0_1(a910) | c2_1(a910) | (~c1_1(a910)) | c2_1(a912) | c1_1(a912) | (~c1_1(a957)) | c3_1(a912)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5179, 4876, 4877, 4875])).
% 2.18/2.38 tff(5181,plain,
% 2.18/2.38 (hskp21),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5180, 5165, 5005, 5004, 5164, 5003, 5163, 5156, 5124, 5125, 5155, 5123])).
% 2.18/2.38 tff(5182,plain,
% 2.18/2.38 (~c3_1(a910)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3510, 5181, 4906, 4907, 5004, 4905, 5003])).
% 2.18/2.38 tff(5183,plain,
% 2.18/2.38 (hskp25),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5107, 5182])).
% 2.18/2.38 tff(5184,plain,
% 2.18/2.38 (~c3_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1692, 5183])).
% 2.18/2.38 tff(5185,plain,
% 2.18/2.38 (~c1_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1698, 5183])).
% 2.18/2.38 tff(5186,plain,
% 2.18/2.38 (~c0_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1841, 5183])).
% 2.18/2.38 tff(5187,plain,
% 2.18/2.38 ($false),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[2645, 112, 5126, 5186, 5185, 5184, 5122, 5128, 151, 5127])).
% 2.18/2.38 tff(5188,plain,(hskp17), inference(lemma,lemma(discharge,[]))).
% 2.18/2.38 tff(5189,plain,
% 2.18/2.38 (~c3_1(a928)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[828, 5188])).
% 2.18/2.38 tff(5190,plain,
% 2.18/2.38 (~c2_1(a928)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[834, 5188])).
% 2.18/2.38 tff(5191,plain,
% 2.18/2.38 (c1_1(a928)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[842, 5188])).
% 2.18/2.38 tff(5192,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a928) | c3_1(a928) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a928) | c3_1(a928) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a928)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5193,plain,
% 2.18/2.38 ((hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928))) <=> (hskp31 | c2_1(a928) | c3_1(a928) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a928)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5194,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | c2_1(a928) | c3_1(a928) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a928))))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5193])).
% 2.18/2.38 tff(5195,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a928) | c3_1(a928) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a928)))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5194, 5192])).
% 2.18/2.38 tff(5196,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a928) | c2_1(a928) | (~c1_1(a928)))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5197,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp31 | c2_1(a928) | c3_1(a928) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c1_1(a928))),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5196, 5195])).
% 2.18/2.38 tff(5198,plain,
% 2.18/2.38 (hskp31),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5197, 112, 5191, 4876, 4877, 5190, 5189, 4875, 10])).
% 2.18/2.38 tff(5199,plain,
% 2.18/2.38 (c1_1(a957)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3827, 5198])).
% 2.18/2.38 tff(5200,plain,
% 2.18/2.38 (c3_1(a957)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3835, 5198])).
% 2.18/2.38 tff(5201,plain,
% 2.18/2.38 (c2_1(a957)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3843, 5198])).
% 2.18/2.38 tff(5202,plain,
% 2.18/2.38 (hskp25),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1686, 112, 5191, 5190, 5189, 30])).
% 2.18/2.38 tff(5203,plain,
% 2.18/2.38 (~c1_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1698, 5202])).
% 2.18/2.38 tff(5204,plain,
% 2.18/2.38 (~c0_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1841, 5202])).
% 2.18/2.38 tff(5205,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5206,plain,
% 2.18/2.38 ((hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958))) <=> (hskp1 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5207,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958))))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5206])).
% 2.18/2.38 tff(5208,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5207, 5205])).
% 2.18/2.38 tff(5209,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a958) | c1_1(a958) | (~c2_1(a958)))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5210,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a958) | c1_1(a958) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958))),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5209, 5208])).
% 2.18/2.38 tff(5211,plain,
% 2.18/2.38 (~c2_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5210, 112, 152, 4876, 4877, 5204, 5203, 3342, 4879])).
% 2.18/2.38 tff(5212,plain,
% 2.18/2.38 (hskp20 | hskp1),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3546, 112, 4876, 4877, 4875, 42])).
% 2.18/2.38 tff(5213,plain,
% 2.18/2.38 (hskp20),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5212, 152])).
% 2.18/2.38 tff(5214,plain,
% 2.18/2.38 (~c0_1(a937)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1004, 5213])).
% 2.18/2.38 tff(5215,plain,
% 2.18/2.38 (c2_1(a937)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1012, 5213])).
% 2.18/2.38 tff(5216,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a937) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a937) | (~c2_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a937) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a937) | (~c2_1(a937)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5217,plain,
% 2.18/2.38 ((hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a937) | c1_1(a937) | (~c2_1(a937))) <=> (hskp1 | c0_1(a937) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a937) | (~c2_1(a937)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5218,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a937) | c1_1(a937) | (~c2_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a937) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a937) | (~c2_1(a937))))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5217])).
% 2.18/2.38 tff(5219,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a937) | c1_1(a937) | (~c2_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a937) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a937) | (~c2_1(a937)))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5218, 5216])).
% 2.18/2.38 tff(5220,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c0_1(a937) | c1_1(a937) | (~c2_1(a937)))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5221,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a937) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a898)) | c1_1(a937) | (~c2_1(a937))),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5220, 5219])).
% 2.18/2.38 tff(5222,plain,
% 2.18/2.38 (c1_1(a937)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5221, 112, 152, 5215, 4876, 4877, 5214, 3342, 4879])).
% 2.18/2.38 tff(5223,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c0_1(a937) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a937)) | (~c2_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c0_1(a937) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a937)) | (~c2_1(a937)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5224,plain,
% 2.18/2.38 ((hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a937) | (~c2_1(a937)) | (~c1_1(a937))) <=> (hskp14 | c0_1(a937) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a937)) | (~c2_1(a937)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5225,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a937) | (~c2_1(a937)) | (~c1_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | c0_1(a937) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a937)) | (~c2_1(a937))))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5224])).
% 2.18/2.38 tff(5226,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a937) | (~c2_1(a937)) | (~c1_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c0_1(a937) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a937)) | (~c2_1(a937)))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5225, 5223])).
% 2.18/2.38 tff(5227,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a898) | c3_1(a898) | (~c0_1(a898)) | c0_1(a937) | (~c2_1(a937)) | (~c1_1(a937)))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5228,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp14 | c0_1(a937) | c2_1(a898) | (~ndr1_0) | c3_1(a898) | (~c0_1(a898)) | (~c1_1(a937)) | (~c2_1(a937))),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5227, 5226])).
% 2.18/2.38 tff(5229,plain,
% 2.18/2.38 (hskp14),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5228, 112, 5215, 4876, 5214, 4875, 373, 5222, 4879])).
% 2.18/2.38 tff(5230,plain,
% 2.18/2.38 (~c1_1(a918)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[672, 5229])).
% 2.18/2.38 tff(5231,plain,
% 2.18/2.38 (c3_1(a918)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[742, 5229])).
% 2.18/2.38 tff(5232,plain,
% 2.18/2.38 (c0_1(a918)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[734, 5229])).
% 2.18/2.38 tff(5233,plain,
% 2.18/2.38 (hskp18),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4964, 112, 5232, 5231, 4876, 5230, 4875, 753, 4879])).
% 2.18/2.38 tff(5234,plain,
% 2.18/2.38 (~c1_1(a929)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[771, 5233])).
% 2.18/2.38 tff(5235,plain,
% 2.18/2.38 (c2_1(a929)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[781, 5233])).
% 2.18/2.38 tff(5236,plain,
% 2.18/2.38 (c0_1(a929)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[789, 5233])).
% 2.18/2.38 tff(5237,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5238,plain,
% 2.18/2.38 ((hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929))) <=> (hskp7 | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.18/2.38 inference(rewrite,[status(thm)],[])).
% 2.18/2.38 tff(5239,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929))))),
% 2.18/2.38 inference(monotonicity,[status(thm)],[5238])).
% 2.18/2.38 tff(5240,plain,
% 2.18/2.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.18/2.38 inference(transitivity,[status(thm)],[5239, 5237])).
% 2.18/2.38 tff(5241,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c1_1(a929) | (~c2_1(a929)) | (~c0_1(a929)))),
% 2.18/2.38 inference(quant_inst,[status(thm)],[])).
% 2.18/2.38 tff(5242,plain,
% 2.18/2.38 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a929) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a929)) | (~c0_1(a929))),
% 2.18/2.38 inference(modus_ponens,[status(thm)],[5241, 5240])).
% 2.18/2.38 tff(5243,plain,
% 2.18/2.38 (hskp7),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[5242, 112, 5236, 5235, 4876, 4877, 5234, 4875, 576])).
% 2.18/2.38 tff(5244,plain,
% 2.18/2.38 (~c0_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4676, 5243])).
% 2.18/2.38 tff(5245,plain,
% 2.18/2.38 (c3_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[512, 5243])).
% 2.18/2.38 tff(5246,plain,
% 2.18/2.38 (c2_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1343, 112, 5232, 5231, 5245, 4876, 4877, 5230, 5244, 4875, 271])).
% 2.18/2.38 tff(5247,plain,
% 2.18/2.38 (~c3_1(a958)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[1692, 5202])).
% 2.18/2.38 tff(5248,plain,
% 2.18/2.38 (c0_1(a928)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3998, 112, 5191, 5245, 5203, 5247, 5190, 5244, 1721, 5246, 5211])).
% 2.18/2.38 tff(5249,plain,
% 2.18/2.38 (~c1_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4222, 5243])).
% 2.18/2.38 tff(5250,plain,
% 2.18/2.38 ($false),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[3866, 112, 152, 5191, 5189, 5244, 5249, 3342, 5246, 5248])).
% 2.18/2.38 tff(5251,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 2.18/2.38 tff(5252,plain,
% 2.18/2.38 (~c0_1(a899)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[292, 5251])).
% 2.18/2.38 tff(5253,plain,
% 2.18/2.38 (c1_1(a899)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[308, 5251])).
% 2.18/2.38 tff(5254,plain,
% 2.18/2.38 (c2_1(a899)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[300, 5251])).
% 2.18/2.38 tff(5255,plain,
% 2.18/2.38 (hskp7),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4722, 5254, 5188, 5253, 5252])).
% 2.18/2.38 tff(5256,plain,
% 2.18/2.38 (~c0_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4676, 5255])).
% 2.18/2.38 tff(5257,plain,
% 2.18/2.38 (~c1_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4222, 5255])).
% 2.18/2.38 tff(5258,plain,
% 2.18/2.38 (c0_1(a928)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4003, 5257, 5191, 5190, 5254, 5256, 5189, 5252, 5201, 5200, 5199])).
% 2.18/2.38 tff(5259,plain,
% 2.18/2.38 (hskp14),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4021, 112, 5253, 5254, 5190, 5189, 5252, 373, 5258])).
% 2.18/2.38 tff(5260,plain,
% 2.18/2.38 (~c1_1(a918)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[672, 5259])).
% 2.18/2.38 tff(5261,plain,
% 2.18/2.38 (c3_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[512, 5255])).
% 2.18/2.38 tff(5262,plain,
% 2.18/2.38 (c3_1(a918)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[742, 5259])).
% 2.18/2.38 tff(5263,plain,
% 2.18/2.38 (c0_1(a918)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[734, 5259])).
% 2.18/2.38 tff(5264,plain,
% 2.18/2.38 (c2_1(a907)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4058, 112, 5191, 5263, 5262, 5261, 5190, 5260, 5256, 271, 5258])).
% 2.18/2.38 tff(5265,plain,
% 2.18/2.38 (hskp18),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[4038, 5260, 5252, 5190, 5189, 5258, 5254, 5253])).
% 2.18/2.38 tff(5266,plain,
% 2.18/2.38 (~c1_1(a929)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[771, 5265])).
% 2.18/2.38 tff(5267,plain,
% 2.18/2.38 (c2_1(a929)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[781, 5265])).
% 2.18/2.38 tff(5268,plain,
% 2.18/2.38 (c0_1(a929)),
% 2.18/2.38 inference(unit_resolution,[status(thm)],[789, 5265])).
% 2.18/2.39 tff(5269,plain,
% 2.18/2.39 (hskp3),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[1095, 112, 5268, 5267, 5261, 5266, 5256, 5257, 1032])).
% 2.18/2.39 tff(5270,plain,
% 2.18/2.39 (~c3_1(a903)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[1101, 5269])).
% 2.18/2.39 tff(5271,plain,
% 2.18/2.39 (c2_1(a903)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[1119, 5269])).
% 2.18/2.39 tff(5272,plain,
% 2.18/2.39 (c0_1(a903)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[1111, 5269])).
% 2.18/2.39 tff(5273,plain,
% 2.18/2.39 (c2_1(a958)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[4084, 112, 5261, 5272, 5271, 5204, 5247, 5257, 5270, 4070, 5264])).
% 2.18/2.39 tff(5274,plain,
% 2.18/2.39 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))),
% 2.18/2.39 inference(rewrite,[status(thm)],[])).
% 2.18/2.39 tff(5275,plain,
% 2.18/2.39 ((hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958))) <=> (hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))),
% 2.18/2.39 inference(rewrite,[status(thm)],[])).
% 2.18/2.39 tff(5276,plain,
% 2.18/2.39 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958))))),
% 2.18/2.39 inference(monotonicity,[status(thm)],[5275])).
% 2.18/2.39 tff(5277,plain,
% 2.18/2.39 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958)))),
% 2.18/2.39 inference(transitivity,[status(thm)],[5276, 5274])).
% 2.18/2.39 tff(5278,plain,
% 2.18/2.39 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a898) | (~c1_1(a898)) | (~c0_1(a898)) | c3_1(a958) | c1_1(a958) | (~c2_1(a958)))),
% 2.18/2.39 inference(quant_inst,[status(thm)],[])).
% 2.18/2.39 tff(5279,plain,
% 2.18/2.39 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp21 | c1_1(a958) | c3_1(a958) | c2_1(a898) | (~ndr1_0) | (~c0_1(a898)) | (~c1_1(a898)) | (~c2_1(a958))),
% 2.18/2.39 inference(modus_ponens,[status(thm)],[5278, 5277])).
% 2.18/2.39 tff(5280,plain,
% 2.18/2.39 (hskp21 | (~c2_1(a958))),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[5279, 112, 4876, 4877, 5203, 5247, 4875, 402])).
% 2.18/2.39 tff(5281,plain,
% 2.18/2.39 (hskp21),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[5280, 5273])).
% 2.18/2.39 tff(5282,plain,
% 2.18/2.39 (c0_1(a938)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[430, 5281])).
% 2.18/2.39 tff(5283,plain,
% 2.18/2.39 (~c2_1(a938)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[422, 5281])).
% 2.18/2.39 tff(5284,plain,
% 2.18/2.39 (~hskp16),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[4165, 5283, 5257, 5261, 5264, 5263, 5262, 5273, 5260, 5203, 5247, 5256, 5282])).
% 2.18/2.39 tff(5285,plain,
% 2.18/2.39 (hskp16 | hskp10),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[4172, 112, 5272, 5271, 5270, 1906])).
% 2.18/2.39 tff(5286,plain,
% 2.18/2.39 (hskp10),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[5285, 5284])).
% 2.18/2.39 tff(5287,plain,
% 2.18/2.39 (~c2_1(a910)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[2348, 5286])).
% 2.18/2.39 tff(5288,plain,
% 2.18/2.39 (~c0_1(a910)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[2354, 5286])).
% 2.18/2.39 tff(5289,plain,
% 2.18/2.39 (c1_1(a910)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[2362, 5286])).
% 2.18/2.39 tff(5290,plain,
% 2.18/2.39 (hskp11),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[5016, 5289, 5288, 5287])).
% 2.18/2.39 tff(5291,plain,
% 2.18/2.39 (~c1_1(a912)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[2146, 5290])).
% 2.18/2.39 tff(5292,plain,
% 2.18/2.39 (~c3_1(a938)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[416, 5281])).
% 2.18/2.39 tff(5293,plain,
% 2.18/2.39 (~hskp22),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[4100, 5273, 5261, 5247, 5256, 5203, 5264])).
% 2.18/2.39 tff(5294,plain,
% 2.18/2.39 (~c2_1(a912)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[1679, 5290])).
% 2.18/2.39 tff(5295,plain,
% 2.18/2.39 (~c1_1(a938)),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[4214, 5294, 5272, 5271, 5257, 5270, 5264, 5293, 5261, 5283, 5292, 5256, 5291])).
% 2.18/2.39 tff(5296,plain,
% 2.18/2.39 ($false),
% 2.18/2.39 inference(unit_resolution,[status(thm)],[4127, 112, 5293, 5282, 5261, 5283, 5257, 4111, 5264, 5295])).
% 2.18/2.39 % SZS output end Proof
% 2.18/2.39 % E exiting
%------------------------------------------------------------------------------