%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN450-1 : 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 05:39:09 AM UTC 2025
% Result : Unsatisfiable 0.59s 0.77s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN450-1 : TPTP v9.0.0. Released v2.1.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n014.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 12:36:09 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.59/0.77 % SZS status Unsatisfiable
% 0.59/0.77 % SZS output start Proof
% 0.59/0.77 tff(c3_1_type, type, (
% 0.59/0.77 c3_1: $i > $o)).
% 0.59/0.77 tff(a643_type, type, (
% 0.59/0.77 a643: $i)).
% 0.59/0.77 tff(c2_1_type, type, (
% 0.59/0.77 c2_1: $i > $o)).
% 0.59/0.77 tff(a675_type, type, (
% 0.59/0.77 a675: $i)).
% 0.59/0.77 tff(hskp17_type, type, (
% 0.59/0.77 hskp17: $o)).
% 0.59/0.77 tff(c0_1_type, type, (
% 0.59/0.77 c0_1: $i > $o)).
% 0.59/0.77 tff(a647_type, type, (
% 0.59/0.77 a647: $i)).
% 0.59/0.77 tff(hskp5_type, type, (
% 0.59/0.77 hskp5: $o)).
% 0.59/0.77 tff(c1_1_type, type, (
% 0.59/0.77 c1_1: $i > $o)).
% 0.59/0.77 tff(hskp2_type, type, (
% 0.59/0.77 hskp2: $o)).
% 0.59/0.77 tff(a665_type, type, (
% 0.59/0.77 a665: $i)).
% 0.59/0.77 tff(ndr1_0_type, type, (
% 0.59/0.77 ndr1_0: $o)).
% 0.59/0.77 tff(hskp14_type, type, (
% 0.59/0.77 hskp14: $o)).
% 0.59/0.77 tff(hskp1_type, type, (
% 0.59/0.77 hskp1: $o)).
% 0.59/0.77 tff(hskp28_type, type, (
% 0.59/0.77 hskp28: $o)).
% 0.59/0.77 tff(a651_type, type, (
% 0.59/0.77 a651: $i)).
% 0.59/0.77 tff(hskp7_type, type, (
% 0.59/0.77 hskp7: $o)).
% 0.59/0.77 tff(a641_type, type, (
% 0.59/0.77 a641: $i)).
% 0.59/0.77 tff(hskp0_type, type, (
% 0.59/0.77 hskp0: $o)).
% 0.59/0.77 tff(a642_type, type, (
% 0.59/0.77 a642: $i)).
% 0.59/0.77 tff(a648_type, type, (
% 0.59/0.77 a648: $i)).
% 0.59/0.77 tff(hskp6_type, type, (
% 0.59/0.77 hskp6: $o)).
% 0.59/0.77 tff(a698_type, type, (
% 0.59/0.77 a698: $i)).
% 0.59/0.77 tff(hskp24_type, type, (
% 0.59/0.77 hskp24: $o)).
% 0.59/0.77 tff(hskp20_type, type, (
% 0.59/0.77 hskp20: $o)).
% 0.59/0.77 tff(a686_type, type, (
% 0.59/0.77 a686: $i)).
% 0.59/0.77 tff(a695_type, type, (
% 0.59/0.77 a695: $i)).
% 0.59/0.77 tff(a676_type, type, (
% 0.59/0.77 a676: $i)).
% 0.59/0.77 tff(hskp18_type, type, (
% 0.59/0.77 hskp18: $o)).
% 0.59/0.77 tff(hskp23_type, type, (
% 0.59/0.77 hskp23: $o)).
% 0.59/0.77 tff(a660_type, type, (
% 0.59/0.77 a660: $i)).
% 0.59/0.77 tff(hskp12_type, type, (
% 0.59/0.77 hskp12: $o)).
% 0.59/0.77 tff(a657_type, type, (
% 0.59/0.77 a657: $i)).
% 0.59/0.77 tff(hskp11_type, type, (
% 0.59/0.77 hskp11: $o)).
% 0.59/0.77 tff(a693_type, type, (
% 0.59/0.77 a693: $i)).
% 0.59/0.77 tff(hskp22_type, type, (
% 0.59/0.77 hskp22: $o)).
% 0.59/0.77 tff(hskp4_type, type, (
% 0.59/0.77 hskp4: $o)).
% 0.59/0.77 tff(a671_type, type, (
% 0.59/0.77 a671: $i)).
% 0.59/0.77 tff(a646_type, type, (
% 0.59/0.77 a646: $i)).
% 0.59/0.77 tff(a710_type, type, (
% 0.59/0.77 a710: $i)).
% 0.59/0.77 tff(hskp25_type, type, (
% 0.59/0.77 hskp25: $o)).
% 0.59/0.77 tff(a655_type, type, (
% 0.59/0.77 a655: $i)).
% 0.59/0.77 tff(hskp27_type, type, (
% 0.59/0.77 hskp27: $o)).
% 0.59/0.77 tff(a645_type, type, (
% 0.59/0.77 a645: $i)).
% 0.59/0.77 tff(hskp3_type, type, (
% 0.59/0.77 hskp3: $o)).
% 0.59/0.77 tff(a640_type, type, (
% 0.59/0.77 a640: $i)).
% 0.59/0.77 tff(hskp26_type, type, (
% 0.59/0.77 hskp26: $o)).
% 0.59/0.77 tff(a652_type, type, (
% 0.59/0.77 a652: $i)).
% 0.59/0.77 tff(hskp8_type, type, (
% 0.59/0.77 hskp8: $o)).
% 0.59/0.77 tff(a672_type, type, (
% 0.59/0.77 a672: $i)).
% 0.59/0.77 tff(hskp16_type, type, (
% 0.59/0.77 hskp16: $o)).
% 0.59/0.77 tff(a682_type, type, (
% 0.59/0.77 a682: $i)).
% 0.59/0.77 tff(hskp19_type, type, (
% 0.59/0.77 hskp19: $o)).
% 0.59/0.77 tff(1,assumption,(~hskp17), introduced(assumption)).
% 0.59/0.77 tff(2,assumption,(~hskp5), introduced(assumption)).
% 0.59/0.77 tff(3,plain,
% 0.59/0.77 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(4,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[3])).
% 0.59/0.77 tff(5,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(6,plain,
% 0.59/0.77 (^[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)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(7,plain,
% 0.59/0.77 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[6])).
% 0.59/0.77 tff(8,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.59/0.77 tff(9,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.59/0.77 tff(10,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.59/0.77 tff(11,plain,(
% 0.59/0.77 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.59/0.77 inference(skolemize,[status(sab)],[10])).
% 0.59/0.77 tff(12,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.59/0.77 tff(13,plain,
% 0.59/0.77 (^[U: $i] : refl((hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(14,plain,
% 0.59/0.77 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[13])).
% 0.59/0.77 tff(15,plain,
% 0.59/0.77 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(16,plain,
% 0.59/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7) <=> ((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7))), rewrite(((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7) <=> (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7) <=> (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(17,plain,
% 0.59/0.77 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7) <=> ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[16])).
% 0.59/0.77 tff(18,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.59/0.77 tff(19,plain,
% 0.59/0.77 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.59/0.77 tff(20,plain,
% 0.59/0.77 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.59/0.77 tff(21,plain,(
% 0.59/0.77 ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.77 inference(skolemize,[status(sab)],[20])).
% 0.59/0.77 tff(22,plain,
% 0.59/0.77 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.59/0.77 tff(23,assumption,(~hskp0), introduced(assumption)).
% 0.59/0.77 tff(24,assumption,(~hskp2), introduced(assumption)).
% 0.59/0.77 tff(25,plain,
% 0.59/0.77 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(26,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[25])).
% 0.59/0.77 tff(27,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(28,plain,
% 0.59/0.77 (^[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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(29,plain,
% 0.59/0.77 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[28])).
% 0.59/0.77 tff(30,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.59/0.77 tff(31,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.59/0.77 tff(32,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.59/0.77 tff(33,plain,(
% 0.59/0.77 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.59/0.77 inference(skolemize,[status(sab)],[32])).
% 0.59/0.77 tff(34,plain,
% 0.59/0.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.59/0.77 tff(35,plain,
% 0.59/0.77 (^[U: $i] : refl((hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(36,plain,
% 0.59/0.77 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[35])).
% 0.59/0.77 tff(37,plain,
% 0.59/0.77 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(38,plain,
% 0.59/0.77 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(39,plain,
% 0.59/0.78 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[38])).
% 0.59/0.78 tff(40,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.59/0.78 tff(41,plain,
% 0.59/0.78 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.59/0.78 tff(42,plain,
% 0.59/0.78 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.59/0.78 tff(43,plain,(
% 0.59/0.78 ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.59/0.78 inference(skolemize,[status(sab)],[42])).
% 0.59/0.78 tff(44,plain,
% 0.59/0.78 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.59/0.78 tff(45,assumption,(hskp14), introduced(assumption)).
% 0.59/0.78 tff(46,plain,
% 0.59/0.78 (((~hskp14) | (~c1_1(a665))) <=> ((~hskp14) | (~c1_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(47,plain,
% 0.59/0.78 (((~c1_1(a665)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(48,axiom,((~c1_1(a665)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.59/0.78 tff(49,plain,
% 0.59/0.78 ((~hskp14) | (~c1_1(a665))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.59/0.78 tff(50,plain,
% 0.59/0.78 ((~hskp14) | (~c1_1(a665))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.59/0.78 tff(51,plain,
% 0.59/0.78 (~c1_1(a665)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[50, 45])).
% 0.59/0.78 tff(52,plain,
% 0.59/0.78 (((~hskp14) | (~c0_1(a665))) <=> ((~hskp14) | (~c0_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(53,plain,
% 0.59/0.78 (((~c0_1(a665)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(54,axiom,((~c0_1(a665)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.59/0.78 tff(55,plain,
% 0.59/0.78 ((~hskp14) | (~c0_1(a665))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.59/0.78 tff(56,plain,
% 0.59/0.78 ((~hskp14) | (~c0_1(a665))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.59/0.78 tff(57,plain,
% 0.59/0.78 (~c0_1(a665)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[56, 45])).
% 0.59/0.78 tff(58,plain,
% 0.59/0.78 (((~hskp14) | c2_1(a665)) <=> ((~hskp14) | c2_1(a665))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(59,axiom,((~hskp14) | c2_1(a665)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.59/0.78 tff(60,plain,
% 0.59/0.78 ((~hskp14) | c2_1(a665)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.59/0.78 tff(61,plain,
% 0.59/0.78 ((~hskp14) | c2_1(a665)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[60, 58])).
% 0.59/0.78 tff(62,plain,
% 0.59/0.78 ((~hskp14) | c2_1(a665)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.59/0.78 tff(63,plain,
% 0.59/0.78 ((~hskp14) | c2_1(a665)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.59/0.78 tff(64,plain,
% 0.59/0.78 ((~hskp14) | c2_1(a665)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.59/0.78 tff(65,plain,
% 0.59/0.78 (c2_1(a665)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[64, 45])).
% 0.59/0.78 tff(66,assumption,(~ndr1_0), introduced(assumption)).
% 0.59/0.78 tff(67,plain,
% 0.59/0.78 ((ndr1_0 | (~hskp0)) <=> (ndr1_0 | (~hskp0))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(68,plain,
% 0.59/0.78 (((~hskp0) | ndr1_0) <=> (ndr1_0 | (~hskp0))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(69,axiom,((~hskp0) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 0.59/0.78 tff(70,plain,
% 0.59/0.78 (ndr1_0 | (~hskp0)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.59/0.78 tff(71,plain,
% 0.59/0.78 (ndr1_0 | (~hskp0)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.59/0.78 tff(72,plain,
% 0.59/0.78 (~hskp0),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[71, 66])).
% 0.59/0.78 tff(73,plain,
% 0.59/0.78 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(74,plain,
% 0.59/0.78 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(75,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 0.59/0.78 tff(76,plain,
% 0.59/0.78 (ndr1_0 | (~hskp24)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.59/0.78 tff(77,plain,
% 0.59/0.78 (ndr1_0 | (~hskp24)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.59/0.78 tff(78,plain,
% 0.59/0.78 (~hskp24),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[77, 66])).
% 0.59/0.78 tff(79,plain,
% 0.59/0.78 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(80,plain,
% 0.59/0.78 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(81,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 0.59/0.78 tff(82,plain,
% 0.59/0.78 (ndr1_0 | (~hskp20)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.59/0.78 tff(83,plain,
% 0.59/0.78 (ndr1_0 | (~hskp20)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.59/0.78 tff(84,plain,
% 0.59/0.78 (~hskp20),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[83, 66])).
% 0.59/0.78 tff(85,plain,
% 0.59/0.78 ((hskp24 | hskp20 | hskp0) <=> (hskp24 | hskp20 | hskp0)),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(86,plain,
% 0.59/0.78 (((hskp20 | hskp24) | hskp0) <=> (hskp24 | hskp20 | hskp0)),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(87,axiom,((hskp20 | hskp24) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.59/0.78 tff(88,plain,
% 0.59/0.78 (hskp24 | hskp20 | hskp0),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.59/0.78 tff(89,plain,
% 0.59/0.78 (hskp24 | hskp20 | hskp0),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.59/0.78 tff(90,plain,
% 0.59/0.78 (hskp24 | hskp20 | hskp0),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.59/0.78 tff(91,plain,
% 0.59/0.78 (hskp24 | hskp20 | hskp0),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.59/0.78 tff(92,plain,
% 0.59/0.78 (hskp24 | hskp20 | hskp0),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.59/0.78 tff(93,plain,
% 0.59/0.78 ($false),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[92, 84, 78, 23])).
% 0.59/0.78 tff(94,plain,(ndr1_0 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.59/0.78 tff(95,plain,
% 0.59/0.78 ($false),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[94, 72, 66])).
% 0.59/0.78 tff(96,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.59/0.78 tff(97,plain,
% 0.59/0.78 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(98,plain,
% 0.59/0.78 ((hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665))) <=> (hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(99,plain,
% 0.59/0.78 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[98])).
% 0.59/0.78 tff(100,plain,
% 0.59/0.78 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))),
% 0.59/0.78 inference(transitivity,[status(thm)],[99, 97])).
% 0.59/0.78 tff(101,plain,
% 0.59/0.78 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665)))),
% 0.59/0.78 inference(quant_inst,[status(thm)],[])).
% 0.59/0.78 tff(102,plain,
% 0.59/0.78 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.59/0.78 tff(103,plain,
% 0.59/0.78 (hskp6),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[102, 96, 24, 65, 57, 51, 44])).
% 0.59/0.78 tff(104,plain,
% 0.59/0.78 (((~hskp6) | (~c3_1(a648))) <=> ((~hskp6) | (~c3_1(a648)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(105,plain,
% 0.59/0.78 (((~c3_1(a648)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a648)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(106,axiom,((~c3_1(a648)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.59/0.78 tff(107,plain,
% 0.59/0.78 ((~hskp6) | (~c3_1(a648))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.59/0.78 tff(108,plain,
% 0.59/0.78 ((~hskp6) | (~c3_1(a648))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.59/0.78 tff(109,plain,
% 0.59/0.78 (~c3_1(a648)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.59/0.78 tff(110,plain,
% 0.59/0.78 (((~hskp6) | (~c2_1(a648))) <=> ((~hskp6) | (~c2_1(a648)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(111,plain,
% 0.59/0.78 (((~c2_1(a648)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a648)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(112,axiom,((~c2_1(a648)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.59/0.78 tff(113,plain,
% 0.59/0.78 ((~hskp6) | (~c2_1(a648))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.59/0.78 tff(114,plain,
% 0.59/0.78 ((~hskp6) | (~c2_1(a648))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.59/0.78 tff(115,plain,
% 0.59/0.78 (~c2_1(a648)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[114, 103])).
% 0.59/0.78 tff(116,plain,
% 0.59/0.78 (^[U: $i] : refl((hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(117,plain,
% 0.59/0.78 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[116])).
% 0.59/0.78 tff(118,plain,
% 0.59/0.78 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(119,plain,
% 0.59/0.78 (^[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)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp0))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(120,plain,
% 0.59/0.78 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[119])).
% 0.59/0.78 tff(121,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.59/0.78 tff(122,plain,
% 0.59/0.78 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.59/0.78 tff(123,plain,
% 0.59/0.78 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.59/0.78 tff(124,plain,(
% 0.59/0.78 ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.59/0.78 inference(skolemize,[status(sab)],[123])).
% 0.59/0.78 tff(125,plain,
% 0.59/0.78 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.59/0.78 tff(126,plain,
% 0.59/0.78 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(127,plain,
% 0.59/0.78 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665)) <=> (hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(128,plain,
% 0.59/0.78 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665)))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[127])).
% 0.59/0.78 tff(129,plain,
% 0.59/0.78 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))),
% 0.59/0.78 inference(transitivity,[status(thm)],[128, 126])).
% 0.59/0.78 tff(130,plain,
% 0.59/0.78 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665))),
% 0.59/0.78 inference(quant_inst,[status(thm)],[])).
% 0.59/0.78 tff(131,plain,
% 0.59/0.78 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.59/0.78 tff(132,plain,
% 0.59/0.78 (c3_1(a665)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[131, 96, 24, 23, 57, 51, 125])).
% 0.59/0.78 tff(133,plain,
% 0.59/0.78 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(134,plain,
% 0.59/0.78 ((hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665))) <=> (hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(135,plain,
% 0.59/0.78 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[134])).
% 0.59/0.78 tff(136,plain,
% 0.59/0.78 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.59/0.78 inference(transitivity,[status(thm)],[135, 133])).
% 0.59/0.78 tff(137,plain,
% 0.59/0.78 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.59/0.78 inference(quant_inst,[status(thm)],[])).
% 0.59/0.78 tff(138,plain,
% 0.59/0.78 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.59/0.78 tff(139,plain,
% 0.59/0.78 (hskp7 | (~c3_1(a665))),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[138, 96, 1, 65, 51, 22])).
% 0.59/0.78 tff(140,plain,
% 0.59/0.78 (hskp7),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[139, 132])).
% 0.59/0.78 tff(141,plain,
% 0.59/0.78 (((~hskp7) | (~c1_1(a651))) <=> ((~hskp7) | (~c1_1(a651)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(142,plain,
% 0.59/0.78 (((~c1_1(a651)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a651)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(143,axiom,((~c1_1(a651)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.59/0.78 tff(144,plain,
% 0.59/0.78 ((~hskp7) | (~c1_1(a651))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.59/0.78 tff(145,plain,
% 0.59/0.78 ((~hskp7) | (~c1_1(a651))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[144, 141])).
% 0.59/0.78 tff(146,plain,
% 0.59/0.78 (~c1_1(a651)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[145, 140])).
% 0.59/0.78 tff(147,plain,
% 0.59/0.78 (((~hskp7) | (~c0_1(a651))) <=> ((~hskp7) | (~c0_1(a651)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(148,plain,
% 0.59/0.78 (((~c0_1(a651)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a651)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(149,axiom,((~c0_1(a651)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.59/0.78 tff(150,plain,
% 0.59/0.78 ((~hskp7) | (~c0_1(a651))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.59/0.78 tff(151,plain,
% 0.59/0.78 ((~hskp7) | (~c0_1(a651))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[150, 147])).
% 0.59/0.78 tff(152,plain,
% 0.59/0.78 (~c0_1(a651)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[151, 140])).
% 0.59/0.78 tff(153,plain,
% 0.59/0.78 (((~hskp7) | c3_1(a651)) <=> ((~hskp7) | c3_1(a651))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(154,axiom,((~hskp7) | c3_1(a651)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.59/0.78 tff(155,plain,
% 0.59/0.78 ((~hskp7) | c3_1(a651)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.59/0.78 tff(156,plain,
% 0.59/0.78 ((~hskp7) | c3_1(a651)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[155, 153])).
% 0.59/0.78 tff(157,plain,
% 0.59/0.78 ((~hskp7) | c3_1(a651)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[156, 153])).
% 0.59/0.78 tff(158,plain,
% 0.59/0.78 ((~hskp7) | c3_1(a651)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.59/0.78 tff(159,plain,
% 0.59/0.78 ((~hskp7) | c3_1(a651)),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[158, 153])).
% 0.59/0.78 tff(160,plain,
% 0.59/0.78 (c3_1(a651)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[159, 140])).
% 0.59/0.78 tff(161,plain,
% 0.59/0.78 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(162,plain,
% 0.59/0.78 ((hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(163,plain,
% 0.59/0.78 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[162])).
% 0.59/0.78 tff(164,plain,
% 0.59/0.78 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))),
% 0.59/0.78 inference(transitivity,[status(thm)],[163, 161])).
% 0.59/0.78 tff(165,plain,
% 0.59/0.78 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 0.59/0.78 inference(quant_inst,[status(thm)],[])).
% 0.59/0.78 tff(166,plain,
% 0.59/0.78 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.59/0.78 tff(167,plain,
% 0.59/0.78 (~c1_1(a648)),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[166, 96, 24, 160, 152, 146, 115, 109, 34])).
% 0.59/0.78 tff(168,plain,
% 0.59/0.78 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(169,plain,
% 0.59/0.78 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[168])).
% 0.59/0.78 tff(170,plain,
% 0.59/0.78 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(171,plain,
% 0.59/0.78 (^[V: $i, U: $i] : 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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(172,plain,
% 0.59/0.78 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[171])).
% 0.59/0.78 tff(173,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.59/0.78 tff(174,plain,
% 0.59/0.78 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.59/0.78 tff(175,plain,
% 0.59/0.78 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.59/0.78 tff(176,plain,(
% 0.59/0.78 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.78 inference(skolemize,[status(sab)],[175])).
% 0.59/0.78 tff(177,plain,
% 0.59/0.78 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.59/0.78 tff(178,plain,
% 0.59/0.78 (^[U: $i] : refl((hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(179,plain,
% 0.59/0.78 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[178])).
% 0.59/0.78 tff(180,plain,
% 0.59/0.78 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(181,plain,
% 0.59/0.78 (^[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)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5) <=> (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5) <=> (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(182,plain,
% 0.59/0.78 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[181])).
% 0.59/0.78 tff(183,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.59/0.78 tff(184,plain,
% 0.59/0.78 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.59/0.78 tff(185,plain,
% 0.59/0.78 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.59/0.78 tff(186,plain,(
% 0.59/0.78 ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.78 inference(skolemize,[status(sab)],[185])).
% 0.59/0.78 tff(187,plain,
% 0.59/0.78 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.59/0.78 tff(188,plain,
% 0.59/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(189,plain,
% 0.59/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_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)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[188])).
% 0.59/0.78 tff(190,plain,
% 0.59/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_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)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(191,plain,
% 0.59/0.78 (^[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)) | (~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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.59/0.78 inference(bind,[status(th)],[])).
% 0.59/0.78 tff(192,plain,
% 0.59/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_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)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.59/0.78 inference(quant_intro,[status(thm)],[191])).
% 0.59/0.78 tff(193,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.59/0.78 tff(194,plain,
% 0.59/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.59/0.78 tff(195,plain,
% 0.59/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.59/0.78 tff(196,plain,(
% 0.59/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.59/0.78 inference(skolemize,[status(sab)],[195])).
% 0.59/0.78 tff(197,plain,
% 0.59/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.59/0.78 tff(198,assumption,(~hskp20), introduced(assumption)).
% 0.59/0.78 tff(199,plain,
% 0.59/0.78 ((hskp20 | hskp18 | hskp2) <=> (hskp20 | hskp18 | hskp2)),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(200,plain,
% 0.59/0.78 (((hskp18 | hskp2) | hskp20) <=> (hskp20 | hskp18 | hskp2)),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(201,axiom,((hskp18 | hskp2) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 0.59/0.78 tff(202,plain,
% 0.59/0.78 (hskp20 | hskp18 | hskp2),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.59/0.78 tff(203,plain,
% 0.59/0.78 (hskp20 | hskp18 | hskp2),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[202, 199])).
% 0.59/0.78 tff(204,plain,
% 0.59/0.78 (hskp20 | hskp18 | hskp2),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.59/0.78 tff(205,plain,
% 0.59/0.78 (hskp20 | hskp18 | hskp2),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[204, 199])).
% 0.59/0.78 tff(206,plain,
% 0.59/0.78 (hskp20 | hskp18 | hskp2),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[205, 199])).
% 0.59/0.78 tff(207,plain,
% 0.59/0.78 (hskp18),
% 0.59/0.78 inference(unit_resolution,[status(thm)],[206, 198, 24])).
% 0.59/0.78 tff(208,plain,
% 0.59/0.78 (((~hskp18) | (~c2_1(a676))) <=> ((~hskp18) | (~c2_1(a676)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(209,plain,
% 0.59/0.78 (((~c2_1(a676)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a676)))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(210,axiom,((~c2_1(a676)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.59/0.78 tff(211,plain,
% 0.59/0.78 ((~hskp18) | (~c2_1(a676))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.59/0.78 tff(212,plain,
% 0.59/0.78 ((~hskp18) | (~c2_1(a676))),
% 0.59/0.78 inference(modus_ponens,[status(thm)],[211, 208])).
% 0.59/0.79 tff(213,plain,
% 0.59/0.79 (~c2_1(a676)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[212, 207])).
% 0.59/0.79 tff(214,plain,
% 0.59/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(215,plain,
% 0.59/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[214])).
% 0.59/0.79 tff(216,plain,
% 0.59/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(217,plain,
% 0.59/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(218,plain,
% 0.59/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[217])).
% 0.59/0.79 tff(219,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.59/0.79 tff(220,plain,
% 0.59/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.59/0.79 tff(221,plain,
% 0.59/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.59/0.79 tff(222,plain,(
% 0.59/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.59/0.79 inference(skolemize,[status(sab)],[221])).
% 0.59/0.79 tff(223,plain,
% 0.59/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.59/0.79 tff(224,assumption,(~c3_1(a647)), introduced(assumption)).
% 0.59/0.79 tff(225,plain,
% 0.59/0.79 (hskp24),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[92, 198, 23])).
% 0.59/0.79 tff(226,plain,
% 0.59/0.79 (((~hskp24) | (~c2_1(a698))) <=> ((~hskp24) | (~c2_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(227,plain,
% 0.59/0.79 (((~c2_1(a698)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(228,axiom,((~c2_1(a698)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.59/0.79 tff(229,plain,
% 0.59/0.79 ((~hskp24) | (~c2_1(a698))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.59/0.79 tff(230,plain,
% 0.59/0.79 ((~hskp24) | (~c2_1(a698))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[229, 226])).
% 0.59/0.79 tff(231,plain,
% 0.59/0.79 (~c2_1(a698)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[230, 225])).
% 0.59/0.79 tff(232,plain,
% 0.59/0.79 (((~hskp24) | c1_1(a698)) <=> ((~hskp24) | c1_1(a698))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(233,axiom,((~hskp24) | c1_1(a698)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.59/0.79 tff(234,plain,
% 0.59/0.79 ((~hskp24) | c1_1(a698)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.59/0.79 tff(235,plain,
% 0.59/0.79 ((~hskp24) | c1_1(a698)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[234, 232])).
% 0.59/0.79 tff(236,plain,
% 0.59/0.79 ((~hskp24) | c1_1(a698)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[235, 232])).
% 0.59/0.79 tff(237,plain,
% 0.59/0.79 ((~hskp24) | c1_1(a698)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.59/0.79 tff(238,plain,
% 0.59/0.79 ((~hskp24) | c1_1(a698)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[237, 232])).
% 0.59/0.79 tff(239,plain,
% 0.59/0.79 (c1_1(a698)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[238, 225])).
% 0.59/0.79 tff(240,plain,
% 0.59/0.79 (((~hskp24) | (~c0_1(a698))) <=> ((~hskp24) | (~c0_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(241,plain,
% 0.59/0.79 (((~c0_1(a698)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(242,axiom,((~c0_1(a698)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.59/0.79 tff(243,plain,
% 0.59/0.79 ((~hskp24) | (~c0_1(a698))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.59/0.79 tff(244,plain,
% 0.59/0.79 ((~hskp24) | (~c0_1(a698))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.59/0.79 tff(245,plain,
% 0.59/0.79 (~c0_1(a698)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[244, 225])).
% 0.59/0.79 tff(246,assumption,(~c0_1(a647)), introduced(assumption)).
% 0.59/0.79 tff(247,plain,
% 0.59/0.79 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(248,plain,
% 0.59/0.79 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647)) <=> (hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(249,plain,
% 0.59/0.79 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0)))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[248])).
% 0.59/0.79 tff(250,plain,
% 0.59/0.79 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))),
% 0.59/0.79 inference(transitivity,[status(thm)],[249, 247])).
% 0.59/0.79 tff(251,plain,
% 0.59/0.79 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(252,plain,
% 0.59/0.79 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.59/0.79 tff(253,plain,
% 0.59/0.79 (c1_1(a647) | c0_1(a647)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[252, 96, 24, 23, 224, 125])).
% 0.59/0.79 tff(254,plain,
% 0.59/0.79 (c1_1(a647)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[253, 246])).
% 0.59/0.79 tff(255,assumption,(c1_1(a647)), introduced(assumption)).
% 0.59/0.79 tff(256,assumption,(c3_1(a698)), introduced(assumption)).
% 0.59/0.79 tff(257,plain,
% 0.59/0.79 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(258,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[257])).
% 0.59/0.79 tff(259,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(260,plain,
% 0.59/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(261,plain,
% 0.59/0.79 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[260])).
% 0.59/0.79 tff(262,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.59/0.79 tff(263,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.59/0.79 tff(264,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.59/0.79 tff(265,plain,(
% 0.59/0.79 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(skolemize,[status(sab)],[264])).
% 0.59/0.79 tff(266,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.59/0.79 tff(267,assumption,(~c2_1(a698)), introduced(assumption)).
% 0.59/0.79 tff(268,assumption,(c1_1(a698)), introduced(assumption)).
% 0.59/0.79 tff(269,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(270,plain,
% 0.59/0.79 ((hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(271,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[270])).
% 0.59/0.79 tff(272,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.59/0.79 inference(transitivity,[status(thm)],[271, 269])).
% 0.59/0.79 tff(273,plain,
% 0.59/0.79 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(274,plain,
% 0.59/0.79 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.59/0.79 tff(275,plain,
% 0.59/0.79 (hskp6 | c0_1(a647) | (~c1_1(a647)) | (~c3_1(a698))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[274, 96, 268, 267, 224, 266])).
% 0.59/0.79 tff(276,plain,
% 0.59/0.79 (hskp6),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[275, 256, 246, 255])).
% 0.59/0.79 tff(277,plain,
% 0.59/0.79 (~c3_1(a648)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[108, 276])).
% 0.59/0.79 tff(278,plain,
% 0.59/0.79 (~c2_1(a648)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[114, 276])).
% 0.59/0.79 tff(279,plain,
% 0.59/0.79 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(280,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[279])).
% 0.59/0.79 tff(281,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(282,plain,
% 0.59/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(283,plain,
% 0.59/0.79 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[282])).
% 0.59/0.79 tff(284,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.59/0.79 tff(285,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.59/0.79 tff(286,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.59/0.79 tff(287,plain,(
% 0.59/0.79 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(skolemize,[status(sab)],[286])).
% 0.59/0.79 tff(288,plain,
% 0.59/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[287, 280])).
% 0.59/0.79 tff(289,assumption,(~c0_1(a698)), introduced(assumption)).
% 0.59/0.79 tff(290,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(291,plain,
% 0.59/0.79 ((hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(292,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[291])).
% 0.59/0.79 tff(293,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.59/0.79 inference(transitivity,[status(thm)],[292, 290])).
% 0.59/0.79 tff(294,plain,
% 0.59/0.79 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(295,plain,
% 0.59/0.79 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.59/0.79 tff(296,plain,
% 0.59/0.79 (hskp11 | c0_1(a647) | (~c1_1(a647)) | (~c3_1(a698))),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[295, 96, 268, 289, 224, 288])).
% 0.59/0.79 tff(297,plain,
% 0.59/0.79 (hskp11),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[296, 256, 246, 255])).
% 0.59/0.79 tff(298,plain,
% 0.59/0.79 (((~hskp11) | (~c3_1(a657))) <=> ((~hskp11) | (~c3_1(a657)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(299,plain,
% 0.59/0.79 (((~c3_1(a657)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a657)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(300,axiom,((~c3_1(a657)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.59/0.79 tff(301,plain,
% 0.59/0.79 ((~hskp11) | (~c3_1(a657))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.59/0.79 tff(302,plain,
% 0.59/0.79 ((~hskp11) | (~c3_1(a657))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[301, 298])).
% 0.59/0.79 tff(303,plain,
% 0.59/0.79 (~c3_1(a657)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[302, 297])).
% 0.59/0.79 tff(304,plain,
% 0.59/0.79 (((~hskp6) | c0_1(a648)) <=> ((~hskp6) | c0_1(a648))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(305,axiom,((~hskp6) | c0_1(a648)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.59/0.79 tff(306,plain,
% 0.59/0.79 ((~hskp6) | c0_1(a648)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.59/0.79 tff(307,plain,
% 0.59/0.79 ((~hskp6) | c0_1(a648)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[306, 304])).
% 0.59/0.79 tff(308,plain,
% 0.59/0.79 ((~hskp6) | c0_1(a648)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[307, 304])).
% 0.59/0.79 tff(309,plain,
% 0.59/0.79 ((~hskp6) | c0_1(a648)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.59/0.79 tff(310,plain,
% 0.59/0.79 ((~hskp6) | c0_1(a648)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[309, 304])).
% 0.59/0.79 tff(311,plain,
% 0.59/0.79 (c0_1(a648)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[310, 276])).
% 0.59/0.79 tff(312,plain,
% 0.59/0.79 (((~hskp11) | c2_1(a657)) <=> ((~hskp11) | c2_1(a657))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(313,axiom,((~hskp11) | c2_1(a657)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.59/0.79 tff(314,plain,
% 0.59/0.79 ((~hskp11) | c2_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.59/0.79 tff(315,plain,
% 0.59/0.79 ((~hskp11) | c2_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[314, 312])).
% 0.59/0.79 tff(316,plain,
% 0.59/0.79 ((~hskp11) | c2_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[315, 312])).
% 0.59/0.79 tff(317,plain,
% 0.59/0.79 ((~hskp11) | c2_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[316, 312])).
% 0.59/0.79 tff(318,plain,
% 0.59/0.79 ((~hskp11) | c2_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[317, 312])).
% 0.59/0.79 tff(319,plain,
% 0.59/0.79 (c2_1(a657)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[318, 297])).
% 0.59/0.79 tff(320,plain,
% 0.59/0.79 (((~hskp11) | c0_1(a657)) <=> ((~hskp11) | c0_1(a657))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(321,axiom,((~hskp11) | c0_1(a657)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.59/0.79 tff(322,plain,
% 0.59/0.79 ((~hskp11) | c0_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.59/0.79 tff(323,plain,
% 0.59/0.79 ((~hskp11) | c0_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[322, 320])).
% 0.59/0.79 tff(324,plain,
% 0.59/0.79 ((~hskp11) | c0_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[323, 320])).
% 0.59/0.79 tff(325,plain,
% 0.59/0.79 ((~hskp11) | c0_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.59/0.79 tff(326,plain,
% 0.59/0.79 ((~hskp11) | c0_1(a657)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[325, 320])).
% 0.59/0.79 tff(327,plain,
% 0.59/0.79 (c0_1(a657)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[326, 297])).
% 0.59/0.79 tff(328,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(329,plain,
% 0.59/0.79 (((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648))) <=> (c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(330,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[329])).
% 0.59/0.79 tff(331,plain,
% 0.59/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.59/0.79 inference(transitivity,[status(thm)],[330, 328])).
% 0.59/0.79 tff(332,plain,
% 0.59/0.79 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(333,plain,
% 0.59/0.79 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.59/0.79 tff(334,plain,
% 0.59/0.79 ($false),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[333, 96, 327, 319, 311, 303, 278, 277, 177])).
% 0.59/0.79 tff(335,plain,((~c3_1(a698)) | c0_1(a647) | (~c1_1(a647)) | (~c1_1(a698)) | c0_1(a698) | c3_1(a647) | c2_1(a698)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.79 tff(336,plain,
% 0.59/0.79 (~c3_1(a698)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[335, 246, 254, 239, 245, 224, 231])).
% 0.59/0.79 tff(337,assumption,(~c3_1(a698)), introduced(assumption)).
% 0.59/0.79 tff(338,assumption,(hskp7), introduced(assumption)).
% 0.59/0.79 tff(339,plain,
% 0.59/0.79 (~c0_1(a651)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[151, 338])).
% 0.59/0.79 tff(340,plain,
% 0.59/0.79 (~c1_1(a651)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[145, 338])).
% 0.59/0.79 tff(341,assumption,(~c1_1(a651)), introduced(assumption)).
% 0.59/0.79 tff(342,assumption,(~c0_1(a651)), introduced(assumption)).
% 0.59/0.80 tff(343,plain,
% 0.59/0.80 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(344,plain,
% 0.59/0.80 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651)) <=> (hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(345,plain,
% 0.59/0.80 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0)))),
% 0.59/0.80 inference(monotonicity,[status(thm)],[344])).
% 0.59/0.80 tff(346,plain,
% 0.59/0.80 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))),
% 0.59/0.80 inference(transitivity,[status(thm)],[345, 343])).
% 0.59/0.80 tff(347,plain,
% 0.59/0.80 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(348,plain,
% 0.59/0.80 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.59/0.80 tff(349,plain,
% 0.59/0.80 (c3_1(a651) | c0_1(a651)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[348, 96, 24, 23, 341, 125])).
% 0.59/0.80 tff(350,plain,
% 0.59/0.80 (c3_1(a651)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[349, 342])).
% 0.59/0.80 tff(351,plain,
% 0.59/0.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(352,plain,
% 0.59/0.80 ((hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(353,plain,
% 0.59/0.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698)))),
% 0.59/0.80 inference(monotonicity,[status(thm)],[352])).
% 0.59/0.80 tff(354,plain,
% 0.59/0.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))),
% 0.59/0.80 inference(transitivity,[status(thm)],[353, 351])).
% 0.59/0.80 tff(355,plain,
% 0.59/0.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(356,plain,
% 0.59/0.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.63/0.80 tff(357,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[356, 96, 24, 268, 350, 267, 342, 341, 34, 337])).
% 0.63/0.80 tff(358,plain,(c0_1(a651) | hskp2 | (~c1_1(a698)) | c2_1(a698) | c1_1(a651) | c3_1(a698) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(359,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[358, 340, 339, 268, 267, 24, 337, 23])).
% 0.63/0.80 tff(360,plain,((~hskp7) | (~c1_1(a698)) | c2_1(a698) | hskp2 | c3_1(a698) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(361,plain,
% 0.63/0.80 (~hskp7),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[360, 336, 231, 24, 239, 23])).
% 0.63/0.80 tff(362,assumption,(hskp1), introduced(assumption)).
% 0.63/0.80 tff(363,plain,
% 0.63/0.80 (((~hskp1) | (~c1_1(a642))) <=> ((~hskp1) | (~c1_1(a642)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(364,plain,
% 0.63/0.80 (((~c1_1(a642)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a642)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(365,axiom,((~c1_1(a642)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.63/0.80 tff(366,plain,
% 0.63/0.80 ((~hskp1) | (~c1_1(a642))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.63/0.80 tff(367,plain,
% 0.63/0.80 ((~hskp1) | (~c1_1(a642))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[366, 363])).
% 0.63/0.80 tff(368,plain,
% 0.63/0.80 (~c1_1(a642)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[367, 362])).
% 0.63/0.80 tff(369,assumption,(~hskp7), introduced(assumption)).
% 0.63/0.80 tff(370,plain,
% 0.63/0.80 (((~hskp1) | c0_1(a642)) <=> ((~hskp1) | c0_1(a642))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(371,axiom,((~hskp1) | c0_1(a642)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.63/0.80 tff(372,plain,
% 0.63/0.80 ((~hskp1) | c0_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.63/0.80 tff(373,plain,
% 0.63/0.80 ((~hskp1) | c0_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[372, 370])).
% 0.63/0.80 tff(374,plain,
% 0.63/0.80 ((~hskp1) | c0_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[373, 370])).
% 0.63/0.80 tff(375,plain,
% 0.63/0.80 ((~hskp1) | c0_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[374, 370])).
% 0.63/0.80 tff(376,plain,
% 0.63/0.80 ((~hskp1) | c0_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[375, 370])).
% 0.63/0.80 tff(377,plain,
% 0.63/0.80 (c0_1(a642)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[376, 362])).
% 0.63/0.80 tff(378,plain,
% 0.63/0.80 (((~hskp1) | c3_1(a642)) <=> ((~hskp1) | c3_1(a642))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(379,axiom,((~hskp1) | c3_1(a642)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.63/0.80 tff(380,plain,
% 0.63/0.80 ((~hskp1) | c3_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.63/0.80 tff(381,plain,
% 0.63/0.80 ((~hskp1) | c3_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[380, 378])).
% 0.63/0.80 tff(382,plain,
% 0.63/0.80 ((~hskp1) | c3_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[381, 378])).
% 0.63/0.80 tff(383,plain,
% 0.63/0.80 ((~hskp1) | c3_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[382, 378])).
% 0.63/0.80 tff(384,plain,
% 0.63/0.80 ((~hskp1) | c3_1(a642)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[383, 378])).
% 0.63/0.80 tff(385,plain,
% 0.63/0.80 (c3_1(a642)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[384, 362])).
% 0.63/0.80 tff(386,assumption,(~c1_1(a642)), introduced(assumption)).
% 0.63/0.80 tff(387,assumption,(c3_1(a642)), introduced(assumption)).
% 0.63/0.80 tff(388,plain,
% 0.63/0.80 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(389,plain,
% 0.63/0.80 ((hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642))) <=> (hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(390,plain,
% 0.63/0.80 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[389])).
% 0.63/0.80 tff(391,plain,
% 0.63/0.80 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[390, 388])).
% 0.63/0.80 tff(392,plain,
% 0.63/0.80 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(393,plain,
% 0.63/0.80 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.63/0.80 tff(394,plain,
% 0.63/0.80 (hskp7 | (~c2_1(a642))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[393, 96, 1, 387, 386, 22])).
% 0.63/0.80 tff(395,plain,
% 0.63/0.80 (~c2_1(a642)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[394, 369])).
% 0.63/0.80 tff(396,plain,
% 0.63/0.80 (^[U: $i] : refl((hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(397,plain,
% 0.63/0.80 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[396])).
% 0.63/0.80 tff(398,plain,
% 0.63/0.80 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(399,plain,
% 0.63/0.80 (^[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)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22) <=> (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(400,plain,
% 0.63/0.80 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[399])).
% 0.63/0.80 tff(401,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.63/0.80 tff(402,plain,
% 0.63/0.80 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.63/0.80 tff(403,plain,
% 0.63/0.80 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.63/0.80 tff(404,plain,(
% 0.63/0.80 ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[403])).
% 0.63/0.80 tff(405,plain,
% 0.63/0.80 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[404, 397])).
% 0.63/0.80 tff(406,assumption,(c0_1(a642)), introduced(assumption)).
% 0.63/0.80 tff(407,plain,
% 0.63/0.80 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(408,plain,
% 0.63/0.80 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(409,plain,
% 0.63/0.80 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.63/0.80 tff(410,plain,
% 0.63/0.80 (hskp22 | c2_1(a642)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[409, 96, 198, 406, 387, 405])).
% 0.63/0.80 tff(411,plain,
% 0.63/0.80 (hskp22),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[410, 395])).
% 0.63/0.80 tff(412,plain,
% 0.63/0.80 (((~hskp22) | (~c0_1(a693))) <=> ((~hskp22) | (~c0_1(a693)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(413,plain,
% 0.63/0.80 (((~c0_1(a693)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a693)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(414,axiom,((~c0_1(a693)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.63/0.80 tff(415,plain,
% 0.63/0.80 ((~hskp22) | (~c0_1(a693))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.63/0.80 tff(416,plain,
% 0.63/0.80 ((~hskp22) | (~c0_1(a693))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[415, 412])).
% 0.63/0.80 tff(417,plain,
% 0.63/0.80 (~c0_1(a693)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[416, 411])).
% 0.63/0.80 tff(418,plain,
% 0.63/0.80 (((~hskp22) | c2_1(a693)) <=> ((~hskp22) | c2_1(a693))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(419,axiom,((~hskp22) | c2_1(a693)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.63/0.80 tff(420,plain,
% 0.63/0.80 ((~hskp22) | c2_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.63/0.80 tff(421,plain,
% 0.63/0.80 ((~hskp22) | c2_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[420, 418])).
% 0.63/0.80 tff(422,plain,
% 0.63/0.80 ((~hskp22) | c2_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[421, 418])).
% 0.63/0.80 tff(423,plain,
% 0.63/0.80 ((~hskp22) | c2_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[422, 418])).
% 0.63/0.80 tff(424,plain,
% 0.63/0.80 ((~hskp22) | c2_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[423, 418])).
% 0.63/0.80 tff(425,plain,
% 0.63/0.80 (c2_1(a693)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[424, 411])).
% 0.63/0.80 tff(426,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(427,plain,
% 0.63/0.80 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(428,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[427])).
% 0.63/0.80 tff(429,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[428, 426])).
% 0.63/0.80 tff(430,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(431,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.63/0.80 tff(432,plain,
% 0.63/0.80 (~c1_1(a693)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[431, 96, 425, 255, 406, 417, 246, 224, 386, 223, 395])).
% 0.63/0.80 tff(433,plain,
% 0.63/0.80 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(434,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[433])).
% 0.63/0.80 tff(435,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(436,plain,
% 0.63/0.80 (^[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)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~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)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(437,plain,
% 0.63/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[436])).
% 0.63/0.80 tff(438,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)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.63/0.80 tff(439,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.63/0.80 tff(440,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[439, 435])).
% 0.63/0.80 tff(441,plain,(
% 0.63/0.80 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[440])).
% 0.63/0.80 tff(442,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[441, 434])).
% 0.63/0.80 tff(443,plain,
% 0.63/0.80 (((~hskp22) | c3_1(a693)) <=> ((~hskp22) | c3_1(a693))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(444,axiom,((~hskp22) | c3_1(a693)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.63/0.80 tff(445,plain,
% 0.63/0.80 ((~hskp22) | c3_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.63/0.80 tff(446,plain,
% 0.63/0.80 ((~hskp22) | c3_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[445, 443])).
% 0.63/0.80 tff(447,plain,
% 0.63/0.80 ((~hskp22) | c3_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[446, 443])).
% 0.63/0.80 tff(448,plain,
% 0.63/0.80 ((~hskp22) | c3_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[447, 443])).
% 0.63/0.80 tff(449,plain,
% 0.63/0.80 ((~hskp22) | c3_1(a693)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[448, 443])).
% 0.63/0.80 tff(450,plain,
% 0.63/0.80 (c3_1(a693)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[449, 411])).
% 0.63/0.80 tff(451,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(452,plain,
% 0.63/0.80 ((hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693))) <=> (hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(453,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[452])).
% 0.63/0.80 tff(454,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[453, 451])).
% 0.63/0.80 tff(455,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(456,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.63/0.80 tff(457,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[456, 96, 369, 450, 406, 387, 417, 442, 395, 432])).
% 0.63/0.80 tff(458,plain,(hskp7 | (~c0_1(a642)) | (~c3_1(a642)) | (~c1_1(a647)) | c0_1(a647) | c3_1(a647) | c1_1(a642) | hskp20 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(459,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[458, 385, 377, 369, 255, 246, 224, 368, 198, 1])).
% 0.63/0.80 tff(460,plain,((~hskp1) | hskp7 | (~c1_1(a647)) | c0_1(a647) | c3_1(a647) | hskp20 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(461,plain,
% 0.63/0.80 (~hskp1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[460, 361, 254, 246, 224, 198, 1])).
% 0.63/0.80 tff(462,plain,
% 0.63/0.80 ((hskp17 | hskp14 | hskp1) <=> (hskp17 | hskp14 | hskp1)),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(463,plain,
% 0.63/0.80 (((hskp1 | hskp14) | hskp17) <=> (hskp17 | hskp14 | hskp1)),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(464,axiom,((hskp1 | hskp14) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.63/0.80 tff(465,plain,
% 0.63/0.80 (hskp17 | hskp14 | hskp1),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.63/0.80 tff(466,plain,
% 0.63/0.80 (hskp17 | hskp14 | hskp1),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[465, 462])).
% 0.63/0.80 tff(467,plain,
% 0.63/0.80 (hskp17 | hskp14 | hskp1),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[466, 462])).
% 0.63/0.80 tff(468,plain,
% 0.63/0.80 (hskp17 | hskp14 | hskp1),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[467, 462])).
% 0.63/0.80 tff(469,plain,
% 0.63/0.80 (hskp17 | hskp14 | hskp1),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[468, 462])).
% 0.63/0.80 tff(470,plain,
% 0.63/0.80 (hskp14),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[469, 461, 1])).
% 0.63/0.80 tff(471,plain,
% 0.63/0.80 (~c0_1(a665)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[56, 470])).
% 0.63/0.80 tff(472,plain,
% 0.63/0.80 (~c1_1(a665)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[50, 470])).
% 0.63/0.80 tff(473,assumption,(~c1_1(a665)), introduced(assumption)).
% 0.63/0.80 tff(474,assumption,(~c0_1(a665)), introduced(assumption)).
% 0.63/0.80 tff(475,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(476,plain,
% 0.63/0.80 ((hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665))) <=> (hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(477,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698)))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[476])).
% 0.63/0.81 tff(478,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))),
% 0.63/0.81 inference(transitivity,[status(thm)],[477, 475])).
% 0.63/0.81 tff(479,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(480,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.63/0.81 tff(481,plain,
% 0.63/0.81 (c1_1(a665) | (~c3_1(a665))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[480, 96, 24, 268, 267, 474, 34, 337])).
% 0.63/0.81 tff(482,plain,
% 0.63/0.81 (~c3_1(a665)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[481, 473])).
% 0.63/0.81 tff(483,plain,
% 0.63/0.81 (c1_1(a665) | c3_1(a665)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[131, 96, 24, 23, 474, 125])).
% 0.63/0.81 tff(484,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[483, 482, 473])).
% 0.63/0.81 tff(485,plain,(c1_1(a665) | hskp2 | hskp0 | c0_1(a665) | (~c1_1(a698)) | c2_1(a698) | c3_1(a698)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(486,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[485, 472, 471, 23, 336, 239, 231, 24])).
% 0.63/0.81 tff(487,plain,(c0_1(a647) | hskp0 | hskp2 | hskp17 | c3_1(a647) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(488,plain,
% 0.63/0.81 (c0_1(a647)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[487, 224, 24, 1, 23, 198])).
% 0.63/0.81 tff(489,plain,
% 0.63/0.81 (((~hskp5) | (~c0_1(a647))) <=> ((~hskp5) | (~c0_1(a647)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(490,plain,
% 0.63/0.81 (((~c0_1(a647)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a647)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(491,axiom,((~c0_1(a647)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.63/0.81 tff(492,plain,
% 0.63/0.81 ((~hskp5) | (~c0_1(a647))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.63/0.81 tff(493,plain,
% 0.63/0.81 ((~hskp5) | (~c0_1(a647))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[492, 489])).
% 0.63/0.81 tff(494,plain,
% 0.63/0.81 (~hskp5),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[493, 488])).
% 0.63/0.81 tff(495,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(496,plain,
% 0.63/0.81 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647))) <=> (hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(497,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647)))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[496])).
% 0.63/0.81 tff(498,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))),
% 0.63/0.81 inference(transitivity,[status(thm)],[497, 495])).
% 0.63/0.81 tff(499,plain,
% 0.63/0.81 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(500,plain,
% 0.63/0.81 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.63/0.81 tff(501,plain,
% 0.63/0.81 (hskp5 | (~c0_1(a647)) | c2_1(a647)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[500, 96, 198, 224, 187])).
% 0.63/0.81 tff(502,plain,
% 0.63/0.81 (c2_1(a647)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[501, 494, 488])).
% 0.63/0.81 tff(503,plain,
% 0.63/0.81 (^[U: $i] : refl((hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(504,plain,
% 0.63/0.81 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[503])).
% 0.63/0.81 tff(505,plain,
% 0.63/0.81 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(506,plain,
% 0.63/0.81 (^[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)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20) <=> ((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(507,plain,
% 0.63/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[506])).
% 0.63/0.81 tff(508,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.63/0.81 tff(509,plain,
% 0.63/0.81 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.63/0.81 tff(510,plain,
% 0.63/0.81 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[509, 505])).
% 0.63/0.81 tff(511,plain,(
% 0.63/0.81 ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(skolemize,[status(sab)],[510])).
% 0.63/0.81 tff(512,plain,
% 0.63/0.81 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[511, 504])).
% 0.63/0.81 tff(513,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(514,plain,
% 0.63/0.81 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647))) <=> (hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(515,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[514])).
% 0.63/0.81 tff(516,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[515, 513])).
% 0.63/0.81 tff(517,plain,
% 0.63/0.81 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(518,plain,
% 0.63/0.81 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[517, 516])).
% 0.63/0.81 tff(519,plain,
% 0.63/0.81 (hskp12 | (~c0_1(a647)) | (~c2_1(a647))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[518, 96, 198, 224, 512])).
% 0.63/0.81 tff(520,plain,
% 0.63/0.81 (hskp12),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[519, 502, 488])).
% 0.63/0.81 tff(521,plain,
% 0.63/0.81 (((~hskp12) | (~c2_1(a660))) <=> ((~hskp12) | (~c2_1(a660)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(522,plain,
% 0.63/0.81 (((~c2_1(a660)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a660)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(523,axiom,((~c2_1(a660)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.63/0.81 tff(524,plain,
% 0.63/0.81 ((~hskp12) | (~c2_1(a660))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.63/0.81 tff(525,plain,
% 0.63/0.81 ((~hskp12) | (~c2_1(a660))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[524, 521])).
% 0.63/0.81 tff(526,plain,
% 0.63/0.81 (~c2_1(a660)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[525, 520])).
% 0.63/0.81 tff(527,plain,
% 0.63/0.81 (((~hskp12) | (~c1_1(a660))) <=> ((~hskp12) | (~c1_1(a660)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(528,plain,
% 0.63/0.81 (((~c1_1(a660)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a660)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(529,axiom,((~c1_1(a660)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.63/0.81 tff(530,plain,
% 0.63/0.81 ((~hskp12) | (~c1_1(a660))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.63/0.81 tff(531,plain,
% 0.63/0.81 ((~hskp12) | (~c1_1(a660))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[530, 527])).
% 0.63/0.81 tff(532,plain,
% 0.63/0.81 (~c1_1(a660)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[531, 520])).
% 0.63/0.81 tff(533,plain,
% 0.63/0.81 (((~hskp18) | c0_1(a676)) <=> ((~hskp18) | c0_1(a676))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(534,axiom,((~hskp18) | c0_1(a676)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.63/0.81 tff(535,plain,
% 0.63/0.81 ((~hskp18) | c0_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.63/0.81 tff(536,plain,
% 0.63/0.81 ((~hskp18) | c0_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[535, 533])).
% 0.63/0.81 tff(537,plain,
% 0.63/0.81 ((~hskp18) | c0_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[536, 533])).
% 0.63/0.81 tff(538,plain,
% 0.63/0.81 ((~hskp18) | c0_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[537, 533])).
% 0.63/0.81 tff(539,plain,
% 0.63/0.81 ((~hskp18) | c0_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[538, 533])).
% 0.63/0.81 tff(540,plain,
% 0.63/0.81 (c0_1(a676)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[539, 207])).
% 0.63/0.81 tff(541,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(542,plain,
% 0.63/0.81 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676))) <=> (hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(543,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676)))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[542])).
% 0.63/0.81 tff(544,plain,
% 0.63/0.81 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))),
% 0.63/0.81 inference(transitivity,[status(thm)],[543, 541])).
% 0.63/0.81 tff(545,plain,
% 0.63/0.81 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(546,plain,
% 0.63/0.81 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.63/0.81 tff(547,plain,
% 0.63/0.81 (hskp5 | c3_1(a676)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[546, 96, 198, 540, 213, 187])).
% 0.63/0.81 tff(548,plain,
% 0.63/0.81 (c3_1(a676)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[547, 494])).
% 0.63/0.81 tff(549,plain,
% 0.63/0.81 (^[U: $i] : refl((hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(550,plain,
% 0.63/0.81 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[549])).
% 0.63/0.81 tff(551,plain,
% 0.63/0.81 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(552,plain,
% 0.63/0.81 (^[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)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23) <=> (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(553,plain,
% 0.63/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[552])).
% 0.63/0.81 tff(554,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.63/0.81 tff(555,plain,
% 0.63/0.81 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.63/0.81 tff(556,plain,
% 0.63/0.81 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[555, 551])).
% 0.63/0.81 tff(557,plain,(
% 0.63/0.81 ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(skolemize,[status(sab)],[556])).
% 0.63/0.81 tff(558,plain,
% 0.63/0.81 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[557, 550])).
% 0.63/0.81 tff(559,plain,
% 0.63/0.81 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(560,plain,
% 0.63/0.81 ((hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676))) <=> (hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(561,plain,
% 0.63/0.81 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[560])).
% 0.63/0.81 tff(562,plain,
% 0.63/0.81 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[561, 559])).
% 0.63/0.81 tff(563,plain,
% 0.63/0.81 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(564,plain,
% 0.63/0.81 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.63/0.81 tff(565,plain,
% 0.63/0.81 (hskp23 | hskp5 | (~c3_1(a676))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[564, 96, 540, 213, 558])).
% 0.63/0.81 tff(566,plain,
% 0.63/0.81 (hskp23),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[565, 548, 494])).
% 0.63/0.81 tff(567,plain,
% 0.63/0.81 (((~hskp23) | (~c3_1(a695))) <=> ((~hskp23) | (~c3_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(568,plain,
% 0.63/0.81 (((~c3_1(a695)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(569,axiom,((~c3_1(a695)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.63/0.81 tff(570,plain,
% 0.63/0.81 ((~hskp23) | (~c3_1(a695))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.63/0.81 tff(571,plain,
% 0.63/0.81 ((~hskp23) | (~c3_1(a695))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[570, 567])).
% 0.63/0.81 tff(572,plain,
% 0.63/0.81 (~c3_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[571, 566])).
% 0.63/0.81 tff(573,plain,
% 0.63/0.81 (((~hskp23) | (~c0_1(a695))) <=> ((~hskp23) | (~c0_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(574,plain,
% 0.63/0.81 (((~c0_1(a695)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(575,axiom,((~c0_1(a695)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.63/0.81 tff(576,plain,
% 0.63/0.81 ((~hskp23) | (~c0_1(a695))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.63/0.81 tff(577,plain,
% 0.63/0.81 ((~hskp23) | (~c0_1(a695))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[576, 573])).
% 0.63/0.81 tff(578,plain,
% 0.63/0.81 (~c0_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[577, 566])).
% 0.63/0.81 tff(579,plain,
% 0.63/0.81 (((~hskp12) | c0_1(a660)) <=> ((~hskp12) | c0_1(a660))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(580,axiom,((~hskp12) | c0_1(a660)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.63/0.81 tff(581,plain,
% 0.63/0.81 ((~hskp12) | c0_1(a660)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.63/0.81 tff(582,plain,
% 0.63/0.81 ((~hskp12) | c0_1(a660)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[581, 579])).
% 0.63/0.81 tff(583,plain,
% 0.63/0.81 ((~hskp12) | c0_1(a660)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[582, 579])).
% 0.63/0.81 tff(584,plain,
% 0.63/0.81 ((~hskp12) | c0_1(a660)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[583, 579])).
% 0.63/0.81 tff(585,plain,
% 0.63/0.81 ((~hskp12) | c0_1(a660)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[584, 579])).
% 0.63/0.81 tff(586,plain,
% 0.63/0.81 (c0_1(a660)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[585, 520])).
% 0.63/0.81 tff(587,plain,
% 0.63/0.81 (((~hskp23) | c2_1(a695)) <=> ((~hskp23) | c2_1(a695))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(588,axiom,((~hskp23) | c2_1(a695)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.63/0.81 tff(589,plain,
% 0.63/0.81 ((~hskp23) | c2_1(a695)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.63/0.81 tff(590,plain,
% 0.63/0.81 ((~hskp23) | c2_1(a695)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[589, 587])).
% 0.63/0.81 tff(591,plain,
% 0.63/0.81 ((~hskp23) | c2_1(a695)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[590, 587])).
% 0.63/0.81 tff(592,plain,
% 0.63/0.81 ((~hskp23) | c2_1(a695)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[591, 587])).
% 0.63/0.81 tff(593,plain,
% 0.63/0.81 ((~hskp23) | c2_1(a695)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[592, 587])).
% 0.63/0.81 tff(594,plain,
% 0.63/0.81 (c2_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[593, 566])).
% 0.63/0.81 tff(595,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(596,plain,
% 0.63/0.81 (((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695))) <=> (c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(597,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[596])).
% 0.63/0.81 tff(598,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[597, 595])).
% 0.63/0.81 tff(599,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(600,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.63/0.81 tff(601,plain,
% 0.63/0.81 (~c1_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[600, 96, 594, 586, 578, 572, 532, 526, 223])).
% 0.63/0.81 tff(602,plain,
% 0.63/0.81 (((~hskp18) | c1_1(a676)) <=> ((~hskp18) | c1_1(a676))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(603,axiom,((~hskp18) | c1_1(a676)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.63/0.81 tff(604,plain,
% 0.63/0.81 ((~hskp18) | c1_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.63/0.81 tff(605,plain,
% 0.63/0.81 ((~hskp18) | c1_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[604, 602])).
% 0.63/0.81 tff(606,plain,
% 0.63/0.81 ((~hskp18) | c1_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[605, 602])).
% 0.63/0.81 tff(607,plain,
% 0.63/0.81 ((~hskp18) | c1_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[606, 602])).
% 0.63/0.81 tff(608,plain,
% 0.63/0.81 ((~hskp18) | c1_1(a676)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[607, 602])).
% 0.63/0.81 tff(609,plain,
% 0.63/0.81 (c1_1(a676)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[608, 207])).
% 0.63/0.81 tff(610,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(611,plain,
% 0.63/0.81 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695)) <=> (c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(612,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[611])).
% 0.63/0.81 tff(613,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[612, 610])).
% 0.63/0.81 tff(614,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(615,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.63/0.81 tff(616,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[615, 96, 594, 540, 609, 578, 572, 213, 197, 601])).
% 0.63/0.81 tff(617,plain,(c3_1(a647) | hskp20 | hskp2 | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(618,plain,
% 0.63/0.81 (c3_1(a647)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[617, 198, 24, 1, 23])).
% 0.63/0.81 tff(619,plain,
% 0.63/0.81 (((~hskp5) | (~c3_1(a647))) <=> ((~hskp5) | (~c3_1(a647)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(620,plain,
% 0.63/0.81 (((~c3_1(a647)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a647)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(621,axiom,((~c3_1(a647)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.63/0.81 tff(622,plain,
% 0.63/0.81 ((~hskp5) | (~c3_1(a647))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.63/0.81 tff(623,plain,
% 0.63/0.81 ((~hskp5) | (~c3_1(a647))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[622, 619])).
% 0.63/0.81 tff(624,plain,
% 0.63/0.81 (~hskp5),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[623, 618])).
% 0.63/0.81 tff(625,plain,
% 0.63/0.81 (c3_1(a676)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[547, 624])).
% 0.63/0.81 tff(626,plain,
% 0.63/0.81 (hskp23),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[565, 625, 624])).
% 0.63/0.81 tff(627,plain,
% 0.63/0.81 (~c3_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[571, 626])).
% 0.63/0.81 tff(628,plain,
% 0.63/0.81 (~c0_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[577, 626])).
% 0.63/0.81 tff(629,plain,
% 0.63/0.81 (c2_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[593, 626])).
% 0.63/0.81 tff(630,plain,
% 0.63/0.81 (c1_1(a695)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[615, 96, 629, 540, 609, 628, 627, 213, 197])).
% 0.63/0.81 tff(631,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(632,plain,
% 0.63/0.81 ((hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695))) <=> (hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(633,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[632])).
% 0.63/0.81 tff(634,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[633, 631])).
% 0.63/0.81 tff(635,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(636,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.63/0.82 tff(637,plain,
% 0.63/0.82 (hskp6),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[636, 96, 609, 628, 627, 213, 266, 625, 630])).
% 0.63/0.82 tff(638,plain,
% 0.63/0.82 (~c3_1(a648)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[108, 637])).
% 0.63/0.82 tff(639,plain,
% 0.63/0.82 (~c2_1(a648)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[114, 637])).
% 0.63/0.82 tff(640,plain,
% 0.63/0.82 (c0_1(a648)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[310, 637])).
% 0.63/0.82 tff(641,plain,
% 0.63/0.82 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(642,plain,
% 0.63/0.82 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648))) <=> (hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(643,plain,
% 0.63/0.82 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[642])).
% 0.63/0.82 tff(644,plain,
% 0.63/0.82 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[643, 641])).
% 0.63/0.82 tff(645,plain,
% 0.63/0.82 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(646,plain,
% 0.63/0.82 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.63/0.82 tff(647,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[646, 96, 198, 624, 640, 639, 638, 187])).
% 0.63/0.82 tff(648,plain,(hskp20 | hskp2 | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(649,plain,
% 0.63/0.82 (hskp20),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[648, 1, 24, 23])).
% 0.63/0.82 tff(650,plain,
% 0.63/0.82 (((~hskp20) | (~c3_1(a686))) <=> ((~hskp20) | (~c3_1(a686)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(651,plain,
% 0.63/0.82 (((~c3_1(a686)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a686)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(652,axiom,((~c3_1(a686)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.63/0.82 tff(653,plain,
% 0.63/0.82 ((~hskp20) | (~c3_1(a686))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.63/0.82 tff(654,plain,
% 0.63/0.82 ((~hskp20) | (~c3_1(a686))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[653, 650])).
% 0.63/0.82 tff(655,plain,
% 0.63/0.82 (~c3_1(a686)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[654, 649])).
% 0.63/0.82 tff(656,plain,
% 0.63/0.82 (c0_1(a648)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[310, 103])).
% 0.63/0.82 tff(657,plain,
% 0.63/0.82 (((~hskp20) | c2_1(a686)) <=> ((~hskp20) | c2_1(a686))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(658,axiom,((~hskp20) | c2_1(a686)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.63/0.82 tff(659,plain,
% 0.63/0.82 ((~hskp20) | c2_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.63/0.82 tff(660,plain,
% 0.63/0.82 ((~hskp20) | c2_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[659, 657])).
% 0.63/0.82 tff(661,plain,
% 0.63/0.82 ((~hskp20) | c2_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[660, 657])).
% 0.63/0.82 tff(662,plain,
% 0.63/0.82 ((~hskp20) | c2_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[661, 657])).
% 0.63/0.82 tff(663,plain,
% 0.63/0.82 ((~hskp20) | c2_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[662, 657])).
% 0.63/0.82 tff(664,plain,
% 0.63/0.82 (c2_1(a686)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[663, 649])).
% 0.63/0.82 tff(665,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(666,plain,
% 0.63/0.82 (((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648))) <=> (c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(667,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[666])).
% 0.63/0.82 tff(668,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[667, 665])).
% 0.63/0.82 tff(669,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(670,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.63/0.82 tff(671,plain,
% 0.63/0.82 (~c0_1(a686)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[670, 96, 664, 656, 655, 115, 109, 177])).
% 0.63/0.82 tff(672,plain,
% 0.63/0.82 (((~hskp20) | c1_1(a686)) <=> ((~hskp20) | c1_1(a686))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(673,axiom,((~hskp20) | c1_1(a686)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.63/0.82 tff(674,plain,
% 0.63/0.82 ((~hskp20) | c1_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[673, 672])).
% 0.63/0.82 tff(675,plain,
% 0.63/0.82 ((~hskp20) | c1_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[674, 672])).
% 0.63/0.82 tff(676,plain,
% 0.63/0.82 ((~hskp20) | c1_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[675, 672])).
% 0.63/0.82 tff(677,plain,
% 0.63/0.82 ((~hskp20) | c1_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[676, 672])).
% 0.63/0.82 tff(678,plain,
% 0.63/0.82 ((~hskp20) | c1_1(a686)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[677, 672])).
% 0.63/0.82 tff(679,plain,
% 0.63/0.82 (c1_1(a686)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[678, 649])).
% 0.63/0.82 tff(680,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(681,plain,
% 0.63/0.82 (((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686))) <=> (c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(682,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[681])).
% 0.63/0.82 tff(683,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[682, 680])).
% 0.63/0.82 tff(684,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(685,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.63/0.82 tff(686,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[685, 96, 679, 664, 656, 655, 115, 223, 671, 167])).
% 0.63/0.82 tff(687,plain,((~hskp14) | hskp2 | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(688,plain,
% 0.63/0.82 (~hskp14),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[687, 1, 24, 23])).
% 0.63/0.82 tff(689,plain,
% 0.63/0.82 ((hskp24 | hskp17 | hskp14) <=> (hskp24 | hskp17 | hskp14)),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(690,plain,
% 0.63/0.82 (((hskp24 | hskp14) | hskp17) <=> (hskp24 | hskp17 | hskp14)),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(691,plain,
% 0.63/0.82 ((hskp24 | hskp14) <=> (hskp24 | hskp14)),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(692,plain,
% 0.63/0.82 (((hskp24 | hskp14) | hskp17) <=> ((hskp24 | hskp14) | hskp17)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[691])).
% 0.63/0.82 tff(693,plain,
% 0.63/0.82 (((hskp24 | hskp14) | hskp17) <=> (hskp24 | hskp17 | hskp14)),
% 0.63/0.82 inference(transitivity,[status(thm)],[692, 690])).
% 0.63/0.82 tff(694,axiom,((hskp24 | hskp14) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.63/0.82 tff(695,plain,
% 0.63/0.82 (hskp24 | hskp17 | hskp14),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.63/0.82 tff(696,plain,
% 0.63/0.82 (hskp24 | hskp17 | hskp14),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[695, 689])).
% 0.63/0.82 tff(697,plain,
% 0.63/0.82 (hskp24 | hskp17 | hskp14),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[696, 689])).
% 0.63/0.82 tff(698,plain,
% 0.63/0.82 (hskp24 | hskp17 | hskp14),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[697, 689])).
% 0.63/0.82 tff(699,plain,
% 0.63/0.82 (hskp24 | hskp17 | hskp14),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[698, 689])).
% 0.63/0.82 tff(700,plain,
% 0.63/0.82 (hskp24),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[699, 688, 1])).
% 0.63/0.82 tff(701,plain,
% 0.63/0.82 (c1_1(a698)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[238, 700])).
% 0.63/0.82 tff(702,plain,
% 0.63/0.82 (~c2_1(a698)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[230, 700])).
% 0.63/0.82 tff(703,plain,
% 0.63/0.82 (hskp1),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[469, 688, 1])).
% 0.63/0.82 tff(704,plain,
% 0.63/0.82 (~c1_1(a642)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[367, 703])).
% 0.63/0.82 tff(705,plain,
% 0.63/0.82 (c3_1(a642)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[384, 703])).
% 0.63/0.82 tff(706,plain,
% 0.63/0.82 (hskp7 | (~c2_1(a642))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[393, 96, 1, 705, 704, 22])).
% 0.63/0.82 tff(707,plain,
% 0.63/0.82 (~c2_1(a642)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[706, 369])).
% 0.63/0.82 tff(708,plain,
% 0.63/0.82 (c0_1(a642)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[376, 703])).
% 0.63/0.82 tff(709,plain,
% 0.63/0.82 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(710,plain,
% 0.63/0.82 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(711,plain,
% 0.63/0.82 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.63/0.82 tff(712,plain,
% 0.63/0.82 (hskp23 | hskp5 | c2_1(a642)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[711, 96, 708, 705, 558])).
% 0.63/0.82 tff(713,plain,
% 0.63/0.82 (hskp23),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[712, 707, 2])).
% 0.63/0.82 tff(714,plain,
% 0.63/0.82 (~c3_1(a695)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[571, 713])).
% 0.63/0.82 tff(715,plain,
% 0.63/0.82 (~c0_1(a695)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[577, 713])).
% 0.63/0.82 tff(716,plain,
% 0.63/0.82 (c2_1(a695)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[593, 713])).
% 0.63/0.82 tff(717,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(718,plain,
% 0.63/0.82 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695))) <=> (c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(719,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[718])).
% 0.63/0.82 tff(720,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[719, 717])).
% 0.63/0.82 tff(721,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(722,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.63/0.82 tff(723,plain,
% 0.63/0.82 (~c1_1(a695)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[722, 96, 716, 708, 715, 714, 704, 223, 707])).
% 0.63/0.82 tff(724,plain,
% 0.63/0.82 (^[U: $i] : refl((hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(725,plain,
% 0.63/0.82 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[724])).
% 0.63/0.82 tff(726,plain,
% 0.63/0.82 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(727,plain,
% 0.63/0.82 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(728,plain,
% 0.63/0.82 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[727])).
% 0.63/0.82 tff(729,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.63/0.82 tff(730,plain,
% 0.63/0.82 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.63/0.82 tff(731,plain,
% 0.63/0.82 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[730, 726])).
% 0.63/0.82 tff(732,plain,(
% 0.63/0.82 ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.82 inference(skolemize,[status(sab)],[731])).
% 0.63/0.82 tff(733,plain,
% 0.63/0.82 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[732, 725])).
% 0.63/0.82 tff(734,assumption,(~hskp28), introduced(assumption)).
% 0.63/0.82 tff(735,plain,
% 0.63/0.82 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(736,plain,
% 0.63/0.82 ((hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642))) <=> (hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(737,plain,
% 0.63/0.82 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[736])).
% 0.63/0.82 tff(738,plain,
% 0.63/0.82 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[737, 735])).
% 0.63/0.82 tff(739,plain,
% 0.63/0.82 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(740,plain,
% 0.63/0.82 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[739, 738])).
% 0.63/0.82 tff(741,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[740, 96, 734, 1, 377, 385, 368, 733])).
% 0.63/0.82 tff(742,plain,((~hskp1) | hskp28 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(743,plain,
% 0.63/0.82 (hskp28),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[742, 703, 1])).
% 0.63/0.82 tff(744,plain,
% 0.63/0.82 (((~hskp28) | c2_1(a671)) <=> ((~hskp28) | c2_1(a671))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(745,axiom,((~hskp28) | c2_1(a671)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.63/0.82 tff(746,plain,
% 0.63/0.82 ((~hskp28) | c2_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.63/0.82 tff(747,plain,
% 0.63/0.82 ((~hskp28) | c2_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[746, 744])).
% 0.63/0.82 tff(748,plain,
% 0.63/0.82 ((~hskp28) | c2_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[747, 744])).
% 0.63/0.82 tff(749,plain,
% 0.63/0.82 ((~hskp28) | c2_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[748, 744])).
% 0.63/0.82 tff(750,plain,
% 0.63/0.82 ((~hskp28) | c2_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[749, 744])).
% 0.63/0.82 tff(751,plain,
% 0.63/0.82 (c2_1(a671)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[750, 743])).
% 0.63/0.82 tff(752,plain,
% 0.63/0.82 (((~hskp28) | c1_1(a671)) <=> ((~hskp28) | c1_1(a671))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(753,axiom,((~hskp28) | c1_1(a671)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.63/0.82 tff(754,plain,
% 0.63/0.82 ((~hskp28) | c1_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.63/0.82 tff(755,plain,
% 0.63/0.82 ((~hskp28) | c1_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[754, 752])).
% 0.63/0.82 tff(756,plain,
% 0.63/0.82 ((~hskp28) | c1_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[755, 752])).
% 0.63/0.82 tff(757,plain,
% 0.63/0.82 ((~hskp28) | c1_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[756, 752])).
% 0.63/0.82 tff(758,plain,
% 0.63/0.82 ((~hskp28) | c1_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[757, 752])).
% 0.63/0.82 tff(759,plain,
% 0.63/0.82 (c1_1(a671)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[758, 743])).
% 0.63/0.82 tff(760,plain,
% 0.63/0.82 (((~hskp28) | c0_1(a671)) <=> ((~hskp28) | c0_1(a671))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(761,axiom,((~hskp28) | c0_1(a671)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.63/0.82 tff(762,plain,
% 0.63/0.82 ((~hskp28) | c0_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.63/0.82 tff(763,plain,
% 0.63/0.82 ((~hskp28) | c0_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[762, 760])).
% 0.63/0.82 tff(764,plain,
% 0.63/0.82 ((~hskp28) | c0_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[763, 760])).
% 0.63/0.82 tff(765,plain,
% 0.63/0.82 ((~hskp28) | c0_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[764, 760])).
% 0.63/0.82 tff(766,plain,
% 0.63/0.82 ((~hskp28) | c0_1(a671)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[765, 760])).
% 0.63/0.82 tff(767,plain,
% 0.63/0.82 (c0_1(a671)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[766, 743])).
% 0.63/0.82 tff(768,assumption,(hskp4), introduced(assumption)).
% 0.63/0.82 tff(769,plain,
% 0.63/0.82 (((~hskp4) | (~c3_1(a646))) <=> ((~hskp4) | (~c3_1(a646)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(770,plain,
% 0.63/0.82 (((~c3_1(a646)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a646)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(771,axiom,((~c3_1(a646)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.63/0.82 tff(772,plain,
% 0.63/0.82 ((~hskp4) | (~c3_1(a646))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[771, 770])).
% 0.63/0.82 tff(773,plain,
% 0.63/0.82 ((~hskp4) | (~c3_1(a646))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[772, 769])).
% 0.63/0.82 tff(774,plain,
% 0.63/0.82 (~c3_1(a646)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[773, 768])).
% 0.63/0.82 tff(775,plain,
% 0.63/0.82 (((~hskp4) | (~c1_1(a646))) <=> ((~hskp4) | (~c1_1(a646)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(776,plain,
% 0.63/0.82 (((~c1_1(a646)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a646)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(777,axiom,((~c1_1(a646)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.63/0.82 tff(778,plain,
% 0.63/0.82 ((~hskp4) | (~c1_1(a646))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.63/0.82 tff(779,plain,
% 0.63/0.82 ((~hskp4) | (~c1_1(a646))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[778, 775])).
% 0.63/0.82 tff(780,plain,
% 0.63/0.82 (~c1_1(a646)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[779, 768])).
% 0.63/0.82 tff(781,plain,
% 0.63/0.82 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(782,plain,
% 0.63/0.82 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646)) <=> (hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(783,plain,
% 0.63/0.82 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646)))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[782])).
% 0.63/0.82 tff(784,plain,
% 0.63/0.82 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))),
% 0.63/0.82 inference(transitivity,[status(thm)],[783, 781])).
% 0.63/0.82 tff(785,plain,
% 0.63/0.82 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(786,plain,
% 0.63/0.82 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.63/0.82 tff(787,plain,
% 0.63/0.82 (c0_1(a646)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[786, 96, 24, 23, 780, 774, 125])).
% 0.63/0.82 tff(788,plain,
% 0.63/0.82 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(789,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[788])).
% 0.63/0.82 tff(790,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(791,plain,
% 0.63/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(792,plain,
% 0.63/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[791])).
% 0.63/0.82 tff(793,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.63/0.82 tff(794,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[793, 792])).
% 0.63/0.82 tff(795,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[794, 790])).
% 0.63/0.82 tff(796,plain,(
% 0.63/0.82 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.82 inference(skolemize,[status(sab)],[795])).
% 0.63/0.82 tff(797,plain,
% 0.63/0.82 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[796, 789])).
% 0.63/0.83 tff(798,assumption,(c2_1(a671)), introduced(assumption)).
% 0.63/0.83 tff(799,assumption,(c1_1(a671)), introduced(assumption)).
% 0.63/0.83 tff(800,assumption,(c0_1(a671)), introduced(assumption)).
% 0.63/0.83 tff(801,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(802,plain,
% 0.63/0.83 ((hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646))) <=> (hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(803,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[802])).
% 0.63/0.83 tff(804,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[803, 801])).
% 0.63/0.83 tff(805,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(806,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.63/0.83 tff(807,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[806, 96, 369, 800, 799, 798, 780, 774, 797, 787])).
% 0.63/0.83 tff(808,plain,((~hskp4) | hskp7 | (~c0_1(a671)) | (~c1_1(a671)) | (~c2_1(a671)) | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(809,plain,
% 0.63/0.83 (~hskp4),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[808, 369, 767, 759, 751, 24, 23])).
% 0.63/0.83 tff(810,plain,
% 0.63/0.83 (^[U: $i] : refl((hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(811,plain,
% 0.63/0.83 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[810])).
% 0.63/0.83 tff(812,plain,
% 0.63/0.83 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(813,plain,
% 0.63/0.83 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4) <=> ((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4) <=> (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(814,plain,
% 0.63/0.83 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[813])).
% 0.63/0.83 tff(815,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.63/0.83 tff(816,plain,
% 0.63/0.83 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.63/0.83 tff(817,plain,
% 0.63/0.83 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[816, 812])).
% 0.63/0.83 tff(818,plain,(
% 0.63/0.83 ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[817])).
% 0.63/0.83 tff(819,plain,
% 0.63/0.83 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[818, 811])).
% 0.63/0.83 tff(820,plain,
% 0.63/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(821,plain,
% 0.63/0.83 ((hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642))) <=> (hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(822,plain,
% 0.63/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[821])).
% 0.63/0.83 tff(823,plain,
% 0.63/0.83 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[822, 820])).
% 0.63/0.83 tff(824,plain,
% 0.63/0.83 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(825,plain,
% 0.63/0.83 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.63/0.83 tff(826,plain,
% 0.63/0.83 (hskp18 | hskp4),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[825, 96, 708, 705, 704, 819])).
% 0.63/0.83 tff(827,plain,
% 0.63/0.83 (hskp18),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[826, 809])).
% 0.63/0.83 tff(828,plain,
% 0.63/0.83 (~c2_1(a676)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[212, 827])).
% 0.63/0.83 tff(829,plain,
% 0.63/0.83 (c1_1(a676)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[608, 827])).
% 0.63/0.83 tff(830,plain,
% 0.63/0.83 (c0_1(a676)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[539, 827])).
% 0.63/0.83 tff(831,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[615, 96, 716, 830, 829, 715, 714, 828, 197, 723])).
% 0.63/0.83 tff(832,plain,(hskp7 | hskp5 | hskp2 | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(833,plain,
% 0.63/0.83 (hskp7),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[832, 2, 24, 23, 1])).
% 0.63/0.83 tff(834,plain,
% 0.63/0.83 (c3_1(a698)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[360, 833, 702, 24, 701, 23])).
% 0.63/0.83 tff(835,assumption,(hskp23), introduced(assumption)).
% 0.63/0.83 tff(836,plain,
% 0.63/0.83 (~c3_1(a695)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[571, 835])).
% 0.63/0.83 tff(837,plain,
% 0.63/0.83 (~c0_1(a695)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[577, 835])).
% 0.63/0.83 tff(838,plain,
% 0.63/0.83 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(839,plain,
% 0.63/0.83 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695)) <=> (hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(840,plain,
% 0.63/0.83 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695)))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[839])).
% 0.63/0.83 tff(841,plain,
% 0.63/0.83 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))),
% 0.63/0.83 inference(transitivity,[status(thm)],[840, 838])).
% 0.63/0.83 tff(842,plain,
% 0.63/0.83 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(843,plain,
% 0.63/0.83 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.63/0.83 tff(844,plain,
% 0.63/0.83 (c1_1(a695)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[843, 96, 24, 23, 837, 836, 125])).
% 0.63/0.83 tff(845,plain,
% 0.63/0.83 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(846,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_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) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[845])).
% 0.63/0.83 tff(847,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_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) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(848,plain,
% 0.63/0.83 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(849,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[848])).
% 0.63/0.83 tff(850,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.63/0.83 tff(851,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.63/0.83 tff(852,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[851, 847])).
% 0.63/0.83 tff(853,plain,(
% 0.63/0.83 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[852])).
% 0.63/0.83 tff(854,plain,
% 0.63/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[853, 846])).
% 0.63/0.83 tff(855,plain,
% 0.63/0.83 (c2_1(a695)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[593, 835])).
% 0.63/0.83 tff(856,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(857,plain,
% 0.63/0.83 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695))) <=> (c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(858,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[857])).
% 0.63/0.83 tff(859,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[858, 856])).
% 0.63/0.83 tff(860,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(861,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.63/0.83 tff(862,plain,
% 0.63/0.83 ((~c2_1(a642)) | (~c1_1(a695))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[861, 96, 800, 799, 798, 855, 387, 837, 386, 854])).
% 0.63/0.83 tff(863,plain,
% 0.63/0.83 (~c2_1(a642)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[862, 844])).
% 0.63/0.83 tff(864,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[722, 96, 855, 406, 837, 836, 386, 223, 863, 844])).
% 0.63/0.83 tff(865,plain,((~hskp23) | (~c0_1(a642)) | c1_1(a642) | (~c0_1(a671)) | (~c1_1(a671)) | (~c2_1(a671)) | (~c3_1(a642)) | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(866,plain,
% 0.63/0.83 (~hskp23),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[865, 708, 704, 767, 759, 751, 705, 24, 23])).
% 0.63/0.83 tff(867,plain,
% 0.63/0.83 (^[U: $i] : refl((hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(868,plain,
% 0.63/0.83 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[867])).
% 0.63/0.83 tff(869,plain,
% 0.63/0.83 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(870,plain,
% 0.63/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25) <=> ((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(871,plain,
% 0.63/0.83 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[870])).
% 0.63/0.83 tff(872,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.63/0.83 tff(873,plain,
% 0.63/0.83 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.63/0.83 tff(874,plain,
% 0.63/0.83 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[873, 869])).
% 0.63/0.83 tff(875,plain,(
% 0.63/0.83 ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[874])).
% 0.63/0.83 tff(876,plain,
% 0.63/0.83 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[875, 868])).
% 0.63/0.83 tff(877,plain,
% 0.63/0.83 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(878,plain,
% 0.63/0.83 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(879,plain,
% 0.63/0.83 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[878, 877])).
% 0.63/0.83 tff(880,plain,
% 0.63/0.83 (hskp25 | hskp23),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[879, 96, 767, 759, 751, 876])).
% 0.63/0.83 tff(881,plain,
% 0.63/0.83 (hskp25),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[880, 866])).
% 0.63/0.83 tff(882,plain,
% 0.63/0.83 (((~hskp25) | (~c3_1(a710))) <=> ((~hskp25) | (~c3_1(a710)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(883,plain,
% 0.63/0.83 (((~c3_1(a710)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a710)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(884,axiom,((~c3_1(a710)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.63/0.83 tff(885,plain,
% 0.63/0.83 ((~hskp25) | (~c3_1(a710))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.63/0.83 tff(886,plain,
% 0.63/0.83 ((~hskp25) | (~c3_1(a710))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[885, 882])).
% 0.63/0.83 tff(887,plain,
% 0.63/0.83 (~c3_1(a710)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[886, 881])).
% 0.63/0.83 tff(888,plain,
% 0.63/0.83 (((~hskp25) | (~c0_1(a710))) <=> ((~hskp25) | (~c0_1(a710)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(889,plain,
% 0.63/0.83 (((~c0_1(a710)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a710)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(890,axiom,((~c0_1(a710)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.63/0.83 tff(891,plain,
% 0.63/0.83 ((~hskp25) | (~c0_1(a710))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.63/0.83 tff(892,plain,
% 0.63/0.83 ((~hskp25) | (~c0_1(a710))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[891, 888])).
% 0.63/0.83 tff(893,plain,
% 0.63/0.83 (~c0_1(a710)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[892, 881])).
% 0.63/0.83 tff(894,plain,
% 0.63/0.83 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(895,plain,
% 0.63/0.83 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710)) <=> (hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(896,plain,
% 0.63/0.83 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710)))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[895])).
% 0.63/0.83 tff(897,plain,
% 0.63/0.83 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))),
% 0.63/0.83 inference(transitivity,[status(thm)],[896, 894])).
% 0.63/0.83 tff(898,plain,
% 0.63/0.83 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(899,plain,
% 0.63/0.83 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.63/0.83 tff(900,plain,
% 0.63/0.83 (c1_1(a710)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[899, 96, 24, 23, 893, 887, 125])).
% 0.63/0.83 tff(901,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(902,plain,
% 0.63/0.83 ((hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710))) <=> (hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(903,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[902])).
% 0.63/0.83 tff(904,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[903, 901])).
% 0.63/0.83 tff(905,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(906,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[905, 904])).
% 0.63/0.83 tff(907,plain,
% 0.63/0.83 (hskp6 | (~c3_1(a698))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[906, 96, 701, 893, 887, 702, 266, 900])).
% 0.63/0.83 tff(908,plain,
% 0.63/0.83 (hskp6),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[907, 834])).
% 0.63/0.83 tff(909,plain,
% 0.63/0.83 (~c3_1(a648)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[108, 908])).
% 0.63/0.83 tff(910,plain,
% 0.63/0.83 (~c2_1(a648)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[114, 908])).
% 0.63/0.83 tff(911,plain,
% 0.63/0.83 (~c1_1(a651)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[145, 833])).
% 0.63/0.83 tff(912,plain,
% 0.63/0.83 (~c0_1(a651)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[151, 833])).
% 0.63/0.83 tff(913,plain,
% 0.63/0.83 (c3_1(a651)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[159, 833])).
% 0.63/0.83 tff(914,plain,
% 0.63/0.83 (~c1_1(a648)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[166, 96, 24, 913, 912, 911, 910, 909, 34])).
% 0.63/0.83 tff(915,plain,
% 0.63/0.83 (c2_1(a642)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[712, 2, 866])).
% 0.63/0.83 tff(916,plain,
% 0.63/0.83 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(917,plain,
% 0.63/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[916])).
% 0.63/0.84 tff(918,plain,
% 0.63/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(919,plain,
% 0.63/0.84 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(920,plain,
% 0.67/0.84 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_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) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[919])).
% 0.67/0.84 tff(921,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.67/0.84 tff(922,plain,
% 0.67/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.67/0.84 tff(923,plain,
% 0.67/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[922, 918])).
% 0.67/0.84 tff(924,plain,(
% 0.67/0.84 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.67/0.84 inference(skolemize,[status(sab)],[923])).
% 0.67/0.84 tff(925,plain,
% 0.67/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[924, 917])).
% 0.67/0.84 tff(926,plain,
% 0.67/0.84 (~c0_1(a698)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[244, 700])).
% 0.67/0.84 tff(927,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(928,plain,
% 0.67/0.84 ((hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710))) <=> (hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(929,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[928])).
% 0.67/0.84 tff(930,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[929, 927])).
% 0.67/0.84 tff(931,plain,
% 0.67/0.84 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(932,plain,
% 0.67/0.84 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.67/0.84 tff(933,plain,
% 0.67/0.84 (hskp11 | (~c3_1(a698))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[932, 96, 701, 893, 887, 926, 288, 900])).
% 0.67/0.84 tff(934,plain,
% 0.67/0.84 (hskp11),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[933, 834])).
% 0.67/0.84 tff(935,plain,
% 0.67/0.84 (~c3_1(a657)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[302, 934])).
% 0.67/0.84 tff(936,plain,
% 0.67/0.84 (c0_1(a648)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[310, 908])).
% 0.67/0.84 tff(937,plain,
% 0.67/0.84 (c2_1(a657)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[318, 934])).
% 0.67/0.84 tff(938,plain,
% 0.67/0.84 (c0_1(a657)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[326, 934])).
% 0.67/0.84 tff(939,plain,
% 0.67/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(940,plain,
% 0.67/0.84 (((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648))) <=> (c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(941,plain,
% 0.67/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[940])).
% 0.67/0.84 tff(942,plain,
% 0.67/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[941, 939])).
% 0.67/0.84 tff(943,plain,
% 0.67/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(944,plain,
% 0.67/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[943, 942])).
% 0.67/0.84 tff(945,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[944, 96, 938, 937, 936, 708, 935, 909, 704, 925, 915, 914])).
% 0.67/0.84 tff(946,plain,(hskp5 | hskp2 | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.84 tff(947,plain,
% 0.67/0.84 (hskp5),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[946, 1, 23, 24])).
% 0.67/0.84 tff(948,plain,
% 0.67/0.84 (~c0_1(a647)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[493, 947])).
% 0.67/0.84 tff(949,plain,
% 0.67/0.84 (~c3_1(a647)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[623, 947])).
% 0.67/0.84 tff(950,plain,
% 0.67/0.84 (~c3_1(a698)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[335, 254, 701, 246, 926, 224, 702])).
% 0.67/0.84 tff(951,plain,
% 0.67/0.84 (~hskp7),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[360, 950, 702, 24, 701, 23])).
% 0.67/0.84 tff(952,plain,
% 0.67/0.84 (~c2_1(a642)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[706, 951])).
% 0.67/0.84 tff(953,assumption,(~c2_1(a642)), introduced(assumption)).
% 0.67/0.84 tff(954,assumption,(~c0_1(a686)), introduced(assumption)).
% 0.67/0.84 tff(955,assumption,(~c3_1(a686)), introduced(assumption)).
% 0.67/0.84 tff(956,assumption,(c2_1(a686)), introduced(assumption)).
% 0.67/0.84 tff(957,assumption,(c1_1(a686)), introduced(assumption)).
% 0.67/0.84 tff(958,plain,
% 0.67/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(959,plain,
% 0.67/0.84 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686))) <=> (c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(960,plain,
% 0.67/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[959])).
% 0.67/0.84 tff(961,plain,
% 0.67/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[960, 958])).
% 0.67/0.84 tff(962,plain,
% 0.67/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(963,plain,
% 0.67/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.67/0.84 tff(964,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[963, 96, 957, 956, 406, 955, 386, 223, 954, 953])).
% 0.67/0.84 tff(965,plain,(c0_1(a686) | (~c1_1(a686)) | (~c2_1(a686)) | (~c0_1(a642)) | c3_1(a686) | c1_1(a642) | c2_1(a642)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.84 tff(966,plain,
% 0.67/0.84 (c0_1(a686)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[965, 952, 664, 708, 655, 704, 679])).
% 0.67/0.84 tff(967,plain,
% 0.67/0.84 (~hskp4),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[808, 951, 767, 759, 751, 24, 23])).
% 0.67/0.84 tff(968,plain,
% 0.67/0.84 (hskp18),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[826, 967])).
% 0.67/0.84 tff(969,plain,
% 0.67/0.84 (~c2_1(a676)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[212, 968])).
% 0.67/0.84 tff(970,plain,
% 0.67/0.84 (c0_1(a676)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[539, 968])).
% 0.67/0.84 tff(971,assumption,(~c3_1(a676)), introduced(assumption)).
% 0.67/0.84 tff(972,assumption,(c0_1(a686)), introduced(assumption)).
% 0.67/0.84 tff(973,assumption,(~c2_1(a676)), introduced(assumption)).
% 0.67/0.84 tff(974,assumption,(c0_1(a676)), introduced(assumption)).
% 0.67/0.84 tff(975,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(976,plain,
% 0.67/0.84 (((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676))) <=> (c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(977,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[976])).
% 0.67/0.84 tff(978,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[977, 975])).
% 0.67/0.84 tff(979,plain,
% 0.67/0.84 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(980,plain,
% 0.67/0.84 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.67/0.84 tff(981,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[980, 96, 956, 974, 955, 973, 177, 972, 971])).
% 0.67/0.84 tff(982,plain,(c3_1(a676) | (~c2_1(a686)) | (~c0_1(a676)) | c3_1(a686) | c2_1(a676) | (~c0_1(a686))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.84 tff(983,plain,
% 0.67/0.84 (c3_1(a676)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[982, 970, 664, 655, 969, 966])).
% 0.67/0.84 tff(984,plain,
% 0.67/0.84 (c1_1(a676)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[608, 968])).
% 0.67/0.84 tff(985,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(986,plain,
% 0.67/0.84 ((hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(987,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[986])).
% 0.67/0.84 tff(988,plain,
% 0.67/0.84 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[987, 985])).
% 0.67/0.84 tff(989,plain,
% 0.67/0.84 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(990,plain,
% 0.67/0.84 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.67/0.84 tff(991,plain,
% 0.67/0.84 (hskp6 | (~c3_1(a676))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[990, 96, 984, 254, 969, 246, 224, 266])).
% 0.67/0.84 tff(992,plain,
% 0.67/0.84 (hskp6),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[991, 983])).
% 0.67/0.84 tff(993,plain,
% 0.67/0.84 (~c3_1(a648)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[108, 992])).
% 0.67/0.84 tff(994,plain,
% 0.67/0.84 (~c2_1(a648)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[114, 992])).
% 0.67/0.84 tff(995,plain,
% 0.67/0.84 (c0_1(a648)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[310, 992])).
% 0.67/0.84 tff(996,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[670, 96, 664, 995, 655, 994, 993, 177, 966])).
% 0.67/0.84 tff(997,plain,(c0_1(a647) | c3_1(a647) | hskp2 | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.84 tff(998,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[997, 949, 948, 24, 23, 1])).
% 0.67/0.84 tff(999,plain,(hskp17 | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.67/0.84 tff(1000,plain,
% 0.67/0.84 (hskp17),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[999, 24, 23])).
% 0.67/0.84 tff(1001,plain,
% 0.67/0.84 (((~hskp17) | (~c1_1(a675))) <=> ((~hskp17) | (~c1_1(a675)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(1002,plain,
% 0.67/0.84 (((~c1_1(a675)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a675)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(1003,axiom,((~c1_1(a675)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.67/0.84 tff(1004,plain,
% 0.67/0.84 ((~hskp17) | (~c1_1(a675))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.67/0.84 tff(1005,plain,
% 0.67/0.84 ((~hskp17) | (~c1_1(a675))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[1004, 1001])).
% 0.67/0.84 tff(1006,plain,
% 0.67/0.84 (~c1_1(a675)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[1005, 1000])).
% 0.67/0.84 tff(1007,plain,
% 0.67/0.84 (((~hskp17) | (~c3_1(a675))) <=> ((~hskp17) | (~c3_1(a675)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(1008,plain,
% 0.67/0.84 (((~c3_1(a675)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a675)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(1009,axiom,((~c3_1(a675)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.67/0.84 tff(1010,plain,
% 0.67/0.84 ((~hskp17) | (~c3_1(a675))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.67/0.84 tff(1011,plain,
% 0.67/0.84 ((~hskp17) | (~c3_1(a675))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[1010, 1007])).
% 0.67/0.84 tff(1012,plain,
% 0.67/0.84 (~c3_1(a675)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[1011, 1000])).
% 0.67/0.84 tff(1013,assumption,(~c3_1(a675)), introduced(assumption)).
% 0.67/0.84 tff(1014,assumption,(~c1_1(a675)), introduced(assumption)).
% 0.67/0.84 tff(1015,plain,
% 0.67/0.84 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(1016,plain,
% 0.67/0.84 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675)) <=> (hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(1017,plain,
% 0.67/0.84 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675)))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[1016])).
% 0.67/0.84 tff(1018,plain,
% 0.67/0.84 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))),
% 0.67/0.84 inference(transitivity,[status(thm)],[1017, 1015])).
% 0.67/0.84 tff(1019,plain,
% 0.67/0.84 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(1020,plain,
% 0.67/0.84 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675)),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.67/0.84 tff(1021,plain,
% 0.67/0.84 (c3_1(a675) | c0_1(a675)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[1020, 96, 24, 23, 1014, 125])).
% 0.67/0.84 tff(1022,plain,
% 0.67/0.84 (c0_1(a675)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[1021, 1013])).
% 0.67/0.84 tff(1023,plain,
% 0.67/0.84 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(1024,plain,
% 0.67/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_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)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[1023])).
% 0.67/0.84 tff(1025,plain,
% 0.67/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_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)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(1026,plain,
% 0.67/0.84 (^[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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | 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) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(1027,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[1026])).
% 0.67/0.85 tff(1028,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.67/0.85 tff(1029,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.67/0.85 tff(1030,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1029, 1025])).
% 0.67/0.85 tff(1031,plain,(
% 0.67/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.67/0.85 inference(skolemize,[status(sab)],[1030])).
% 0.67/0.85 tff(1032,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1031, 1024])).
% 0.67/0.85 tff(1033,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1034,plain,
% 0.67/0.85 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698))) <=> (c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1035,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1034])).
% 0.67/0.85 tff(1036,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1035, 1033])).
% 0.67/0.85 tff(1037,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1038,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 0.67/0.85 tff(1039,plain,
% 0.67/0.85 (~c3_1(a698)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1038, 96, 239, 540, 609, 245, 213, 1014, 1013, 1032, 1022])).
% 0.67/0.85 tff(1040,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1041,plain,
% 0.67/0.85 (((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675))) <=> (c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1042,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1041])).
% 0.67/0.85 tff(1043,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1042, 1040])).
% 0.67/0.85 tff(1044,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1045,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.67/0.85 tff(1046,plain,
% 0.67/0.85 (~c2_1(a675)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1045, 96, 1014, 1013, 925, 1022])).
% 0.67/0.85 tff(1047,plain,
% 0.67/0.85 (((~hskp17) | c2_1(a675)) <=> ((~hskp17) | c2_1(a675))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1048,axiom,((~hskp17) | c2_1(a675)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.67/0.85 tff(1049,plain,
% 0.67/0.85 ((~hskp17) | c2_1(a675)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.67/0.85 tff(1050,plain,
% 0.67/0.85 ((~hskp17) | c2_1(a675)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1049, 1047])).
% 0.67/0.85 tff(1051,plain,
% 0.67/0.85 ((~hskp17) | c2_1(a675)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1050, 1047])).
% 0.67/0.85 tff(1052,plain,
% 0.67/0.85 ((~hskp17) | c2_1(a675)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1051, 1047])).
% 0.67/0.85 tff(1053,plain,
% 0.67/0.85 ((~hskp17) | c2_1(a675)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1052, 1047])).
% 0.67/0.85 tff(1054,plain,
% 0.67/0.85 (~hskp17),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1053, 1046])).
% 0.67/0.85 tff(1055,plain,
% 0.67/0.85 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1056,plain,
% 0.67/0.85 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675))) <=> (hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1057,plain,
% 0.67/0.85 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1056])).
% 0.67/0.85 tff(1058,plain,
% 0.67/0.85 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1057, 1055])).
% 0.67/0.85 tff(1059,plain,
% 0.67/0.85 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1060,plain,
% 0.67/0.85 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.67/0.85 tff(1061,plain,
% 0.67/0.85 (hskp20 | hskp5 | c2_1(a675)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1060, 96, 1013, 187, 1022])).
% 0.67/0.85 tff(1062,plain,
% 0.67/0.85 (hskp5),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1061, 198, 1046])).
% 0.67/0.85 tff(1063,plain,
% 0.67/0.85 (~c3_1(a647)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[623, 1062])).
% 0.67/0.85 tff(1064,plain,
% 0.67/0.85 (~c0_1(a647)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[493, 1062])).
% 0.67/0.85 tff(1065,plain,
% 0.67/0.85 (((~hskp5) | c1_1(a647)) <=> ((~hskp5) | c1_1(a647))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1066,axiom,((~hskp5) | c1_1(a647)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.67/0.85 tff(1067,plain,
% 0.67/0.85 ((~hskp5) | c1_1(a647)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.67/0.85 tff(1068,plain,
% 0.67/0.85 ((~hskp5) | c1_1(a647)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1067, 1065])).
% 0.67/0.85 tff(1069,plain,
% 0.67/0.85 ((~hskp5) | c1_1(a647)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1068, 1065])).
% 0.67/0.85 tff(1070,plain,
% 0.67/0.85 ((~hskp5) | c1_1(a647)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1069, 1065])).
% 0.67/0.85 tff(1071,plain,
% 0.67/0.85 ((~hskp5) | c1_1(a647)),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1070, 1065])).
% 0.67/0.85 tff(1072,plain,
% 0.67/0.85 (c1_1(a647)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1071, 1062])).
% 0.67/0.85 tff(1073,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1074,plain,
% 0.67/0.85 (((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1075,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1074])).
% 0.67/0.85 tff(1076,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1075, 1073])).
% 0.67/0.85 tff(1077,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1078,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.67/0.85 tff(1079,plain,
% 0.67/0.85 (~c2_1(a647)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1078, 96, 1046, 1072, 1014, 1064, 1063, 223, 1022])).
% 0.67/0.85 tff(1080,assumption,(~c2_1(a647)), introduced(assumption)).
% 0.67/0.85 tff(1081,plain,
% 0.67/0.85 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(1082,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[1081])).
% 0.67/0.85 tff(1083,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1084,plain,
% 0.67/0.85 (^[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))) | (~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)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_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)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_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)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(1085,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[1084])).
% 0.67/0.85 tff(1086,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.67/0.85 tff(1087,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.67/0.85 tff(1088,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1087, 1083])).
% 0.67/0.85 tff(1089,plain,(
% 0.67/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.67/0.85 inference(skolemize,[status(sab)],[1088])).
% 0.67/0.85 tff(1090,plain,
% 0.67/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1089, 1082])).
% 0.67/0.85 tff(1091,assumption,(c0_1(a675)), introduced(assumption)).
% 0.67/0.85 tff(1092,plain,
% 0.67/0.85 (~c2_1(a675)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1045, 96, 1014, 1013, 925, 1091])).
% 0.67/0.85 tff(1093,assumption,(hskp28), introduced(assumption)).
% 0.67/0.85 tff(1094,plain,
% 0.67/0.85 (c1_1(a671)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[758, 1093])).
% 0.67/0.85 tff(1095,plain,
% 0.67/0.85 (c0_1(a671)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[766, 1093])).
% 0.67/0.85 tff(1096,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1097,plain,
% 0.67/0.85 (((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647)) <=> (c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1098,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1097])).
% 0.67/0.85 tff(1099,plain,
% 0.67/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1098, 1096])).
% 0.67/0.85 tff(1100,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1101,plain,
% 0.67/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 0.67/0.85 tff(1102,plain,
% 0.67/0.85 (~c3_1(a671)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1101, 96, 1095, 1094, 1092, 1014, 1013, 246, 224, 1090, 1080])).
% 0.67/0.85 tff(1103,plain,
% 0.67/0.85 (c2_1(a671)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[750, 1093])).
% 0.67/0.85 tff(1104,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1105,plain,
% 0.67/0.85 (((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675))) <=> (c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1106,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[1105])).
% 0.67/0.85 tff(1107,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[1106, 1104])).
% 0.67/0.85 tff(1108,plain,
% 0.67/0.85 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(1109,plain,
% 0.67/0.85 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.67/0.85 tff(1110,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1109, 96, 1095, 1103, 1092, 1013, 177, 1091, 1102])).
% 0.67/0.85 tff(1111,plain,((~hskp28) | c3_1(a675) | (~c0_1(a675)) | c1_1(a675) | c0_1(a647) | c3_1(a647) | c2_1(a647)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(1112,plain,
% 0.67/0.85 (~hskp28),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1111, 1064, 1022, 1014, 1013, 1063, 1079])).
% 0.67/0.85 tff(1113,plain,
% 0.67/0.85 (~hskp1),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[742, 1112, 1054])).
% 0.67/0.85 tff(1114,plain,
% 0.67/0.85 (hskp14),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[469, 1113, 1054])).
% 0.67/0.85 tff(1115,plain,
% 0.67/0.85 (~c0_1(a665)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[56, 1114])).
% 0.67/0.85 tff(1116,plain,
% 0.67/0.85 (~c1_1(a665)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[50, 1114])).
% 0.67/0.85 tff(1117,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[485, 1116, 1115, 23, 24, 239, 231, 1039])).
% 0.67/0.85 tff(1118,plain,(hskp20 | hskp0 | hskp2 | c1_1(a675) | c3_1(a675)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(1119,plain,
% 0.67/0.85 (hskp20),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[1118, 1013, 24, 1014, 23])).
% 0.67/0.85 tff(1120,plain,
% 0.67/0.85 (~c3_1(a686)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[654, 1119])).
% 0.67/0.85 tff(1121,plain,
% 0.67/0.85 (c2_1(a686)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[663, 1119])).
% 0.67/0.85 tff(1122,plain,
% 0.67/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(1123,plain,
% 0.67/0.85 (((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675))) <=> (c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1124,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1123])).
% 0.67/0.86 tff(1125,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1124, 1122])).
% 0.67/0.86 tff(1126,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1127,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.67/0.86 tff(1128,plain,
% 0.67/0.86 (~c0_1(a686)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1127, 96, 1121, 1046, 1120, 1013, 177, 1022])).
% 0.67/0.86 tff(1129,plain,
% 0.67/0.86 (c1_1(a686)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[678, 1119])).
% 0.67/0.86 tff(1130,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1131,plain,
% 0.67/0.86 (((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686))) <=> (c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1132,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1131])).
% 0.67/0.86 tff(1133,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1132, 1130])).
% 0.67/0.86 tff(1134,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1135,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.67/0.86 tff(1136,plain,
% 0.67/0.86 ($false),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1135, 96, 1129, 1121, 1046, 1120, 1014, 223, 1022, 1128])).
% 0.67/0.86 tff(1137,plain,(c3_1(a675) | c1_1(a675) | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.67/0.86 tff(1138,plain,
% 0.67/0.86 ($false),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1137, 1012, 1006, 24, 23])).
% 0.67/0.86 tff(1139,plain,(hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.67/0.86 tff(1140,plain,
% 0.67/0.86 (hskp2),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1139, 23])).
% 0.67/0.86 tff(1141,plain,
% 0.67/0.86 (((~hskp2) | (~c0_1(a643))) <=> ((~hskp2) | (~c0_1(a643)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1142,plain,
% 0.67/0.86 (((~c0_1(a643)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a643)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1143,axiom,((~c0_1(a643)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.67/0.86 tff(1144,plain,
% 0.67/0.86 ((~hskp2) | (~c0_1(a643))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 0.67/0.86 tff(1145,plain,
% 0.67/0.86 ((~hskp2) | (~c0_1(a643))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1144, 1141])).
% 0.67/0.86 tff(1146,plain,
% 0.67/0.86 (~c0_1(a643)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1145, 1140])).
% 0.67/0.86 tff(1147,plain,
% 0.67/0.86 (((~hskp2) | c2_1(a643)) <=> ((~hskp2) | c2_1(a643))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1148,axiom,((~hskp2) | c2_1(a643)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.67/0.86 tff(1149,plain,
% 0.67/0.86 ((~hskp2) | c2_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.67/0.86 tff(1150,plain,
% 0.67/0.86 ((~hskp2) | c2_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1149, 1147])).
% 0.67/0.86 tff(1151,plain,
% 0.67/0.86 ((~hskp2) | c2_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1150, 1147])).
% 0.67/0.86 tff(1152,plain,
% 0.67/0.86 ((~hskp2) | c2_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1151, 1147])).
% 0.67/0.86 tff(1153,plain,
% 0.67/0.86 ((~hskp2) | c2_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1152, 1147])).
% 0.67/0.86 tff(1154,plain,
% 0.67/0.86 (c2_1(a643)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1153, 1140])).
% 0.67/0.86 tff(1155,plain,
% 0.67/0.86 (((~hskp2) | c1_1(a643)) <=> ((~hskp2) | c1_1(a643))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1156,axiom,((~hskp2) | c1_1(a643)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.67/0.86 tff(1157,plain,
% 0.67/0.86 ((~hskp2) | c1_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.67/0.86 tff(1158,plain,
% 0.67/0.86 ((~hskp2) | c1_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1157, 1155])).
% 0.67/0.86 tff(1159,plain,
% 0.67/0.86 ((~hskp2) | c1_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1158, 1155])).
% 0.67/0.86 tff(1160,plain,
% 0.67/0.86 ((~hskp2) | c1_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1159, 1155])).
% 0.67/0.86 tff(1161,plain,
% 0.67/0.86 ((~hskp2) | c1_1(a643)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1160, 1155])).
% 0.67/0.86 tff(1162,plain,
% 0.67/0.86 (c1_1(a643)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1161, 1140])).
% 0.67/0.86 tff(1163,assumption,(c1_1(a643)), introduced(assumption)).
% 0.67/0.86 tff(1164,assumption,(~c0_1(a643)), introduced(assumption)).
% 0.67/0.86 tff(1165,assumption,(c2_1(a643)), introduced(assumption)).
% 0.67/0.86 tff(1166,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1167,plain,
% 0.67/0.86 ((hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665))) <=> (hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1168,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665)))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1167])).
% 0.67/0.86 tff(1169,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1168, 1166])).
% 0.67/0.86 tff(1170,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1171,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 0.67/0.86 tff(1172,plain,
% 0.67/0.86 (c3_1(a665)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1171, 96, 2, 65, 57, 51, 12])).
% 0.67/0.86 tff(1173,plain,
% 0.67/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(1174,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[1173])).
% 0.67/0.86 tff(1175,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1176,plain,
% 0.67/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(1177,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[1176])).
% 0.67/0.86 tff(1178,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.67/0.86 tff(1179,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 0.67/0.86 tff(1180,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1179, 1175])).
% 0.67/0.86 tff(1181,plain,(
% 0.67/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.67/0.86 inference(skolemize,[status(sab)],[1180])).
% 0.67/0.86 tff(1182,plain,
% 0.67/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1181, 1174])).
% 0.67/0.86 tff(1183,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1184,plain,
% 0.67/0.86 (((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1185,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1184])).
% 0.67/0.86 tff(1186,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1185, 1183])).
% 0.67/0.86 tff(1187,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1188,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.67/0.86 tff(1189,plain,
% 0.67/0.86 (~c3_1(a643)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1188, 96, 65, 1163, 1165, 51, 1164, 1182, 1172])).
% 0.67/0.86 tff(1190,plain,
% 0.67/0.86 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(1191,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[1190])).
% 0.67/0.86 tff(1192,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1193,plain,
% 0.67/0.86 (^[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) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(1194,plain,
% 0.67/0.86 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[1193])).
% 0.67/0.86 tff(1195,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.67/0.86 tff(1196,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 0.67/0.86 tff(1197,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1196, 1192])).
% 0.67/0.86 tff(1198,plain,(
% 0.67/0.86 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(skolemize,[status(sab)],[1197])).
% 0.67/0.86 tff(1199,plain,
% 0.67/0.86 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1198, 1191])).
% 0.67/0.86 tff(1200,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1201,plain,
% 0.67/0.86 ((hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643))) <=> (hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1202,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1201])).
% 0.67/0.86 tff(1203,plain,
% 0.67/0.86 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1202, 1200])).
% 0.67/0.86 tff(1204,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1205,plain,
% 0.67/0.86 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.67/0.86 tff(1206,plain,
% 0.67/0.86 (hskp27),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1205, 96, 65, 1163, 51, 1164, 1199, 1189, 1172])).
% 0.67/0.86 tff(1207,plain,
% 0.67/0.86 (((~hskp27) | c3_1(a655)) <=> ((~hskp27) | c3_1(a655))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1208,axiom,((~hskp27) | c3_1(a655)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.67/0.86 tff(1209,plain,
% 0.67/0.86 ((~hskp27) | c3_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 0.67/0.86 tff(1210,plain,
% 0.67/0.86 ((~hskp27) | c3_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1209, 1207])).
% 0.67/0.86 tff(1211,plain,
% 0.67/0.86 ((~hskp27) | c3_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1210, 1207])).
% 0.67/0.86 tff(1212,plain,
% 0.67/0.86 ((~hskp27) | c3_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1211, 1207])).
% 0.67/0.86 tff(1213,plain,
% 0.67/0.86 ((~hskp27) | c3_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1212, 1207])).
% 0.67/0.86 tff(1214,plain,
% 0.67/0.86 (c3_1(a655)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1213, 1206])).
% 0.67/0.86 tff(1215,plain,
% 0.67/0.86 (((~hskp27) | c2_1(a655)) <=> ((~hskp27) | c2_1(a655))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1216,axiom,((~hskp27) | c2_1(a655)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.67/0.86 tff(1217,plain,
% 0.67/0.86 ((~hskp27) | c2_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 0.67/0.86 tff(1218,plain,
% 0.67/0.86 ((~hskp27) | c2_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1217, 1215])).
% 0.67/0.86 tff(1219,plain,
% 0.67/0.86 ((~hskp27) | c2_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1218, 1215])).
% 0.67/0.86 tff(1220,plain,
% 0.67/0.86 ((~hskp27) | c2_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1219, 1215])).
% 0.67/0.86 tff(1221,plain,
% 0.67/0.86 ((~hskp27) | c2_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1220, 1215])).
% 0.67/0.86 tff(1222,plain,
% 0.67/0.86 (c2_1(a655)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1221, 1206])).
% 0.67/0.86 tff(1223,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1224,plain,
% 0.67/0.86 (((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1225,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1224])).
% 0.67/0.86 tff(1226,plain,
% 0.67/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1225, 1223])).
% 0.67/0.86 tff(1227,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1228,plain,
% 0.67/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.67/0.86 tff(1229,plain,
% 0.67/0.86 (~c1_1(a655)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1228, 96, 1222, 1214, 65, 1163, 1165, 51, 1164, 1182, 1172])).
% 0.67/0.86 tff(1230,plain,
% 0.67/0.86 (((~hskp27) | c0_1(a655)) <=> ((~hskp27) | c0_1(a655))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1231,axiom,((~hskp27) | c0_1(a655)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.67/0.86 tff(1232,plain,
% 0.67/0.86 ((~hskp27) | c0_1(a655)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.67/0.86 tff(1233,plain,
% 0.67/0.86 ((~hskp27) | c0_1(a655)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1232, 1230])).
% 0.67/0.87 tff(1234,plain,
% 0.67/0.87 ((~hskp27) | c0_1(a655)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1233, 1230])).
% 0.67/0.87 tff(1235,plain,
% 0.67/0.87 ((~hskp27) | c0_1(a655)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1234, 1230])).
% 0.67/0.87 tff(1236,plain,
% 0.67/0.87 ((~hskp27) | c0_1(a655)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1235, 1230])).
% 0.67/0.87 tff(1237,plain,
% 0.67/0.87 (c0_1(a655)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1236, 1206])).
% 0.67/0.87 tff(1238,plain,
% 0.67/0.87 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1239,plain,
% 0.67/0.87 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1240,plain,
% 0.67/0.87 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 0.67/0.87 tff(1241,plain,
% 0.67/0.87 (hskp28 | c1_1(a655)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1240, 96, 1, 1237, 1214, 733])).
% 0.67/0.87 tff(1242,plain,
% 0.67/0.87 (hskp28),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1241, 1229])).
% 0.67/0.87 tff(1243,plain,
% 0.67/0.87 (c2_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[750, 1242])).
% 0.67/0.87 tff(1244,plain,
% 0.67/0.87 (c1_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[758, 1242])).
% 0.67/0.87 tff(1245,plain,
% 0.67/0.87 (c0_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[766, 1242])).
% 0.67/0.87 tff(1246,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1247,plain,
% 0.67/0.87 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1248,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1247])).
% 0.67/0.87 tff(1249,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1248, 1246])).
% 0.67/0.87 tff(1250,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1251,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.67/0.87 tff(1252,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1251, 96, 1245, 1244, 1243, 1222, 1214, 1163, 1165, 1164, 854, 1229])).
% 0.67/0.87 tff(1253,plain,((~hskp14) | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643) | hskp17 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(1254,plain,
% 0.67/0.87 (~hskp14),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1253, 2, 1165, 1164, 1, 1163])).
% 0.67/0.87 tff(1255,plain,
% 0.67/0.87 (hskp1),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[469, 1254, 1])).
% 0.67/0.87 tff(1256,plain,
% 0.67/0.87 (~c1_1(a642)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[367, 1255])).
% 0.67/0.87 tff(1257,plain,
% 0.67/0.87 (c3_1(a642)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[384, 1255])).
% 0.67/0.87 tff(1258,plain,
% 0.67/0.87 (hskp28),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[742, 1255, 1])).
% 0.67/0.87 tff(1259,plain,
% 0.67/0.87 (c2_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[750, 1258])).
% 0.67/0.87 tff(1260,plain,
% 0.67/0.87 (c1_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[758, 1258])).
% 0.67/0.87 tff(1261,plain,
% 0.67/0.87 (c0_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[766, 1258])).
% 0.67/0.87 tff(1262,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1263,plain,
% 0.67/0.87 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1264,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1263])).
% 0.67/0.87 tff(1265,plain,
% 0.67/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1264, 1262])).
% 0.67/0.87 tff(1266,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1267,plain,
% 0.67/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 0.67/0.87 tff(1268,plain,
% 0.67/0.87 (~c2_1(a642)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1267, 96, 1261, 1260, 1259, 1163, 1165, 1257, 1164, 1256, 854])).
% 0.67/0.87 tff(1269,plain,
% 0.67/0.87 (c0_1(a642)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[376, 1255])).
% 0.67/0.87 tff(1270,plain,
% 0.67/0.87 (hskp23),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[711, 96, 2, 1269, 1257, 558, 1268])).
% 0.67/0.87 tff(1271,plain,
% 0.67/0.87 (~c3_1(a695)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[571, 1270])).
% 0.67/0.87 tff(1272,plain,
% 0.67/0.87 (~c0_1(a695)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[577, 1270])).
% 0.67/0.87 tff(1273,plain,
% 0.67/0.87 (c2_1(a695)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[593, 1270])).
% 0.67/0.87 tff(1274,plain,
% 0.67/0.87 (~c1_1(a695)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[722, 96, 1273, 1269, 1272, 1271, 1256, 223, 1268])).
% 0.67/0.87 tff(1275,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1276,plain,
% 0.67/0.87 ((hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695))) <=> (hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1277,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1276])).
% 0.67/0.87 tff(1278,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1277, 1275])).
% 0.67/0.87 tff(1279,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1280,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 0.67/0.87 tff(1281,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1280, 96, 2, 1273, 1272, 1271, 12, 1274])).
% 0.67/0.87 tff(1282,plain,(hskp5 | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(1283,plain,
% 0.67/0.87 (hskp5),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1282, 1, 1154, 1146, 1162])).
% 0.67/0.87 tff(1284,plain,
% 0.67/0.87 (~c0_1(a647)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[493, 1283])).
% 0.67/0.87 tff(1285,plain,
% 0.67/0.87 (~c3_1(a647)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[623, 1283])).
% 0.67/0.87 tff(1286,assumption,(~hskp1), introduced(assumption)).
% 0.67/0.87 tff(1287,assumption,(c3_1(a665)), introduced(assumption)).
% 0.67/0.87 tff(1288,plain,
% 0.67/0.87 (hskp14),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[469, 1286, 1])).
% 0.67/0.87 tff(1289,plain,
% 0.67/0.87 (~c1_1(a665)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[50, 1288])).
% 0.67/0.87 tff(1290,plain,
% 0.67/0.87 (c2_1(a665)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[64, 1288])).
% 0.67/0.87 tff(1291,plain,
% 0.67/0.87 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(1292,plain,
% 0.67/0.87 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[1291])).
% 0.67/0.87 tff(1293,plain,
% 0.67/0.87 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1294,plain,
% 0.67/0.87 (^[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) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(1295,plain,
% 0.67/0.87 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[1294])).
% 0.67/0.87 tff(1296,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.67/0.87 tff(1297,plain,
% 0.67/0.87 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 0.67/0.87 tff(1298,plain,
% 0.67/0.87 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 0.67/0.87 tff(1299,plain,(
% 0.67/0.87 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.67/0.87 inference(skolemize,[status(sab)],[1298])).
% 0.67/0.87 tff(1300,plain,
% 0.67/0.87 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1299, 1292])).
% 0.67/0.87 tff(1301,plain,
% 0.67/0.87 (~c0_1(a665)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[56, 1288])).
% 0.67/0.87 tff(1302,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1303,plain,
% 0.67/0.87 ((hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647)) <=> (hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1304,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1303])).
% 0.67/0.87 tff(1305,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1304, 1302])).
% 0.67/0.87 tff(1306,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1307,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 0.67/0.87 tff(1308,plain,
% 0.67/0.87 (c1_1(a647) | (~c3_1(a665))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1307, 96, 1286, 1290, 1301, 246, 224, 1300])).
% 0.67/0.87 tff(1309,plain,
% 0.67/0.87 (c1_1(a647)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1308, 1287])).
% 0.67/0.87 tff(1310,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1311,plain,
% 0.67/0.87 ((hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1312,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1311])).
% 0.67/0.87 tff(1313,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1312, 1310])).
% 0.67/0.87 tff(1314,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1315,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.67/0.87 tff(1316,plain,
% 0.67/0.87 (hskp27 | (~c1_1(a647)) | (~c3_1(a665))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1315, 96, 1290, 1289, 246, 224, 1199])).
% 0.67/0.87 tff(1317,plain,
% 0.67/0.87 (hskp27),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1316, 1309, 1287])).
% 0.67/0.87 tff(1318,plain,
% 0.67/0.87 (c3_1(a655)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1213, 1317])).
% 0.67/0.87 tff(1319,plain,
% 0.67/0.87 (c2_1(a655)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1221, 1317])).
% 0.67/0.87 tff(1320,plain,
% 0.67/0.87 (~c1_1(a655)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1228, 96, 1319, 1318, 1290, 1163, 1165, 1289, 1164, 1182, 1287])).
% 0.67/0.87 tff(1321,plain,
% 0.67/0.87 (c0_1(a655)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1236, 1317])).
% 0.67/0.87 tff(1322,plain,
% 0.67/0.87 (hskp28 | c1_1(a655)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1240, 96, 1, 1321, 1318, 733])).
% 0.67/0.87 tff(1323,plain,
% 0.67/0.87 (hskp28),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1322, 1320])).
% 0.67/0.87 tff(1324,plain,
% 0.67/0.87 (c2_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[750, 1323])).
% 0.67/0.87 tff(1325,plain,
% 0.67/0.87 (c1_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[758, 1323])).
% 0.67/0.87 tff(1326,plain,
% 0.67/0.87 (c0_1(a671)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[766, 1323])).
% 0.67/0.87 tff(1327,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1251, 96, 1326, 1325, 1324, 1319, 1318, 1163, 1165, 1164, 854, 1320])).
% 0.67/0.87 tff(1328,plain,((~c3_1(a665)) | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643) | hskp17 | c0_1(a647) | c3_1(a647) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(1329,plain,
% 0.67/0.87 (~c3_1(a665)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1328, 1286, 1165, 1164, 1, 246, 224, 1163])).
% 0.67/0.87 tff(1330,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1331,plain,
% 0.67/0.87 ((hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665)) <=> (hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1332,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665)))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1331])).
% 0.67/0.87 tff(1333,plain,
% 0.67/0.87 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1332, 1330])).
% 0.67/0.87 tff(1334,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1335,plain,
% 0.67/0.87 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 0.67/0.87 tff(1336,plain,
% 0.67/0.87 (~c3_1(a643)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1335, 96, 1286, 1165, 1301, 1289, 1164, 1300, 1329])).
% 0.67/0.87 tff(1337,plain,
% 0.67/0.87 (hskp5 | c3_1(a665)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1171, 96, 1290, 1301, 1289, 12])).
% 0.67/0.87 tff(1338,plain,
% 0.67/0.87 (hskp5),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1337, 1329])).
% 0.67/0.87 tff(1339,plain,
% 0.67/0.87 (c1_1(a647)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1071, 1338])).
% 0.67/0.87 tff(1340,assumption,(~c3_1(a643)), introduced(assumption)).
% 0.67/0.87 tff(1341,assumption,(~hskp6), introduced(assumption)).
% 0.67/0.87 tff(1342,plain,
% 0.67/0.87 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(1343,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[1342])).
% 0.67/0.87 tff(1344,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1345,plain,
% 0.67/0.87 (^[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)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3) <=> ((hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(1346,plain,
% 0.67/0.87 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[1345])).
% 0.67/0.87 tff(1347,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.67/0.87 tff(1348,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 0.67/0.87 tff(1349,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1348, 1344])).
% 0.67/0.87 tff(1350,plain,(
% 0.67/0.87 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.67/0.87 inference(skolemize,[status(sab)],[1349])).
% 0.67/0.87 tff(1351,plain,
% 0.67/0.87 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1350, 1343])).
% 0.67/0.87 tff(1352,plain,
% 0.67/0.87 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1353,plain,
% 0.67/0.87 ((hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643))) <=> (hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1354,plain,
% 0.67/0.87 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643)))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1353])).
% 0.67/0.87 tff(1355,plain,
% 0.67/0.87 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1354, 1352])).
% 0.67/0.87 tff(1356,plain,
% 0.67/0.87 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1357,plain,
% 0.67/0.87 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 0.67/0.87 tff(1358,plain,
% 0.67/0.87 (hskp6 | hskp3 | c3_1(a643)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1357, 96, 1165, 1164, 1351])).
% 0.67/0.87 tff(1359,plain,
% 0.67/0.87 (hskp3),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1358, 1341, 1340])).
% 0.67/0.87 tff(1360,plain,
% 0.67/0.87 (((~hskp3) | (~c2_1(a645))) <=> ((~hskp3) | (~c2_1(a645)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1361,plain,
% 0.67/0.87 (((~c2_1(a645)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a645)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1362,axiom,((~c2_1(a645)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.67/0.88 tff(1363,plain,
% 0.67/0.88 ((~hskp3) | (~c2_1(a645))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 0.67/0.88 tff(1364,plain,
% 0.67/0.88 ((~hskp3) | (~c2_1(a645))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1363, 1360])).
% 0.67/0.88 tff(1365,plain,
% 0.67/0.88 (~c2_1(a645)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1364, 1359])).
% 0.67/0.88 tff(1366,plain,
% 0.67/0.88 (((~hskp3) | c3_1(a645)) <=> ((~hskp3) | c3_1(a645))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1367,axiom,((~hskp3) | c3_1(a645)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.67/0.88 tff(1368,plain,
% 0.67/0.88 ((~hskp3) | c3_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 0.67/0.88 tff(1369,plain,
% 0.67/0.88 ((~hskp3) | c3_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1368, 1366])).
% 0.67/0.88 tff(1370,plain,
% 0.67/0.88 ((~hskp3) | c3_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1369, 1366])).
% 0.67/0.88 tff(1371,plain,
% 0.67/0.88 ((~hskp3) | c3_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1370, 1366])).
% 0.67/0.88 tff(1372,plain,
% 0.67/0.88 ((~hskp3) | c3_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1371, 1366])).
% 0.67/0.88 tff(1373,plain,
% 0.67/0.88 (c3_1(a645)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1372, 1359])).
% 0.67/0.88 tff(1374,plain,
% 0.67/0.88 (((~hskp3) | c1_1(a645)) <=> ((~hskp3) | c1_1(a645))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1375,axiom,((~hskp3) | c1_1(a645)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.67/0.88 tff(1376,plain,
% 0.67/0.88 ((~hskp3) | c1_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 0.67/0.88 tff(1377,plain,
% 0.67/0.88 ((~hskp3) | c1_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1376, 1374])).
% 0.67/0.88 tff(1378,plain,
% 0.67/0.88 ((~hskp3) | c1_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1377, 1374])).
% 0.67/0.88 tff(1379,plain,
% 0.67/0.88 ((~hskp3) | c1_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1378, 1374])).
% 0.67/0.88 tff(1380,plain,
% 0.67/0.88 ((~hskp3) | c1_1(a645)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1379, 1374])).
% 0.67/0.88 tff(1381,plain,
% 0.67/0.88 (c1_1(a645)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1380, 1359])).
% 0.67/0.88 tff(1382,plain,
% 0.67/0.88 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1383,plain,
% 0.67/0.88 ((hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1384,plain,
% 0.67/0.88 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[1383])).
% 0.67/0.88 tff(1385,plain,
% 0.67/0.88 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))),
% 0.67/0.88 inference(transitivity,[status(thm)],[1384, 1382])).
% 0.67/0.88 tff(1386,plain,
% 0.67/0.88 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(1387,plain,
% 0.67/0.88 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 0.67/0.88 tff(1388,plain,
% 0.67/0.88 ($false),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1387, 96, 1341, 255, 1381, 1373, 246, 224, 1365, 266])).
% 0.67/0.88 tff(1389,plain,(hskp6 | (~c1_1(a647)) | c0_1(a647) | c3_1(a647) | c3_1(a643) | (~c2_1(a643)) | c0_1(a643)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.88 tff(1390,plain,
% 0.67/0.88 (hskp6),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1389, 1339, 246, 224, 1336, 1165, 1164])).
% 0.67/0.88 tff(1391,plain,
% 0.67/0.88 (~c2_1(a648)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[114, 1390])).
% 0.67/0.88 tff(1392,plain,
% 0.67/0.88 (c0_1(a648)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[310, 1390])).
% 0.67/0.88 tff(1393,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1394,plain,
% 0.67/0.88 (((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1395,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[1394])).
% 0.67/0.88 tff(1396,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))),
% 0.67/0.88 inference(transitivity,[status(thm)],[1395, 1393])).
% 0.67/0.88 tff(1397,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(1398,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 0.67/0.88 tff(1399,plain,
% 0.67/0.88 (c1_1(a648)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1398, 96, 1392, 1339, 1163, 1165, 1391, 246, 224, 1164, 223])).
% 0.67/0.88 tff(1400,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1401,plain,
% 0.67/0.88 (((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665)) <=> (c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1402,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665)))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[1401])).
% 0.67/0.88 tff(1403,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))),
% 0.67/0.88 inference(transitivity,[status(thm)],[1402, 1400])).
% 0.67/0.88 tff(1404,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(1405,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.67/0.88 tff(1406,plain,
% 0.67/0.88 ($false),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1405, 96, 1290, 1392, 1301, 1289, 1391, 197, 1329, 1399])).
% 0.67/0.88 tff(1407,plain,(hskp1 | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a647) | c3_1(a647) | c0_1(a643) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.88 tff(1408,plain,
% 0.67/0.88 (hskp1),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1407, 246, 1154, 1162, 224, 1146, 1])).
% 0.67/0.88 tff(1409,plain,
% 0.67/0.88 (~c1_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[367, 1408])).
% 0.67/0.88 tff(1410,plain,
% 0.67/0.88 (c3_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[384, 1408])).
% 0.67/0.88 tff(1411,plain,
% 0.67/0.88 (hskp28),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[742, 1408, 1])).
% 0.67/0.88 tff(1412,plain,
% 0.67/0.88 (c2_1(a671)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[750, 1411])).
% 0.67/0.88 tff(1413,plain,
% 0.67/0.88 (c1_1(a671)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[758, 1411])).
% 0.67/0.88 tff(1414,plain,
% 0.67/0.88 (c0_1(a671)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[766, 1411])).
% 0.67/0.88 tff(1415,plain,
% 0.67/0.88 (~c2_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1267, 96, 1414, 1413, 1412, 1162, 1154, 1410, 1146, 1409, 854])).
% 0.67/0.88 tff(1416,plain,
% 0.67/0.88 (c0_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[376, 1408])).
% 0.67/0.88 tff(1417,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1418,plain,
% 0.67/0.88 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1419,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[1418])).
% 0.67/0.88 tff(1420,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))),
% 0.67/0.88 inference(transitivity,[status(thm)],[1419, 1417])).
% 0.67/0.88 tff(1421,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(1422,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 0.67/0.88 tff(1423,plain,
% 0.67/0.88 (~c1_1(a647)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1422, 96, 1162, 1154, 1416, 246, 224, 1146, 1409, 223, 1415])).
% 0.67/0.88 tff(1424,plain,
% 0.67/0.88 (~c3_1(a665)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[138, 96, 1, 369, 1290, 1289, 22])).
% 0.67/0.88 tff(1425,plain,
% 0.67/0.88 ((hskp18 | hskp7 | hskp1) <=> (hskp18 | hskp7 | hskp1)),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1426,plain,
% 0.67/0.88 (((hskp18 | hskp1) | hskp7) <=> (hskp18 | hskp7 | hskp1)),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1427,plain,
% 0.67/0.88 ((hskp18 | hskp1) <=> (hskp18 | hskp1)),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1428,plain,
% 0.67/0.88 (((hskp18 | hskp1) | hskp7) <=> ((hskp18 | hskp1) | hskp7)),
% 0.67/0.88 inference(monotonicity,[status(thm)],[1427])).
% 0.67/0.88 tff(1429,plain,
% 0.67/0.88 (((hskp18 | hskp1) | hskp7) <=> (hskp18 | hskp7 | hskp1)),
% 0.67/0.88 inference(transitivity,[status(thm)],[1428, 1426])).
% 0.67/0.88 tff(1430,axiom,((hskp18 | hskp1) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 0.67/0.88 tff(1431,plain,
% 0.67/0.88 (hskp18 | hskp7 | hskp1),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 0.67/0.88 tff(1432,plain,
% 0.67/0.88 (hskp18 | hskp7 | hskp1),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1431, 1425])).
% 0.67/0.88 tff(1433,plain,
% 0.67/0.88 (hskp18 | hskp7 | hskp1),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1432, 1425])).
% 0.67/0.88 tff(1434,plain,
% 0.67/0.88 (hskp18 | hskp7 | hskp1),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1433, 1425])).
% 0.67/0.88 tff(1435,plain,
% 0.67/0.88 (hskp18 | hskp7 | hskp1),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1434, 1425])).
% 0.67/0.88 tff(1436,plain,
% 0.67/0.88 (hskp18),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1435, 1286, 369])).
% 0.67/0.88 tff(1437,plain,
% 0.67/0.88 (~c2_1(a676)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[212, 1436])).
% 0.67/0.88 tff(1438,plain,
% 0.67/0.88 (c1_1(a676)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[608, 1436])).
% 0.67/0.88 tff(1439,plain,
% 0.67/0.88 (c0_1(a676)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[539, 1436])).
% 0.67/0.88 tff(1440,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1441,plain,
% 0.67/0.88 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665)) <=> (c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1442,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[1441])).
% 0.67/0.88 tff(1443,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))),
% 0.67/0.88 inference(transitivity,[status(thm)],[1442, 1440])).
% 0.67/0.88 tff(1444,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(1445,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 0.67/0.88 tff(1446,plain,
% 0.67/0.88 ($false),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1445, 96, 1439, 1438, 1290, 1437, 1301, 1289, 197, 1424])).
% 0.67/0.88 tff(1447,plain,(hskp1 | hskp17 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.67/0.88 tff(1448,plain,
% 0.67/0.88 (hskp1),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1447, 369, 1])).
% 0.67/0.88 tff(1449,plain,
% 0.67/0.88 (~c1_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[367, 1448])).
% 0.67/0.88 tff(1450,plain,
% 0.67/0.88 (c3_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[384, 1448])).
% 0.67/0.88 tff(1451,plain,
% 0.67/0.88 (~c2_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[393, 96, 1, 369, 1450, 1449, 22])).
% 0.67/0.88 tff(1452,plain,
% 0.67/0.88 (c0_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[376, 1448])).
% 0.67/0.88 tff(1453,plain,
% 0.67/0.88 (~c1_1(a647)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1422, 96, 1163, 1165, 1452, 246, 224, 1164, 1449, 223, 1451])).
% 0.67/0.88 tff(1454,plain,
% 0.67/0.88 (~hskp5),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1071, 1453])).
% 0.67/0.88 tff(1455,plain,
% 0.67/0.88 (hskp23 | hskp5 | c2_1(a642)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[711, 96, 1452, 1450, 558])).
% 0.67/0.88 tff(1456,plain,
% 0.67/0.88 (hskp23),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1455, 1454, 1451])).
% 0.67/0.88 tff(1457,plain,
% 0.67/0.88 (~c3_1(a695)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[571, 1456])).
% 0.67/0.88 tff(1458,plain,
% 0.67/0.88 (~c0_1(a695)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[577, 1456])).
% 0.67/0.88 tff(1459,plain,
% 0.67/0.88 (c2_1(a695)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[593, 1456])).
% 0.67/0.88 tff(1460,plain,
% 0.67/0.88 (~c1_1(a695)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[722, 96, 1459, 1452, 1458, 1457, 1449, 223, 1451])).
% 0.67/0.88 tff(1461,plain,
% 0.67/0.88 ($false),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1280, 96, 1454, 1459, 1458, 1457, 12, 1460])).
% 0.67/0.88 tff(1462,plain,(hskp7 | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a647) | c3_1(a647) | c0_1(a643) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.88 tff(1463,plain,
% 0.67/0.88 (hskp7),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1462, 246, 1154, 1162, 224, 1146, 1])).
% 0.67/0.88 tff(1464,plain,
% 0.67/0.88 (~c1_1(a651)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[145, 1463])).
% 0.67/0.88 tff(1465,plain,
% 0.67/0.88 (c3_1(a651)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[159, 1463])).
% 0.67/0.88 tff(1466,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1467,plain,
% 0.67/0.88 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1468,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[1467])).
% 0.67/0.88 tff(1469,plain,
% 0.67/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.88 inference(transitivity,[status(thm)],[1468, 1466])).
% 0.67/0.88 tff(1470,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(1471,plain,
% 0.67/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 0.67/0.88 tff(1472,plain,
% 0.67/0.88 (~c2_1(a651)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[1471, 96, 1414, 1413, 1412, 1465, 1162, 1154, 1464, 1146, 854])).
% 0.67/0.88 tff(1473,plain,
% 0.67/0.88 (^[U: $i] : refl((hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.67/0.88 inference(bind,[status(th)],[])).
% 0.67/0.88 tff(1474,plain,
% 0.67/0.88 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.88 inference(quant_intro,[status(thm)],[1473])).
% 0.67/0.88 tff(1475,plain,
% 0.67/0.88 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(1476,plain,
% 0.67/0.88 (^[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)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.67/0.88 inference(bind,[status(th)],[])).
% 0.67/0.88 tff(1477,plain,
% 0.67/0.88 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.88 inference(quant_intro,[status(thm)],[1476])).
% 0.67/0.88 tff(1478,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.67/0.88 tff(1479,plain,
% 0.67/0.88 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 0.67/0.88 tff(1480,plain,
% 0.67/0.88 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1479, 1475])).
% 0.67/0.88 tff(1481,plain,(
% 0.67/0.88 ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.88 inference(skolemize,[status(sab)],[1480])).
% 0.67/0.88 tff(1482,plain,
% 0.67/0.88 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[1481, 1474])).
% 0.67/0.88 tff(1483,plain,
% 0.67/0.88 (~c0_1(a651)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[151, 1463])).
% 0.67/0.88 tff(1484,plain,
% 0.67/0.88 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1485,plain,
% 0.67/0.89 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651)) <=> (hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1486,plain,
% 0.67/0.89 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651)))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1485])).
% 0.67/0.89 tff(1487,plain,
% 0.67/0.89 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1486, 1484])).
% 0.67/0.89 tff(1488,plain,
% 0.67/0.89 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1489,plain,
% 0.67/0.89 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 0.67/0.89 tff(1490,plain,
% 0.67/0.89 (hskp26 | c2_1(a651)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1489, 96, 23, 1483, 1464, 1482])).
% 0.67/0.89 tff(1491,plain,
% 0.67/0.89 (hskp26),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1490, 1472])).
% 0.67/0.89 tff(1492,plain,
% 0.67/0.89 (((~hskp26) | c3_1(a640)) <=> ((~hskp26) | c3_1(a640))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1493,axiom,((~hskp26) | c3_1(a640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.67/0.89 tff(1494,plain,
% 0.67/0.89 ((~hskp26) | c3_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.67/0.89 tff(1495,plain,
% 0.67/0.89 ((~hskp26) | c3_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1494, 1492])).
% 0.67/0.89 tff(1496,plain,
% 0.67/0.89 ((~hskp26) | c3_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1495, 1492])).
% 0.67/0.89 tff(1497,plain,
% 0.67/0.89 ((~hskp26) | c3_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1496, 1492])).
% 0.67/0.89 tff(1498,plain,
% 0.67/0.89 ((~hskp26) | c3_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1497, 1492])).
% 0.67/0.89 tff(1499,plain,
% 0.67/0.89 (c3_1(a640)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1498, 1491])).
% 0.67/0.89 tff(1500,plain,
% 0.67/0.89 (((~hskp26) | c1_1(a640)) <=> ((~hskp26) | c1_1(a640))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1501,axiom,((~hskp26) | c1_1(a640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.67/0.89 tff(1502,plain,
% 0.67/0.89 ((~hskp26) | c1_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 0.67/0.89 tff(1503,plain,
% 0.67/0.89 ((~hskp26) | c1_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1502, 1500])).
% 0.67/0.89 tff(1504,plain,
% 0.67/0.89 ((~hskp26) | c1_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1503, 1500])).
% 0.67/0.89 tff(1505,plain,
% 0.67/0.89 ((~hskp26) | c1_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1504, 1500])).
% 0.67/0.89 tff(1506,plain,
% 0.67/0.89 ((~hskp26) | c1_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1505, 1500])).
% 0.67/0.89 tff(1507,plain,
% 0.67/0.89 (c1_1(a640)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1506, 1491])).
% 0.67/0.89 tff(1508,plain,
% 0.67/0.89 (((~hskp26) | c0_1(a640)) <=> ((~hskp26) | c0_1(a640))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1509,axiom,((~hskp26) | c0_1(a640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.67/0.89 tff(1510,plain,
% 0.67/0.89 ((~hskp26) | c0_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 0.67/0.89 tff(1511,plain,
% 0.67/0.89 ((~hskp26) | c0_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1510, 1508])).
% 0.67/0.89 tff(1512,plain,
% 0.67/0.89 ((~hskp26) | c0_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1511, 1508])).
% 0.67/0.89 tff(1513,plain,
% 0.67/0.89 ((~hskp26) | c0_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1512, 1508])).
% 0.67/0.89 tff(1514,plain,
% 0.67/0.89 ((~hskp26) | c0_1(a640)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1513, 1508])).
% 0.67/0.89 tff(1515,plain,
% 0.67/0.89 (c0_1(a640)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1514, 1491])).
% 0.67/0.89 tff(1516,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1517,plain,
% 0.67/0.89 (((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647)) <=> (c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1518,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640))))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1517])).
% 0.67/0.89 tff(1519,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1518, 1516])).
% 0.67/0.89 tff(1520,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1521,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 0.67/0.89 tff(1522,plain,
% 0.67/0.89 (c2_1(a647)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1521, 96, 1515, 1507, 1499, 1423, 246, 224, 1090])).
% 0.67/0.89 tff(1523,plain,
% 0.67/0.89 (~hskp5),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1071, 1423])).
% 0.67/0.89 tff(1524,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1525,plain,
% 0.67/0.89 ((hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647))) <=> (hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1526,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1525])).
% 0.67/0.89 tff(1527,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1526, 1524])).
% 0.67/0.89 tff(1528,plain,
% 0.67/0.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647)))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1529,plain,
% 0.67/0.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 0.67/0.89 tff(1530,plain,
% 0.67/0.89 ($false),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1529, 96, 1523, 1423, 246, 224, 12, 1522])).
% 0.67/0.89 tff(1531,plain,(c0_1(a647) | c3_1(a647) | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.89 tff(1532,plain,
% 0.67/0.89 ($false),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1531, 1285, 1284, 23, 1])).
% 0.67/0.89 tff(1533,plain,(hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.67/0.89 tff(1534,plain,
% 0.67/0.89 (hskp17),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1533, 23])).
% 0.67/0.89 tff(1535,plain,
% 0.67/0.89 (~c3_1(a675)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1011, 1534])).
% 0.67/0.89 tff(1536,plain,
% 0.67/0.89 (~c1_1(a675)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1005, 1534])).
% 0.67/0.89 tff(1537,plain,
% 0.67/0.89 (c2_1(a675)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1053, 1534])).
% 0.67/0.89 tff(1538,assumption,(c2_1(a675)), introduced(assumption)).
% 0.67/0.89 tff(1539,plain,
% 0.67/0.89 (~c0_1(a675)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1045, 96, 1538, 1014, 1013, 925])).
% 0.67/0.89 tff(1540,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1541,plain,
% 0.67/0.89 ((hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675))) <=> (hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1542,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1541])).
% 0.67/0.89 tff(1543,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1542, 1540])).
% 0.67/0.89 tff(1544,plain,
% 0.67/0.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1545,plain,
% 0.67/0.89 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 0.67/0.89 tff(1546,plain,
% 0.67/0.89 (hskp5),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1545, 96, 1538, 1014, 1013, 12, 1539])).
% 0.67/0.89 tff(1547,plain,
% 0.67/0.89 (~c0_1(a647)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[493, 1546])).
% 0.67/0.89 tff(1548,plain,
% 0.67/0.89 (~c3_1(a647)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[623, 1546])).
% 0.67/0.89 tff(1549,plain,
% 0.67/0.89 (c1_1(a647)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1071, 1546])).
% 0.67/0.89 tff(1550,plain,
% 0.67/0.89 (hskp6),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1389, 1340, 1549, 1548, 1547, 1165, 1164])).
% 0.67/0.89 tff(1551,plain,
% 0.67/0.89 (~c2_1(a648)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[114, 1550])).
% 0.67/0.89 tff(1552,plain,
% 0.67/0.89 (c0_1(a648)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[310, 1550])).
% 0.67/0.89 tff(1553,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1554,plain,
% 0.67/0.89 (((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643))) <=> (c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1555,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648))))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1554])).
% 0.67/0.89 tff(1556,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1555, 1553])).
% 0.67/0.89 tff(1557,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1558,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 0.67/0.89 tff(1559,plain,
% 0.67/0.89 (c1_1(a648)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1558, 96, 1552, 1163, 1165, 1551, 1164, 223, 1340])).
% 0.67/0.89 tff(1560,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1561,plain,
% 0.67/0.89 (((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675)) <=> (c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1562,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675)))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1561])).
% 0.67/0.89 tff(1563,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1562, 1560])).
% 0.67/0.89 tff(1564,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1565,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 0.67/0.89 tff(1566,plain,
% 0.67/0.89 ($false),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1565, 96, 1538, 1552, 1014, 1013, 1551, 197, 1539, 1559])).
% 0.67/0.89 tff(1567,plain,(c3_1(a643) | (~c2_1(a675)) | c1_1(a675) | c3_1(a675) | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.89 tff(1568,plain,
% 0.67/0.89 (c3_1(a643)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1567, 1537, 1536, 1535, 1162, 1154, 1146])).
% 0.67/0.89 tff(1569,plain,
% 0.67/0.89 (~c0_1(a675)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1045, 96, 1537, 1536, 1535, 925])).
% 0.67/0.89 tff(1570,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1571,plain,
% 0.67/0.89 ((hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675)) <=> (hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1572,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675)))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1571])).
% 0.67/0.89 tff(1573,plain,
% 0.67/0.89 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1572, 1570])).
% 0.67/0.89 tff(1574,plain,
% 0.67/0.89 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1575,plain,
% 0.67/0.89 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 0.67/0.89 tff(1576,plain,
% 0.67/0.89 (hskp1 | (~c3_1(a643))),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1575, 96, 1154, 1536, 1535, 1146, 1300, 1569])).
% 0.67/0.89 tff(1577,plain,
% 0.67/0.89 (hskp1),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1576, 1568])).
% 0.67/0.89 tff(1578,plain,
% 0.67/0.89 (~c1_1(a642)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[367, 1577])).
% 0.67/0.89 tff(1579,plain,
% 0.67/0.89 (c3_1(a642)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[384, 1577])).
% 0.67/0.89 tff(1580,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1581,plain,
% 0.67/0.89 (((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1582,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1581])).
% 0.67/0.89 tff(1583,plain,
% 0.67/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1582, 1580])).
% 0.67/0.89 tff(1584,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1585,plain,
% 0.67/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 0.67/0.89 tff(1586,plain,
% 0.67/0.89 (~c2_1(a642)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1585, 96, 1162, 1154, 1579, 1146, 1578, 1182, 1568])).
% 0.67/0.89 tff(1587,plain,
% 0.67/0.89 (hskp5),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1545, 96, 1537, 1536, 1535, 12, 1569])).
% 0.67/0.89 tff(1588,plain,
% 0.67/0.89 (~c3_1(a647)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[623, 1587])).
% 0.67/0.89 tff(1589,plain,
% 0.67/0.89 (~c0_1(a647)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[493, 1587])).
% 0.67/0.89 tff(1590,plain,
% 0.67/0.89 (c0_1(a642)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[376, 1577])).
% 0.67/0.89 tff(1591,plain,
% 0.67/0.89 (c1_1(a647)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1071, 1587])).
% 0.67/0.89 tff(1592,plain,
% 0.67/0.89 ($false),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1422, 96, 1591, 1162, 1154, 1590, 1589, 1588, 1146, 1578, 223, 1586])).
% 0.67/0.89 tff(1593,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 0.67/0.89 tff(1594,plain,
% 0.67/0.89 (((~hskp0) | (~c1_1(a641))) <=> ((~hskp0) | (~c1_1(a641)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1595,plain,
% 0.67/0.89 (((~c1_1(a641)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a641)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1596,axiom,((~c1_1(a641)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.67/0.89 tff(1597,plain,
% 0.67/0.89 ((~hskp0) | (~c1_1(a641))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 0.67/0.89 tff(1598,plain,
% 0.67/0.89 ((~hskp0) | (~c1_1(a641))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1597, 1594])).
% 0.67/0.89 tff(1599,plain,
% 0.67/0.89 (~c1_1(a641)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1598, 1593])).
% 0.67/0.89 tff(1600,plain,
% 0.67/0.89 (((~hskp0) | c3_1(a641)) <=> ((~hskp0) | c3_1(a641))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1601,axiom,((~hskp0) | c3_1(a641)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.67/0.89 tff(1602,plain,
% 0.67/0.89 ((~hskp0) | c3_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 0.67/0.89 tff(1603,plain,
% 0.67/0.89 ((~hskp0) | c3_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1602, 1600])).
% 0.67/0.89 tff(1604,plain,
% 0.67/0.89 ((~hskp0) | c3_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1603, 1600])).
% 0.67/0.89 tff(1605,plain,
% 0.67/0.89 ((~hskp0) | c3_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1604, 1600])).
% 0.67/0.89 tff(1606,plain,
% 0.67/0.89 ((~hskp0) | c3_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1605, 1600])).
% 0.67/0.89 tff(1607,plain,
% 0.67/0.89 (c3_1(a641)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1606, 1593])).
% 0.67/0.89 tff(1608,plain,
% 0.67/0.89 (((~hskp0) | c2_1(a641)) <=> ((~hskp0) | c2_1(a641))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1609,axiom,((~hskp0) | c2_1(a641)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.67/0.89 tff(1610,plain,
% 0.67/0.89 ((~hskp0) | c2_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 0.67/0.89 tff(1611,plain,
% 0.67/0.89 ((~hskp0) | c2_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1610, 1608])).
% 0.67/0.89 tff(1612,plain,
% 0.67/0.89 ((~hskp0) | c2_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1611, 1608])).
% 0.67/0.89 tff(1613,plain,
% 0.67/0.89 ((~hskp0) | c2_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1612, 1608])).
% 0.67/0.89 tff(1614,plain,
% 0.67/0.89 ((~hskp0) | c2_1(a641)),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1613, 1608])).
% 0.67/0.89 tff(1615,plain,
% 0.67/0.89 (c2_1(a641)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1614, 1593])).
% 0.67/0.89 tff(1616,plain,
% 0.67/0.89 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1617,plain,
% 0.67/0.89 ((hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641))) <=> (hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1618,plain,
% 0.67/0.89 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))))),
% 0.67/0.89 inference(monotonicity,[status(thm)],[1617])).
% 0.67/0.89 tff(1619,plain,
% 0.67/0.89 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.89 inference(transitivity,[status(thm)],[1618, 1616])).
% 0.67/0.89 tff(1620,plain,
% 0.67/0.89 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.89 inference(quant_inst,[status(thm)],[])).
% 0.67/0.89 tff(1621,plain,
% 0.67/0.89 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))),
% 0.67/0.89 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 0.67/0.89 tff(1622,plain,
% 0.67/0.89 (hskp17 | hskp7),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1621, 96, 1615, 1607, 1599, 22])).
% 0.67/0.89 tff(1623,plain,
% 0.67/0.89 (hskp7),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[1622, 1])).
% 0.67/0.89 tff(1624,plain,
% 0.67/0.89 (~c1_1(a651)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[145, 1623])).
% 0.67/0.89 tff(1625,plain,
% 0.67/0.89 (~c0_1(a651)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[151, 1623])).
% 0.67/0.89 tff(1626,plain,
% 0.67/0.89 (c3_1(a651)),
% 0.67/0.89 inference(unit_resolution,[status(thm)],[159, 1623])).
% 0.67/0.89 tff(1627,plain,
% 0.67/0.89 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.67/0.89 inference(bind,[status(th)],[])).
% 0.67/0.89 tff(1628,plain,
% 0.67/0.89 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.67/0.89 inference(quant_intro,[status(thm)],[1627])).
% 0.67/0.89 tff(1629,plain,
% 0.67/0.89 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.67/0.89 inference(rewrite,[status(thm)],[])).
% 0.67/0.89 tff(1630,plain,
% 0.67/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.67/0.90 inference(bind,[status(th)],[])).
% 0.67/0.90 tff(1631,plain,
% 0.67/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.67/0.90 inference(quant_intro,[status(thm)],[1630])).
% 0.67/0.90 tff(1632,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.67/0.90 tff(1633,plain,
% 0.67/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 0.67/0.90 tff(1634,plain,
% 0.67/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1633, 1629])).
% 0.67/0.90 tff(1635,plain,(
% 0.67/0.90 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.67/0.90 inference(skolemize,[status(sab)],[1634])).
% 0.67/0.90 tff(1636,plain,
% 0.67/0.90 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1635, 1628])).
% 0.67/0.90 tff(1637,assumption,(c3_1(a651)), introduced(assumption)).
% 0.67/0.90 tff(1638,plain,
% 0.67/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1639,plain,
% 0.67/0.90 ((hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1640,plain,
% 0.67/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.67/0.90 inference(monotonicity,[status(thm)],[1639])).
% 0.67/0.90 tff(1641,plain,
% 0.67/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.90 inference(transitivity,[status(thm)],[1640, 1638])).
% 0.67/0.90 tff(1642,plain,
% 0.67/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 0.67/0.90 inference(quant_inst,[status(thm)],[])).
% 0.67/0.90 tff(1643,plain,
% 0.67/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.67/0.90 tff(1644,plain,
% 0.67/0.90 (hskp8),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1643, 96, 1095, 1094, 1103, 1637, 342, 341, 1636])).
% 0.67/0.90 tff(1645,plain,
% 0.67/0.90 (((~hskp8) | (~c2_1(a652))) <=> ((~hskp8) | (~c2_1(a652)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1646,plain,
% 0.67/0.90 (((~c2_1(a652)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a652)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1647,axiom,((~c2_1(a652)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.67/0.90 tff(1648,plain,
% 0.67/0.90 ((~hskp8) | (~c2_1(a652))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 0.67/0.90 tff(1649,plain,
% 0.67/0.90 ((~hskp8) | (~c2_1(a652))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1648, 1645])).
% 0.67/0.90 tff(1650,plain,
% 0.67/0.90 (~c2_1(a652)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1649, 1644])).
% 0.67/0.90 tff(1651,plain,
% 0.67/0.90 (((~hskp8) | c3_1(a652)) <=> ((~hskp8) | c3_1(a652))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1652,axiom,((~hskp8) | c3_1(a652)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.67/0.90 tff(1653,plain,
% 0.67/0.90 ((~hskp8) | c3_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 0.67/0.90 tff(1654,plain,
% 0.67/0.90 ((~hskp8) | c3_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1653, 1651])).
% 0.67/0.90 tff(1655,plain,
% 0.67/0.90 ((~hskp8) | c3_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1654, 1651])).
% 0.67/0.90 tff(1656,plain,
% 0.67/0.90 ((~hskp8) | c3_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1655, 1651])).
% 0.67/0.90 tff(1657,plain,
% 0.67/0.90 ((~hskp8) | c3_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1656, 1651])).
% 0.67/0.90 tff(1658,plain,
% 0.67/0.90 (c3_1(a652)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1657, 1644])).
% 0.67/0.90 tff(1659,plain,
% 0.67/0.90 (((~hskp8) | c0_1(a652)) <=> ((~hskp8) | c0_1(a652))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1660,axiom,((~hskp8) | c0_1(a652)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.67/0.90 tff(1661,plain,
% 0.67/0.90 ((~hskp8) | c0_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 0.67/0.90 tff(1662,plain,
% 0.67/0.90 ((~hskp8) | c0_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1661, 1659])).
% 0.67/0.90 tff(1663,plain,
% 0.67/0.90 ((~hskp8) | c0_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1662, 1659])).
% 0.67/0.90 tff(1664,plain,
% 0.67/0.90 ((~hskp8) | c0_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1663, 1659])).
% 0.67/0.90 tff(1665,plain,
% 0.67/0.90 ((~hskp8) | c0_1(a652)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1664, 1659])).
% 0.67/0.90 tff(1666,plain,
% 0.67/0.90 (c0_1(a652)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1665, 1644])).
% 0.67/0.90 tff(1667,plain,
% 0.67/0.90 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1668,plain,
% 0.67/0.90 ((hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652))) <=> (hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1669,plain,
% 0.67/0.90 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652))))),
% 0.67/0.90 inference(monotonicity,[status(thm)],[1668])).
% 0.67/0.90 tff(1670,plain,
% 0.67/0.90 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))),
% 0.67/0.90 inference(transitivity,[status(thm)],[1669, 1667])).
% 0.67/0.90 tff(1671,plain,
% 0.67/0.90 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652)))),
% 0.67/0.90 inference(quant_inst,[status(thm)],[])).
% 0.67/0.90 tff(1672,plain,
% 0.67/0.90 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 0.67/0.90 tff(1673,plain,
% 0.67/0.90 (hskp23),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1672, 96, 2, 1666, 1658, 1650, 558])).
% 0.67/0.90 tff(1674,plain,
% 0.67/0.90 (~c0_1(a695)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[577, 1673])).
% 0.67/0.90 tff(1675,plain,
% 0.67/0.90 (c2_1(a695)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[593, 1673])).
% 0.67/0.90 tff(1676,plain,
% 0.67/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1677,plain,
% 0.67/0.90 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695))) <=> (c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1678,plain,
% 0.67/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.67/0.90 inference(monotonicity,[status(thm)],[1677])).
% 0.67/0.90 tff(1679,plain,
% 0.67/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.90 inference(transitivity,[status(thm)],[1678, 1676])).
% 0.67/0.90 tff(1680,plain,
% 0.67/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 0.67/0.90 inference(quant_inst,[status(thm)],[])).
% 0.67/0.90 tff(1681,plain,
% 0.67/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 0.67/0.90 tff(1682,plain,
% 0.67/0.90 (~c1_1(a695)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1681, 96, 1095, 1094, 1103, 1675, 1615, 1607, 1674, 1599, 854])).
% 0.67/0.90 tff(1683,plain,
% 0.67/0.90 (~c3_1(a695)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[571, 1673])).
% 0.67/0.90 tff(1684,plain,
% 0.67/0.90 ($false),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1280, 96, 2, 1675, 1674, 1683, 12, 1682])).
% 0.67/0.90 tff(1685,plain,((~hskp28) | hskp5 | (~c3_1(a651)) | c0_1(a651) | c1_1(a651)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.90 tff(1686,plain,
% 0.67/0.90 (~hskp28),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1685, 2, 1626, 1625, 1624])).
% 0.67/0.90 tff(1687,plain,
% 0.67/0.90 (~hskp1),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[742, 1686, 1])).
% 0.67/0.90 tff(1688,plain,
% 0.67/0.90 (hskp14),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[469, 1687, 1])).
% 0.67/0.90 tff(1689,plain,
% 0.67/0.90 (~c1_1(a665)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[50, 1688])).
% 0.67/0.90 tff(1690,plain,
% 0.67/0.90 (~c0_1(a665)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[56, 1688])).
% 0.67/0.90 tff(1691,plain,
% 0.67/0.90 (c2_1(a665)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[64, 1688])).
% 0.67/0.90 tff(1692,plain,
% 0.67/0.90 (c3_1(a665)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1171, 96, 2, 1691, 1690, 1689, 12])).
% 0.67/0.90 tff(1693,plain,
% 0.67/0.90 (^[U: $i] : refl((hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.67/0.90 inference(bind,[status(th)],[])).
% 0.67/0.90 tff(1694,plain,
% 0.67/0.90 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.67/0.90 inference(quant_intro,[status(thm)],[1693])).
% 0.67/0.90 tff(1695,plain,
% 0.67/0.90 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1696,plain,
% 0.67/0.90 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | 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)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16) <=> (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16) <=> (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.67/0.90 inference(bind,[status(th)],[])).
% 0.67/0.90 tff(1697,plain,
% 0.67/0.90 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16) <=> ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.67/0.90 inference(quant_intro,[status(thm)],[1696])).
% 0.67/0.90 tff(1698,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.67/0.90 tff(1699,plain,
% 0.67/0.90 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.67/0.90 tff(1700,plain,
% 0.67/0.90 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1699, 1695])).
% 0.67/0.90 tff(1701,plain,(
% 0.67/0.90 ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.67/0.90 inference(skolemize,[status(sab)],[1700])).
% 0.67/0.90 tff(1702,plain,
% 0.67/0.90 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1701, 1694])).
% 0.67/0.90 tff(1703,plain,
% 0.67/0.90 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.67/0.90 inference(bind,[status(th)],[])).
% 0.67/0.90 tff(1704,plain,
% 0.67/0.90 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.67/0.90 inference(quant_intro,[status(thm)],[1703])).
% 0.67/0.90 tff(1705,plain,
% 0.67/0.90 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1706,plain,
% 0.67/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19) <=> ((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.67/0.90 inference(bind,[status(th)],[])).
% 0.67/0.90 tff(1707,plain,
% 0.67/0.90 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.67/0.90 inference(quant_intro,[status(thm)],[1706])).
% 0.67/0.90 tff(1708,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.67/0.90 tff(1709,plain,
% 0.67/0.90 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 0.67/0.90 tff(1710,plain,
% 0.67/0.90 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1709, 1705])).
% 0.67/0.90 tff(1711,plain,(
% 0.67/0.90 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.67/0.90 inference(skolemize,[status(sab)],[1710])).
% 0.67/0.90 tff(1712,plain,
% 0.67/0.90 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1711, 1704])).
% 0.67/0.90 tff(1713,plain,
% 0.67/0.90 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1714,plain,
% 0.67/0.90 ((hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641))) <=> (hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1715,plain,
% 0.67/0.90 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))))),
% 0.67/0.90 inference(monotonicity,[status(thm)],[1714])).
% 0.67/0.90 tff(1716,plain,
% 0.67/0.90 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.90 inference(transitivity,[status(thm)],[1715, 1713])).
% 0.67/0.90 tff(1717,plain,
% 0.67/0.90 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))),
% 0.67/0.90 inference(quant_inst,[status(thm)],[])).
% 0.67/0.90 tff(1718,plain,
% 0.67/0.90 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 0.67/0.90 tff(1719,plain,
% 0.67/0.90 (hskp19 | hskp17),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1718, 96, 1615, 1607, 1599, 1712])).
% 0.67/0.90 tff(1720,plain,
% 0.67/0.90 (hskp19),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1719, 1])).
% 0.67/0.90 tff(1721,plain,
% 0.67/0.90 (((~hskp19) | (~c2_1(a682))) <=> ((~hskp19) | (~c2_1(a682)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1722,plain,
% 0.67/0.90 (((~c2_1(a682)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a682)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1723,axiom,((~c2_1(a682)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.67/0.90 tff(1724,plain,
% 0.67/0.90 ((~hskp19) | (~c2_1(a682))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 0.67/0.90 tff(1725,plain,
% 0.67/0.90 ((~hskp19) | (~c2_1(a682))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1724, 1721])).
% 0.67/0.90 tff(1726,plain,
% 0.67/0.90 (~c2_1(a682)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1725, 1720])).
% 0.67/0.90 tff(1727,plain,
% 0.67/0.90 (((~hskp19) | (~c1_1(a682))) <=> ((~hskp19) | (~c1_1(a682)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1728,plain,
% 0.67/0.90 (((~c1_1(a682)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a682)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1729,axiom,((~c1_1(a682)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.67/0.90 tff(1730,plain,
% 0.67/0.90 ((~hskp19) | (~c1_1(a682))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 0.67/0.90 tff(1731,plain,
% 0.67/0.90 ((~hskp19) | (~c1_1(a682))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1730, 1727])).
% 0.67/0.90 tff(1732,plain,
% 0.67/0.90 (~c1_1(a682)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1731, 1720])).
% 0.67/0.90 tff(1733,plain,
% 0.67/0.90 (((~hskp19) | c3_1(a682)) <=> ((~hskp19) | c3_1(a682))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1734,axiom,((~hskp19) | c3_1(a682)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.67/0.90 tff(1735,plain,
% 0.67/0.90 ((~hskp19) | c3_1(a682)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 0.67/0.90 tff(1736,plain,
% 0.67/0.90 ((~hskp19) | c3_1(a682)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1735, 1733])).
% 0.67/0.90 tff(1737,plain,
% 0.67/0.90 ((~hskp19) | c3_1(a682)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1736, 1733])).
% 0.67/0.90 tff(1738,plain,
% 0.67/0.90 ((~hskp19) | c3_1(a682)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1737, 1733])).
% 0.67/0.90 tff(1739,plain,
% 0.67/0.90 ((~hskp19) | c3_1(a682)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1738, 1733])).
% 0.67/0.90 tff(1740,plain,
% 0.67/0.90 (c3_1(a682)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1739, 1720])).
% 0.67/0.90 tff(1741,plain,
% 0.67/0.90 (((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))) <=> ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1742,plain,
% 0.67/0.90 ((hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682))) <=> (hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1743,plain,
% 0.67/0.90 (((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682)))) <=> ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682))))),
% 0.67/0.90 inference(monotonicity,[status(thm)],[1742])).
% 0.67/0.90 tff(1744,plain,
% 0.67/0.90 (((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682)))) <=> ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))),
% 0.67/0.90 inference(transitivity,[status(thm)],[1743, 1741])).
% 0.67/0.90 tff(1745,plain,
% 0.67/0.90 ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682)))),
% 0.67/0.90 inference(quant_inst,[status(thm)],[])).
% 0.67/0.90 tff(1746,plain,
% 0.67/0.90 ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 0.67/0.90 tff(1747,plain,
% 0.67/0.90 (hskp28 | hskp16),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1746, 96, 1740, 1732, 1726, 1702])).
% 0.67/0.90 tff(1748,plain,
% 0.67/0.90 (hskp16),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1747, 1686])).
% 0.67/0.90 tff(1749,plain,
% 0.67/0.90 (((~hskp16) | (~c3_1(a672))) <=> ((~hskp16) | (~c3_1(a672)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1750,plain,
% 0.67/0.90 (((~c3_1(a672)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a672)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1751,axiom,((~c3_1(a672)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.67/0.90 tff(1752,plain,
% 0.67/0.90 ((~hskp16) | (~c3_1(a672))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 0.67/0.90 tff(1753,plain,
% 0.67/0.90 ((~hskp16) | (~c3_1(a672))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1752, 1749])).
% 0.67/0.90 tff(1754,plain,
% 0.67/0.90 (~c3_1(a672)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1753, 1748])).
% 0.67/0.90 tff(1755,plain,
% 0.67/0.90 (((~hskp16) | (~c2_1(a672))) <=> ((~hskp16) | (~c2_1(a672)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1756,plain,
% 0.67/0.90 (((~c2_1(a672)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a672)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1757,axiom,((~c2_1(a672)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.67/0.90 tff(1758,plain,
% 0.67/0.90 ((~hskp16) | (~c2_1(a672))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 0.67/0.90 tff(1759,plain,
% 0.67/0.90 ((~hskp16) | (~c2_1(a672))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1758, 1755])).
% 0.67/0.90 tff(1760,plain,
% 0.67/0.90 (~c2_1(a672)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1759, 1748])).
% 0.67/0.90 tff(1761,plain,
% 0.67/0.90 (((~hskp16) | c1_1(a672)) <=> ((~hskp16) | c1_1(a672))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1762,axiom,((~hskp16) | c1_1(a672)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.67/0.90 tff(1763,plain,
% 0.67/0.90 ((~hskp16) | c1_1(a672)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 0.67/0.90 tff(1764,plain,
% 0.67/0.90 ((~hskp16) | c1_1(a672)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1763, 1761])).
% 0.67/0.90 tff(1765,plain,
% 0.67/0.90 ((~hskp16) | c1_1(a672)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1764, 1761])).
% 0.67/0.90 tff(1766,plain,
% 0.67/0.90 ((~hskp16) | c1_1(a672)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1765, 1761])).
% 0.67/0.90 tff(1767,plain,
% 0.67/0.90 ((~hskp16) | c1_1(a672)),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1766, 1761])).
% 0.67/0.90 tff(1768,plain,
% 0.67/0.90 (c1_1(a672)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1767, 1748])).
% 0.67/0.90 tff(1769,plain,
% 0.67/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1770,plain,
% 0.67/0.90 ((hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665))) <=> (hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))),
% 0.67/0.90 inference(rewrite,[status(thm)],[])).
% 0.67/0.90 tff(1771,plain,
% 0.67/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672))))),
% 0.67/0.90 inference(monotonicity,[status(thm)],[1770])).
% 0.67/0.90 tff(1772,plain,
% 0.67/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))),
% 0.67/0.90 inference(transitivity,[status(thm)],[1771, 1769])).
% 0.67/0.90 tff(1773,plain,
% 0.67/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))),
% 0.67/0.90 inference(quant_inst,[status(thm)],[])).
% 0.67/0.90 tff(1774,plain,
% 0.67/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672))),
% 0.67/0.90 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 0.67/0.90 tff(1775,plain,
% 0.67/0.90 ($false),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1774, 96, 24, 1768, 1760, 1754, 1690, 1689, 34, 1692])).
% 0.67/0.90 tff(1776,plain,(hskp5 | hskp2 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.90 tff(1777,plain,
% 0.67/0.90 (hskp2),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1776, 2, 1])).
% 0.67/0.90 tff(1778,plain,
% 0.67/0.90 (c1_1(a643)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1161, 1777])).
% 0.67/0.90 tff(1779,plain,
% 0.67/0.90 (c2_1(a643)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1153, 1777])).
% 0.67/0.90 tff(1780,plain,
% 0.67/0.90 (~c0_1(a643)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1145, 1777])).
% 0.67/0.90 tff(1781,plain,
% 0.67/0.90 ($false),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1282, 1780, 1779, 1, 2, 1778])).
% 0.67/0.90 tff(1782,plain,(hskp5 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.90 tff(1783,plain,
% 0.67/0.90 (hskp5),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1782, 1])).
% 0.67/0.90 tff(1784,plain,
% 0.67/0.90 (~c0_1(a647)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[493, 1783])).
% 0.67/0.90 tff(1785,plain,
% 0.67/0.90 (~c3_1(a647)),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[623, 1783])).
% 0.67/0.90 tff(1786,plain,
% 0.67/0.90 (hskp5),
% 0.67/0.90 inference(unit_resolution,[status(thm)],[1776, 24, 1])).
% 0.67/0.91 tff(1787,plain,
% 0.67/0.91 (c1_1(a647)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1071, 1786])).
% 0.67/0.91 tff(1788,plain,
% 0.67/0.91 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1789,plain,
% 0.67/0.91 ((hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1790,plain,
% 0.67/0.91 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651))))),
% 0.67/0.91 inference(monotonicity,[status(thm)],[1789])).
% 0.67/0.91 tff(1791,plain,
% 0.67/0.91 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))),
% 0.67/0.91 inference(transitivity,[status(thm)],[1790, 1788])).
% 0.67/0.91 tff(1792,plain,
% 0.67/0.91 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 0.67/0.91 inference(quant_inst,[status(thm)],[])).
% 0.67/0.91 tff(1793,plain,
% 0.67/0.91 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 0.67/0.91 tff(1794,plain,
% 0.67/0.91 ($false),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1793, 96, 24, 1637, 255, 342, 341, 224, 34, 1080])).
% 0.67/0.91 tff(1795,plain,(c2_1(a647) | hskp2 | (~c3_1(a651)) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | c3_1(a647)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.91 tff(1796,plain,
% 0.67/0.91 (c2_1(a647)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1795, 24, 1626, 1787, 1625, 1624, 224])).
% 0.67/0.91 tff(1797,plain,
% 0.67/0.91 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1798,plain,
% 0.67/0.91 ((hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1799,plain,
% 0.67/0.91 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647))))),
% 0.67/0.91 inference(monotonicity,[status(thm)],[1798])).
% 0.67/0.91 tff(1800,plain,
% 0.67/0.91 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))),
% 0.67/0.91 inference(transitivity,[status(thm)],[1799, 1797])).
% 0.67/0.91 tff(1801,plain,
% 0.67/0.91 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.67/0.91 inference(quant_inst,[status(thm)],[])).
% 0.67/0.91 tff(1802,plain,
% 0.67/0.91 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 0.67/0.91 tff(1803,plain,
% 0.67/0.91 (hskp27 | c0_1(a647) | (~c1_1(a647))),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1802, 96, 1615, 1607, 224, 1599, 1199])).
% 0.67/0.91 tff(1804,plain,
% 0.67/0.91 (hskp27),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1803, 1787, 246])).
% 0.67/0.91 tff(1805,plain,
% 0.67/0.91 (c3_1(a655)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1213, 1804])).
% 0.67/0.91 tff(1806,plain,
% 0.67/0.91 (c2_1(a655)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1221, 1804])).
% 0.67/0.91 tff(1807,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1808,plain,
% 0.67/0.91 (((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647))) <=> (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1809,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))))),
% 0.67/0.91 inference(monotonicity,[status(thm)],[1808])).
% 0.67/0.91 tff(1810,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 0.67/0.91 inference(transitivity,[status(thm)],[1809, 1807])).
% 0.67/0.91 tff(1811,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))),
% 0.67/0.91 inference(quant_inst,[status(thm)],[])).
% 0.67/0.91 tff(1812,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 0.67/0.91 tff(1813,plain,
% 0.67/0.91 ((~c2_1(a647)) | (~c1_1(a655))),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1812, 96, 1806, 1805, 1787, 1615, 1607, 246, 1599, 1182])).
% 0.67/0.91 tff(1814,plain,
% 0.67/0.91 (~c1_1(a655)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1813, 1796])).
% 0.67/0.91 tff(1815,plain,
% 0.67/0.91 (c0_1(a655)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1236, 1804])).
% 0.67/0.91 tff(1816,plain,
% 0.67/0.91 (hskp28 | c1_1(a655)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1240, 96, 1, 1815, 1805, 733])).
% 0.67/0.91 tff(1817,plain,
% 0.67/0.91 (hskp28),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1816, 1814])).
% 0.67/0.91 tff(1818,plain,
% 0.67/0.91 (c2_1(a671)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[750, 1817])).
% 0.67/0.91 tff(1819,plain,
% 0.67/0.91 (c1_1(a671)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[758, 1817])).
% 0.67/0.91 tff(1820,plain,
% 0.67/0.91 (c0_1(a671)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[766, 1817])).
% 0.67/0.91 tff(1821,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1822,plain,
% 0.67/0.91 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647))) <=> (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1823,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.67/0.91 inference(monotonicity,[status(thm)],[1822])).
% 0.67/0.91 tff(1824,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.91 inference(transitivity,[status(thm)],[1823, 1821])).
% 0.67/0.91 tff(1825,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))),
% 0.67/0.91 inference(quant_inst,[status(thm)],[])).
% 0.67/0.91 tff(1826,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 0.67/0.91 tff(1827,plain,
% 0.67/0.91 ($false),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1826, 96, 1820, 1819, 1818, 1787, 1615, 1607, 246, 1599, 854, 1796])).
% 0.67/0.91 tff(1828,plain,(hskp2 | c0_1(a647) | hskp17 | c3_1(a647)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.91 tff(1829,plain,
% 0.67/0.91 (hskp2),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1828, 246, 1, 224])).
% 0.67/0.91 tff(1830,plain,
% 0.67/0.91 (~c0_1(a643)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1145, 1829])).
% 0.67/0.91 tff(1831,plain,
% 0.67/0.91 (c2_1(a643)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1153, 1829])).
% 0.67/0.91 tff(1832,plain,
% 0.67/0.91 (c1_1(a643)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1161, 1829])).
% 0.67/0.91 tff(1833,plain,
% 0.67/0.91 (hskp1),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1407, 1831, 1, 1832, 224, 1830, 246])).
% 0.67/0.91 tff(1834,plain,
% 0.67/0.91 (hskp28),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[742, 1833, 1])).
% 0.67/0.91 tff(1835,plain,
% 0.67/0.91 (c2_1(a671)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[750, 1834])).
% 0.67/0.91 tff(1836,plain,
% 0.67/0.91 (c1_1(a671)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[758, 1834])).
% 0.67/0.91 tff(1837,plain,
% 0.67/0.91 (c0_1(a671)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[766, 1834])).
% 0.67/0.91 tff(1838,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1839,plain,
% 0.67/0.91 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1840,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.67/0.91 inference(monotonicity,[status(thm)],[1839])).
% 0.67/0.91 tff(1841,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.67/0.91 inference(transitivity,[status(thm)],[1840, 1838])).
% 0.67/0.91 tff(1842,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.91 inference(quant_inst,[status(thm)],[])).
% 0.67/0.91 tff(1843,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 0.67/0.91 tff(1844,plain,
% 0.67/0.91 ($false),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1843, 96, 1837, 1836, 1835, 1832, 1831, 1615, 1607, 1830, 1599, 854])).
% 0.67/0.91 tff(1845,plain,(c0_1(a647) | hskp17 | c3_1(a647)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.91 tff(1846,plain,
% 0.67/0.91 ($false),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1845, 1785, 1784, 1])).
% 0.67/0.91 tff(1847,plain,(hskp17), inference(lemma,lemma(discharge,[]))).
% 0.67/0.91 tff(1848,plain,
% 0.67/0.91 (c2_1(a675)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1053, 1847])).
% 0.67/0.91 tff(1849,plain,
% 0.67/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.67/0.91 inference(bind,[status(th)],[])).
% 0.67/0.91 tff(1850,plain,
% 0.67/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_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) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.67/0.91 inference(quant_intro,[status(thm)],[1849])).
% 0.67/0.91 tff(1851,plain,
% 0.67/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_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) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1852,plain,
% 0.67/0.91 (^[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)) | (~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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.67/0.91 inference(bind,[status(th)],[])).
% 0.67/0.91 tff(1853,plain,
% 0.67/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_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) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.67/0.91 inference(quant_intro,[status(thm)],[1852])).
% 0.67/0.91 tff(1854,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.67/0.91 tff(1855,plain,
% 0.67/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 0.67/0.91 tff(1856,plain,
% 0.67/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1855, 1851])).
% 0.67/0.91 tff(1857,plain,(
% 0.67/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.67/0.91 inference(skolemize,[status(sab)],[1856])).
% 0.67/0.91 tff(1858,plain,
% 0.67/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1857, 1850])).
% 0.67/0.91 tff(1859,plain,
% 0.67/0.91 (~c3_1(a675)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1011, 1847])).
% 0.67/0.91 tff(1860,plain,
% 0.67/0.91 (~c1_1(a675)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1005, 1847])).
% 0.67/0.91 tff(1861,assumption,(hskp18), introduced(assumption)).
% 0.67/0.91 tff(1862,plain,
% 0.67/0.91 (~c2_1(a676)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[212, 1861])).
% 0.67/0.91 tff(1863,plain,
% 0.67/0.91 (c1_1(a676)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[608, 1861])).
% 0.67/0.91 tff(1864,plain,
% 0.67/0.91 (c0_1(a676)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[539, 1861])).
% 0.67/0.91 tff(1865,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1866,plain,
% 0.67/0.91 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675))) <=> (c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))),
% 0.67/0.91 inference(rewrite,[status(thm)],[])).
% 0.67/0.91 tff(1867,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676))))),
% 0.67/0.91 inference(monotonicity,[status(thm)],[1866])).
% 0.67/0.91 tff(1868,plain,
% 0.67/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))),
% 0.67/0.91 inference(transitivity,[status(thm)],[1867, 1865])).
% 0.67/0.91 tff(1869,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))),
% 0.67/0.91 inference(quant_inst,[status(thm)],[])).
% 0.67/0.91 tff(1870,plain,
% 0.67/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676))),
% 0.67/0.91 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 0.67/0.91 tff(1871,plain,
% 0.67/0.91 ($false),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1870, 96, 1864, 1863, 1848, 1615, 1607, 1862, 1860, 1859, 1599, 1858])).
% 0.67/0.91 tff(1872,plain,(~hskp18), inference(lemma,lemma(discharge,[]))).
% 0.67/0.91 tff(1873,plain,
% 0.67/0.91 (~c0_1(a675)),
% 0.67/0.91 inference(unit_resolution,[status(thm)],[1045, 96, 1848, 1860, 1859, 925])).
% 0.67/0.91 tff(1874,plain,
% 0.67/0.91 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.92 inference(rewrite,[status(thm)],[])).
% 0.67/0.92 tff(1875,plain,
% 0.67/0.92 ((hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675))) <=> (hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.92 inference(rewrite,[status(thm)],[])).
% 0.67/0.92 tff(1876,plain,
% 0.67/0.92 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)))),
% 0.67/0.92 inference(monotonicity,[status(thm)],[1875])).
% 0.67/0.92 tff(1877,plain,
% 0.67/0.92 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 0.67/0.92 inference(transitivity,[status(thm)],[1876, 1874])).
% 0.67/0.92 tff(1878,plain,
% 0.67/0.92 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675)))),
% 0.67/0.92 inference(quant_inst,[status(thm)],[])).
% 0.67/0.92 tff(1879,plain,
% 0.67/0.92 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)),
% 0.67/0.92 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 0.67/0.92 tff(1880,plain,
% 0.67/0.92 (hskp6 | hskp2 | c0_1(a675)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1879, 96, 1848, 1860, 44])).
% 0.67/0.92 tff(1881,plain,
% 0.67/0.92 (hskp6),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1880, 24, 1873])).
% 0.67/0.92 tff(1882,plain,
% 0.67/0.92 (~c2_1(a648)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[114, 1881])).
% 0.67/0.92 tff(1883,plain,
% 0.67/0.92 (~c3_1(a648)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[108, 1881])).
% 0.67/0.92 tff(1884,assumption,(hskp20), introduced(assumption)).
% 0.67/0.92 tff(1885,plain,
% 0.67/0.92 (~c3_1(a686)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[654, 1884])).
% 0.67/0.92 tff(1886,assumption,(ndr1_0), introduced(assumption)).
% 0.67/0.92 tff(1887,assumption,(~c1_1(a641)), introduced(assumption)).
% 0.67/0.92 tff(1888,assumption,(c3_1(a641)), introduced(assumption)).
% 0.67/0.92 tff(1889,assumption,(c2_1(a641)), introduced(assumption)).
% 0.67/0.92 tff(1890,assumption,(~c3_1(a648)), introduced(assumption)).
% 0.67/0.92 tff(1891,assumption,(~c2_1(a648)), introduced(assumption)).
% 0.67/0.92 tff(1892,plain,
% 0.67/0.92 (c1_1(a686)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[678, 1884])).
% 0.67/0.92 tff(1893,plain,
% 0.67/0.92 (c2_1(a686)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[663, 1884])).
% 0.67/0.92 tff(1894,plain,
% 0.67/0.92 ((~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675))),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1045, 1014, 1013, 925])).
% 0.67/0.92 tff(1895,plain,
% 0.67/0.92 (~c0_1(a675)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1894, 1538, 1886])).
% 0.67/0.92 tff(1896,plain,
% 0.67/0.92 (hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1879, 1014, 44])).
% 0.67/0.92 tff(1897,plain,
% 0.67/0.92 (hskp6),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1896, 1538, 1886, 24, 1895])).
% 0.67/0.92 tff(1898,plain,
% 0.67/0.92 (c0_1(a648)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[310, 1897])).
% 0.67/0.92 tff(1899,plain,
% 0.67/0.92 ((~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686))),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[670, 955, 1891, 1890, 177])).
% 0.67/0.92 tff(1900,plain,
% 0.67/0.92 (~c0_1(a686)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1899, 1898, 1886, 956])).
% 0.67/0.92 tff(1901,plain,
% 0.67/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))),
% 0.67/0.92 inference(rewrite,[status(thm)],[])).
% 0.67/0.92 tff(1902,plain,
% 0.67/0.92 (((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675))) <=> (c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))),
% 0.67/0.92 inference(rewrite,[status(thm)],[])).
% 0.67/0.92 tff(1903,plain,
% 0.67/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675))))),
% 0.67/0.92 inference(monotonicity,[status(thm)],[1902])).
% 0.67/0.92 tff(1904,plain,
% 0.67/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))),
% 0.67/0.92 inference(transitivity,[status(thm)],[1903, 1901])).
% 0.67/0.92 tff(1905,plain,
% 0.67/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))),
% 0.67/0.92 inference(quant_inst,[status(thm)],[])).
% 0.67/0.92 tff(1906,plain,
% 0.67/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675))),
% 0.67/0.92 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 0.67/0.92 tff(1907,plain,
% 0.67/0.92 (c1_1(a675) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675))),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1906, 1013, 1891, 1887, 1858])).
% 0.67/0.92 tff(1908,plain,
% 0.67/0.92 (~c1_1(a648)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1907, 1898, 1886, 1889, 1888, 1014, 1538])).
% 0.67/0.92 tff(1909,plain,
% 0.67/0.92 ($false),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[685, 1886, 957, 956, 1898, 955, 1891, 223, 1908, 1900])).
% 0.67/0.92 tff(1910,plain,((~c2_1(a675)) | (~ndr1_0) | (~c1_1(a686)) | (~c2_1(a686)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~c2_1(a641)) | (~c3_1(a641)) | c1_1(a675) | c3_1(a675) | c1_1(a641) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.67/0.92 tff(1911,plain,
% 0.67/0.92 ($false),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1910, 1893, 1892, 24, 1538, 955, 1891, 1890, 1889, 1888, 1014, 1013, 1887, 1886])).
% 0.67/0.92 tff(1912,plain,((~hskp20) | hskp2 | (~c2_1(a675)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~c2_1(a641)) | (~c3_1(a641)) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.92 tff(1913,plain,
% 0.67/0.92 ((~hskp20) | hskp2 | (~c2_1(a675)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~c2_1(a641)) | (~c3_1(a641)) | c1_1(a675) | c3_1(a675) | c1_1(a641)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1912, 96])).
% 0.67/0.92 tff(1914,plain,
% 0.67/0.92 ((~hskp20) | hskp2 | (~c2_1(a675)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | c1_1(a675) | c3_1(a675)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1913, 1615, 1607, 1599])).
% 0.67/0.92 tff(1915,plain,
% 0.67/0.92 ($false),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1914, 1885, 1884, 1848, 24, 1883, 1882, 1860, 1859])).
% 0.67/0.92 tff(1916,plain,((~hskp20) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.67/0.92 tff(1917,plain,
% 0.67/0.92 (~hskp20),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1916, 24])).
% 0.67/0.92 tff(1918,plain,
% 0.67/0.92 ($false),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[206, 1917, 24, 1872])).
% 0.67/0.92 tff(1919,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 0.67/0.92 tff(1920,plain,
% 0.67/0.92 (c2_1(a643)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1153, 1919])).
% 0.67/0.92 tff(1921,plain,
% 0.67/0.92 (~c0_1(a643)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1145, 1919])).
% 0.67/0.92 tff(1922,plain,
% 0.67/0.92 (c1_1(a643)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1161, 1919])).
% 0.67/0.92 tff(1923,plain,
% 0.67/0.92 (c3_1(a643)),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1567, 1922, 1860, 1859, 1921, 1920, 1848])).
% 0.67/0.92 tff(1924,plain,
% 0.67/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 0.67/0.92 inference(rewrite,[status(thm)],[])).
% 0.67/0.92 tff(1925,plain,
% 0.67/0.92 (((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 0.67/0.92 inference(rewrite,[status(thm)],[])).
% 0.67/0.92 tff(1926,plain,
% 0.67/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))))),
% 0.67/0.92 inference(monotonicity,[status(thm)],[1925])).
% 0.67/0.92 tff(1927,plain,
% 0.67/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 0.67/0.92 inference(transitivity,[status(thm)],[1926, 1924])).
% 0.67/0.92 tff(1928,plain,
% 0.67/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 0.67/0.92 inference(quant_inst,[status(thm)],[])).
% 0.67/0.92 tff(1929,plain,
% 0.67/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))),
% 0.67/0.92 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 0.67/0.92 tff(1930,plain,
% 0.67/0.92 ($false),
% 0.67/0.92 inference(unit_resolution,[status(thm)],[1929, 96, 1922, 1920, 1615, 1607, 1921, 1599, 1182, 1923])).
% 0.67/0.92 % SZS output end Proof
% 0.67/0.92 % E exiting
%------------------------------------------------------------------------------