%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN455-1 : 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 05:39:10 AM UTC 2025
% Result : Unsatisfiable 1.23s 1.44s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SYN455-1 : TPTP v9.0.0. Released v2.1.0.
% 0.10/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n014.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Jun 20 12:36:24 EDT 2025
% 0.10/0.31 % CPUTime :
% 1.23/1.44 % SZS status Unsatisfiable
% 1.23/1.44 % SZS output start Proof
% 1.23/1.44 tff(c1_1_type, type, (
% 1.23/1.44 c1_1: $i > $o)).
% 1.23/1.44 tff(c2_1_type, type, (
% 1.23/1.44 c2_1: $i > $o)).
% 1.23/1.44 tff(c3_1_type, type, (
% 1.23/1.44 c3_1: $i > $o)).
% 1.23/1.44 tff(ndr1_0_type, type, (
% 1.23/1.44 ndr1_0: $o)).
% 1.23/1.44 tff(a908_type, type, (
% 1.23/1.44 a908: $i)).
% 1.23/1.44 tff(hskp7_type, type, (
% 1.23/1.44 hskp7: $o)).
% 1.23/1.44 tff(a924_type, type, (
% 1.23/1.44 a924: $i)).
% 1.23/1.44 tff(c0_1_type, type, (
% 1.23/1.44 c0_1: $i > $o)).
% 1.23/1.44 tff(hskp13_type, type, (
% 1.23/1.44 hskp13: $o)).
% 1.23/1.44 tff(hskp15_type, type, (
% 1.23/1.44 hskp15: $o)).
% 1.23/1.44 tff(a900_type, type, (
% 1.23/1.44 a900: $i)).
% 1.23/1.44 tff(hskp27_type, type, (
% 1.23/1.44 hskp27: $o)).
% 1.23/1.44 tff(hskp10_type, type, (
% 1.23/1.44 hskp10: $o)).
% 1.23/1.44 tff(a912_type, type, (
% 1.23/1.44 a912: $i)).
% 1.23/1.44 tff(a906_type, type, (
% 1.23/1.44 a906: $i)).
% 1.23/1.44 tff(a946_type, type, (
% 1.23/1.44 a946: $i)).
% 1.23/1.44 tff(a917_type, type, (
% 1.23/1.44 a917: $i)).
% 1.23/1.44 tff(hskp12_type, type, (
% 1.23/1.44 hskp12: $o)).
% 1.23/1.44 tff(hskp5_type, type, (
% 1.23/1.44 hskp5: $o)).
% 1.23/1.44 tff(a902_type, type, (
% 1.23/1.44 a902: $i)).
% 1.23/1.44 tff(hskp1_type, type, (
% 1.23/1.44 hskp1: $o)).
% 1.23/1.44 tff(a914_type, type, (
% 1.23/1.44 a914: $i)).
% 1.23/1.44 tff(a916_type, type, (
% 1.23/1.44 a916: $i)).
% 1.23/1.44 tff(hskp28_type, type, (
% 1.23/1.44 hskp28: $o)).
% 1.23/1.44 tff(hskp11_type, type, (
% 1.23/1.44 hskp11: $o)).
% 1.23/1.44 tff(hskp26_type, type, (
% 1.23/1.44 hskp26: $o)).
% 1.23/1.44 tff(hskp21_type, type, (
% 1.23/1.44 hskp21: $o)).
% 1.23/1.44 tff(a907_type, type, (
% 1.23/1.44 a907: $i)).
% 1.23/1.44 tff(hskp6_type, type, (
% 1.23/1.44 hskp6: $o)).
% 1.23/1.44 tff(a921_type, type, (
% 1.23/1.44 a921: $i)).
% 1.23/1.44 tff(a903_type, type, (
% 1.23/1.44 a903: $i)).
% 1.23/1.44 tff(hskp2_type, type, (
% 1.23/1.44 hskp2: $o)).
% 1.23/1.44 tff(a936_type, type, (
% 1.23/1.44 a936: $i)).
% 1.23/1.44 tff(hskp17_type, type, (
% 1.23/1.44 hskp17: $o)).
% 1.23/1.44 tff(hskp14_type, type, (
% 1.23/1.44 hskp14: $o)).
% 1.23/1.44 tff(a923_type, type, (
% 1.23/1.44 a923: $i)).
% 1.23/1.44 tff(a901_type, type, (
% 1.23/1.44 a901: $i)).
% 1.23/1.44 tff(hskp0_type, type, (
% 1.23/1.44 hskp0: $o)).
% 1.23/1.44 tff(a910_type, type, (
% 1.23/1.44 a910: $i)).
% 1.23/1.44 tff(hskp9_type, type, (
% 1.23/1.44 hskp9: $o)).
% 1.23/1.44 tff(a942_type, type, (
% 1.23/1.44 a942: $i)).
% 1.23/1.44 tff(hskp30_type, type, (
% 1.23/1.44 hskp30: $o)).
% 1.23/1.44 tff(a937_type, type, (
% 1.23/1.44 a937: $i)).
% 1.23/1.44 tff(hskp18_type, type, (
% 1.23/1.44 hskp18: $o)).
% 1.23/1.44 tff(a939_type, type, (
% 1.23/1.44 a939: $i)).
% 1.23/1.44 tff(hskp20_type, type, (
% 1.23/1.44 hskp20: $o)).
% 1.23/1.44 tff(a960_type, type, (
% 1.23/1.44 a960: $i)).
% 1.23/1.44 tff(hskp25_type, type, (
% 1.23/1.44 hskp25: $o)).
% 1.23/1.44 tff(a979_type, type, (
% 1.23/1.44 a979: $i)).
% 1.23/1.44 tff(a926_type, type, (
% 1.23/1.44 a926: $i)).
% 1.23/1.44 tff(hskp16_type, type, (
% 1.23/1.44 hskp16: $o)).
% 1.23/1.44 tff(hskp4_type, type, (
% 1.23/1.44 hskp4: $o)).
% 1.23/1.44 tff(a905_type, type, (
% 1.23/1.44 a905: $i)).
% 1.23/1.44 tff(a954_type, type, (
% 1.23/1.44 a954: $i)).
% 1.23/1.44 tff(hskp23_type, type, (
% 1.23/1.44 hskp23: $o)).
% 1.23/1.44 tff(a909_type, type, (
% 1.23/1.44 a909: $i)).
% 1.23/1.44 tff(hskp8_type, type, (
% 1.23/1.44 hskp8: $o)).
% 1.23/1.44 tff(1,plain,
% 1.23/1.44 (^[V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(2,plain,
% 1.23/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[1])).
% 1.23/1.44 tff(3,plain,
% 1.23/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(4,plain,
% 1.23/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(5,plain,
% 1.23/1.44 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[4])).
% 1.23/1.44 tff(6,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.23/1.44 tff(7,plain,
% 1.23/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.23/1.44 tff(8,plain,
% 1.23/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.23/1.44 tff(9,plain,(
% 1.23/1.44 ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(skolemize,[status(sab)],[8])).
% 1.23/1.44 tff(10,plain,
% 1.23/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.23/1.44 tff(11,plain,
% 1.23/1.44 (^[U: $i] : refl((hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(12,plain,
% 1.23/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[11])).
% 1.23/1.44 tff(13,plain,
% 1.23/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(14,plain,
% 1.23/1.44 (^[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)) | 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)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(15,plain,
% 1.23/1.44 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[14])).
% 1.23/1.44 tff(16,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.23/1.44 tff(17,plain,
% 1.23/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.23/1.44 tff(18,plain,
% 1.23/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.23/1.44 tff(19,plain,(
% 1.23/1.44 ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.23/1.44 inference(skolemize,[status(sab)],[18])).
% 1.23/1.44 tff(20,plain,
% 1.23/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.23/1.44 tff(21,assumption,(~hskp7), introduced(assumption)).
% 1.23/1.44 tff(22,plain,
% 1.23/1.44 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(23,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[22])).
% 1.23/1.44 tff(24,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(25,plain,
% 1.23/1.44 (^[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))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(26,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[25])).
% 1.23/1.44 tff(27,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.23/1.44 tff(28,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.23/1.44 tff(29,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.23/1.44 tff(30,plain,(
% 1.23/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.23/1.44 inference(skolemize,[status(sab)],[29])).
% 1.23/1.44 tff(31,plain,
% 1.23/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.23/1.44 tff(32,assumption,(~hskp12), introduced(assumption)).
% 1.23/1.44 tff(33,plain,
% 1.23/1.44 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(34,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[33])).
% 1.23/1.44 tff(35,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(36,plain,
% 1.23/1.44 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(37,plain,
% 1.23/1.44 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[36])).
% 1.23/1.44 tff(38,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.23/1.44 tff(39,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.23/1.44 tff(40,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.23/1.44 tff(41,plain,(
% 1.23/1.44 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.23/1.44 inference(skolemize,[status(sab)],[40])).
% 1.23/1.44 tff(42,plain,
% 1.23/1.44 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.23/1.44 tff(43,assumption,(~hskp5), introduced(assumption)).
% 1.23/1.44 tff(44,plain,
% 1.23/1.44 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(45,plain,
% 1.23/1.44 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[44])).
% 1.23/1.44 tff(46,plain,
% 1.23/1.44 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(47,plain,
% 1.23/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(48,plain,
% 1.23/1.44 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[47])).
% 1.23/1.44 tff(49,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.23/1.44 tff(50,plain,
% 1.23/1.44 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.23/1.44 tff(51,plain,
% 1.23/1.44 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.23/1.44 tff(52,plain,(
% 1.23/1.44 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.44 inference(skolemize,[status(sab)],[51])).
% 1.23/1.44 tff(53,plain,
% 1.23/1.44 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.23/1.44 tff(54,plain,
% 1.23/1.44 (^[U: $i] : refl((hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(55,plain,
% 1.23/1.44 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[54])).
% 1.23/1.44 tff(56,plain,
% 1.23/1.44 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(57,plain,
% 1.23/1.44 (^[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) | hskp7) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.23/1.44 inference(bind,[status(th)],[])).
% 1.23/1.44 tff(58,plain,
% 1.23/1.44 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp7) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.23/1.44 inference(quant_intro,[status(thm)],[57])).
% 1.23/1.44 tff(59,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.23/1.44 tff(60,plain,
% 1.23/1.44 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.23/1.44 tff(61,plain,
% 1.23/1.44 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.23/1.44 tff(62,plain,(
% 1.23/1.44 ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.23/1.44 inference(skolemize,[status(sab)],[61])).
% 1.23/1.44 tff(63,plain,
% 1.23/1.44 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.23/1.44 tff(64,assumption,(hskp11), introduced(assumption)).
% 1.23/1.44 tff(65,plain,
% 1.23/1.44 (((~hskp11) | (~c2_1(a914))) <=> ((~hskp11) | (~c2_1(a914)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(66,plain,
% 1.23/1.44 (((~c2_1(a914)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a914)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(67,axiom,((~c2_1(a914)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.23/1.44 tff(68,plain,
% 1.23/1.44 ((~hskp11) | (~c2_1(a914))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.23/1.44 tff(69,plain,
% 1.23/1.44 ((~hskp11) | (~c2_1(a914))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[68, 65])).
% 1.23/1.44 tff(70,plain,
% 1.23/1.44 (~c2_1(a914)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[69, 64])).
% 1.23/1.44 tff(71,plain,
% 1.23/1.44 (((~hskp11) | c3_1(a914)) <=> ((~hskp11) | c3_1(a914))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(72,axiom,((~hskp11) | c3_1(a914)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.23/1.44 tff(73,plain,
% 1.23/1.44 ((~hskp11) | c3_1(a914)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.23/1.44 tff(74,plain,
% 1.23/1.44 ((~hskp11) | c3_1(a914)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[73, 71])).
% 1.23/1.44 tff(75,plain,
% 1.23/1.44 ((~hskp11) | c3_1(a914)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[74, 71])).
% 1.23/1.45 tff(76,plain,
% 1.23/1.45 ((~hskp11) | c3_1(a914)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.23/1.45 tff(77,plain,
% 1.23/1.45 ((~hskp11) | c3_1(a914)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[76, 71])).
% 1.23/1.45 tff(78,plain,
% 1.23/1.45 (c3_1(a914)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[77, 64])).
% 1.23/1.45 tff(79,plain,
% 1.23/1.45 (((~hskp11) | c0_1(a914)) <=> ((~hskp11) | c0_1(a914))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(80,axiom,((~hskp11) | c0_1(a914)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.23/1.45 tff(81,plain,
% 1.23/1.45 ((~hskp11) | c0_1(a914)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.23/1.45 tff(82,plain,
% 1.23/1.45 ((~hskp11) | c0_1(a914)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[81, 79])).
% 1.23/1.45 tff(83,plain,
% 1.23/1.45 ((~hskp11) | c0_1(a914)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[82, 79])).
% 1.23/1.45 tff(84,plain,
% 1.23/1.45 ((~hskp11) | c0_1(a914)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.23/1.45 tff(85,plain,
% 1.23/1.45 ((~hskp11) | c0_1(a914)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[84, 79])).
% 1.23/1.45 tff(86,plain,
% 1.23/1.45 (c0_1(a914)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[85, 64])).
% 1.23/1.45 tff(87,assumption,(~ndr1_0), introduced(assumption)).
% 1.23/1.45 tff(88,plain,
% 1.23/1.45 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(89,plain,
% 1.23/1.45 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(90,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 1.23/1.45 tff(91,plain,
% 1.23/1.45 (ndr1_0 | (~hskp5)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.23/1.45 tff(92,plain,
% 1.23/1.45 (ndr1_0 | (~hskp5)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[91, 88])).
% 1.23/1.45 tff(93,plain,
% 1.23/1.45 (~hskp5),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[92, 87])).
% 1.23/1.45 tff(94,plain,
% 1.23/1.45 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(95,plain,
% 1.23/1.45 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(96,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.23/1.45 tff(97,plain,
% 1.23/1.45 (ndr1_0 | (~hskp26)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.23/1.45 tff(98,plain,
% 1.23/1.45 (ndr1_0 | (~hskp26)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[97, 94])).
% 1.23/1.45 tff(99,plain,
% 1.23/1.45 (~hskp26),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[98, 87])).
% 1.23/1.45 tff(100,plain,
% 1.23/1.45 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(101,plain,
% 1.23/1.45 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(102,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 1.23/1.45 tff(103,plain,
% 1.23/1.45 (ndr1_0 | (~hskp21)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.23/1.45 tff(104,plain,
% 1.23/1.45 (ndr1_0 | (~hskp21)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[103, 100])).
% 1.23/1.45 tff(105,plain,
% 1.23/1.45 (~hskp21),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[104, 87])).
% 1.23/1.45 tff(106,plain,
% 1.23/1.45 ((hskp26 | hskp21 | hskp5) <=> (hskp26 | hskp21 | hskp5)),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(107,plain,
% 1.23/1.45 (((hskp26 | hskp5) | hskp21) <=> (hskp26 | hskp21 | hskp5)),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(108,axiom,((hskp26 | hskp5) | hskp21), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 1.23/1.45 tff(109,plain,
% 1.23/1.45 (hskp26 | hskp21 | hskp5),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.23/1.45 tff(110,plain,
% 1.23/1.45 (hskp26 | hskp21 | hskp5),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[109, 106])).
% 1.23/1.45 tff(111,plain,
% 1.23/1.45 (hskp26 | hskp21 | hskp5),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.23/1.45 tff(112,plain,
% 1.23/1.45 (hskp26 | hskp21 | hskp5),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[111, 106])).
% 1.23/1.45 tff(113,plain,
% 1.23/1.45 (hskp26 | hskp21 | hskp5),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[112, 106])).
% 1.23/1.45 tff(114,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[113, 105, 99, 93])).
% 1.23/1.45 tff(115,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(116,plain,
% 1.23/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(117,plain,
% 1.23/1.45 ((hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(118,plain,
% 1.23/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[117])).
% 1.23/1.45 tff(119,plain,
% 1.23/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[118, 116])).
% 1.23/1.45 tff(120,plain,
% 1.23/1.45 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(121,plain,
% 1.23/1.45 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.23/1.45 tff(122,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[121, 115, 21, 43, 86, 78, 70, 63])).
% 1.23/1.45 tff(123,plain,((~hskp11) | hskp7 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(124,plain,
% 1.23/1.45 (~hskp11),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[123, 21, 43])).
% 1.23/1.45 tff(125,assumption,(hskp27), introduced(assumption)).
% 1.23/1.45 tff(126,plain,
% 1.23/1.45 (((~hskp27) | c3_1(a900)) <=> ((~hskp27) | c3_1(a900))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(127,axiom,((~hskp27) | c3_1(a900)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.23/1.45 tff(128,plain,
% 1.23/1.45 ((~hskp27) | c3_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.23/1.45 tff(129,plain,
% 1.23/1.45 ((~hskp27) | c3_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[128, 126])).
% 1.23/1.45 tff(130,plain,
% 1.23/1.45 ((~hskp27) | c3_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[129, 126])).
% 1.23/1.45 tff(131,plain,
% 1.23/1.45 ((~hskp27) | c3_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[130, 126])).
% 1.23/1.45 tff(132,plain,
% 1.23/1.45 ((~hskp27) | c3_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[131, 126])).
% 1.23/1.45 tff(133,plain,
% 1.23/1.45 (c3_1(a900)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[132, 125])).
% 1.23/1.45 tff(134,plain,
% 1.23/1.45 (((~hskp27) | c2_1(a900)) <=> ((~hskp27) | c2_1(a900))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(135,axiom,((~hskp27) | c2_1(a900)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.23/1.45 tff(136,plain,
% 1.23/1.45 ((~hskp27) | c2_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.23/1.45 tff(137,plain,
% 1.23/1.45 ((~hskp27) | c2_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[136, 134])).
% 1.23/1.45 tff(138,plain,
% 1.23/1.45 ((~hskp27) | c2_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[137, 134])).
% 1.23/1.45 tff(139,plain,
% 1.23/1.45 ((~hskp27) | c2_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.23/1.45 tff(140,plain,
% 1.23/1.45 ((~hskp27) | c2_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[139, 134])).
% 1.23/1.45 tff(141,plain,
% 1.23/1.45 (c2_1(a900)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[140, 125])).
% 1.23/1.45 tff(142,plain,
% 1.23/1.45 (((~hskp27) | c1_1(a900)) <=> ((~hskp27) | c1_1(a900))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(143,axiom,((~hskp27) | c1_1(a900)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.23/1.45 tff(144,plain,
% 1.23/1.45 ((~hskp27) | c1_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.23/1.45 tff(145,plain,
% 1.23/1.45 ((~hskp27) | c1_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[144, 142])).
% 1.23/1.45 tff(146,plain,
% 1.23/1.45 ((~hskp27) | c1_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[145, 142])).
% 1.23/1.45 tff(147,plain,
% 1.23/1.45 ((~hskp27) | c1_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[146, 142])).
% 1.23/1.45 tff(148,plain,
% 1.23/1.45 ((~hskp27) | c1_1(a900)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[147, 142])).
% 1.23/1.45 tff(149,plain,
% 1.23/1.45 (c1_1(a900)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[148, 125])).
% 1.23/1.45 tff(150,assumption,(~hskp11), introduced(assumption)).
% 1.23/1.45 tff(151,plain,
% 1.23/1.45 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(152,plain,
% 1.23/1.45 ((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(153,plain,
% 1.23/1.45 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[152])).
% 1.23/1.45 tff(154,plain,
% 1.23/1.45 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[153, 151])).
% 1.23/1.45 tff(155,plain,
% 1.23/1.45 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(156,plain,
% 1.23/1.45 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.23/1.45 tff(157,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[156, 115, 32, 150, 149, 141, 133, 53])).
% 1.23/1.45 tff(158,plain,((~hskp27) | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(159,plain,
% 1.23/1.45 (~hskp27),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[158, 124, 32])).
% 1.23/1.45 tff(160,plain,
% 1.23/1.45 (^[U: $i] : refl((hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(161,plain,
% 1.23/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[160])).
% 1.23/1.45 tff(162,plain,
% 1.23/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(163,plain,
% 1.23/1.45 (^[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)) | 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))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | 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) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10) <=> (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10) <=> (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(164,plain,
% 1.23/1.45 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10) <=> ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[163])).
% 1.23/1.45 tff(165,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.23/1.45 tff(166,plain,
% 1.23/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.23/1.45 tff(167,plain,
% 1.23/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[166, 162])).
% 1.23/1.45 tff(168,plain,(
% 1.23/1.45 ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.45 inference(skolemize,[status(sab)],[167])).
% 1.23/1.45 tff(169,plain,
% 1.23/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[168, 161])).
% 1.23/1.45 tff(170,plain,
% 1.23/1.45 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(171,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[170])).
% 1.23/1.45 tff(172,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(173,plain,
% 1.23/1.45 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~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)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(174,plain,
% 1.23/1.45 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[173])).
% 1.23/1.45 tff(175,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.23/1.45 tff(176,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.23/1.45 tff(177,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.23/1.45 tff(178,plain,(
% 1.23/1.45 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.23/1.45 inference(skolemize,[status(sab)],[177])).
% 1.23/1.45 tff(179,plain,
% 1.23/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[178, 171])).
% 1.23/1.45 tff(180,assumption,(~hskp21), introduced(assumption)).
% 1.23/1.45 tff(181,plain,
% 1.23/1.45 (^[U: $i] : refl((hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(182,plain,
% 1.23/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[181])).
% 1.23/1.45 tff(183,plain,
% 1.23/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(184,plain,
% 1.23/1.45 (^[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)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp12))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp12) <=> (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12) <=> (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.23/1.45 inference(bind,[status(th)],[])).
% 1.23/1.45 tff(185,plain,
% 1.23/1.45 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12) <=> ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.23/1.45 inference(quant_intro,[status(thm)],[184])).
% 1.23/1.45 tff(186,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.29/1.45 tff(187,plain,
% 1.29/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.29/1.45 tff(188,plain,
% 1.29/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[187, 183])).
% 1.29/1.45 tff(189,plain,(
% 1.29/1.45 ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.29/1.45 inference(skolemize,[status(sab)],[188])).
% 1.29/1.45 tff(190,plain,
% 1.29/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[189, 182])).
% 1.29/1.45 tff(191,plain,
% 1.29/1.45 ((hskp21 | hskp13 | hskp12) <=> (hskp21 | hskp13 | hskp12)),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(192,plain,
% 1.29/1.45 (((hskp12 | hskp13) | hskp21) <=> (hskp21 | hskp13 | hskp12)),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(193,axiom,((hskp12 | hskp13) | hskp21), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.29/1.45 tff(194,plain,
% 1.29/1.45 (hskp21 | hskp13 | hskp12),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.29/1.45 tff(195,plain,
% 1.29/1.45 (hskp21 | hskp13 | hskp12),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[194, 191])).
% 1.29/1.45 tff(196,plain,
% 1.29/1.45 (hskp21 | hskp13 | hskp12),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[195, 191])).
% 1.29/1.45 tff(197,plain,
% 1.29/1.45 (hskp21 | hskp13 | hskp12),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[196, 191])).
% 1.29/1.45 tff(198,plain,
% 1.29/1.45 (hskp21 | hskp13 | hskp12),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[197, 191])).
% 1.29/1.45 tff(199,plain,
% 1.29/1.45 (hskp13),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[198, 32, 180])).
% 1.29/1.45 tff(200,plain,
% 1.29/1.45 (((~hskp13) | (~c3_1(a921))) <=> ((~hskp13) | (~c3_1(a921)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(201,plain,
% 1.29/1.45 (((~c3_1(a921)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a921)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(202,axiom,((~c3_1(a921)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.29/1.45 tff(203,plain,
% 1.29/1.45 ((~hskp13) | (~c3_1(a921))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.29/1.45 tff(204,plain,
% 1.29/1.45 ((~hskp13) | (~c3_1(a921))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[203, 200])).
% 1.29/1.45 tff(205,plain,
% 1.29/1.45 (~c3_1(a921)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[204, 199])).
% 1.29/1.45 tff(206,plain,
% 1.29/1.45 (((~hskp13) | (~c0_1(a921))) <=> ((~hskp13) | (~c0_1(a921)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(207,plain,
% 1.29/1.45 (((~c0_1(a921)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a921)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(208,axiom,((~c0_1(a921)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.29/1.45 tff(209,plain,
% 1.29/1.45 ((~hskp13) | (~c0_1(a921))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.29/1.45 tff(210,plain,
% 1.29/1.45 ((~hskp13) | (~c0_1(a921))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[209, 206])).
% 1.29/1.45 tff(211,plain,
% 1.29/1.45 (~c0_1(a921)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[210, 199])).
% 1.29/1.45 tff(212,plain,
% 1.29/1.45 (((~hskp13) | c2_1(a921)) <=> ((~hskp13) | c2_1(a921))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(213,axiom,((~hskp13) | c2_1(a921)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.29/1.45 tff(214,plain,
% 1.29/1.45 ((~hskp13) | c2_1(a921)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.29/1.45 tff(215,plain,
% 1.29/1.45 ((~hskp13) | c2_1(a921)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[214, 212])).
% 1.29/1.45 tff(216,plain,
% 1.29/1.45 ((~hskp13) | c2_1(a921)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[215, 212])).
% 1.29/1.45 tff(217,plain,
% 1.29/1.45 ((~hskp13) | c2_1(a921)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[216, 212])).
% 1.29/1.45 tff(218,plain,
% 1.29/1.45 ((~hskp13) | c2_1(a921)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[217, 212])).
% 1.29/1.45 tff(219,plain,
% 1.29/1.45 (c2_1(a921)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[218, 199])).
% 1.29/1.45 tff(220,plain,
% 1.29/1.45 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(221,plain,
% 1.29/1.45 ((hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921))) <=> (hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(222,plain,
% 1.29/1.45 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))))),
% 1.29/1.45 inference(monotonicity,[status(thm)],[221])).
% 1.29/1.45 tff(223,plain,
% 1.29/1.45 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.29/1.45 inference(transitivity,[status(thm)],[222, 220])).
% 1.29/1.45 tff(224,plain,
% 1.29/1.45 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))),
% 1.29/1.45 inference(quant_inst,[status(thm)],[])).
% 1.29/1.45 tff(225,plain,
% 1.29/1.45 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.29/1.45 tff(226,plain,
% 1.29/1.45 (hskp28),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[225, 115, 32, 219, 211, 205, 190])).
% 1.29/1.45 tff(227,plain,
% 1.29/1.45 (((~hskp28) | c0_1(a916)) <=> ((~hskp28) | c0_1(a916))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(228,axiom,((~hskp28) | c0_1(a916)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.29/1.45 tff(229,plain,
% 1.29/1.45 ((~hskp28) | c0_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.29/1.45 tff(230,plain,
% 1.29/1.45 ((~hskp28) | c0_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[229, 227])).
% 1.29/1.45 tff(231,plain,
% 1.29/1.45 ((~hskp28) | c0_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[230, 227])).
% 1.29/1.45 tff(232,plain,
% 1.29/1.45 ((~hskp28) | c0_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[231, 227])).
% 1.29/1.45 tff(233,plain,
% 1.29/1.45 ((~hskp28) | c0_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[232, 227])).
% 1.29/1.45 tff(234,plain,
% 1.29/1.45 (c0_1(a916)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[233, 226])).
% 1.29/1.45 tff(235,plain,
% 1.29/1.45 (((~hskp28) | c3_1(a916)) <=> ((~hskp28) | c3_1(a916))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(236,axiom,((~hskp28) | c3_1(a916)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.29/1.45 tff(237,plain,
% 1.29/1.45 ((~hskp28) | c3_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.29/1.45 tff(238,plain,
% 1.29/1.45 ((~hskp28) | c3_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[237, 235])).
% 1.29/1.45 tff(239,plain,
% 1.29/1.45 ((~hskp28) | c3_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[238, 235])).
% 1.29/1.45 tff(240,plain,
% 1.29/1.45 ((~hskp28) | c3_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[239, 235])).
% 1.29/1.45 tff(241,plain,
% 1.29/1.45 ((~hskp28) | c3_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[240, 235])).
% 1.29/1.45 tff(242,plain,
% 1.29/1.45 (c3_1(a916)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[241, 226])).
% 1.29/1.45 tff(243,plain,
% 1.29/1.45 (((~hskp28) | c1_1(a916)) <=> ((~hskp28) | c1_1(a916))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(244,axiom,((~hskp28) | c1_1(a916)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.29/1.45 tff(245,plain,
% 1.29/1.45 ((~hskp28) | c1_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.29/1.45 tff(246,plain,
% 1.29/1.45 ((~hskp28) | c1_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[245, 243])).
% 1.29/1.45 tff(247,plain,
% 1.29/1.45 ((~hskp28) | c1_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[246, 243])).
% 1.29/1.45 tff(248,plain,
% 1.29/1.45 ((~hskp28) | c1_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[247, 243])).
% 1.29/1.45 tff(249,plain,
% 1.29/1.45 ((~hskp28) | c1_1(a916)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[248, 243])).
% 1.29/1.45 tff(250,plain,
% 1.29/1.45 (c1_1(a916)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[249, 226])).
% 1.29/1.45 tff(251,assumption,(hskp5), introduced(assumption)).
% 1.29/1.45 tff(252,plain,
% 1.29/1.45 (((~hskp5) | c2_1(a906)) <=> ((~hskp5) | c2_1(a906))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(253,axiom,((~hskp5) | c2_1(a906)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.29/1.45 tff(254,plain,
% 1.29/1.45 ((~hskp5) | c2_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.29/1.45 tff(255,plain,
% 1.29/1.45 ((~hskp5) | c2_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[254, 252])).
% 1.29/1.45 tff(256,plain,
% 1.29/1.45 ((~hskp5) | c2_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[255, 252])).
% 1.29/1.45 tff(257,plain,
% 1.29/1.45 ((~hskp5) | c2_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[256, 252])).
% 1.29/1.45 tff(258,plain,
% 1.29/1.45 ((~hskp5) | c2_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[257, 252])).
% 1.29/1.45 tff(259,plain,
% 1.29/1.45 (c2_1(a906)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[258, 251])).
% 1.29/1.45 tff(260,plain,
% 1.29/1.45 (((~hskp5) | (~c3_1(a906))) <=> ((~hskp5) | (~c3_1(a906)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(261,plain,
% 1.29/1.45 (((~c3_1(a906)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a906)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(262,axiom,((~c3_1(a906)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.29/1.45 tff(263,plain,
% 1.29/1.45 ((~hskp5) | (~c3_1(a906))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.29/1.45 tff(264,plain,
% 1.29/1.45 ((~hskp5) | (~c3_1(a906))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[263, 260])).
% 1.29/1.45 tff(265,plain,
% 1.29/1.45 (~c3_1(a906)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[264, 251])).
% 1.29/1.45 tff(266,plain,
% 1.29/1.45 (((~hskp5) | c0_1(a906)) <=> ((~hskp5) | c0_1(a906))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(267,axiom,((~hskp5) | c0_1(a906)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.29/1.45 tff(268,plain,
% 1.29/1.45 ((~hskp5) | c0_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.29/1.45 tff(269,plain,
% 1.29/1.45 ((~hskp5) | c0_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[268, 266])).
% 1.29/1.45 tff(270,plain,
% 1.29/1.45 ((~hskp5) | c0_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[269, 266])).
% 1.29/1.45 tff(271,plain,
% 1.29/1.45 ((~hskp5) | c0_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[270, 266])).
% 1.29/1.45 tff(272,plain,
% 1.29/1.45 ((~hskp5) | c0_1(a906)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[271, 266])).
% 1.29/1.45 tff(273,plain,
% 1.29/1.45 (c0_1(a906)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[272, 251])).
% 1.29/1.45 tff(274,plain,
% 1.29/1.45 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_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) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.29/1.45 inference(bind,[status(th)],[])).
% 1.29/1.45 tff(275,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.45 inference(quant_intro,[status(thm)],[274])).
% 1.29/1.45 tff(276,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(277,plain,
% 1.29/1.45 (^[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)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_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) | c3_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) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_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) | c3_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) | c3_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)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.29/1.45 inference(bind,[status(th)],[])).
% 1.29/1.45 tff(278,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.45 inference(quant_intro,[status(thm)],[277])).
% 1.29/1.45 tff(279,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.29/1.45 tff(280,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[279, 278])).
% 1.29/1.45 tff(281,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[280, 276])).
% 1.29/1.45 tff(282,plain,(
% 1.29/1.45 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.45 inference(skolemize,[status(sab)],[281])).
% 1.29/1.45 tff(283,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[282, 275])).
% 1.29/1.45 tff(284,assumption,(c0_1(a906)), introduced(assumption)).
% 1.29/1.45 tff(285,assumption,(c2_1(a906)), introduced(assumption)).
% 1.29/1.45 tff(286,assumption,(~c3_1(a906)), introduced(assumption)).
% 1.29/1.45 tff(287,assumption,(~hskp10), introduced(assumption)).
% 1.29/1.45 tff(288,assumption,(hskp12), introduced(assumption)).
% 1.29/1.45 tff(289,plain,
% 1.29/1.45 (((~hskp12) | (~c2_1(a917))) <=> ((~hskp12) | (~c2_1(a917)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(290,plain,
% 1.29/1.45 (((~c2_1(a917)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a917)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(291,axiom,((~c2_1(a917)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.29/1.45 tff(292,plain,
% 1.29/1.45 ((~hskp12) | (~c2_1(a917))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.29/1.45 tff(293,plain,
% 1.29/1.45 ((~hskp12) | (~c2_1(a917))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[292, 289])).
% 1.29/1.45 tff(294,plain,
% 1.29/1.45 (~c2_1(a917)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[293, 288])).
% 1.29/1.45 tff(295,plain,
% 1.29/1.45 (((~hskp12) | c1_1(a917)) <=> ((~hskp12) | c1_1(a917))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(296,axiom,((~hskp12) | c1_1(a917)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.29/1.45 tff(297,plain,
% 1.29/1.45 ((~hskp12) | c1_1(a917)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.29/1.45 tff(298,plain,
% 1.29/1.45 ((~hskp12) | c1_1(a917)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[297, 295])).
% 1.29/1.45 tff(299,plain,
% 1.29/1.45 ((~hskp12) | c1_1(a917)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[298, 295])).
% 1.29/1.45 tff(300,plain,
% 1.29/1.45 ((~hskp12) | c1_1(a917)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[299, 295])).
% 1.29/1.45 tff(301,plain,
% 1.29/1.45 ((~hskp12) | c1_1(a917)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[300, 295])).
% 1.29/1.45 tff(302,plain,
% 1.29/1.45 (c1_1(a917)),
% 1.29/1.45 inference(unit_resolution,[status(thm)],[301, 288])).
% 1.29/1.45 tff(303,plain,
% 1.29/1.45 (((~hskp12) | c3_1(a917)) <=> ((~hskp12) | c3_1(a917))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(304,axiom,((~hskp12) | c3_1(a917)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.29/1.45 tff(305,plain,
% 1.29/1.45 ((~hskp12) | c3_1(a917)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[304, 303])).
% 1.29/1.45 tff(306,plain,
% 1.29/1.45 ((~hskp12) | c3_1(a917)),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[305, 303])).
% 1.29/1.46 tff(307,plain,
% 1.29/1.46 ((~hskp12) | c3_1(a917)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[306, 303])).
% 1.29/1.46 tff(308,plain,
% 1.29/1.46 ((~hskp12) | c3_1(a917)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[307, 303])).
% 1.29/1.46 tff(309,plain,
% 1.29/1.46 ((~hskp12) | c3_1(a917)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[308, 303])).
% 1.29/1.46 tff(310,plain,
% 1.29/1.46 (c3_1(a917)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[309, 288])).
% 1.29/1.46 tff(311,plain,
% 1.29/1.46 (^[U: $i] : refl((hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(312,plain,
% 1.29/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[311])).
% 1.29/1.46 tff(313,plain,
% 1.29/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(314,plain,
% 1.29/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21) <=> (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(315,plain,
% 1.29/1.46 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[314])).
% 1.29/1.46 tff(316,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.29/1.46 tff(317,plain,
% 1.29/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.29/1.46 tff(318,plain,
% 1.29/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[317, 313])).
% 1.29/1.46 tff(319,plain,(
% 1.29/1.46 ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.46 inference(skolemize,[status(sab)],[318])).
% 1.29/1.46 tff(320,plain,
% 1.29/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[319, 312])).
% 1.29/1.46 tff(321,assumption,(~c2_1(a917)), introduced(assumption)).
% 1.29/1.46 tff(322,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(323,plain,
% 1.29/1.46 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917))) <=> (hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(324,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[323])).
% 1.29/1.46 tff(325,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[324, 322])).
% 1.29/1.46 tff(326,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(327,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[326, 325])).
% 1.29/1.46 tff(328,plain,
% 1.29/1.46 (hskp10 | (~c3_1(a917)) | (~c1_1(a917))),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[327, 115, 180, 321, 320])).
% 1.29/1.46 tff(329,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[328, 310, 302, 287])).
% 1.29/1.46 tff(330,plain,((~hskp12) | hskp10 | hskp21 | c2_1(a917)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(331,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[330, 294, 288, 180, 287])).
% 1.29/1.46 tff(332,plain,((~hskp12) | hskp21 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(333,plain,
% 1.29/1.46 (~hskp12),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[332, 287, 180])).
% 1.29/1.46 tff(334,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(335,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(336,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[335, 334])).
% 1.29/1.46 tff(337,plain,
% 1.29/1.46 (hskp10 | c2_1(a916)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[336, 115, 180, 250, 242, 320])).
% 1.29/1.46 tff(338,plain,
% 1.29/1.46 (c2_1(a916)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[337, 287])).
% 1.29/1.46 tff(339,plain,
% 1.29/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(340,plain,
% 1.29/1.46 ((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(341,plain,
% 1.29/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[340])).
% 1.29/1.46 tff(342,plain,
% 1.29/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[341, 339])).
% 1.29/1.46 tff(343,plain,
% 1.29/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(344,plain,
% 1.29/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.29/1.46 tff(345,plain,
% 1.29/1.46 (hskp11 | (~c2_1(a916))),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[344, 115, 32, 250, 242, 53])).
% 1.29/1.46 tff(346,plain,
% 1.29/1.46 (hskp11),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[345, 338])).
% 1.29/1.46 tff(347,plain,
% 1.29/1.46 (c0_1(a914)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[85, 346])).
% 1.29/1.46 tff(348,plain,
% 1.29/1.46 (c3_1(a914)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[77, 346])).
% 1.29/1.46 tff(349,plain,
% 1.29/1.46 (~c2_1(a914)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[69, 346])).
% 1.29/1.46 tff(350,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(351,plain,
% 1.29/1.46 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914))) <=> (hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(352,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[351])).
% 1.29/1.46 tff(353,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[352, 350])).
% 1.29/1.46 tff(354,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(355,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.29/1.46 tff(356,plain,
% 1.29/1.46 (~c1_1(a914)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[355, 115, 180, 287, 348, 349, 320])).
% 1.29/1.46 tff(357,assumption,(hskp6), introduced(assumption)).
% 1.29/1.46 tff(358,plain,
% 1.29/1.46 (((~hskp6) | (~c2_1(a907))) <=> ((~hskp6) | (~c2_1(a907)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(359,plain,
% 1.29/1.46 (((~c2_1(a907)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a907)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(360,axiom,((~c2_1(a907)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.29/1.46 tff(361,plain,
% 1.29/1.46 ((~hskp6) | (~c2_1(a907))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[360, 359])).
% 1.29/1.46 tff(362,plain,
% 1.29/1.46 ((~hskp6) | (~c2_1(a907))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[361, 358])).
% 1.29/1.46 tff(363,plain,
% 1.29/1.46 (~c2_1(a907)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[362, 357])).
% 1.29/1.46 tff(364,plain,
% 1.29/1.46 (((~hskp6) | c1_1(a907)) <=> ((~hskp6) | c1_1(a907))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(365,axiom,((~hskp6) | c1_1(a907)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.29/1.46 tff(366,plain,
% 1.29/1.46 ((~hskp6) | c1_1(a907)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[365, 364])).
% 1.29/1.46 tff(367,plain,
% 1.29/1.46 ((~hskp6) | c1_1(a907)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[366, 364])).
% 1.29/1.46 tff(368,plain,
% 1.29/1.46 ((~hskp6) | c1_1(a907)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[367, 364])).
% 1.29/1.46 tff(369,plain,
% 1.29/1.46 ((~hskp6) | c1_1(a907)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[368, 364])).
% 1.29/1.46 tff(370,plain,
% 1.29/1.46 ((~hskp6) | c1_1(a907)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[369, 364])).
% 1.29/1.46 tff(371,plain,
% 1.29/1.46 (c1_1(a907)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[370, 357])).
% 1.29/1.46 tff(372,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(373,plain,
% 1.29/1.46 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907))) <=> (hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(374,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[373])).
% 1.29/1.46 tff(375,plain,
% 1.29/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[374, 372])).
% 1.29/1.46 tff(376,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(377,plain,
% 1.29/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.29/1.46 tff(378,plain,
% 1.29/1.46 (~c3_1(a907)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[377, 115, 180, 287, 371, 363, 320])).
% 1.29/1.46 tff(379,assumption,(~c1_1(a914)), introduced(assumption)).
% 1.29/1.46 tff(380,assumption,(c3_1(a914)), introduced(assumption)).
% 1.29/1.46 tff(381,assumption,(c0_1(a914)), introduced(assumption)).
% 1.29/1.46 tff(382,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(383,plain,
% 1.29/1.46 ((hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(384,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[383])).
% 1.29/1.46 tff(385,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[384, 382])).
% 1.29/1.46 tff(386,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(387,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.29/1.46 tff(388,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[387, 115, 180, 381, 380, 371, 363, 179, 379, 378])).
% 1.29/1.46 tff(389,plain,((~hskp6) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | c1_1(a914) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(390,plain,
% 1.29/1.46 (~hskp6),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[389, 356, 180, 348, 347, 287])).
% 1.29/1.46 tff(391,plain,
% 1.29/1.46 (^[U: $i] : refl((hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(392,plain,
% 1.29/1.46 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[391])).
% 1.29/1.46 tff(393,plain,
% 1.29/1.46 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(394,plain,
% 1.29/1.46 (^[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)) | 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)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(395,plain,
% 1.29/1.46 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[394])).
% 1.29/1.46 tff(396,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.29/1.46 tff(397,plain,
% 1.29/1.46 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.29/1.46 tff(398,plain,
% 1.29/1.46 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[397, 393])).
% 1.29/1.46 tff(399,plain,(
% 1.29/1.46 ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.29/1.46 inference(skolemize,[status(sab)],[398])).
% 1.29/1.46 tff(400,plain,
% 1.29/1.46 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[399, 392])).
% 1.29/1.46 tff(401,plain,
% 1.29/1.46 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(402,plain,
% 1.29/1.46 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914))) <=> (hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(403,plain,
% 1.29/1.46 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[402])).
% 1.29/1.46 tff(404,plain,
% 1.29/1.46 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[403, 401])).
% 1.29/1.46 tff(405,plain,
% 1.29/1.46 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(406,plain,
% 1.29/1.46 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.29/1.46 tff(407,plain,
% 1.29/1.46 (hskp17),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[406, 115, 32, 347, 349, 400, 356])).
% 1.29/1.46 tff(408,plain,
% 1.29/1.46 (((~hskp17) | (~c3_1(a936))) <=> ((~hskp17) | (~c3_1(a936)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(409,plain,
% 1.29/1.46 (((~c3_1(a936)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a936)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(410,axiom,((~c3_1(a936)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.29/1.46 tff(411,plain,
% 1.29/1.46 ((~hskp17) | (~c3_1(a936))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.29/1.46 tff(412,plain,
% 1.29/1.46 ((~hskp17) | (~c3_1(a936))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[411, 408])).
% 1.29/1.46 tff(413,plain,
% 1.29/1.46 (~c3_1(a936)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[412, 407])).
% 1.29/1.46 tff(414,assumption,(hskp7), introduced(assumption)).
% 1.29/1.46 tff(415,plain,
% 1.29/1.46 (((~hskp7) | (~c3_1(a908))) <=> ((~hskp7) | (~c3_1(a908)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(416,plain,
% 1.29/1.46 (((~c3_1(a908)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a908)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(417,axiom,((~c3_1(a908)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.29/1.46 tff(418,plain,
% 1.29/1.46 ((~hskp7) | (~c3_1(a908))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.29/1.46 tff(419,plain,
% 1.29/1.46 ((~hskp7) | (~c3_1(a908))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[418, 415])).
% 1.29/1.46 tff(420,plain,
% 1.29/1.46 (~c3_1(a908)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[419, 414])).
% 1.29/1.46 tff(421,plain,
% 1.29/1.46 (((~hskp7) | (~c2_1(a908))) <=> ((~hskp7) | (~c2_1(a908)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(422,plain,
% 1.29/1.46 (((~c2_1(a908)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a908)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(423,axiom,((~c2_1(a908)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.29/1.46 tff(424,plain,
% 1.29/1.46 ((~hskp7) | (~c2_1(a908))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[423, 422])).
% 1.29/1.46 tff(425,plain,
% 1.29/1.46 ((~hskp7) | (~c2_1(a908))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[424, 421])).
% 1.29/1.46 tff(426,plain,
% 1.29/1.46 (~c2_1(a908)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[425, 414])).
% 1.29/1.46 tff(427,plain,
% 1.29/1.46 (((~hskp7) | c1_1(a908)) <=> ((~hskp7) | c1_1(a908))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(428,axiom,((~hskp7) | c1_1(a908)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.29/1.46 tff(429,plain,
% 1.29/1.46 ((~hskp7) | c1_1(a908)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.29/1.46 tff(430,plain,
% 1.29/1.46 ((~hskp7) | c1_1(a908)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[429, 427])).
% 1.29/1.46 tff(431,plain,
% 1.29/1.46 ((~hskp7) | c1_1(a908)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[430, 427])).
% 1.29/1.46 tff(432,plain,
% 1.29/1.46 ((~hskp7) | c1_1(a908)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[431, 427])).
% 1.29/1.46 tff(433,plain,
% 1.29/1.46 ((~hskp7) | c1_1(a908)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[432, 427])).
% 1.29/1.46 tff(434,plain,
% 1.29/1.46 (c1_1(a908)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[433, 414])).
% 1.29/1.46 tff(435,assumption,(c3_1(a916)), introduced(assumption)).
% 1.29/1.46 tff(436,assumption,(c1_1(a916)), introduced(assumption)).
% 1.29/1.46 tff(437,assumption,(c0_1(a916)), introduced(assumption)).
% 1.29/1.46 tff(438,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(439,plain,
% 1.29/1.46 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(440,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[439])).
% 1.29/1.46 tff(441,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[440, 438])).
% 1.29/1.46 tff(442,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(443,plain,
% 1.31/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[442, 441])).
% 1.31/1.47 tff(444,plain,
% 1.31/1.47 ($false),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[443, 115, 437, 436, 435, 434, 284, 285, 426, 420, 286, 31])).
% 1.31/1.47 tff(445,plain,((~hskp7) | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916)) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.47 tff(446,plain,
% 1.31/1.47 (~hskp7),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[445, 234, 250, 242, 284, 285, 286])).
% 1.31/1.47 tff(447,plain,
% 1.31/1.47 (((~hskp17) | (~c2_1(a936))) <=> ((~hskp17) | (~c2_1(a936)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(448,plain,
% 1.31/1.47 (((~c2_1(a936)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a936)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(449,axiom,((~c2_1(a936)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.31/1.47 tff(450,plain,
% 1.31/1.47 ((~hskp17) | (~c2_1(a936))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.31/1.47 tff(451,plain,
% 1.31/1.47 ((~hskp17) | (~c2_1(a936))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[450, 447])).
% 1.31/1.47 tff(452,plain,
% 1.31/1.47 (~c2_1(a936)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[451, 407])).
% 1.31/1.47 tff(453,plain,
% 1.31/1.47 (((~hskp17) | (~c1_1(a936))) <=> ((~hskp17) | (~c1_1(a936)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(454,plain,
% 1.31/1.47 (((~c1_1(a936)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a936)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(455,axiom,((~c1_1(a936)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.31/1.47 tff(456,plain,
% 1.31/1.47 ((~hskp17) | (~c1_1(a936))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[455, 454])).
% 1.31/1.47 tff(457,plain,
% 1.31/1.47 ((~hskp17) | (~c1_1(a936))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[456, 453])).
% 1.31/1.47 tff(458,plain,
% 1.31/1.47 (~c1_1(a936)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[457, 407])).
% 1.31/1.47 tff(459,assumption,(~c0_1(a936)), introduced(assumption)).
% 1.31/1.47 tff(460,plain,
% 1.31/1.47 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(461,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[460])).
% 1.31/1.47 tff(462,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(463,plain,
% 1.31/1.47 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(464,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[463])).
% 1.31/1.47 tff(465,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.31/1.47 tff(466,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[465, 464])).
% 1.31/1.47 tff(467,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[466, 462])).
% 1.31/1.47 tff(468,plain,(
% 1.31/1.47 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(skolemize,[status(sab)],[467])).
% 1.31/1.47 tff(469,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[468, 461])).
% 1.31/1.47 tff(470,assumption,(~c2_1(a936)), introduced(assumption)).
% 1.31/1.47 tff(471,assumption,(~c1_1(a936)), introduced(assumption)).
% 1.31/1.47 tff(472,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(473,plain,
% 1.31/1.47 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(474,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936)))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[473])).
% 1.31/1.47 tff(475,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))),
% 1.31/1.47 inference(transitivity,[status(thm)],[474, 472])).
% 1.31/1.47 tff(476,plain,
% 1.31/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(477,plain,
% 1.31/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[476, 475])).
% 1.31/1.47 tff(478,plain,
% 1.31/1.47 ((~c1_1(a906)) | c0_1(a936)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[477, 115, 284, 285, 471, 470, 286, 469])).
% 1.31/1.47 tff(479,plain,
% 1.31/1.47 (~c1_1(a906)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[478, 459])).
% 1.31/1.47 tff(480,plain,
% 1.31/1.47 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(481,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_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) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[480])).
% 1.31/1.47 tff(482,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_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) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(483,plain,
% 1.31/1.47 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(484,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_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) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[483])).
% 1.31/1.47 tff(485,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.31/1.47 tff(486,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.31/1.47 tff(487,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[486, 482])).
% 1.31/1.47 tff(488,plain,(
% 1.31/1.47 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(skolemize,[status(sab)],[487])).
% 1.31/1.47 tff(489,plain,
% 1.31/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[488, 481])).
% 1.31/1.47 tff(490,assumption,(~c3_1(a921)), introduced(assumption)).
% 1.31/1.47 tff(491,assumption,(~c0_1(a921)), introduced(assumption)).
% 1.31/1.47 tff(492,assumption,(c2_1(a921)), introduced(assumption)).
% 1.31/1.47 tff(493,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(494,plain,
% 1.31/1.47 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(495,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936)))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[494])).
% 1.31/1.47 tff(496,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))),
% 1.31/1.47 inference(transitivity,[status(thm)],[495, 493])).
% 1.31/1.47 tff(497,plain,
% 1.31/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(498,plain,
% 1.31/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[497, 496])).
% 1.31/1.47 tff(499,plain,
% 1.31/1.47 ($false),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[498, 115, 492, 284, 471, 470, 491, 490, 286, 489, 479, 459])).
% 1.31/1.47 tff(500,plain,(c0_1(a936) | (~c2_1(a921)) | (~c0_1(a906)) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.47 tff(501,plain,
% 1.31/1.47 (c0_1(a936)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[500, 458, 284, 219, 452, 211, 205, 286, 285])).
% 1.31/1.47 tff(502,assumption,(c0_1(a936)), introduced(assumption)).
% 1.31/1.47 tff(503,assumption,(~hskp6), introduced(assumption)).
% 1.31/1.47 tff(504,plain,
% 1.31/1.47 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(505,plain,
% 1.31/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[504])).
% 1.31/1.47 tff(506,plain,
% 1.31/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(507,plain,
% 1.31/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(508,plain,
% 1.31/1.47 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[507])).
% 1.31/1.47 tff(509,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.31/1.47 tff(510,plain,
% 1.31/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.31/1.47 tff(511,plain,
% 1.31/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[510, 506])).
% 1.31/1.47 tff(512,plain,(
% 1.31/1.47 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.47 inference(skolemize,[status(sab)],[511])).
% 1.31/1.47 tff(513,plain,
% 1.31/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[512, 505])).
% 1.31/1.47 tff(514,assumption,(hskp14), introduced(assumption)).
% 1.31/1.47 tff(515,plain,
% 1.31/1.47 (((~hskp14) | (~c1_1(a923))) <=> ((~hskp14) | (~c1_1(a923)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(516,plain,
% 1.31/1.47 (((~c1_1(a923)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a923)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(517,axiom,((~c1_1(a923)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.31/1.47 tff(518,plain,
% 1.31/1.47 ((~hskp14) | (~c1_1(a923))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.31/1.47 tff(519,plain,
% 1.31/1.47 ((~hskp14) | (~c1_1(a923))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[518, 515])).
% 1.31/1.47 tff(520,plain,
% 1.31/1.47 (~c1_1(a923)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[519, 514])).
% 1.31/1.47 tff(521,plain,
% 1.31/1.47 (((~hskp14) | (~c0_1(a923))) <=> ((~hskp14) | (~c0_1(a923)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(522,plain,
% 1.31/1.47 (((~c0_1(a923)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a923)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(523,axiom,((~c0_1(a923)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.31/1.47 tff(524,plain,
% 1.31/1.47 ((~hskp14) | (~c0_1(a923))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[523, 522])).
% 1.31/1.47 tff(525,plain,
% 1.31/1.47 ((~hskp14) | (~c0_1(a923))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[524, 521])).
% 1.31/1.47 tff(526,plain,
% 1.31/1.47 (~c0_1(a923)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[525, 514])).
% 1.31/1.47 tff(527,plain,
% 1.31/1.47 (((~hskp14) | c3_1(a923)) <=> ((~hskp14) | c3_1(a923))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(528,axiom,((~hskp14) | c3_1(a923)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.31/1.47 tff(529,plain,
% 1.31/1.47 ((~hskp14) | c3_1(a923)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.31/1.47 tff(530,plain,
% 1.31/1.47 ((~hskp14) | c3_1(a923)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[529, 527])).
% 1.31/1.47 tff(531,plain,
% 1.31/1.47 ((~hskp14) | c3_1(a923)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[530, 527])).
% 1.31/1.47 tff(532,plain,
% 1.31/1.47 ((~hskp14) | c3_1(a923)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[531, 527])).
% 1.31/1.47 tff(533,plain,
% 1.31/1.47 ((~hskp14) | c3_1(a923)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[532, 527])).
% 1.31/1.47 tff(534,plain,
% 1.31/1.47 (c3_1(a923)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[533, 514])).
% 1.31/1.47 tff(535,plain,
% 1.31/1.47 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(536,plain,
% 1.31/1.47 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923))) <=> (hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(537,plain,
% 1.31/1.47 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[536])).
% 1.31/1.47 tff(538,plain,
% 1.31/1.47 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[537, 535])).
% 1.31/1.47 tff(539,plain,
% 1.31/1.47 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(540,plain,
% 1.31/1.47 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.31/1.47 tff(541,plain,
% 1.31/1.47 ($false),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[540, 115, 21, 503, 534, 526, 520, 513])).
% 1.31/1.47 tff(542,plain,((~hskp14) | hskp7 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.31/1.47 tff(543,plain,
% 1.31/1.47 (~hskp14),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[542, 503, 21])).
% 1.31/1.47 tff(544,plain,
% 1.31/1.47 (^[U: $i] : refl((hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(545,plain,
% 1.31/1.47 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[544])).
% 1.31/1.47 tff(546,plain,
% 1.31/1.47 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(547,plain,
% 1.31/1.47 (^[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)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp14))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14) <=> (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(548,plain,
% 1.31/1.47 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14) <=> ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[547])).
% 1.31/1.47 tff(549,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.31/1.47 tff(550,plain,
% 1.31/1.47 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[549, 548])).
% 1.31/1.47 tff(551,plain,
% 1.31/1.47 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[550, 546])).
% 1.31/1.47 tff(552,plain,(
% 1.31/1.47 ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.47 inference(skolemize,[status(sab)],[551])).
% 1.31/1.47 tff(553,plain,
% 1.31/1.48 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[552, 545])).
% 1.31/1.48 tff(554,assumption,(~c3_1(a936)), introduced(assumption)).
% 1.31/1.48 tff(555,plain,
% 1.31/1.48 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(556,plain,
% 1.31/1.48 ((hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936))) <=> (hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(557,plain,
% 1.31/1.48 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[556])).
% 1.31/1.48 tff(558,plain,
% 1.31/1.48 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[557, 555])).
% 1.31/1.48 tff(559,plain,
% 1.31/1.48 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(560,plain,
% 1.31/1.48 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[559, 558])).
% 1.31/1.48 tff(561,plain,
% 1.31/1.48 (hskp14 | hskp6 | (~c0_1(a936))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[560, 115, 470, 554, 553])).
% 1.31/1.48 tff(562,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[561, 543, 503, 502])).
% 1.31/1.48 tff(563,plain,(hskp6 | (~c0_1(a936)) | c2_1(a936) | c3_1(a936) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(564,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[563, 501, 452, 446, 413, 390])).
% 1.31/1.48 tff(565,plain,(hskp10 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(566,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[565, 333, 287, 286, 285, 180, 284])).
% 1.31/1.48 tff(567,plain,(hskp10 | c3_1(a906) | (~c2_1(a906)) | hskp21 | (~c0_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(568,plain,
% 1.31/1.48 (hskp10),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[567, 286, 285, 180, 284])).
% 1.31/1.48 tff(569,plain,
% 1.31/1.48 (((~hskp10) | (~c0_1(a912))) <=> ((~hskp10) | (~c0_1(a912)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(570,plain,
% 1.31/1.48 (((~c0_1(a912)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a912)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(571,axiom,((~c0_1(a912)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.31/1.48 tff(572,plain,
% 1.31/1.48 ((~hskp10) | (~c0_1(a912))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.31/1.48 tff(573,plain,
% 1.31/1.48 ((~hskp10) | (~c0_1(a912))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[572, 569])).
% 1.31/1.48 tff(574,plain,
% 1.31/1.48 (~c0_1(a912)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[573, 568])).
% 1.31/1.48 tff(575,plain,
% 1.31/1.48 (^[U: $i] : refl((hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(576,plain,
% 1.31/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[575])).
% 1.31/1.48 tff(577,plain,
% 1.31/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(578,plain,
% 1.31/1.48 (^[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)) | hskp2) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0))), rewrite(((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(579,plain,
% 1.31/1.48 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[578])).
% 1.31/1.48 tff(580,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.31/1.48 tff(581,plain,
% 1.31/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.31/1.48 tff(582,plain,
% 1.31/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[581, 577])).
% 1.31/1.48 tff(583,plain,(
% 1.31/1.48 ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.31/1.48 inference(skolemize,[status(sab)],[582])).
% 1.31/1.48 tff(584,plain,
% 1.31/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[583, 576])).
% 1.31/1.48 tff(585,assumption,(~hskp2), introduced(assumption)).
% 1.31/1.48 tff(586,plain,
% 1.31/1.48 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(587,plain,
% 1.31/1.48 ((hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921))) <=> (hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(588,plain,
% 1.31/1.48 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[587])).
% 1.31/1.48 tff(589,plain,
% 1.31/1.48 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[588, 586])).
% 1.31/1.48 tff(590,plain,
% 1.31/1.48 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(591,plain,
% 1.31/1.48 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.31/1.48 tff(592,plain,
% 1.31/1.48 (hskp0),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[591, 115, 585, 219, 211, 205, 584])).
% 1.31/1.48 tff(593,plain,
% 1.31/1.48 (((~hskp0) | (~c3_1(a901))) <=> ((~hskp0) | (~c3_1(a901)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(594,plain,
% 1.31/1.48 (((~c3_1(a901)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a901)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(595,axiom,((~c3_1(a901)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.31/1.48 tff(596,plain,
% 1.31/1.48 ((~hskp0) | (~c3_1(a901))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.31/1.48 tff(597,plain,
% 1.31/1.48 ((~hskp0) | (~c3_1(a901))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[596, 593])).
% 1.31/1.48 tff(598,plain,
% 1.31/1.48 (~c3_1(a901)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[597, 592])).
% 1.31/1.48 tff(599,plain,
% 1.31/1.48 (((~hskp0) | (~c1_1(a901))) <=> ((~hskp0) | (~c1_1(a901)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(600,plain,
% 1.31/1.48 (((~c1_1(a901)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a901)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(601,axiom,((~c1_1(a901)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.31/1.48 tff(602,plain,
% 1.31/1.48 ((~hskp0) | (~c1_1(a901))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[601, 600])).
% 1.31/1.48 tff(603,plain,
% 1.31/1.48 ((~hskp0) | (~c1_1(a901))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[602, 599])).
% 1.31/1.48 tff(604,plain,
% 1.31/1.48 (~c1_1(a901)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[603, 592])).
% 1.31/1.48 tff(605,plain,
% 1.31/1.48 (((~hskp0) | (~c0_1(a901))) <=> ((~hskp0) | (~c0_1(a901)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(606,plain,
% 1.31/1.48 (((~c0_1(a901)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a901)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(607,axiom,((~c0_1(a901)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.31/1.48 tff(608,plain,
% 1.31/1.48 ((~hskp0) | (~c0_1(a901))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[607, 606])).
% 1.31/1.48 tff(609,plain,
% 1.31/1.48 ((~hskp0) | (~c0_1(a901))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[608, 605])).
% 1.31/1.48 tff(610,plain,
% 1.31/1.48 (~c0_1(a901)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[609, 592])).
% 1.31/1.48 tff(611,assumption,(~c0_1(a912)), introduced(assumption)).
% 1.31/1.48 tff(612,plain,
% 1.31/1.48 (hskp10),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[565, 32, 286, 285, 180, 284])).
% 1.31/1.48 tff(613,plain,
% 1.31/1.48 (((~hskp10) | c2_1(a912)) <=> ((~hskp10) | c2_1(a912))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(614,axiom,((~hskp10) | c2_1(a912)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.31/1.48 tff(615,plain,
% 1.31/1.48 ((~hskp10) | c2_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.31/1.48 tff(616,plain,
% 1.31/1.48 ((~hskp10) | c2_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[615, 613])).
% 1.31/1.48 tff(617,plain,
% 1.31/1.48 ((~hskp10) | c2_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[616, 613])).
% 1.31/1.48 tff(618,plain,
% 1.31/1.48 ((~hskp10) | c2_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[617, 613])).
% 1.31/1.48 tff(619,plain,
% 1.31/1.48 ((~hskp10) | c2_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[618, 613])).
% 1.31/1.48 tff(620,plain,
% 1.31/1.48 (c2_1(a912)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[619, 612])).
% 1.31/1.48 tff(621,plain,
% 1.31/1.48 (((~hskp10) | c1_1(a912)) <=> ((~hskp10) | c1_1(a912))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(622,axiom,((~hskp10) | c1_1(a912)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.31/1.48 tff(623,plain,
% 1.31/1.48 ((~hskp10) | c1_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[622, 621])).
% 1.31/1.48 tff(624,plain,
% 1.31/1.48 ((~hskp10) | c1_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[623, 621])).
% 1.31/1.48 tff(625,plain,
% 1.31/1.48 ((~hskp10) | c1_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[624, 621])).
% 1.31/1.48 tff(626,plain,
% 1.31/1.48 ((~hskp10) | c1_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[625, 621])).
% 1.31/1.48 tff(627,plain,
% 1.31/1.48 ((~hskp10) | c1_1(a912)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[626, 621])).
% 1.31/1.48 tff(628,plain,
% 1.31/1.48 (c1_1(a912)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[627, 612])).
% 1.31/1.48 tff(629,assumption,(c2_1(a912)), introduced(assumption)).
% 1.31/1.48 tff(630,assumption,(c1_1(a912)), introduced(assumption)).
% 1.31/1.48 tff(631,plain,
% 1.31/1.48 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(632,plain,
% 1.31/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[631])).
% 1.31/1.48 tff(633,plain,
% 1.31/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(634,plain,
% 1.31/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(635,plain,
% 1.31/1.48 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[634])).
% 1.31/1.48 tff(636,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.31/1.48 tff(637,plain,
% 1.31/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.31/1.48 tff(638,plain,
% 1.31/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[637, 633])).
% 1.31/1.48 tff(639,plain,(
% 1.31/1.48 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.31/1.48 inference(skolemize,[status(sab)],[638])).
% 1.31/1.48 tff(640,plain,
% 1.31/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[639, 632])).
% 1.31/1.48 tff(641,plain,
% 1.31/1.48 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(642,plain,
% 1.31/1.48 ((hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(643,plain,
% 1.31/1.48 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[642])).
% 1.31/1.48 tff(644,plain,
% 1.31/1.48 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[643, 641])).
% 1.31/1.48 tff(645,plain,
% 1.31/1.48 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(646,plain,
% 1.31/1.48 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.31/1.48 tff(647,plain,
% 1.31/1.48 (hskp14 | hskp7 | (~c2_1(a912)) | (~c1_1(a912))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[646, 115, 611, 640])).
% 1.31/1.48 tff(648,plain,
% 1.31/1.48 (hskp14),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[647, 21, 630, 629])).
% 1.31/1.48 tff(649,plain,
% 1.31/1.48 (~c1_1(a923)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[519, 648])).
% 1.31/1.48 tff(650,plain,
% 1.31/1.48 (~c0_1(a923)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[525, 648])).
% 1.31/1.48 tff(651,plain,
% 1.31/1.48 (c3_1(a923)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[533, 648])).
% 1.31/1.48 tff(652,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[540, 115, 21, 503, 651, 650, 649, 513])).
% 1.31/1.48 tff(653,plain,(hskp7 | hskp6 | (~c1_1(a912)) | (~c2_1(a912)) | c0_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(654,plain,
% 1.31/1.48 (hskp6),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[653, 628, 446, 620, 611])).
% 1.31/1.48 tff(655,plain,
% 1.31/1.48 (~c2_1(a907)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[362, 654])).
% 1.31/1.48 tff(656,plain,
% 1.31/1.48 (((~hskp6) | c0_1(a907)) <=> ((~hskp6) | c0_1(a907))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(657,axiom,((~hskp6) | c0_1(a907)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.31/1.48 tff(658,plain,
% 1.31/1.48 ((~hskp6) | c0_1(a907)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[657, 656])).
% 1.31/1.48 tff(659,plain,
% 1.31/1.48 ((~hskp6) | c0_1(a907)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[658, 656])).
% 1.31/1.48 tff(660,plain,
% 1.31/1.48 ((~hskp6) | c0_1(a907)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[659, 656])).
% 1.31/1.48 tff(661,plain,
% 1.31/1.48 ((~hskp6) | c0_1(a907)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[660, 656])).
% 1.31/1.48 tff(662,plain,
% 1.31/1.48 ((~hskp6) | c0_1(a907)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[661, 656])).
% 1.31/1.48 tff(663,plain,
% 1.31/1.48 (c0_1(a907)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[662, 654])).
% 1.31/1.48 tff(664,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(665,plain,
% 1.31/1.48 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c0_1(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(666,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[665])).
% 1.31/1.48 tff(667,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[666, 664])).
% 1.31/1.48 tff(668,plain,
% 1.31/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(669,plain,
% 1.31/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[668, 667])).
% 1.31/1.48 tff(670,plain,
% 1.31/1.48 (c3_1(a907)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[669, 115, 628, 620, 663, 611, 655, 610, 604, 598, 283])).
% 1.31/1.48 tff(671,plain,
% 1.31/1.48 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(672,plain,
% 1.31/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[671])).
% 1.31/1.48 tff(673,plain,
% 1.31/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(674,plain,
% 1.31/1.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(675,plain,
% 1.31/1.48 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_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) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[674])).
% 1.31/1.48 tff(676,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.31/1.48 tff(677,plain,
% 1.31/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[676, 675])).
% 1.31/1.48 tff(678,plain,
% 1.31/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[677, 673])).
% 1.31/1.48 tff(679,plain,(
% 1.31/1.48 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.31/1.48 inference(skolemize,[status(sab)],[678])).
% 1.31/1.48 tff(680,plain,
% 1.31/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[679, 672])).
% 1.31/1.48 tff(681,plain,
% 1.31/1.48 (c1_1(a907)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[370, 654])).
% 1.31/1.48 tff(682,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(683,plain,
% 1.31/1.48 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(684,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[683])).
% 1.31/1.48 tff(685,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[684, 682])).
% 1.31/1.48 tff(686,plain,
% 1.31/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(687,plain,
% 1.31/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.31/1.48 tff(688,plain,
% 1.31/1.48 ((~c3_1(a907)) | c1_1(a921)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[687, 115, 219, 628, 620, 681, 205, 611, 655, 680])).
% 1.31/1.48 tff(689,plain,
% 1.31/1.48 (c1_1(a921)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[688, 670])).
% 1.31/1.48 tff(690,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(691,plain,
% 1.31/1.49 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(692,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[691])).
% 1.31/1.49 tff(693,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[692, 690])).
% 1.31/1.49 tff(694,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(695,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[694, 693])).
% 1.31/1.49 tff(696,plain,
% 1.31/1.49 ((~c2_1(a901)) | (~c3_1(a907))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[695, 115, 628, 620, 681, 611, 655, 604, 598, 680])).
% 1.31/1.49 tff(697,plain,
% 1.31/1.49 (~c2_1(a901)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[696, 670])).
% 1.31/1.49 tff(698,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(699,plain,
% 1.31/1.49 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(700,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[699])).
% 1.31/1.49 tff(701,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[700, 698])).
% 1.31/1.49 tff(702,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(703,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[702, 701])).
% 1.31/1.49 tff(704,plain,
% 1.31/1.49 (c2_1(a901) | (~c1_1(a921))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[703, 115, 219, 284, 285, 205, 286, 610, 604, 469])).
% 1.31/1.49 tff(705,plain,
% 1.31/1.49 ($false),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[704, 697, 689])).
% 1.31/1.49 tff(706,plain,(hskp12 | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c0_1(a912) | hskp21 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.31/1.49 tff(707,plain,
% 1.31/1.49 (hskp2),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[706, 32, 285, 286, 284, 180, 574])).
% 1.31/1.49 tff(708,plain,
% 1.31/1.49 (((~hskp2) | (~c3_1(a903))) <=> ((~hskp2) | (~c3_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(709,plain,
% 1.31/1.49 (((~c3_1(a903)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(710,axiom,((~c3_1(a903)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.31/1.49 tff(711,plain,
% 1.31/1.49 ((~hskp2) | (~c3_1(a903))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.31/1.49 tff(712,plain,
% 1.31/1.49 ((~hskp2) | (~c3_1(a903))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[711, 708])).
% 1.31/1.49 tff(713,plain,
% 1.31/1.49 (~c3_1(a903)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[712, 707])).
% 1.31/1.49 tff(714,plain,
% 1.31/1.49 (((~hskp2) | (~c2_1(a903))) <=> ((~hskp2) | (~c2_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(715,plain,
% 1.31/1.49 (((~c2_1(a903)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(716,axiom,((~c2_1(a903)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.31/1.49 tff(717,plain,
% 1.31/1.49 ((~hskp2) | (~c2_1(a903))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[716, 715])).
% 1.31/1.49 tff(718,plain,
% 1.31/1.49 ((~hskp2) | (~c2_1(a903))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[717, 714])).
% 1.31/1.49 tff(719,plain,
% 1.31/1.49 (~c2_1(a903)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[718, 707])).
% 1.31/1.49 tff(720,plain,
% 1.31/1.49 (((~hskp2) | c0_1(a903)) <=> ((~hskp2) | c0_1(a903))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(721,axiom,((~hskp2) | c0_1(a903)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.31/1.49 tff(722,plain,
% 1.31/1.49 ((~hskp2) | c0_1(a903)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[721, 720])).
% 1.31/1.49 tff(723,plain,
% 1.31/1.49 ((~hskp2) | c0_1(a903)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[722, 720])).
% 1.31/1.49 tff(724,plain,
% 1.31/1.49 ((~hskp2) | c0_1(a903)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[723, 720])).
% 1.31/1.49 tff(725,plain,
% 1.31/1.49 ((~hskp2) | c0_1(a903)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[724, 720])).
% 1.31/1.49 tff(726,plain,
% 1.31/1.49 ((~hskp2) | c0_1(a903)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[725, 720])).
% 1.31/1.49 tff(727,plain,
% 1.31/1.49 (c0_1(a903)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[726, 707])).
% 1.31/1.49 tff(728,plain,
% 1.31/1.49 (c2_1(a912)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[619, 568])).
% 1.31/1.49 tff(729,plain,
% 1.31/1.49 (c1_1(a912)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[627, 568])).
% 1.31/1.49 tff(730,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(731,plain,
% 1.31/1.49 (((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921)) <=> (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(732,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[731])).
% 1.31/1.49 tff(733,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.31/1.49 inference(transitivity,[status(thm)],[732, 730])).
% 1.31/1.49 tff(734,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(735,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.31/1.49 tff(736,plain,
% 1.31/1.49 (c1_1(a921)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[735, 115, 729, 728, 727, 211, 205, 574, 719, 713, 283])).
% 1.31/1.49 tff(737,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(738,plain,
% 1.31/1.49 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903))) <=> (c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(739,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[738])).
% 1.31/1.49 tff(740,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[739, 737])).
% 1.31/1.49 tff(741,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(742,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[741, 740])).
% 1.31/1.49 tff(743,plain,
% 1.31/1.49 (~c1_1(a903)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[742, 115, 234, 250, 242, 284, 285, 286, 719, 713, 31])).
% 1.31/1.49 tff(744,plain,
% 1.31/1.49 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(745,plain,
% 1.31/1.49 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903))) <=> (hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(746,plain,
% 1.31/1.49 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[745])).
% 1.31/1.49 tff(747,plain,
% 1.31/1.49 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[746, 744])).
% 1.31/1.49 tff(748,plain,
% 1.31/1.49 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(749,plain,
% 1.31/1.49 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[748, 747])).
% 1.31/1.49 tff(750,plain,
% 1.31/1.49 (hskp17 | c1_1(a903)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[749, 115, 32, 727, 719, 400])).
% 1.31/1.49 tff(751,plain,
% 1.31/1.49 (hskp17),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[750, 743])).
% 1.31/1.49 tff(752,plain,
% 1.31/1.49 (~c2_1(a936)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[451, 751])).
% 1.31/1.49 tff(753,plain,
% 1.31/1.49 (^[U: $i] : refl((hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(754,plain,
% 1.31/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[753])).
% 1.31/1.49 tff(755,plain,
% 1.31/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(756,plain,
% 1.31/1.49 (^[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)) | 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)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | 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) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp7) <=> (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7) <=> (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(757,plain,
% 1.31/1.49 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7) <=> ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[756])).
% 1.31/1.49 tff(758,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.31/1.49 tff(759,plain,
% 1.31/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.31/1.49 tff(760,plain,
% 1.31/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[759, 755])).
% 1.31/1.49 tff(761,plain,(
% 1.31/1.49 ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[760])).
% 1.31/1.49 tff(762,plain,
% 1.31/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[761, 754])).
% 1.31/1.49 tff(763,plain,
% 1.31/1.49 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(764,plain,
% 1.31/1.49 ((hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903))) <=> (hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(765,plain,
% 1.31/1.49 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[764])).
% 1.31/1.49 tff(766,plain,
% 1.31/1.49 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[765, 763])).
% 1.31/1.49 tff(767,plain,
% 1.31/1.49 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(768,plain,
% 1.31/1.49 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.31/1.49 tff(769,plain,
% 1.31/1.49 (hskp30 | hskp7 | c1_1(a903)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[768, 115, 727, 713, 762])).
% 1.31/1.49 tff(770,plain,
% 1.31/1.49 (hskp30),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[769, 743, 446])).
% 1.31/1.49 tff(771,plain,
% 1.31/1.49 (((~hskp30) | c2_1(a942)) <=> ((~hskp30) | c2_1(a942))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(772,axiom,((~hskp30) | c2_1(a942)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.31/1.49 tff(773,plain,
% 1.31/1.49 ((~hskp30) | c2_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.31/1.49 tff(774,plain,
% 1.31/1.49 ((~hskp30) | c2_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[773, 771])).
% 1.31/1.49 tff(775,plain,
% 1.31/1.49 ((~hskp30) | c2_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[774, 771])).
% 1.31/1.49 tff(776,plain,
% 1.31/1.49 ((~hskp30) | c2_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[775, 771])).
% 1.31/1.49 tff(777,plain,
% 1.31/1.49 ((~hskp30) | c2_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[776, 771])).
% 1.31/1.49 tff(778,plain,
% 1.31/1.49 (c2_1(a942)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[777, 770])).
% 1.31/1.49 tff(779,plain,
% 1.31/1.49 (~c1_1(a936)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[457, 751])).
% 1.31/1.49 tff(780,plain,
% 1.31/1.49 (((~hskp30) | c1_1(a942)) <=> ((~hskp30) | c1_1(a942))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(781,axiom,((~hskp30) | c1_1(a942)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.31/1.49 tff(782,plain,
% 1.31/1.49 ((~hskp30) | c1_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.31/1.49 tff(783,plain,
% 1.31/1.49 ((~hskp30) | c1_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[782, 780])).
% 1.31/1.49 tff(784,plain,
% 1.31/1.49 ((~hskp30) | c1_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[783, 780])).
% 1.31/1.49 tff(785,plain,
% 1.31/1.49 ((~hskp30) | c1_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[784, 780])).
% 1.31/1.49 tff(786,plain,
% 1.31/1.49 ((~hskp30) | c1_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[785, 780])).
% 1.31/1.49 tff(787,plain,
% 1.31/1.49 (c1_1(a942)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[786, 770])).
% 1.31/1.49 tff(788,plain,
% 1.31/1.49 (((~hskp30) | c0_1(a942)) <=> ((~hskp30) | c0_1(a942))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(789,axiom,((~hskp30) | c0_1(a942)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.31/1.49 tff(790,plain,
% 1.31/1.49 ((~hskp30) | c0_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[789, 788])).
% 1.31/1.49 tff(791,plain,
% 1.31/1.49 ((~hskp30) | c0_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[790, 788])).
% 1.31/1.49 tff(792,plain,
% 1.31/1.49 ((~hskp30) | c0_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[791, 788])).
% 1.31/1.49 tff(793,plain,
% 1.31/1.49 ((~hskp30) | c0_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[792, 788])).
% 1.31/1.49 tff(794,plain,
% 1.31/1.49 ((~hskp30) | c0_1(a942)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[793, 788])).
% 1.31/1.49 tff(795,plain,
% 1.31/1.49 (c0_1(a942)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[794, 770])).
% 1.31/1.49 tff(796,plain,
% 1.31/1.49 (c0_1(a936)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[500, 779, 284, 205, 752, 211, 219, 286, 285])).
% 1.31/1.49 tff(797,plain,
% 1.31/1.49 (~c3_1(a936)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[412, 751])).
% 1.31/1.49 tff(798,plain,
% 1.31/1.49 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(799,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[798])).
% 1.31/1.49 tff(800,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(801,plain,
% 1.31/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(802,plain,
% 1.31/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[801])).
% 1.31/1.49 tff(803,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.31/1.49 tff(804,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.31/1.49 tff(805,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[804, 800])).
% 1.31/1.49 tff(806,plain,(
% 1.31/1.49 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[805])).
% 1.31/1.49 tff(807,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[806, 799])).
% 1.31/1.49 tff(808,assumption,(~c1_1(a903)), introduced(assumption)).
% 1.31/1.49 tff(809,assumption,(~c2_1(a903)), introduced(assumption)).
% 1.31/1.49 tff(810,assumption,(~hskp9), introduced(assumption)).
% 1.31/1.49 tff(811,plain,
% 1.31/1.49 (^[U: $i] : refl((hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(812,plain,
% 1.31/1.49 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[811])).
% 1.31/1.49 tff(813,plain,
% 1.31/1.49 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(814,plain,
% 1.31/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp9))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(815,plain,
% 1.31/1.49 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[814])).
% 1.31/1.49 tff(816,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.31/1.49 tff(817,plain,
% 1.31/1.49 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.31/1.49 tff(818,plain,
% 1.31/1.50 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[817, 813])).
% 1.31/1.50 tff(819,plain,(
% 1.31/1.50 ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(skolemize,[status(sab)],[818])).
% 1.31/1.50 tff(820,plain,
% 1.31/1.50 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[819, 812])).
% 1.31/1.50 tff(821,assumption,(~c3_1(a903)), introduced(assumption)).
% 1.31/1.50 tff(822,plain,
% 1.31/1.50 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(823,plain,
% 1.31/1.50 ((hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903)) <=> (hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(824,plain,
% 1.31/1.50 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[823])).
% 1.31/1.50 tff(825,plain,
% 1.31/1.50 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.31/1.50 inference(transitivity,[status(thm)],[824, 822])).
% 1.31/1.50 tff(826,plain,
% 1.31/1.50 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(827,plain,
% 1.31/1.50 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[826, 825])).
% 1.31/1.50 tff(828,plain,
% 1.31/1.50 (hskp27 | hskp9 | c2_1(a903) | c1_1(a903)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[827, 115, 821, 820])).
% 1.31/1.50 tff(829,plain,
% 1.31/1.50 (hskp27),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[828, 810, 809, 808])).
% 1.31/1.50 tff(830,plain,
% 1.31/1.50 (c3_1(a900)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[132, 829])).
% 1.31/1.50 tff(831,plain,
% 1.31/1.50 (c2_1(a900)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[140, 829])).
% 1.31/1.50 tff(832,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(833,plain,
% 1.31/1.50 ((hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936))) <=> (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(834,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[833])).
% 1.31/1.50 tff(835,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[834, 832])).
% 1.31/1.50 tff(836,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(837,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[836, 835])).
% 1.31/1.50 tff(838,plain,
% 1.31/1.50 (~c0_1(a900)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[837, 115, 810, 831, 830, 471, 554, 807, 502])).
% 1.31/1.50 tff(839,assumption,(c2_1(a942)), introduced(assumption)).
% 1.31/1.50 tff(840,assumption,(c0_1(a942)), introduced(assumption)).
% 1.31/1.50 tff(841,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(842,plain,
% 1.31/1.50 ((hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936))) <=> (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(843,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[842])).
% 1.31/1.50 tff(844,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[843, 841])).
% 1.31/1.50 tff(845,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(846,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.31/1.50 tff(847,plain,
% 1.31/1.50 (hskp9 | (~c3_1(a942))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[846, 115, 840, 839, 471, 554, 807, 502])).
% 1.31/1.50 tff(848,plain,
% 1.31/1.50 (~c3_1(a942)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[847, 810])).
% 1.31/1.50 tff(849,plain,
% 1.31/1.50 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(850,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[849])).
% 1.31/1.50 tff(851,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(852,plain,
% 1.31/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(853,plain,
% 1.31/1.50 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[852])).
% 1.31/1.50 tff(854,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.31/1.50 tff(855,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[854, 853])).
% 1.31/1.50 tff(856,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[855, 851])).
% 1.31/1.50 tff(857,plain,(
% 1.31/1.50 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[856])).
% 1.31/1.50 tff(858,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[857, 850])).
% 1.31/1.50 tff(859,assumption,(c1_1(a942)), introduced(assumption)).
% 1.31/1.50 tff(860,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(861,plain,
% 1.31/1.50 ((hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936))) <=> (hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(862,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[861])).
% 1.31/1.50 tff(863,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[862, 860])).
% 1.31/1.50 tff(864,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(865,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.31/1.50 tff(866,plain,
% 1.31/1.50 (hskp0),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[865, 115, 840, 859, 470, 554, 858, 848, 502])).
% 1.31/1.50 tff(867,plain,
% 1.31/1.50 (~c3_1(a901)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[597, 866])).
% 1.31/1.50 tff(868,plain,
% 1.31/1.50 (~c1_1(a901)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[603, 866])).
% 1.31/1.50 tff(869,plain,
% 1.31/1.50 (~c0_1(a901)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[609, 866])).
% 1.31/1.50 tff(870,plain,
% 1.31/1.50 (c1_1(a900)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[148, 829])).
% 1.31/1.50 tff(871,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(872,plain,
% 1.31/1.50 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(873,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[872])).
% 1.31/1.50 tff(874,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.31/1.50 inference(transitivity,[status(thm)],[873, 871])).
% 1.31/1.50 tff(875,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(876,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[875, 874])).
% 1.31/1.50 tff(877,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[876, 115, 870, 831, 470, 554, 869, 868, 867, 283, 502, 838])).
% 1.31/1.50 tff(878,plain,(hskp9 | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | (~c0_1(a942)) | (~c1_1(a942)) | c1_1(a936) | (~c2_1(a942)) | c2_1(a903) | c1_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(879,plain,
% 1.31/1.50 (hskp9),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[878, 797, 713, 796, 795, 787, 779, 778, 719, 743, 752])).
% 1.31/1.50 tff(880,plain,
% 1.31/1.50 (((~hskp9) | (~c3_1(a910))) <=> ((~hskp9) | (~c3_1(a910)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(881,plain,
% 1.31/1.50 (((~c3_1(a910)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a910)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(882,axiom,((~c3_1(a910)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.31/1.50 tff(883,plain,
% 1.31/1.50 ((~hskp9) | (~c3_1(a910))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.31/1.50 tff(884,plain,
% 1.31/1.50 ((~hskp9) | (~c3_1(a910))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[883, 880])).
% 1.31/1.50 tff(885,plain,
% 1.31/1.50 (~c3_1(a910)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[884, 879])).
% 1.31/1.50 tff(886,plain,
% 1.31/1.50 (((~hskp9) | (~c1_1(a910))) <=> ((~hskp9) | (~c1_1(a910)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(887,plain,
% 1.31/1.50 (((~c1_1(a910)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a910)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(888,axiom,((~c1_1(a910)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.31/1.50 tff(889,plain,
% 1.31/1.50 ((~hskp9) | (~c1_1(a910))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[888, 887])).
% 1.31/1.50 tff(890,plain,
% 1.31/1.50 ((~hskp9) | (~c1_1(a910))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[889, 886])).
% 1.31/1.50 tff(891,plain,
% 1.31/1.50 (~c1_1(a910)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[890, 879])).
% 1.31/1.50 tff(892,plain,
% 1.31/1.50 (^[U: $i] : refl((hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(893,plain,
% 1.31/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[892])).
% 1.31/1.50 tff(894,plain,
% 1.31/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(895,plain,
% 1.31/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(896,plain,
% 1.31/1.50 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[895])).
% 1.31/1.50 tff(897,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.31/1.50 tff(898,plain,
% 1.31/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.31/1.50 tff(899,plain,
% 1.31/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[898, 894])).
% 1.31/1.50 tff(900,plain,(
% 1.31/1.50 ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(skolemize,[status(sab)],[899])).
% 1.31/1.50 tff(901,plain,
% 1.31/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[900, 893])).
% 1.31/1.50 tff(902,plain,
% 1.31/1.50 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(903,plain,
% 1.31/1.50 ((hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903)) <=> (hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(904,plain,
% 1.31/1.50 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[903])).
% 1.31/1.50 tff(905,plain,
% 1.31/1.50 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.31/1.50 inference(transitivity,[status(thm)],[904, 902])).
% 1.31/1.50 tff(906,plain,
% 1.31/1.50 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(907,plain,
% 1.31/1.50 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.31/1.50 tff(908,plain,
% 1.31/1.50 (hskp27 | hskp11 | c2_1(a903) | c1_1(a903)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[907, 115, 821, 901])).
% 1.31/1.50 tff(909,plain,
% 1.31/1.50 (hskp27),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[908, 150, 809, 808])).
% 1.31/1.50 tff(910,plain,
% 1.31/1.50 (c3_1(a900)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[132, 909])).
% 1.31/1.50 tff(911,plain,
% 1.31/1.50 (c2_1(a900)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[140, 909])).
% 1.31/1.50 tff(912,plain,
% 1.31/1.50 (c1_1(a900)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[148, 909])).
% 1.31/1.50 tff(913,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[156, 115, 32, 150, 912, 911, 910, 53])).
% 1.31/1.50 tff(914,plain,(hskp11 | hskp12 | c2_1(a903) | c1_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(915,plain,
% 1.31/1.50 (c1_1(a903)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[914, 32, 809, 150, 821])).
% 1.31/1.50 tff(916,plain,
% 1.31/1.50 (hskp28 | hskp12 | c3_1(a921) | (~c2_1(a921))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[225, 115, 491, 190])).
% 1.31/1.50 tff(917,plain,
% 1.31/1.50 (hskp28),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[916, 32, 492, 490])).
% 1.31/1.50 tff(918,plain,
% 1.31/1.50 (c3_1(a916)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[241, 917])).
% 1.31/1.50 tff(919,plain,
% 1.31/1.50 (c1_1(a916)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[249, 917])).
% 1.31/1.50 tff(920,plain,
% 1.31/1.50 (c0_1(a916)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[233, 917])).
% 1.31/1.50 tff(921,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[742, 115, 920, 919, 918, 284, 285, 286, 809, 821, 31, 915])).
% 1.31/1.50 tff(922,plain,(hskp12 | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~c2_1(a921)) | c3_1(a921) | c0_1(a921) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(923,plain,
% 1.31/1.50 (hskp11),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[922, 719, 285, 286, 211, 713, 284, 205, 32, 219])).
% 1.31/1.50 tff(924,plain,
% 1.31/1.50 (~c2_1(a914)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[69, 923])).
% 1.31/1.50 tff(925,plain,
% 1.31/1.50 (((~hskp9) | c2_1(a910)) <=> ((~hskp9) | c2_1(a910))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(926,axiom,((~hskp9) | c2_1(a910)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.31/1.50 tff(927,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a910)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.31/1.50 tff(928,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a910)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[927, 925])).
% 1.31/1.50 tff(929,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a910)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[928, 925])).
% 1.31/1.50 tff(930,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a910)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[929, 925])).
% 1.31/1.50 tff(931,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a910)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[930, 925])).
% 1.31/1.50 tff(932,plain,
% 1.31/1.50 (c2_1(a910)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[931, 879])).
% 1.31/1.50 tff(933,plain,
% 1.31/1.50 (c3_1(a914)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[77, 923])).
% 1.31/1.50 tff(934,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(935,plain,
% 1.31/1.51 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(936,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[935])).
% 1.31/1.51 tff(937,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[936, 934])).
% 1.31/1.51 tff(938,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(939,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[938, 937])).
% 1.31/1.51 tff(940,plain,
% 1.31/1.51 (~c1_1(a914)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[939, 115, 219, 933, 932, 211, 924, 891, 885, 680, 736])).
% 1.31/1.51 tff(941,plain,
% 1.31/1.51 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(942,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[941])).
% 1.31/1.51 tff(943,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(944,plain,
% 1.31/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(945,plain,
% 1.31/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[944])).
% 1.31/1.51 tff(946,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.31/1.51 tff(947,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[946, 945])).
% 1.31/1.51 tff(948,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[947, 943])).
% 1.31/1.51 tff(949,plain,(
% 1.31/1.51 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.31/1.51 inference(skolemize,[status(sab)],[948])).
% 1.31/1.51 tff(950,plain,
% 1.31/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[949, 942])).
% 1.31/1.51 tff(951,plain,
% 1.31/1.51 (c0_1(a914)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[85, 923])).
% 1.31/1.51 tff(952,assumption,(~c1_1(a902)), introduced(assumption)).
% 1.31/1.51 tff(953,plain,
% 1.31/1.51 (hskp10),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[332, 288, 180])).
% 1.31/1.51 tff(954,plain,
% 1.31/1.51 (c2_1(a912)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[619, 953])).
% 1.31/1.51 tff(955,plain,
% 1.31/1.51 (c1_1(a912)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[627, 953])).
% 1.31/1.51 tff(956,plain,
% 1.31/1.51 (hskp7),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[653, 955, 503, 954, 611])).
% 1.31/1.51 tff(957,plain,
% 1.31/1.51 (~c3_1(a908)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[419, 956])).
% 1.31/1.51 tff(958,plain,
% 1.31/1.51 (~c2_1(a908)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[425, 956])).
% 1.31/1.51 tff(959,plain,
% 1.31/1.51 (c1_1(a908)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[433, 956])).
% 1.31/1.51 tff(960,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(961,plain,
% 1.31/1.51 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(962,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[961])).
% 1.31/1.51 tff(963,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[962, 960])).
% 1.31/1.51 tff(964,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(965,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[964, 963])).
% 1.31/1.51 tff(966,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[965, 115, 302, 310, 959, 294, 958, 957, 10])).
% 1.31/1.51 tff(967,plain,((~hskp12) | hskp6 | c0_1(a912) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.31/1.51 tff(968,plain,
% 1.31/1.51 (~hskp12),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[967, 611, 503, 180])).
% 1.31/1.51 tff(969,plain,
% 1.31/1.51 (hskp13),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[198, 968, 180])).
% 1.31/1.51 tff(970,plain,
% 1.31/1.51 (hskp11),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[922, 211, 285, 286, 809, 821, 284, 490, 32, 219])).
% 1.31/1.51 tff(971,plain,
% 1.31/1.51 (~c2_1(a914)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[69, 970])).
% 1.31/1.51 tff(972,plain,
% 1.31/1.51 (hskp28 | hskp12 | c0_1(a921) | (~c2_1(a921))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[225, 115, 490, 190])).
% 1.31/1.51 tff(973,plain,
% 1.31/1.51 (hskp28),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[972, 219, 32, 211])).
% 1.31/1.51 tff(974,plain,
% 1.31/1.51 (c3_1(a916)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[241, 973])).
% 1.31/1.51 tff(975,plain,
% 1.31/1.51 (c1_1(a916)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[249, 973])).
% 1.31/1.51 tff(976,plain,
% 1.31/1.51 (c0_1(a916)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[233, 973])).
% 1.31/1.51 tff(977,assumption,(~c1_1(a912)), introduced(assumption)).
% 1.31/1.51 tff(978,plain,
% 1.31/1.51 (~hskp10),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[627, 977])).
% 1.31/1.51 tff(979,plain,
% 1.31/1.51 (c3_1(a914)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[77, 970])).
% 1.31/1.51 tff(980,plain,
% 1.31/1.51 (hskp10 | (~c1_1(a914))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[355, 115, 180, 979, 971, 320])).
% 1.31/1.51 tff(981,plain,
% 1.31/1.51 (~c1_1(a914)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[980, 978])).
% 1.31/1.51 tff(982,plain,
% 1.31/1.51 (c0_1(a914)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[85, 970])).
% 1.31/1.51 tff(983,plain,
% 1.31/1.51 (hskp17 | c1_1(a914)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[406, 115, 32, 982, 971, 400])).
% 1.31/1.51 tff(984,plain,
% 1.31/1.51 (hskp17),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[983, 981])).
% 1.31/1.51 tff(985,plain,
% 1.31/1.51 (~c3_1(a936)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[412, 984])).
% 1.31/1.51 tff(986,plain,
% 1.31/1.51 (~c2_1(a936)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[451, 984])).
% 1.31/1.51 tff(987,plain,
% 1.31/1.51 (~c1_1(a936)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[457, 984])).
% 1.31/1.51 tff(988,plain,
% 1.31/1.51 (~c1_1(a903)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[742, 115, 976, 975, 974, 284, 285, 286, 809, 821, 31])).
% 1.31/1.51 tff(989,plain,
% 1.31/1.51 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(990,plain,
% 1.31/1.51 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912))) <=> (hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(991,plain,
% 1.31/1.51 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[990])).
% 1.31/1.51 tff(992,plain,
% 1.31/1.51 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[991, 989])).
% 1.31/1.51 tff(993,plain,
% 1.31/1.51 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(994,plain,
% 1.31/1.51 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.31/1.51 tff(995,plain,
% 1.31/1.51 (hskp7 | c1_1(a912) | (~c3_1(a912))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[994, 115, 503, 611, 513])).
% 1.31/1.51 tff(996,plain,
% 1.31/1.51 (~c3_1(a912)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[995, 21, 977])).
% 1.31/1.51 tff(997,assumption,(c0_1(a903)), introduced(assumption)).
% 1.31/1.51 tff(998,plain,
% 1.31/1.51 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(999,plain,
% 1.31/1.51 ((hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903))) <=> (hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1000,plain,
% 1.31/1.51 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[999])).
% 1.31/1.51 tff(1001,plain,
% 1.31/1.51 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[1000, 998])).
% 1.31/1.51 tff(1002,plain,
% 1.31/1.51 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(1003,plain,
% 1.35/1.51 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 1.35/1.51 tff(1004,plain,
% 1.35/1.51 (hskp14 | hskp6 | c2_1(a903) | (~c0_1(a903))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1003, 115, 821, 553])).
% 1.35/1.51 tff(1005,plain,
% 1.35/1.51 (hskp14),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1004, 503, 997, 809])).
% 1.35/1.51 tff(1006,plain,
% 1.35/1.51 (~c1_1(a923)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[519, 1005])).
% 1.35/1.51 tff(1007,plain,
% 1.35/1.51 (~c0_1(a923)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[525, 1005])).
% 1.35/1.51 tff(1008,plain,
% 1.35/1.51 (c3_1(a923)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[533, 1005])).
% 1.35/1.51 tff(1009,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[540, 115, 21, 503, 1008, 1007, 1006, 513])).
% 1.35/1.51 tff(1010,plain,(hskp6 | hskp7 | (~c0_1(a903)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(1011,plain,
% 1.35/1.51 (~c0_1(a903)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1010, 21, 503, 809, 821])).
% 1.35/1.51 tff(1012,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(1013,plain,
% 1.35/1.51 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903)) <=> (c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(1014,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[1013])).
% 1.35/1.51 tff(1015,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.35/1.51 inference(transitivity,[status(thm)],[1014, 1012])).
% 1.35/1.51 tff(1016,plain,
% 1.35/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(1017,plain,
% 1.35/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 1.35/1.51 tff(1018,plain,
% 1.35/1.51 (c0_1(a903) | (~c1_1(a921))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1017, 115, 492, 284, 285, 490, 286, 809, 469, 808])).
% 1.35/1.51 tff(1019,plain,
% 1.35/1.51 (~c1_1(a921)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1018, 1011])).
% 1.35/1.51 tff(1020,plain,
% 1.35/1.51 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.35/1.51 inference(bind,[status(th)],[])).
% 1.35/1.51 tff(1021,plain,
% 1.35/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_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) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.51 inference(quant_intro,[status(thm)],[1020])).
% 1.35/1.51 tff(1022,plain,
% 1.35/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_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) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(1023,plain,
% 1.35/1.51 (^[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)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.35/1.51 inference(bind,[status(th)],[])).
% 1.35/1.51 tff(1024,plain,
% 1.35/1.51 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.51 inference(quant_intro,[status(thm)],[1023])).
% 1.35/1.51 tff(1025,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.35/1.51 tff(1026,plain,
% 1.35/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 1.35/1.51 tff(1027,plain,
% 1.35/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[1026, 1022])).
% 1.35/1.51 tff(1028,plain,(
% 1.35/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.51 inference(skolemize,[status(sab)],[1027])).
% 1.35/1.51 tff(1029,plain,
% 1.35/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[1028, 1021])).
% 1.35/1.51 tff(1030,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(1031,plain,
% 1.35/1.51 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921)) <=> (c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(1032,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[1031])).
% 1.35/1.51 tff(1033,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))),
% 1.35/1.51 inference(transitivity,[status(thm)],[1032, 1030])).
% 1.35/1.51 tff(1034,plain,
% 1.35/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(1035,plain,
% 1.35/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 1.35/1.51 tff(1036,plain,
% 1.35/1.51 (c0_1(a903) | c1_1(a921) | (~c0_1(a936))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1035, 115, 470, 554, 491, 490, 809, 821, 1029])).
% 1.35/1.51 tff(1037,plain,
% 1.35/1.51 (~c0_1(a936)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1036, 1011, 1019])).
% 1.35/1.51 tff(1038,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(1039,plain,
% 1.35/1.51 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903)) <=> (c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(1040,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[1039])).
% 1.35/1.51 tff(1041,plain,
% 1.35/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.35/1.51 inference(transitivity,[status(thm)],[1040, 1038])).
% 1.35/1.51 tff(1042,plain,
% 1.35/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1043,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 1.35/1.52 tff(1044,plain,
% 1.35/1.52 (c0_1(a903) | (~c1_1(a906))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1043, 115, 284, 285, 286, 809, 469, 808])).
% 1.35/1.52 tff(1045,plain,
% 1.35/1.52 (~c1_1(a906)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1044, 1011])).
% 1.35/1.52 tff(1046,assumption,(~c2_1(a912)), introduced(assumption)).
% 1.35/1.52 tff(1047,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1048,plain,
% 1.35/1.52 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1049,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[1048])).
% 1.35/1.52 tff(1050,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.35/1.52 inference(transitivity,[status(thm)],[1049, 1047])).
% 1.35/1.52 tff(1051,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1052,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.35/1.52 tff(1053,plain,
% 1.35/1.52 (c2_1(a912) | (~c1_1(a906))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1052, 115, 977, 284, 285, 611, 286, 469])).
% 1.35/1.52 tff(1054,plain,
% 1.35/1.52 (~c1_1(a906)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1053, 1046])).
% 1.35/1.52 tff(1055,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1056,plain,
% 1.35/1.52 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1057,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[1056])).
% 1.35/1.52 tff(1058,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.35/1.52 inference(transitivity,[status(thm)],[1057, 1055])).
% 1.35/1.52 tff(1059,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1060,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 1.35/1.52 tff(1061,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1060, 115, 492, 977, 1046, 284, 491, 490, 611, 286, 489, 1054])).
% 1.35/1.52 tff(1062,plain,(c2_1(a912) | (~c2_1(a921)) | c1_1(a912) | (~c0_1(a906)) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(1063,plain,
% 1.35/1.52 (c2_1(a912)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1062, 977, 492, 284, 491, 490, 611, 286, 285])).
% 1.35/1.52 tff(1064,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1065,plain,
% 1.35/1.52 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1066,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[1065])).
% 1.35/1.52 tff(1067,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.35/1.52 inference(transitivity,[status(thm)],[1066, 1064])).
% 1.35/1.52 tff(1068,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1069,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.35/1.52 tff(1070,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1069, 115, 1063, 284, 471, 470, 611, 286, 489, 1045, 1037, 996])).
% 1.35/1.52 tff(1071,plain,(hskp7 | (~c0_1(a906)) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~c2_1(a906)) | c1_1(a903) | (~c2_1(a921)) | c1_1(a912) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(1072,plain,
% 1.35/1.52 (hskp7),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1071, 987, 284, 986, 611, 286, 985, 211, 490, 809, 821, 285, 988, 219, 977, 503])).
% 1.35/1.52 tff(1073,plain,
% 1.35/1.52 (~c2_1(a908)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[425, 1072])).
% 1.35/1.52 tff(1074,plain,
% 1.35/1.52 (~c3_1(a908)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[419, 1072])).
% 1.35/1.52 tff(1075,assumption,(~c2_1(a908)), introduced(assumption)).
% 1.35/1.52 tff(1076,assumption,(~c3_1(a908)), introduced(assumption)).
% 1.35/1.52 tff(1077,plain,
% 1.35/1.52 (c2_1(a908) | (~c1_1(a908))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[443, 115, 437, 436, 435, 284, 285, 1076, 286, 31])).
% 1.35/1.52 tff(1078,plain,
% 1.35/1.52 (~c1_1(a908)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1077, 1075])).
% 1.35/1.52 tff(1079,plain,
% 1.35/1.52 (~hskp7),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[433, 1078])).
% 1.35/1.52 tff(1080,plain,
% 1.35/1.52 (~c3_1(a912)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[995, 1079, 977])).
% 1.35/1.52 tff(1081,plain,
% 1.35/1.52 (~c0_1(a903)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1010, 1079, 503, 809, 821])).
% 1.35/1.52 tff(1082,plain,
% 1.35/1.52 (~c1_1(a903)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[742, 115, 437, 436, 435, 284, 285, 286, 809, 821, 31])).
% 1.35/1.52 tff(1083,plain,
% 1.35/1.52 (c0_1(a903) | (~c1_1(a921))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1017, 115, 492, 284, 285, 490, 286, 809, 469, 1082])).
% 1.35/1.52 tff(1084,plain,
% 1.35/1.52 (~c1_1(a921)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1083, 1081])).
% 1.35/1.52 tff(1085,plain,
% 1.35/1.52 (~c0_1(a936)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1036, 1081, 1084])).
% 1.35/1.52 tff(1086,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1087,plain,
% 1.35/1.52 (((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1088,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[1087])).
% 1.35/1.52 tff(1089,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.35/1.52 inference(transitivity,[status(thm)],[1088, 1086])).
% 1.35/1.52 tff(1090,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1091,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 1.35/1.52 tff(1092,plain,
% 1.35/1.52 (~c0_1(a908)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1091, 115, 1063, 1078, 471, 470, 611, 1076, 489, 1085, 1080])).
% 1.35/1.52 tff(1093,plain,
% 1.35/1.52 (c0_1(a903) | (~c1_1(a906))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1043, 115, 284, 285, 286, 809, 469, 1082])).
% 1.35/1.52 tff(1094,plain,
% 1.35/1.52 (~c1_1(a906)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1093, 1081])).
% 1.35/1.52 tff(1095,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1096,plain,
% 1.35/1.52 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908)) <=> (c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1097,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912)))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[1096])).
% 1.35/1.52 tff(1098,plain,
% 1.35/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))),
% 1.35/1.52 inference(transitivity,[status(thm)],[1097, 1095])).
% 1.35/1.52 tff(1099,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1100,plain,
% 1.35/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912)),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 1.35/1.52 tff(1101,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1100, 115, 1063, 1078, 284, 611, 1075, 286, 489, 1094, 1092, 1080])).
% 1.35/1.52 tff(1102,plain,(c2_1(a908) | (~c0_1(a906)) | c0_1(a912) | c3_1(a906) | c1_1(a936) | c2_1(a936) | c3_1(a908) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~c2_1(a906)) | (~c2_1(a921)) | c1_1(a912) | hskp6 | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(1103,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1102, 1074, 1073, 611, 286, 987, 986, 284, 985, 211, 490, 809, 821, 285, 219, 977, 503, 976, 975, 974])).
% 1.35/1.52 tff(1104,plain,(c1_1(a912) | c0_1(a912) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~c2_1(a906)) | hskp6 | hskp12 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(1105,plain,
% 1.35/1.52 (c1_1(a912)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1104, 32, 286, 284, 490, 809, 821, 285, 503, 611, 180])).
% 1.35/1.52 tff(1106,plain,
% 1.35/1.52 (~hskp10),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[619, 1046])).
% 1.35/1.52 tff(1107,plain,
% 1.35/1.52 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1108,plain,
% 1.35/1.52 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912))) <=> (hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1109,plain,
% 1.35/1.52 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[1108])).
% 1.35/1.52 tff(1110,plain,
% 1.35/1.52 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.35/1.52 inference(transitivity,[status(thm)],[1109, 1107])).
% 1.35/1.52 tff(1111,plain,
% 1.35/1.52 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912)))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1112,plain,
% 1.35/1.52 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 1.35/1.52 tff(1113,plain,
% 1.35/1.52 (hskp10 | c2_1(a912) | (~c3_1(a912))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1112, 115, 180, 630, 320])).
% 1.35/1.52 tff(1114,plain,
% 1.35/1.52 (~c3_1(a912)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1113, 1106, 1046])).
% 1.35/1.52 tff(1115,assumption,(~c2_1(a914)), introduced(assumption)).
% 1.35/1.52 tff(1116,plain,
% 1.35/1.52 (hskp10 | (~c1_1(a914))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[355, 115, 180, 380, 1115, 320])).
% 1.35/1.52 tff(1117,plain,
% 1.35/1.52 (~c1_1(a914)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1116, 1106])).
% 1.35/1.52 tff(1118,plain,
% 1.35/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1119,plain,
% 1.35/1.52 ((hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1120,plain,
% 1.35/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[1119])).
% 1.35/1.52 tff(1121,plain,
% 1.35/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.52 inference(transitivity,[status(thm)],[1120, 1118])).
% 1.35/1.52 tff(1122,plain,
% 1.35/1.52 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(1123,plain,
% 1.35/1.52 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.35/1.52 tff(1124,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1123, 115, 180, 381, 380, 630, 1046, 179, 1117, 1114])).
% 1.35/1.52 tff(1125,plain,(c2_1(a912) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | (~c1_1(a912)) | c2_1(a914)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(1126,plain,
% 1.35/1.52 (c2_1(a912)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1125, 982, 180, 979, 1105, 971])).
% 1.35/1.52 tff(1127,plain,
% 1.35/1.52 (hskp7),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[653, 1105, 503, 1126, 611])).
% 1.35/1.52 tff(1128,plain,
% 1.35/1.52 (~c3_1(a908)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[419, 1127])).
% 1.35/1.52 tff(1129,plain,
% 1.35/1.52 (~c2_1(a908)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[425, 1127])).
% 1.35/1.52 tff(1130,plain,
% 1.35/1.52 (c1_1(a908)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[433, 1127])).
% 1.35/1.52 tff(1131,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[443, 115, 976, 975, 974, 1130, 284, 285, 1129, 1128, 286, 31])).
% 1.35/1.52 tff(1132,plain,(hskp12 | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | hskp6 | c0_1(a912) | hskp21 | c3_1(a921) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(1133,plain,
% 1.35/1.52 (c3_1(a921)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1132, 968, 285, 286, 503, 611, 180, 284, 809, 821])).
% 1.35/1.52 tff(1134,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[204, 1133, 969])).
% 1.35/1.52 tff(1135,plain,(c0_1(a912) | (~c2_1(a906)) | c3_1(a906) | hskp6 | hskp21 | (~c0_1(a906)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(1136,plain,
% 1.35/1.52 (c0_1(a912)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1135, 503, 286, 285, 180, 284, 809, 821])).
% 1.35/1.52 tff(1137,plain,
% 1.35/1.52 (~hskp10),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[573, 1136])).
% 1.35/1.52 tff(1138,plain,
% 1.35/1.52 (~hskp12),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[332, 1137, 180])).
% 1.35/1.52 tff(1139,plain,
% 1.35/1.52 (hskp13),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[198, 1138, 180])).
% 1.35/1.52 tff(1140,plain,
% 1.35/1.52 (c2_1(a921)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[218, 1139])).
% 1.35/1.52 tff(1141,plain,
% 1.35/1.52 (~c0_1(a921)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[210, 1139])).
% 1.35/1.52 tff(1142,plain,
% 1.35/1.52 (~c3_1(a921)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[204, 1139])).
% 1.35/1.52 tff(1143,plain,
% 1.35/1.52 (hskp11),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[922, 1142, 285, 286, 809, 821, 284, 1138, 1141, 1140])).
% 1.35/1.52 tff(1144,plain,
% 1.35/1.52 (~c2_1(a914)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[69, 1143])).
% 1.35/1.52 tff(1145,plain,
% 1.35/1.52 (c3_1(a914)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[77, 1143])).
% 1.35/1.52 tff(1146,plain,
% 1.35/1.52 (~c1_1(a914)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[355, 115, 180, 1137, 1145, 1144, 320])).
% 1.35/1.52 tff(1147,plain,
% 1.35/1.52 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.35/1.52 inference(bind,[status(th)],[])).
% 1.35/1.52 tff(1148,plain,
% 1.35/1.52 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.35/1.52 inference(quant_intro,[status(thm)],[1147])).
% 1.35/1.52 tff(1149,plain,
% 1.35/1.52 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(1150,plain,
% 1.35/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.35/1.53 inference(bind,[status(th)],[])).
% 1.35/1.53 tff(1151,plain,
% 1.35/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.35/1.53 inference(quant_intro,[status(thm)],[1150])).
% 1.35/1.53 tff(1152,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.35/1.53 tff(1153,plain,
% 1.35/1.53 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.35/1.53 tff(1154,plain,
% 1.35/1.53 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1153, 1149])).
% 1.35/1.53 tff(1155,plain,(
% 1.35/1.53 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.35/1.53 inference(skolemize,[status(sab)],[1154])).
% 1.35/1.53 tff(1156,plain,
% 1.35/1.53 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1155, 1148])).
% 1.35/1.53 tff(1157,plain,
% 1.35/1.53 (c0_1(a914)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[85, 1143])).
% 1.35/1.53 tff(1158,plain,
% 1.35/1.53 (hskp28),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[225, 115, 1138, 1140, 1141, 1142, 190])).
% 1.35/1.53 tff(1159,plain,
% 1.35/1.53 (c3_1(a916)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[241, 1158])).
% 1.35/1.53 tff(1160,plain,
% 1.35/1.53 (c1_1(a916)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[249, 1158])).
% 1.35/1.53 tff(1161,plain,
% 1.35/1.53 (c0_1(a916)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[233, 1158])).
% 1.35/1.53 tff(1162,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1163,plain,
% 1.35/1.53 ((hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914))) <=> (hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1164,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1163])).
% 1.35/1.53 tff(1165,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1164, 1162])).
% 1.35/1.53 tff(1166,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1167,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 1.35/1.53 tff(1168,plain,
% 1.35/1.53 (hskp15),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1167, 115, 1161, 1160, 1159, 1157, 1144, 1156, 1146])).
% 1.35/1.53 tff(1169,plain,
% 1.35/1.53 (((~hskp15) | (~c1_1(a924))) <=> ((~hskp15) | (~c1_1(a924)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1170,plain,
% 1.35/1.53 (((~c1_1(a924)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a924)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1171,axiom,((~c1_1(a924)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.35/1.53 tff(1172,plain,
% 1.35/1.53 ((~hskp15) | (~c1_1(a924))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.35/1.53 tff(1173,plain,
% 1.35/1.53 ((~hskp15) | (~c1_1(a924))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1172, 1169])).
% 1.35/1.53 tff(1174,plain,
% 1.35/1.53 (~c1_1(a924)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1173, 1168])).
% 1.35/1.53 tff(1175,plain,
% 1.35/1.53 (hskp17 | c1_1(a914)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[406, 115, 1138, 1157, 1144, 400])).
% 1.35/1.53 tff(1176,plain,
% 1.35/1.53 (hskp17),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1175, 1146])).
% 1.35/1.53 tff(1177,plain,
% 1.35/1.53 (~c3_1(a936)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[412, 1176])).
% 1.35/1.53 tff(1178,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1179,plain,
% 1.35/1.53 ((hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1180,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1179])).
% 1.35/1.53 tff(1181,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1180, 1178])).
% 1.35/1.53 tff(1182,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1183,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.35/1.53 tff(1184,plain,
% 1.35/1.53 (~c1_1(a903)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1183, 115, 180, 1157, 1145, 809, 821, 179, 1146])).
% 1.35/1.53 tff(1185,plain,
% 1.35/1.53 (((~hskp15) | (~c0_1(a924))) <=> ((~hskp15) | (~c0_1(a924)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1186,plain,
% 1.35/1.53 (((~c0_1(a924)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a924)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1187,axiom,((~c0_1(a924)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.35/1.53 tff(1188,plain,
% 1.35/1.53 ((~hskp15) | (~c0_1(a924))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 1.35/1.53 tff(1189,plain,
% 1.35/1.53 ((~hskp15) | (~c0_1(a924))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1188, 1185])).
% 1.35/1.53 tff(1190,plain,
% 1.35/1.53 (~c0_1(a924)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1189, 1168])).
% 1.35/1.53 tff(1191,plain,
% 1.35/1.53 (~c2_1(a936)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[451, 1176])).
% 1.35/1.53 tff(1192,plain,
% 1.35/1.53 (~c1_1(a936)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[457, 1176])).
% 1.35/1.53 tff(1193,plain,
% 1.35/1.53 (((~hskp15) | c2_1(a924)) <=> ((~hskp15) | c2_1(a924))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1194,axiom,((~hskp15) | c2_1(a924)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.35/1.53 tff(1195,plain,
% 1.35/1.53 ((~hskp15) | c2_1(a924)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 1.35/1.53 tff(1196,plain,
% 1.35/1.53 ((~hskp15) | c2_1(a924)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1195, 1193])).
% 1.35/1.53 tff(1197,plain,
% 1.35/1.53 ((~hskp15) | c2_1(a924)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1196, 1193])).
% 1.35/1.53 tff(1198,plain,
% 1.35/1.53 ((~hskp15) | c2_1(a924)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1197, 1193])).
% 1.35/1.53 tff(1199,plain,
% 1.35/1.53 ((~hskp15) | c2_1(a924)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1198, 1193])).
% 1.35/1.53 tff(1200,plain,
% 1.35/1.53 (c2_1(a924)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1199, 1168])).
% 1.35/1.53 tff(1201,assumption,(~c1_1(a924)), introduced(assumption)).
% 1.35/1.53 tff(1202,assumption,(~c0_1(a924)), introduced(assumption)).
% 1.35/1.53 tff(1203,plain,
% 1.35/1.53 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1204,plain,
% 1.35/1.53 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924))) <=> (hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1205,plain,
% 1.35/1.53 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1204])).
% 1.35/1.53 tff(1206,plain,
% 1.35/1.53 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1205, 1203])).
% 1.35/1.53 tff(1207,plain,
% 1.35/1.53 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1208,plain,
% 1.35/1.53 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.35/1.53 tff(1209,plain,
% 1.35/1.53 (hskp7 | (~c3_1(a924))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1208, 115, 503, 1202, 1201, 513])).
% 1.35/1.53 tff(1210,plain,
% 1.35/1.53 (~c3_1(a924)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1209, 21])).
% 1.35/1.53 tff(1211,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1212,plain,
% 1.35/1.53 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903)) <=> (c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1213,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1212])).
% 1.35/1.53 tff(1214,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1213, 1211])).
% 1.35/1.53 tff(1215,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1216,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.35/1.53 tff(1217,plain,
% 1.35/1.53 (c0_1(a903) | (~c0_1(a936))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1216, 115, 470, 554, 809, 821, 1029, 808])).
% 1.35/1.53 tff(1218,plain,
% 1.35/1.53 (~c0_1(a936)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1217, 1011])).
% 1.35/1.53 tff(1219,assumption,(c2_1(a924)), introduced(assumption)).
% 1.35/1.53 tff(1220,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1221,plain,
% 1.35/1.53 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1222,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1221])).
% 1.35/1.53 tff(1223,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.35/1.53 tff(1224,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1225,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.35/1.53 tff(1226,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1225, 115, 1219, 284, 471, 470, 1202, 286, 489, 1045, 1218, 1210])).
% 1.35/1.53 tff(1227,plain,(hskp7 | (~c2_1(a924)) | (~c0_1(a906)) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~c2_1(a906)) | c2_1(a903) | c1_1(a903) | c3_1(a936) | c3_1(a903) | hskp6 | c1_1(a924)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(1228,plain,
% 1.35/1.53 (hskp7),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1227, 1200, 284, 1192, 1191, 1190, 286, 285, 809, 1184, 1177, 821, 503, 1174])).
% 1.35/1.53 tff(1229,plain,
% 1.35/1.53 (~c3_1(a908)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[419, 1228])).
% 1.35/1.53 tff(1230,plain,
% 1.35/1.53 (~c2_1(a908)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[425, 1228])).
% 1.35/1.53 tff(1231,plain,
% 1.35/1.53 (c1_1(a908)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[433, 1228])).
% 1.35/1.53 tff(1232,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1233,plain,
% 1.35/1.53 ((hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1234,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1233])).
% 1.35/1.53 tff(1235,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1234, 1232])).
% 1.35/1.53 tff(1236,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1237,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 1.35/1.53 tff(1238,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1237, 115, 180, 1157, 1145, 1231, 1230, 1229, 179, 1146])).
% 1.35/1.53 tff(1239,plain,(hskp6 | hskp21 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(1240,plain,
% 1.35/1.53 (hskp6),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1239, 809, 284, 286, 285, 180, 821])).
% 1.35/1.53 tff(1241,plain,
% 1.35/1.53 (~c2_1(a907)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[362, 1240])).
% 1.35/1.53 tff(1242,assumption,(~hskp13), introduced(assumption)).
% 1.35/1.53 tff(1243,plain,
% 1.35/1.53 (hskp12),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[198, 1242, 180])).
% 1.35/1.53 tff(1244,plain,
% 1.35/1.53 (hskp10),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[332, 1243, 180])).
% 1.35/1.53 tff(1245,plain,
% 1.35/1.53 (~c0_1(a912)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[573, 1244])).
% 1.35/1.53 tff(1246,plain,
% 1.35/1.53 (c2_1(a912)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[619, 1244])).
% 1.35/1.53 tff(1247,plain,
% 1.35/1.53 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1248,plain,
% 1.35/1.53 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912))) <=> (hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1249,plain,
% 1.35/1.53 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1248])).
% 1.35/1.53 tff(1250,plain,
% 1.35/1.53 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1249, 1247])).
% 1.35/1.53 tff(1251,plain,
% 1.35/1.53 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1252,plain,
% 1.35/1.53 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 1.35/1.53 tff(1253,plain,
% 1.35/1.53 (~c3_1(a912)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1252, 115, 1242, 21, 1246, 1245, 20])).
% 1.35/1.53 tff(1254,plain,
% 1.35/1.53 (~c2_1(a917)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[293, 1243])).
% 1.35/1.53 tff(1255,plain,
% 1.35/1.53 (c3_1(a917)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[309, 1243])).
% 1.35/1.53 tff(1256,plain,
% 1.35/1.53 (c1_1(a917)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[301, 1243])).
% 1.35/1.53 tff(1257,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1258,plain,
% 1.35/1.53 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903))) <=> (c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1259,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1258])).
% 1.35/1.53 tff(1260,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1259, 1257])).
% 1.35/1.53 tff(1261,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1262,plain,
% 1.35/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 1.35/1.53 tff(1263,plain,
% 1.35/1.53 (~c1_1(a903)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1262, 115, 1256, 1255, 1254, 809, 821, 10])).
% 1.35/1.53 tff(1264,plain,
% 1.35/1.53 (c1_1(a912)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[627, 1244])).
% 1.35/1.53 tff(1265,plain,
% 1.35/1.53 (hskp14),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[646, 115, 21, 1264, 1246, 1245, 640])).
% 1.35/1.53 tff(1266,plain,
% 1.35/1.53 (~c1_1(a923)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[519, 1265])).
% 1.35/1.53 tff(1267,plain,
% 1.35/1.53 (~c0_1(a923)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[525, 1265])).
% 1.35/1.53 tff(1268,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1269,plain,
% 1.35/1.54 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1270,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1269])).
% 1.35/1.54 tff(1271,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1270, 1268])).
% 1.35/1.54 tff(1272,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1273,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 1.35/1.54 tff(1274,plain,
% 1.35/1.54 (c1_1(a906)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1273, 115, 1256, 1255, 1264, 1246, 285, 1254, 1245, 286, 680])).
% 1.35/1.54 tff(1275,plain,
% 1.35/1.54 (c0_1(a903)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1043, 115, 284, 285, 286, 809, 469, 1274, 1263])).
% 1.35/1.54 tff(1276,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1277,plain,
% 1.35/1.54 (((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923)) <=> (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1278,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1277])).
% 1.35/1.54 tff(1279,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1278, 1276])).
% 1.35/1.54 tff(1280,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1281,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.35/1.54 tff(1282,plain,
% 1.35/1.54 (c2_1(a923)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1281, 115, 1246, 1275, 1267, 1266, 1245, 821, 489, 1263, 1253])).
% 1.35/1.54 tff(1283,plain,
% 1.35/1.54 (c3_1(a923)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[533, 1265])).
% 1.35/1.54 tff(1284,plain,
% 1.35/1.54 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1285,plain,
% 1.35/1.54 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923))) <=> (hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1286,plain,
% 1.35/1.54 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1285])).
% 1.35/1.54 tff(1287,plain,
% 1.35/1.54 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1286, 1284])).
% 1.35/1.54 tff(1288,plain,
% 1.35/1.54 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1289,plain,
% 1.35/1.54 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.35/1.54 tff(1290,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1289, 115, 1242, 21, 1283, 1267, 20, 1282])).
% 1.35/1.54 tff(1291,plain,(hskp13 | hskp7 | c3_1(a903) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a903) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(1292,plain,
% 1.35/1.54 (hskp13),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1291, 21, 821, 284, 285, 286, 809, 180])).
% 1.35/1.54 tff(1293,plain,
% 1.35/1.54 (c2_1(a921)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[218, 1292])).
% 1.35/1.54 tff(1294,plain,
% 1.35/1.54 (~c0_1(a921)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[210, 1292])).
% 1.35/1.54 tff(1295,plain,
% 1.35/1.54 (~c3_1(a921)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[204, 1292])).
% 1.35/1.54 tff(1296,plain,
% 1.35/1.54 (hskp11),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[922, 32, 285, 286, 809, 821, 284, 1295, 1294, 1293])).
% 1.35/1.54 tff(1297,plain,
% 1.35/1.54 (~c2_1(a914)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[69, 1296])).
% 1.35/1.54 tff(1298,plain,
% 1.35/1.54 (hskp28 | hskp12),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[225, 115, 1293, 1294, 1295, 190])).
% 1.35/1.54 tff(1299,plain,
% 1.35/1.54 (hskp28),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1298, 32])).
% 1.35/1.54 tff(1300,plain,
% 1.35/1.54 (c3_1(a916)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[241, 1299])).
% 1.35/1.54 tff(1301,plain,
% 1.35/1.54 (c1_1(a916)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[249, 1299])).
% 1.35/1.54 tff(1302,plain,
% 1.35/1.54 (c0_1(a916)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[233, 1299])).
% 1.35/1.54 tff(1303,plain,
% 1.35/1.54 (~c1_1(a903)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[742, 115, 1302, 1301, 1300, 284, 285, 286, 809, 821, 31])).
% 1.35/1.54 tff(1304,plain,
% 1.35/1.54 (c0_1(a914)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[85, 1296])).
% 1.35/1.54 tff(1305,assumption,(~c2_1(a907)), introduced(assumption)).
% 1.35/1.54 tff(1306,plain,
% 1.35/1.54 (c3_1(a914)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[77, 1296])).
% 1.35/1.54 tff(1307,plain,
% 1.35/1.54 (hskp11),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[914, 808, 809, 32, 821])).
% 1.35/1.54 tff(1308,plain,
% 1.35/1.54 (c0_1(a914)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[85, 1307])).
% 1.35/1.54 tff(1309,plain,
% 1.35/1.54 (c3_1(a914)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[77, 1307])).
% 1.35/1.54 tff(1310,plain,
% 1.35/1.54 (hskp10 | (~c3_1(a914)) | (~c1_1(a914))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[355, 115, 180, 1115, 320])).
% 1.35/1.54 tff(1311,plain,
% 1.35/1.54 (~c1_1(a914)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1310, 287, 1309])).
% 1.35/1.54 tff(1312,plain,
% 1.35/1.54 (hskp17 | hskp12 | c1_1(a914) | (~c0_1(a914))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[406, 115, 1115, 400])).
% 1.35/1.54 tff(1313,plain,
% 1.35/1.54 (hskp17),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1312, 1311, 32, 1308])).
% 1.35/1.54 tff(1314,plain,
% 1.35/1.54 (~c2_1(a936)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[451, 1313])).
% 1.35/1.54 tff(1315,plain,
% 1.35/1.54 (~c1_1(a936)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[457, 1313])).
% 1.35/1.54 tff(1316,assumption,(~hskp18), introduced(assumption)).
% 1.35/1.54 tff(1317,plain,
% 1.35/1.54 (^[U: $i] : refl((hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.35/1.54 inference(bind,[status(th)],[])).
% 1.35/1.54 tff(1318,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.35/1.54 inference(quant_intro,[status(thm)],[1317])).
% 1.35/1.54 tff(1319,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1320,plain,
% 1.35/1.54 (^[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)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.35/1.54 inference(bind,[status(th)],[])).
% 1.35/1.54 tff(1321,plain,
% 1.35/1.54 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.35/1.54 inference(quant_intro,[status(thm)],[1320])).
% 1.35/1.54 tff(1322,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.35/1.54 tff(1323,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 1.35/1.54 tff(1324,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1323, 1319])).
% 1.35/1.54 tff(1325,plain,(
% 1.35/1.54 ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.35/1.54 inference(skolemize,[status(sab)],[1324])).
% 1.35/1.54 tff(1326,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1325, 1318])).
% 1.35/1.54 tff(1327,plain,
% 1.35/1.54 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1328,plain,
% 1.35/1.54 ((hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914))) <=> (hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1329,plain,
% 1.35/1.54 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1328])).
% 1.35/1.54 tff(1330,plain,
% 1.35/1.54 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1329, 1327])).
% 1.35/1.54 tff(1331,plain,
% 1.35/1.54 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1332,plain,
% 1.35/1.54 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914)),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 1.35/1.54 tff(1333,plain,
% 1.35/1.54 (hskp20 | hskp18 | (~c3_1(a914)) | c1_1(a914)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1332, 115, 1115, 1326])).
% 1.35/1.54 tff(1334,plain,
% 1.35/1.54 (hskp20),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1333, 1311, 1316, 1309])).
% 1.35/1.54 tff(1335,plain,
% 1.35/1.54 (((~hskp20) | (~c3_1(a939))) <=> ((~hskp20) | (~c3_1(a939)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1336,plain,
% 1.35/1.54 (((~c3_1(a939)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a939)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1337,axiom,((~c3_1(a939)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.38/1.54 tff(1338,plain,
% 1.38/1.54 ((~hskp20) | (~c3_1(a939))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.38/1.54 tff(1339,plain,
% 1.38/1.54 ((~hskp20) | (~c3_1(a939))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1338, 1335])).
% 1.38/1.54 tff(1340,plain,
% 1.38/1.54 (~c3_1(a939)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1339, 1334])).
% 1.38/1.54 tff(1341,plain,
% 1.38/1.54 (((~hskp20) | (~c1_1(a939))) <=> ((~hskp20) | (~c1_1(a939)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1342,plain,
% 1.38/1.54 (((~c1_1(a939)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a939)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1343,axiom,((~c1_1(a939)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.38/1.54 tff(1344,plain,
% 1.38/1.54 ((~hskp20) | (~c1_1(a939))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.38/1.54 tff(1345,plain,
% 1.38/1.54 ((~hskp20) | (~c1_1(a939))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1344, 1341])).
% 1.38/1.54 tff(1346,plain,
% 1.38/1.54 (~c1_1(a939)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1345, 1334])).
% 1.38/1.54 tff(1347,plain,
% 1.38/1.54 (((~hskp20) | c0_1(a939)) <=> ((~hskp20) | c0_1(a939))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1348,axiom,((~hskp20) | c0_1(a939)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.38/1.54 tff(1349,plain,
% 1.38/1.54 ((~hskp20) | c0_1(a939)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.38/1.54 tff(1350,plain,
% 1.38/1.54 ((~hskp20) | c0_1(a939)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1349, 1347])).
% 1.38/1.54 tff(1351,plain,
% 1.38/1.54 ((~hskp20) | c0_1(a939)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1350, 1347])).
% 1.38/1.54 tff(1352,plain,
% 1.38/1.54 ((~hskp20) | c0_1(a939)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1351, 1347])).
% 1.38/1.54 tff(1353,plain,
% 1.38/1.54 ((~hskp20) | c0_1(a939)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1352, 1347])).
% 1.38/1.54 tff(1354,plain,
% 1.38/1.54 (c0_1(a939)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1353, 1334])).
% 1.38/1.54 tff(1355,plain,
% 1.38/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1356,plain,
% 1.38/1.54 (((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1357,plain,
% 1.38/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1356])).
% 1.38/1.54 tff(1358,plain,
% 1.38/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1357, 1355])).
% 1.38/1.54 tff(1359,plain,
% 1.38/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1360,plain,
% 1.38/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.38/1.54 tff(1361,plain,
% 1.38/1.54 (c0_1(a936)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1360, 115, 1354, 492, 1346, 1340, 1315, 1314, 491, 490, 489])).
% 1.38/1.54 tff(1362,plain,
% 1.38/1.54 (~c3_1(a936)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[412, 1313])).
% 1.38/1.54 tff(1363,plain,
% 1.38/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1364,plain,
% 1.38/1.54 (((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903)) <=> (c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1365,plain,
% 1.38/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1364])).
% 1.38/1.54 tff(1366,plain,
% 1.38/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1365, 1363])).
% 1.38/1.54 tff(1367,plain,
% 1.38/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1368,plain,
% 1.38/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 1.38/1.54 tff(1369,plain,
% 1.38/1.54 (c0_1(a903)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1368, 115, 492, 1315, 1362, 491, 490, 809, 489, 808, 1361])).
% 1.38/1.54 tff(1370,plain,
% 1.38/1.54 (hskp6),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1010, 1369, 21, 809, 821])).
% 1.38/1.54 tff(1371,plain,
% 1.38/1.54 (c1_1(a907)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[370, 1370])).
% 1.38/1.54 tff(1372,plain,
% 1.38/1.54 (hskp10 | (~c3_1(a907)) | (~c1_1(a907))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[377, 115, 180, 1305, 320])).
% 1.38/1.54 tff(1373,plain,
% 1.38/1.54 (~c3_1(a907)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1372, 1371, 287])).
% 1.38/1.54 tff(1374,plain,
% 1.38/1.54 (c3_1(a907) | (~c1_1(a907))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[387, 115, 180, 1308, 1309, 1305, 179, 1311])).
% 1.38/1.54 tff(1375,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1374, 1373, 1371])).
% 1.38/1.54 tff(1376,plain,(hskp10 | hskp21 | c2_1(a907) | hskp7 | c2_1(a903) | c3_1(a903) | (~c2_1(a921)) | c0_1(a921) | c3_1(a921) | c1_1(a903) | hskp18 | c2_1(a914) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1377,plain,
% 1.38/1.54 (hskp18),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1376, 287, 1305, 180, 809, 821, 808, 491, 490, 219, 21, 1115, 32])).
% 1.38/1.54 tff(1378,plain,
% 1.38/1.54 (((~hskp18) | c1_1(a937)) <=> ((~hskp18) | c1_1(a937))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1379,axiom,((~hskp18) | c1_1(a937)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.38/1.54 tff(1380,plain,
% 1.38/1.54 ((~hskp18) | c1_1(a937)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 1.38/1.54 tff(1381,plain,
% 1.38/1.54 ((~hskp18) | c1_1(a937)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1380, 1378])).
% 1.38/1.54 tff(1382,plain,
% 1.38/1.54 ((~hskp18) | c1_1(a937)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1381, 1378])).
% 1.38/1.54 tff(1383,plain,
% 1.38/1.54 ((~hskp18) | c1_1(a937)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1382, 1378])).
% 1.38/1.54 tff(1384,plain,
% 1.38/1.54 ((~hskp18) | c1_1(a937)),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1383, 1378])).
% 1.38/1.54 tff(1385,plain,
% 1.38/1.54 (c1_1(a937)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1384, 1377])).
% 1.38/1.54 tff(1386,plain,
% 1.38/1.54 (((~hskp18) | (~c2_1(a937))) <=> ((~hskp18) | (~c2_1(a937)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1387,plain,
% 1.38/1.54 (((~c2_1(a937)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a937)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1388,axiom,((~c2_1(a937)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.38/1.54 tff(1389,plain,
% 1.38/1.54 ((~hskp18) | (~c2_1(a937))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.38/1.54 tff(1390,plain,
% 1.38/1.54 ((~hskp18) | (~c2_1(a937))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1389, 1386])).
% 1.38/1.54 tff(1391,plain,
% 1.38/1.54 (~c2_1(a937)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1390, 1377])).
% 1.38/1.54 tff(1392,assumption,(~c2_1(a937)), introduced(assumption)).
% 1.38/1.54 tff(1393,assumption,(c1_1(a937)), introduced(assumption)).
% 1.38/1.54 tff(1394,plain,
% 1.38/1.54 (~c1_1(a914)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1310, 287, 380])).
% 1.38/1.54 tff(1395,plain,
% 1.38/1.54 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1396,plain,
% 1.38/1.54 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937))) <=> (hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1397,plain,
% 1.38/1.54 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1396])).
% 1.38/1.54 tff(1398,plain,
% 1.38/1.54 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1397, 1395])).
% 1.38/1.54 tff(1399,plain,
% 1.38/1.54 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1400,plain,
% 1.38/1.54 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 1.38/1.54 tff(1401,plain,
% 1.38/1.54 (hskp10 | (~c3_1(a937)) | (~c1_1(a937))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1400, 115, 180, 1392, 320])).
% 1.38/1.54 tff(1402,plain,
% 1.38/1.54 (~c3_1(a937)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1401, 1393, 287])).
% 1.38/1.54 tff(1403,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1404,plain,
% 1.38/1.54 ((hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(1405,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937))))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[1404])).
% 1.38/1.54 tff(1406,plain,
% 1.38/1.54 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))),
% 1.38/1.54 inference(transitivity,[status(thm)],[1405, 1403])).
% 1.38/1.54 tff(1407,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(1408,plain,
% 1.38/1.54 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 1.38/1.54 tff(1409,plain,
% 1.38/1.54 (c3_1(a937) | (~c1_1(a937))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1408, 115, 180, 381, 380, 1392, 179, 379])).
% 1.38/1.54 tff(1410,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1409, 1402, 1393])).
% 1.38/1.54 tff(1411,plain,((~c1_1(a937)) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a937) | c1_1(a914) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1412,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1411, 1394, 287, 180, 1393, 1392, 381, 380])).
% 1.38/1.54 tff(1413,plain,(hskp10 | hskp21 | (~c1_1(a937)) | c2_1(a937) | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a914)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1414,plain,
% 1.38/1.54 ($false),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1413, 1391, 1385, 180, 287, 381, 380, 1115])).
% 1.38/1.54 tff(1415,plain,(hskp10 | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a914) | c2_1(a907) | c2_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a921) | c3_1(a921) | hskp7 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.54 tff(1416,plain,
% 1.38/1.54 (hskp10),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[1415, 1303, 180, 1306, 1297, 1305, 809, 821, 1304, 1294, 1295, 21, 32])).
% 1.38/1.55 tff(1417,plain,
% 1.38/1.55 (~c0_1(a912)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[573, 1416])).
% 1.38/1.55 tff(1418,plain,
% 1.38/1.55 (c2_1(a912)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[619, 1416])).
% 1.38/1.55 tff(1419,plain,
% 1.38/1.55 (c1_1(a912)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[627, 1416])).
% 1.38/1.55 tff(1420,plain,
% 1.38/1.55 (hskp14),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[646, 115, 21, 1419, 1418, 1417, 640])).
% 1.38/1.55 tff(1421,plain,
% 1.38/1.55 (~c1_1(a923)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[519, 1420])).
% 1.38/1.55 tff(1422,plain,
% 1.38/1.55 (~c0_1(a923)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[525, 1420])).
% 1.38/1.55 tff(1423,plain,
% 1.38/1.55 (c3_1(a923)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[533, 1420])).
% 1.38/1.55 tff(1424,plain,
% 1.38/1.55 (hskp6),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[540, 115, 21, 1423, 1422, 1421, 513])).
% 1.38/1.55 tff(1425,plain,
% 1.38/1.55 (c0_1(a907)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[662, 1424])).
% 1.38/1.55 tff(1426,plain,
% 1.38/1.55 (c1_1(a907)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[370, 1424])).
% 1.38/1.55 tff(1427,assumption,(c1_1(a907)), introduced(assumption)).
% 1.38/1.55 tff(1428,assumption,(c0_1(a907)), introduced(assumption)).
% 1.38/1.55 tff(1429,assumption,(~c0_1(a903)), introduced(assumption)).
% 1.38/1.55 tff(1430,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1431,plain,
% 1.38/1.55 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903)) <=> (c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1432,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1431])).
% 1.38/1.55 tff(1433,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1432, 1430])).
% 1.38/1.55 tff(1434,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1435,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.38/1.55 tff(1436,plain,
% 1.38/1.55 (c0_1(a903) | c1_1(a903) | c3_1(a907) | (~c0_1(a907))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1435, 115, 1305, 809, 821, 1029])).
% 1.38/1.55 tff(1437,plain,
% 1.38/1.55 (c3_1(a907)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1436, 1429, 808, 1428])).
% 1.38/1.55 tff(1438,plain,
% 1.38/1.55 (~c1_1(a921)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1018, 1429])).
% 1.38/1.55 tff(1439,plain,
% 1.38/1.55 ((~c3_1(a907)) | (~c1_1(a907)) | c1_1(a921)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[687, 115, 492, 630, 629, 490, 611, 1305, 680])).
% 1.38/1.55 tff(1440,plain,
% 1.38/1.55 ($false),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1439, 1438, 1437, 1427])).
% 1.38/1.55 tff(1441,plain,(c0_1(a903) | (~c1_1(a907)) | (~c2_1(a921)) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a903) | c1_1(a903) | (~c0_1(a907)) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.55 tff(1442,plain,
% 1.38/1.55 (c0_1(a903)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1441, 1426, 1293, 1419, 1418, 1295, 1417, 1305, 284, 285, 286, 809, 1303, 1425, 821])).
% 1.38/1.55 tff(1443,plain,
% 1.38/1.55 (hskp17 | hskp12 | c1_1(a903) | (~c0_1(a903))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[749, 115, 809, 400])).
% 1.38/1.55 tff(1444,plain,
% 1.38/1.55 (hskp17),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1443, 1442, 32, 1303])).
% 1.38/1.55 tff(1445,plain,
% 1.38/1.55 (~c2_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[451, 1444])).
% 1.38/1.55 tff(1446,plain,
% 1.38/1.55 (hskp30 | hskp7 | c1_1(a903) | (~c0_1(a903))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[768, 115, 821, 762])).
% 1.38/1.55 tff(1447,plain,
% 1.38/1.55 (hskp30),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1446, 1442, 21, 1303])).
% 1.38/1.55 tff(1448,plain,
% 1.38/1.55 (c2_1(a942)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[777, 1447])).
% 1.38/1.55 tff(1449,plain,
% 1.38/1.55 (~c1_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[457, 1444])).
% 1.38/1.55 tff(1450,plain,
% 1.38/1.55 (c1_1(a942)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[786, 1447])).
% 1.38/1.55 tff(1451,plain,
% 1.38/1.55 (c0_1(a942)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[794, 1447])).
% 1.38/1.55 tff(1452,plain,
% 1.38/1.55 (~c3_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[412, 1444])).
% 1.38/1.55 tff(1453,plain,
% 1.38/1.55 ((~c0_1(a903)) | c1_1(a921)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[735, 115, 1419, 1418, 1294, 1295, 1417, 809, 821, 283])).
% 1.38/1.55 tff(1454,plain,
% 1.38/1.55 (c1_1(a921)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1453, 1442])).
% 1.38/1.55 tff(1455,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1456,plain,
% 1.38/1.55 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1457,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936)))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1456])).
% 1.38/1.55 tff(1458,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1457, 1455])).
% 1.38/1.55 tff(1459,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1460,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.38/1.55 tff(1461,plain,
% 1.38/1.55 (c0_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1460, 115, 1293, 284, 285, 1449, 1445, 1295, 286, 469, 1454])).
% 1.38/1.55 tff(1462,plain,
% 1.38/1.55 (hskp9),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[878, 1461, 1303, 1452, 1451, 1450, 1449, 1448, 809, 1445, 821])).
% 1.38/1.55 tff(1463,plain,
% 1.38/1.55 (~c3_1(a910)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[884, 1462])).
% 1.38/1.55 tff(1464,plain,
% 1.38/1.55 (~c1_1(a910)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[890, 1462])).
% 1.38/1.55 tff(1465,plain,
% 1.38/1.55 (c2_1(a910)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[931, 1462])).
% 1.38/1.55 tff(1466,plain,
% 1.38/1.55 (~c1_1(a914)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[939, 115, 1293, 1306, 1465, 1294, 1297, 1464, 1463, 680, 1454])).
% 1.38/1.55 tff(1467,plain,
% 1.38/1.55 (c3_1(a907)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[387, 115, 180, 381, 380, 1427, 1305, 179, 379])).
% 1.38/1.55 tff(1468,plain,
% 1.38/1.55 ((~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[687, 115, 490, 611, 1305, 680])).
% 1.38/1.55 tff(1469,plain,
% 1.38/1.55 (c1_1(a921)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1468, 1467, 492, 629, 630, 1427])).
% 1.38/1.55 tff(1470,plain,
% 1.38/1.55 (hskp17),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1312, 379, 32, 381])).
% 1.38/1.55 tff(1471,plain,
% 1.38/1.55 (~c2_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[451, 1470])).
% 1.38/1.55 tff(1472,plain,
% 1.38/1.55 (~c1_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[457, 1470])).
% 1.38/1.55 tff(1473,plain,
% 1.38/1.55 (hskp20),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1333, 379, 1316, 380])).
% 1.38/1.55 tff(1474,plain,
% 1.38/1.55 (~c3_1(a939)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1339, 1473])).
% 1.38/1.55 tff(1475,plain,
% 1.38/1.55 (~c1_1(a939)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1345, 1473])).
% 1.38/1.55 tff(1476,plain,
% 1.38/1.55 (c0_1(a939)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1353, 1473])).
% 1.38/1.55 tff(1477,plain,
% 1.38/1.55 (c0_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1360, 115, 1476, 492, 1475, 1474, 1472, 1471, 491, 490, 489])).
% 1.38/1.55 tff(1478,assumption,(~c3_1(a910)), introduced(assumption)).
% 1.38/1.55 tff(1479,assumption,(~c1_1(a910)), introduced(assumption)).
% 1.38/1.55 tff(1480,plain,
% 1.38/1.55 (~c3_1(a936)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[412, 1470])).
% 1.38/1.55 tff(1481,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1482,plain,
% 1.38/1.55 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910)) <=> (c2_1(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1483,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1482])).
% 1.38/1.55 tff(1484,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1483, 1481])).
% 1.38/1.55 tff(1485,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1486,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 1.38/1.55 tff(1487,plain,
% 1.38/1.55 (c0_1(a910) | (~c0_1(a936))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1486, 115, 630, 629, 1471, 1480, 611, 1479, 1478, 283])).
% 1.38/1.55 tff(1488,plain,
% 1.38/1.55 (c0_1(a910)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1487, 1477])).
% 1.38/1.55 tff(1489,plain,
% 1.38/1.55 (hskp28),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[972, 32, 492, 491])).
% 1.38/1.55 tff(1490,plain,
% 1.38/1.55 (c3_1(a916)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[241, 1489])).
% 1.38/1.55 tff(1491,plain,
% 1.38/1.55 (c1_1(a916)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[249, 1489])).
% 1.38/1.55 tff(1492,plain,
% 1.38/1.55 (c0_1(a916)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[233, 1489])).
% 1.38/1.55 tff(1493,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1494,plain,
% 1.38/1.55 ((hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1495,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1494])).
% 1.38/1.55 tff(1496,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1495, 1493])).
% 1.38/1.55 tff(1497,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1498,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 1.38/1.55 tff(1499,plain,
% 1.38/1.55 (hskp1),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1498, 115, 1492, 1491, 1490, 381, 380, 950, 379])).
% 1.38/1.55 tff(1500,plain,
% 1.38/1.55 (((~hskp1) | c2_1(a902)) <=> ((~hskp1) | c2_1(a902))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1501,axiom,((~hskp1) | c2_1(a902)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.38/1.55 tff(1502,plain,
% 1.38/1.55 ((~hskp1) | c2_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 1.38/1.55 tff(1503,plain,
% 1.38/1.55 ((~hskp1) | c2_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1502, 1500])).
% 1.38/1.55 tff(1504,plain,
% 1.38/1.55 ((~hskp1) | c2_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1503, 1500])).
% 1.38/1.55 tff(1505,plain,
% 1.38/1.55 ((~hskp1) | c2_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1504, 1500])).
% 1.38/1.55 tff(1506,plain,
% 1.38/1.55 ((~hskp1) | c2_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1505, 1500])).
% 1.38/1.55 tff(1507,plain,
% 1.38/1.55 (c2_1(a902)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1506, 1499])).
% 1.38/1.55 tff(1508,plain,
% 1.38/1.55 (((~hskp1) | c0_1(a902)) <=> ((~hskp1) | c0_1(a902))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1509,axiom,((~hskp1) | c0_1(a902)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.38/1.55 tff(1510,plain,
% 1.38/1.55 ((~hskp1) | c0_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 1.38/1.55 tff(1511,plain,
% 1.38/1.55 ((~hskp1) | c0_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1510, 1508])).
% 1.38/1.55 tff(1512,plain,
% 1.38/1.55 ((~hskp1) | c0_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1511, 1508])).
% 1.38/1.55 tff(1513,plain,
% 1.38/1.55 ((~hskp1) | c0_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1512, 1508])).
% 1.38/1.55 tff(1514,plain,
% 1.38/1.55 ((~hskp1) | c0_1(a902)),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1513, 1508])).
% 1.38/1.55 tff(1515,plain,
% 1.38/1.55 (c0_1(a902)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1514, 1499])).
% 1.38/1.55 tff(1516,plain,
% 1.38/1.55 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(1517,plain,
% 1.38/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[1516])).
% 1.38/1.55 tff(1518,plain,
% 1.38/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1519,plain,
% 1.38/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(1520,plain,
% 1.38/1.55 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[1519])).
% 1.38/1.55 tff(1521,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.38/1.55 tff(1522,plain,
% 1.38/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.38/1.55 tff(1523,plain,
% 1.38/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1522, 1518])).
% 1.38/1.55 tff(1524,plain,(
% 1.38/1.55 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.38/1.55 inference(skolemize,[status(sab)],[1523])).
% 1.38/1.55 tff(1525,plain,
% 1.38/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1524, 1517])).
% 1.38/1.55 tff(1526,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1527,plain,
% 1.38/1.55 ((hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902))) <=> (hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1528,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1527])).
% 1.38/1.55 tff(1529,plain,
% 1.38/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.38/1.55 tff(1530,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(1531,plain,
% 1.38/1.55 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.38/1.55 tff(1532,plain,
% 1.38/1.55 (hskp0 | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1531, 115, 1305, 952, 1525])).
% 1.38/1.55 tff(1533,plain,
% 1.38/1.55 (hskp0),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[1532, 1515, 1427, 1428, 1507])).
% 1.38/1.55 tff(1534,plain,
% 1.38/1.55 (~c3_1(a901)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[597, 1533])).
% 1.38/1.55 tff(1535,plain,
% 1.38/1.55 (~c1_1(a901)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[603, 1533])).
% 1.38/1.55 tff(1536,plain,
% 1.38/1.55 (~c0_1(a901)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[609, 1533])).
% 1.38/1.55 tff(1537,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1538,plain,
% 1.38/1.55 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(1539,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[1538])).
% 1.38/1.55 tff(1540,plain,
% 1.38/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[1539, 1537])).
% 1.38/1.55 tff(1541,plain,
% 1.38/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1542,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 1.38/1.56 tff(1543,plain,
% 1.38/1.56 ((~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1542, 115, 611, 1479, 1478, 1305, 680])).
% 1.38/1.56 tff(1544,plain,
% 1.38/1.56 (~c2_1(a910)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1543, 1467, 629, 630, 1427])).
% 1.38/1.56 tff(1545,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1546,plain,
% 1.38/1.56 (((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1547,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1546])).
% 1.38/1.56 tff(1548,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1547, 1545])).
% 1.38/1.56 tff(1549,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1550,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 1.38/1.56 tff(1551,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1550, 115, 492, 1544, 491, 1478, 1536, 1535, 1534, 283, 1488, 1469])).
% 1.38/1.56 tff(1552,plain,(c1_1(a914) | (~c2_1(a921)) | c0_1(a921) | c3_1(a910) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a907) | c1_1(a902) | (~c1_1(a912)) | (~c2_1(a912)) | c0_1(a912) | c1_1(a910) | c3_1(a921) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | hskp18 | c2_1(a914) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1553,plain,
% 1.38/1.56 (hskp18),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1552, 1466, 1294, 32, 1426, 1425, 1305, 952, 1419, 1418, 1417, 1464, 1295, 180, 1304, 1306, 1463, 1297, 1293])).
% 1.38/1.56 tff(1554,plain,
% 1.38/1.56 (c1_1(a937)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1384, 1553])).
% 1.38/1.56 tff(1555,plain,
% 1.38/1.56 (((~hskp18) | (~c0_1(a937))) <=> ((~hskp18) | (~c0_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1556,plain,
% 1.38/1.56 (((~c0_1(a937)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1557,axiom,((~c0_1(a937)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.38/1.56 tff(1558,plain,
% 1.38/1.56 ((~hskp18) | (~c0_1(a937))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 1.38/1.56 tff(1559,plain,
% 1.38/1.56 ((~hskp18) | (~c0_1(a937))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1558, 1555])).
% 1.38/1.56 tff(1560,plain,
% 1.38/1.56 (~c0_1(a937)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1559, 1553])).
% 1.38/1.56 tff(1561,plain,
% 1.38/1.56 (~c2_1(a937)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1390, 1553])).
% 1.38/1.56 tff(1562,plain,
% 1.38/1.56 (c3_1(a937)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1408, 115, 180, 1393, 381, 380, 1392, 179, 379])).
% 1.38/1.56 tff(1563,plain,
% 1.38/1.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(1564,plain,
% 1.38/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[1563])).
% 1.38/1.56 tff(1565,plain,
% 1.38/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1566,plain,
% 1.38/1.56 (^[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))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(1567,plain,
% 1.38/1.56 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[1566])).
% 1.38/1.56 tff(1568,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.38/1.56 tff(1569,plain,
% 1.38/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 1.38/1.56 tff(1570,plain,
% 1.38/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1569, 1565])).
% 1.38/1.56 tff(1571,plain,(
% 1.38/1.56 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.38/1.56 inference(skolemize,[status(sab)],[1570])).
% 1.38/1.56 tff(1572,plain,
% 1.38/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1571, 1564])).
% 1.38/1.56 tff(1573,plain,
% 1.38/1.56 (hskp1),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1498, 115, 437, 436, 435, 381, 380, 950, 379])).
% 1.38/1.56 tff(1574,plain,
% 1.38/1.56 (c2_1(a902)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1506, 1573])).
% 1.38/1.56 tff(1575,plain,
% 1.38/1.56 (c0_1(a902)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1514, 1573])).
% 1.38/1.56 tff(1576,plain,
% 1.38/1.56 (hskp0),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1532, 1575, 1427, 1428, 1574])).
% 1.38/1.56 tff(1577,plain,
% 1.38/1.56 (~c1_1(a901)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[603, 1576])).
% 1.38/1.56 tff(1578,plain,
% 1.38/1.56 (~c0_1(a901)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[609, 1576])).
% 1.38/1.56 tff(1579,assumption,(~c0_1(a937)), introduced(assumption)).
% 1.38/1.56 tff(1580,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1581,plain,
% 1.38/1.56 (((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1582,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1581])).
% 1.38/1.56 tff(1583,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1582, 1580])).
% 1.38/1.56 tff(1584,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1585,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 1.38/1.56 tff(1586,plain,
% 1.38/1.56 (c2_1(a901)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1585, 115, 1428, 1427, 1579, 1392, 1578, 1577, 1572, 1467, 1562])).
% 1.38/1.56 tff(1587,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1588,plain,
% 1.38/1.56 (((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1589,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1588])).
% 1.38/1.56 tff(1590,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1589, 1587])).
% 1.38/1.56 tff(1591,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1592,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.38/1.56 tff(1593,plain,
% 1.38/1.56 ((~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1592, 115, 1392, 490, 611, 680])).
% 1.38/1.56 tff(1594,plain,
% 1.38/1.56 (c1_1(a921)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1593, 1562, 629, 630, 492, 1393])).
% 1.38/1.56 tff(1595,plain,
% 1.38/1.56 (~c3_1(a901)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[597, 1576])).
% 1.38/1.56 tff(1596,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1597,plain,
% 1.38/1.56 (((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1598,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1597])).
% 1.38/1.56 tff(1599,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1598, 1596])).
% 1.38/1.56 tff(1600,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1601,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 1.38/1.56 tff(1602,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1601, 115, 1393, 492, 1392, 491, 1577, 1595, 680, 1594, 1562, 1586])).
% 1.38/1.56 tff(1603,plain,(c1_1(a914) | (~c1_1(a937)) | (~c2_1(a921)) | c2_1(a937) | c0_1(a921) | (~c0_1(a907)) | (~c1_1(a907)) | c0_1(a937) | c2_1(a907) | c1_1(a902) | (~c2_1(a912)) | (~c1_1(a912)) | c3_1(a921) | c0_1(a912) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1604,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1603, 1561, 1560, 1293, 1300, 1294, 1425, 1426, 1466, 1305, 952, 1418, 1419, 1295, 1417, 180, 1304, 1306, 1302, 1301, 1554])).
% 1.38/1.56 tff(1605,plain,(hskp12 | c2_1(a907) | c1_1(a902) | hskp21 | c2_1(a903) | c3_1(a903) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1606,plain,
% 1.38/1.56 (hskp7),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1605, 32, 952, 180, 809, 821, 284, 285, 286, 1241])).
% 1.38/1.56 tff(1607,plain,
% 1.38/1.56 (~c3_1(a908)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[419, 1606])).
% 1.38/1.56 tff(1608,plain,
% 1.38/1.56 (~c2_1(a908)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[425, 1606])).
% 1.38/1.56 tff(1609,plain,
% 1.38/1.56 (hskp13),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[198, 333, 180])).
% 1.38/1.56 tff(1610,plain,
% 1.38/1.56 (~c0_1(a921)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[210, 1609])).
% 1.38/1.56 tff(1611,plain,
% 1.38/1.56 (~c3_1(a921)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[204, 1609])).
% 1.38/1.56 tff(1612,plain,
% 1.38/1.56 (hskp11),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[922, 219, 285, 286, 809, 821, 284, 490, 491, 32])).
% 1.38/1.56 tff(1613,plain,
% 1.38/1.56 (~c2_1(a914)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[69, 1612])).
% 1.38/1.56 tff(1614,plain,
% 1.38/1.56 (c3_1(a914)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[77, 1612])).
% 1.38/1.56 tff(1615,plain,
% 1.38/1.56 (~c1_1(a914)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[355, 115, 180, 287, 1614, 1613, 320])).
% 1.38/1.56 tff(1616,plain,
% 1.38/1.56 (c0_1(a914)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[85, 1612])).
% 1.38/1.56 tff(1617,plain,
% 1.38/1.56 (hskp28),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[972, 219, 32, 491])).
% 1.38/1.56 tff(1618,plain,
% 1.38/1.56 (c3_1(a916)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[241, 1617])).
% 1.38/1.56 tff(1619,plain,
% 1.38/1.56 (c1_1(a916)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[249, 1617])).
% 1.38/1.56 tff(1620,plain,
% 1.38/1.56 (c0_1(a916)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[233, 1617])).
% 1.38/1.56 tff(1621,plain,
% 1.38/1.56 (~c1_1(a908)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[443, 115, 1620, 1619, 1618, 284, 285, 1075, 1076, 286, 31])).
% 1.38/1.56 tff(1622,plain,
% 1.38/1.56 (~hskp7),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[433, 1621])).
% 1.38/1.56 tff(1623,plain,
% 1.38/1.56 (~c1_1(a903)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[742, 115, 1620, 1619, 1618, 284, 285, 286, 809, 821, 31])).
% 1.38/1.56 tff(1624,plain,
% 1.38/1.56 (hskp18),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1376, 1623, 1305, 180, 809, 821, 287, 491, 490, 219, 1622, 1613, 32])).
% 1.38/1.56 tff(1625,plain,
% 1.38/1.56 (c1_1(a937)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1384, 1624])).
% 1.38/1.56 tff(1626,plain,
% 1.38/1.56 (~c2_1(a937)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1390, 1624])).
% 1.38/1.56 tff(1627,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1411, 1626, 1625, 287, 1614, 1616, 1615, 180])).
% 1.38/1.56 tff(1628,plain,(hskp12 | hskp10 | hskp21 | c2_1(a907) | c2_1(a903) | c3_1(a903) | c0_1(a921) | c3_1(a921) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a908) | c3_1(a908)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1629,plain,
% 1.38/1.56 ($false),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1628, 1611, 1610, 180, 1305, 809, 821, 287, 333, 284, 285, 286, 1075, 1076])).
% 1.38/1.56 tff(1630,plain,(hskp10 | hskp21 | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a908) | c3_1(a908)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.56 tff(1631,plain,
% 1.38/1.56 (hskp10),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1630, 1075, 1305, 809, 821, 284, 285, 286, 180, 1076])).
% 1.38/1.56 tff(1632,plain,
% 1.38/1.56 (~c0_1(a912)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[573, 1631])).
% 1.38/1.56 tff(1633,plain,
% 1.38/1.56 (c2_1(a912)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[619, 1631])).
% 1.38/1.56 tff(1634,plain,
% 1.38/1.56 (c1_1(a912)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[627, 1631])).
% 1.38/1.56 tff(1635,assumption,(~c1_1(a908)), introduced(assumption)).
% 1.38/1.56 tff(1636,plain,
% 1.38/1.56 (~hskp7),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[433, 1635])).
% 1.38/1.56 tff(1637,plain,
% 1.38/1.56 (hskp14 | hskp7),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[646, 115, 630, 629, 611, 640])).
% 1.38/1.56 tff(1638,plain,
% 1.38/1.56 (hskp14),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1637, 1636])).
% 1.38/1.56 tff(1639,plain,
% 1.38/1.56 (~c1_1(a923)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[519, 1638])).
% 1.38/1.56 tff(1640,plain,
% 1.38/1.56 (~c0_1(a923)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[525, 1638])).
% 1.38/1.56 tff(1641,plain,
% 1.38/1.56 (c3_1(a923)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[533, 1638])).
% 1.38/1.56 tff(1642,plain,
% 1.38/1.56 (hskp6),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[540, 115, 1636, 1641, 1640, 1639, 513])).
% 1.38/1.56 tff(1643,plain,
% 1.38/1.56 (c1_1(a907)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[370, 1642])).
% 1.38/1.56 tff(1644,plain,
% 1.38/1.56 (c0_1(a907)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[662, 1642])).
% 1.38/1.56 tff(1645,assumption,(~c0_1(a908)), introduced(assumption)).
% 1.38/1.56 tff(1646,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1647,plain,
% 1.38/1.56 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908)) <=> (c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1648,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908)))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[1647])).
% 1.38/1.56 tff(1649,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))),
% 1.38/1.56 inference(transitivity,[status(thm)],[1648, 1646])).
% 1.38/1.56 tff(1650,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(1651,plain,
% 1.38/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.38/1.56 tff(1652,plain,
% 1.38/1.56 (c1_1(a908) | c2_1(a908) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1651, 115, 1076, 1305, 1029])).
% 1.38/1.56 tff(1653,plain,
% 1.38/1.56 (c3_1(a907)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[1652, 1645, 1075, 1635, 1644])).
% 1.38/1.56 tff(1654,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1655,plain,
% 1.38/1.56 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908)) <=> (c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(1656,plain,
% 1.38/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1655])).
% 1.38/1.57 tff(1657,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1656, 1654])).
% 1.38/1.57 tff(1658,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1659,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.38/1.57 tff(1660,plain,
% 1.38/1.57 (c0_1(a908) | (~c1_1(a921))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1659, 115, 492, 1635, 284, 285, 490, 1075, 286, 469])).
% 1.38/1.57 tff(1661,plain,
% 1.38/1.57 (~c1_1(a921)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1660, 1645])).
% 1.38/1.57 tff(1662,plain,
% 1.38/1.57 ((~c3_1(a907)) | (~c1_1(a907)) | c1_1(a921) | (~c2_1(a921))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[687, 115, 630, 629, 490, 611, 1305, 680])).
% 1.38/1.57 tff(1663,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1662, 1661, 1653, 492, 1643])).
% 1.38/1.57 tff(1664,plain,(c0_1(a908) | (~c2_1(a921)) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c0_1(a912) | c2_1(a907) | c1_1(a908) | (~c0_1(a906)) | (~c2_1(a906)) | c2_1(a908) | c3_1(a906) | c3_1(a908)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(1665,plain,
% 1.38/1.57 (c0_1(a908)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1664, 219, 1634, 1633, 490, 1632, 1305, 1621, 284, 285, 1075, 286, 1076])).
% 1.38/1.57 tff(1666,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1667,plain,
% 1.38/1.57 (((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921)) <=> (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1668,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1667])).
% 1.38/1.57 tff(1669,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1668, 1666])).
% 1.38/1.57 tff(1670,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1671,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 1.38/1.57 tff(1672,plain,
% 1.38/1.57 (c0_1(a921) | (~c0_1(a908)) | c1_1(a921)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1671, 115, 1634, 1633, 490, 1632, 1075, 1076, 283])).
% 1.38/1.57 tff(1673,plain,
% 1.38/1.57 (c1_1(a921)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1672, 1665, 491])).
% 1.38/1.57 tff(1674,plain,
% 1.38/1.57 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1675,plain,
% 1.38/1.57 ((hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908))) <=> (hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1676,plain,
% 1.38/1.57 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1675])).
% 1.38/1.57 tff(1677,plain,
% 1.38/1.57 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1676, 1674])).
% 1.38/1.57 tff(1678,plain,
% 1.38/1.57 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1679,plain,
% 1.38/1.57 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 1.38/1.57 tff(1680,plain,
% 1.38/1.57 (hskp30 | hskp7 | c1_1(a908) | (~c0_1(a908))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1679, 115, 1076, 762])).
% 1.38/1.57 tff(1681,plain,
% 1.38/1.57 (hskp30),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1680, 1665, 1621, 1622])).
% 1.38/1.57 tff(1682,plain,
% 1.38/1.57 (c2_1(a942)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[777, 1681])).
% 1.38/1.57 tff(1683,plain,
% 1.38/1.57 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1684,plain,
% 1.38/1.57 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908))) <=> (hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1685,plain,
% 1.38/1.57 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1684])).
% 1.38/1.57 tff(1686,plain,
% 1.38/1.57 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1685, 1683])).
% 1.38/1.57 tff(1687,plain,
% 1.38/1.57 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1688,plain,
% 1.38/1.57 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 1.38/1.57 tff(1689,plain,
% 1.38/1.57 (hskp17 | hskp12 | c1_1(a908) | (~c0_1(a908))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1688, 115, 1075, 400])).
% 1.38/1.57 tff(1690,plain,
% 1.38/1.57 (hskp17),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1689, 1665, 32, 1621])).
% 1.38/1.57 tff(1691,plain,
% 1.38/1.57 (~c1_1(a936)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[457, 1690])).
% 1.38/1.57 tff(1692,plain,
% 1.38/1.57 (c1_1(a942)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[786, 1681])).
% 1.38/1.57 tff(1693,plain,
% 1.38/1.57 (c0_1(a942)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[794, 1681])).
% 1.38/1.57 tff(1694,plain,
% 1.38/1.57 (~c2_1(a936)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[451, 1690])).
% 1.38/1.57 tff(1695,plain,
% 1.38/1.57 (c0_1(a936)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1460, 115, 219, 284, 285, 1691, 1694, 490, 286, 469, 1673])).
% 1.38/1.57 tff(1696,plain,
% 1.38/1.57 (~c3_1(a936)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[412, 1690])).
% 1.38/1.57 tff(1697,plain,
% 1.38/1.57 (hskp9),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[878, 1694, 1696, 1695, 1693, 1692, 1691, 1682, 809, 1623, 821])).
% 1.38/1.57 tff(1698,plain,
% 1.38/1.57 (~c3_1(a910)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[884, 1697])).
% 1.38/1.57 tff(1699,plain,
% 1.38/1.57 (~c1_1(a910)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[890, 1697])).
% 1.38/1.57 tff(1700,plain,
% 1.38/1.57 (~c1_1(a903)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[742, 115, 1492, 1491, 1490, 284, 285, 286, 809, 821, 31])).
% 1.38/1.57 tff(1701,plain,
% 1.38/1.57 (~c1_1(a908)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[443, 115, 1492, 1491, 1490, 284, 285, 1075, 1076, 286, 31])).
% 1.38/1.57 tff(1702,plain,
% 1.38/1.57 (~hskp7),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[433, 1701])).
% 1.38/1.57 tff(1703,plain,
% 1.38/1.57 (hskp10),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1376, 1702, 1305, 180, 809, 821, 492, 491, 490, 1700, 1316, 1115, 32])).
% 1.38/1.57 tff(1704,plain,
% 1.38/1.57 (c1_1(a912)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[627, 1703])).
% 1.38/1.57 tff(1705,plain,
% 1.38/1.57 (c2_1(a912)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[619, 1703])).
% 1.38/1.57 tff(1706,plain,
% 1.38/1.57 (hskp11),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[914, 1700, 809, 32, 821])).
% 1.38/1.57 tff(1707,plain,
% 1.38/1.57 (c3_1(a914)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[77, 1706])).
% 1.38/1.57 tff(1708,plain,
% 1.38/1.57 (c0_1(a914)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[85, 1706])).
% 1.38/1.57 tff(1709,plain,
% 1.38/1.57 (hskp14),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[647, 1702, 629, 630])).
% 1.38/1.57 tff(1710,plain,
% 1.38/1.57 (~c1_1(a923)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[519, 1709])).
% 1.38/1.57 tff(1711,plain,
% 1.38/1.57 (~c0_1(a923)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[525, 1709])).
% 1.38/1.57 tff(1712,plain,
% 1.38/1.57 (c3_1(a923)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[533, 1709])).
% 1.38/1.57 tff(1713,plain,
% 1.38/1.57 (hskp6),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[540, 115, 1702, 1712, 1711, 1710, 513])).
% 1.38/1.57 tff(1714,plain,
% 1.38/1.57 (c0_1(a907)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[662, 1713])).
% 1.38/1.57 tff(1715,plain,
% 1.38/1.57 (c1_1(a907)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[370, 1713])).
% 1.38/1.57 tff(1716,plain,
% 1.38/1.57 (c1_1(a914)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1552, 1715, 491, 1478, 492, 1714, 1305, 952, 630, 629, 611, 1479, 490, 180, 1708, 1707, 1316, 1115, 32])).
% 1.38/1.57 tff(1717,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1718,plain,
% 1.38/1.57 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1719,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1718])).
% 1.38/1.57 tff(1720,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1719, 1717])).
% 1.38/1.57 tff(1721,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1722,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 1.38/1.57 tff(1723,plain,
% 1.38/1.57 ((~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1722, 115, 490, 1115, 611, 680])).
% 1.38/1.57 tff(1724,plain,
% 1.38/1.57 (c1_1(a921)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1723, 1716, 492, 629, 630, 1707])).
% 1.38/1.57 tff(1725,plain,
% 1.38/1.57 (c0_1(a908) | (~c1_1(a921))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1659, 115, 492, 1701, 284, 285, 490, 1075, 286, 469])).
% 1.38/1.57 tff(1726,plain,
% 1.38/1.57 (c0_1(a908)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1725, 1724])).
% 1.38/1.57 tff(1727,plain,
% 1.38/1.57 ((~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[939, 115, 491, 1115, 1479, 1478, 680])).
% 1.38/1.57 tff(1728,plain,
% 1.38/1.57 (~c2_1(a910)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1727, 1716, 492, 1707, 1724])).
% 1.38/1.57 tff(1729,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1730,plain,
% 1.38/1.57 (((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910)) <=> (c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1731,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910)))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1730])).
% 1.38/1.57 tff(1732,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1731, 1729])).
% 1.38/1.57 tff(1733,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1734,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910)),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 1.38/1.57 tff(1735,plain,
% 1.38/1.57 (c2_1(a910) | c1_1(a910) | (~c0_1(a908)) | c0_1(a910)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1734, 115, 1478, 1075, 1076, 1029])).
% 1.38/1.57 tff(1736,plain,
% 1.38/1.57 (c0_1(a910)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1735, 1728, 1479, 1726])).
% 1.38/1.57 tff(1737,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1738,plain,
% 1.38/1.57 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1739,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1738])).
% 1.38/1.57 tff(1740,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1739, 1737])).
% 1.38/1.57 tff(1741,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1742,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 1.38/1.57 tff(1743,plain,
% 1.38/1.57 (c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1742, 115, 285, 1115, 611, 286, 680])).
% 1.38/1.57 tff(1744,plain,
% 1.38/1.57 (c1_1(a906)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1743, 1716, 629, 1707, 630])).
% 1.38/1.57 tff(1745,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1746,plain,
% 1.38/1.57 ((hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910))) <=> (hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1747,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1746])).
% 1.38/1.57 tff(1748,plain,
% 1.38/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1747, 1745])).
% 1.38/1.57 tff(1749,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1750,plain,
% 1.38/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.38/1.57 tff(1751,plain,
% 1.38/1.57 (hskp0 | c2_1(a910) | (~c1_1(a906)) | (~c0_1(a910))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1750, 115, 284, 1478, 286, 858])).
% 1.38/1.57 tff(1752,plain,
% 1.38/1.57 (hskp0),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1751, 1728, 1744, 1736])).
% 1.38/1.57 tff(1753,plain,
% 1.38/1.57 (~c3_1(a901)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[597, 1752])).
% 1.38/1.57 tff(1754,plain,
% 1.38/1.57 (~c1_1(a901)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[603, 1752])).
% 1.38/1.57 tff(1755,plain,
% 1.38/1.57 (~c0_1(a901)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[609, 1752])).
% 1.38/1.57 tff(1756,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1550, 115, 492, 1728, 491, 1478, 1755, 1754, 1753, 283, 1736, 1724])).
% 1.38/1.57 tff(1757,plain,(hskp12 | (~c2_1(a921)) | c0_1(a921) | c3_1(a910) | (~c0_1(a906)) | c3_1(a906) | c1_1(a910) | c2_1(a908) | c3_1(a908) | (~c2_1(a906)) | c3_1(a921) | (~c2_1(a912)) | (~c1_1(a912)) | c2_1(a914) | c0_1(a912) | c2_1(a907) | c1_1(a902) | hskp21 | hskp18 | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(1758,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1757, 1705, 1704, 491, 1478, 284, 286, 1479, 1075, 1076, 285, 490, 1316, 32, 1115, 611, 1305, 952, 180, 492, 809, 821])).
% 1.38/1.57 tff(1759,plain,(hskp12 | c0_1(a921) | c3_1(a910) | (~c0_1(a906)) | c3_1(a906) | c1_1(a910) | c2_1(a908) | c3_1(a908) | (~c2_1(a906)) | c3_1(a921) | hskp18 | c2_1(a914) | c0_1(a912) | c2_1(a907) | c1_1(a902) | hskp21 | (~c2_1(a921)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.57 tff(1760,plain,
% 1.38/1.57 (hskp18),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1759, 1698, 1632, 284, 286, 1699, 1075, 1076, 285, 490, 491, 32, 1613, 1305, 952, 180, 219, 809, 821])).
% 1.38/1.57 tff(1761,plain,
% 1.38/1.57 (~c2_1(a937)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1390, 1760])).
% 1.38/1.57 tff(1762,plain,
% 1.38/1.57 (c2_1(a910)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[931, 1697])).
% 1.38/1.57 tff(1763,plain,
% 1.38/1.57 (c1_1(a937)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1384, 1760])).
% 1.38/1.57 tff(1764,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1765,plain,
% 1.38/1.57 (((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1766,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[1765])).
% 1.38/1.57 tff(1767,plain,
% 1.38/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[1766, 1764])).
% 1.38/1.57 tff(1768,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(1769,plain,
% 1.38/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 1.38/1.57 tff(1770,plain,
% 1.38/1.57 (~c3_1(a937)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1769, 115, 1763, 219, 1762, 1761, 491, 1699, 1698, 680, 1673])).
% 1.38/1.57 tff(1771,plain,
% 1.38/1.57 (hskp14 | hskp7),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[646, 115, 1634, 1633, 1632, 640])).
% 1.38/1.57 tff(1772,plain,
% 1.38/1.57 (hskp14),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1771, 1622])).
% 1.38/1.57 tff(1773,plain,
% 1.38/1.57 (~c1_1(a923)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[519, 1772])).
% 1.38/1.57 tff(1774,plain,
% 1.38/1.57 (~c0_1(a923)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[525, 1772])).
% 1.38/1.57 tff(1775,plain,
% 1.38/1.57 (c3_1(a923)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[533, 1772])).
% 1.38/1.57 tff(1776,plain,
% 1.38/1.57 (hskp6),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[540, 115, 1622, 1775, 1774, 1773, 513])).
% 1.38/1.57 tff(1777,plain,
% 1.38/1.57 (c1_1(a907)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[370, 1776])).
% 1.38/1.57 tff(1778,plain,
% 1.38/1.57 (c0_1(a907)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[662, 1776])).
% 1.38/1.57 tff(1779,plain,
% 1.38/1.57 (~c0_1(a937)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1559, 1760])).
% 1.38/1.57 tff(1780,plain,
% 1.38/1.57 (c1_1(a914)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[1603, 1779, 219, 1618, 491, 1778, 1777, 1761, 1305, 952, 1633, 1634, 490, 1632, 180, 1616, 1614, 1620, 1619, 1763])).
% 1.38/1.57 tff(1781,plain,
% 1.38/1.57 (^[U: $i] : refl((hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.38/1.57 inference(bind,[status(th)],[])).
% 1.38/1.57 tff(1782,plain,
% 1.38/1.57 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.38/1.57 inference(quant_intro,[status(thm)],[1781])).
% 1.38/1.57 tff(1783,plain,
% 1.38/1.57 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(1784,plain,
% 1.38/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21) <=> (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(1785,plain,
% 1.38/1.58 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21) <=> ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[1784])).
% 1.38/1.58 tff(1786,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.38/1.58 tff(1787,plain,
% 1.38/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.38/1.58 tff(1788,plain,
% 1.38/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1787, 1783])).
% 1.38/1.58 tff(1789,plain,(
% 1.38/1.58 ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.38/1.58 inference(skolemize,[status(sab)],[1788])).
% 1.38/1.58 tff(1790,plain,
% 1.38/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1789, 1782])).
% 1.38/1.58 tff(1791,plain,
% 1.38/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1792,plain,
% 1.38/1.58 ((hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914))) <=> (hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1793,plain,
% 1.38/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[1792])).
% 1.38/1.58 tff(1794,plain,
% 1.38/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[1793, 1791])).
% 1.38/1.58 tff(1795,plain,
% 1.38/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(1796,plain,
% 1.38/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 1.38/1.58 tff(1797,plain,
% 1.38/1.58 (hskp25 | (~c1_1(a914))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1796, 115, 180, 1614, 1613, 1790])).
% 1.38/1.58 tff(1798,plain,
% 1.38/1.58 (hskp25),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1797, 1780])).
% 1.38/1.58 tff(1799,plain,
% 1.38/1.58 (((~hskp25) | (~c1_1(a960))) <=> ((~hskp25) | (~c1_1(a960)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1800,plain,
% 1.38/1.58 (((~c1_1(a960)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a960)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1801,axiom,((~c1_1(a960)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.38/1.58 tff(1802,plain,
% 1.38/1.58 ((~hskp25) | (~c1_1(a960))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 1.38/1.58 tff(1803,plain,
% 1.38/1.58 ((~hskp25) | (~c1_1(a960))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1802, 1799])).
% 1.38/1.58 tff(1804,plain,
% 1.38/1.58 (~c1_1(a960)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1803, 1798])).
% 1.38/1.58 tff(1805,plain,
% 1.38/1.58 (((~hskp25) | c3_1(a960)) <=> ((~hskp25) | c3_1(a960))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1806,axiom,((~hskp25) | c3_1(a960)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.38/1.58 tff(1807,plain,
% 1.38/1.58 ((~hskp25) | c3_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 1.38/1.58 tff(1808,plain,
% 1.38/1.58 ((~hskp25) | c3_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1807, 1805])).
% 1.38/1.58 tff(1809,plain,
% 1.38/1.58 ((~hskp25) | c3_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1808, 1805])).
% 1.38/1.58 tff(1810,plain,
% 1.38/1.58 ((~hskp25) | c3_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1809, 1805])).
% 1.38/1.58 tff(1811,plain,
% 1.38/1.58 ((~hskp25) | c3_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1810, 1805])).
% 1.38/1.58 tff(1812,plain,
% 1.38/1.58 (c3_1(a960)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1811, 1798])).
% 1.38/1.58 tff(1813,plain,
% 1.38/1.58 (((~hskp25) | c0_1(a960)) <=> ((~hskp25) | c0_1(a960))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1814,axiom,((~hskp25) | c0_1(a960)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.38/1.58 tff(1815,plain,
% 1.38/1.58 ((~hskp25) | c0_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.38/1.58 tff(1816,plain,
% 1.38/1.58 ((~hskp25) | c0_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1815, 1813])).
% 1.38/1.58 tff(1817,plain,
% 1.38/1.58 ((~hskp25) | c0_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1816, 1813])).
% 1.38/1.58 tff(1818,plain,
% 1.38/1.58 ((~hskp25) | c0_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1817, 1813])).
% 1.38/1.58 tff(1819,plain,
% 1.38/1.58 ((~hskp25) | c0_1(a960)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1818, 1813])).
% 1.38/1.58 tff(1820,plain,
% 1.38/1.58 (c0_1(a960)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1819, 1798])).
% 1.38/1.58 tff(1821,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1822,plain,
% 1.38/1.58 ((hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1823,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[1822])).
% 1.38/1.58 tff(1824,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[1823, 1821])).
% 1.38/1.58 tff(1825,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(1826,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 1.38/1.58 tff(1827,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1826, 115, 180, 1820, 1812, 1763, 1804, 1761, 179, 1770])).
% 1.38/1.58 tff(1828,plain,(hskp12 | hskp21 | c0_1(a921) | c2_1(a907) | c1_1(a902) | c3_1(a921) | (~c0_1(a906)) | c3_1(a906) | c2_1(a908) | c3_1(a908) | (~c2_1(a906)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(1829,plain,
% 1.38/1.58 (hskp12),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1828, 491, 180, 1305, 952, 490, 284, 286, 1075, 1076, 285, 809, 821])).
% 1.38/1.58 tff(1830,plain,
% 1.38/1.58 (~c2_1(a917)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[293, 1829])).
% 1.38/1.58 tff(1831,plain,
% 1.38/1.58 (c3_1(a917)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[309, 1829])).
% 1.38/1.58 tff(1832,plain,
% 1.38/1.58 (c1_1(a917)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[301, 1829])).
% 1.38/1.58 tff(1833,plain,
% 1.38/1.58 (c1_1(a906)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1273, 115, 1832, 1831, 1634, 1633, 285, 1830, 1632, 286, 680])).
% 1.38/1.58 tff(1834,plain,
% 1.38/1.58 (~c1_1(a908)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[965, 115, 1832, 1831, 1830, 1075, 1076, 10])).
% 1.38/1.58 tff(1835,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1836,plain,
% 1.38/1.58 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908)) <=> (c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1837,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908)))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[1836])).
% 1.38/1.58 tff(1838,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))),
% 1.38/1.58 inference(transitivity,[status(thm)],[1837, 1835])).
% 1.38/1.58 tff(1839,plain,
% 1.38/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(1840,plain,
% 1.38/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.38/1.58 tff(1841,plain,
% 1.38/1.58 (c0_1(a908)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1840, 115, 1834, 284, 285, 1075, 286, 469, 1833])).
% 1.38/1.58 tff(1842,plain,
% 1.38/1.58 (c1_1(a921)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1672, 1841, 491])).
% 1.38/1.58 tff(1843,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1844,plain,
% 1.38/1.58 ((hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908))) <=> (hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1845,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[1844])).
% 1.38/1.58 tff(1846,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[1845, 1843])).
% 1.38/1.58 tff(1847,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(1848,plain,
% 1.38/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 1.38/1.58 tff(1849,plain,
% 1.38/1.58 (hskp0 | c2_1(a908) | (~c1_1(a906)) | (~c0_1(a908))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1848, 115, 284, 1076, 286, 858])).
% 1.38/1.58 tff(1850,plain,
% 1.38/1.58 (hskp0),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1849, 1841, 1075, 1833])).
% 1.38/1.58 tff(1851,plain,
% 1.38/1.58 (~c1_1(a901)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[603, 1850])).
% 1.38/1.58 tff(1852,plain,
% 1.38/1.58 (~c0_1(a901)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[609, 1850])).
% 1.38/1.58 tff(1853,plain,
% 1.38/1.58 (~hskp7),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[433, 1834])).
% 1.38/1.58 tff(1854,plain,
% 1.38/1.58 (hskp14),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1771, 1853])).
% 1.38/1.58 tff(1855,plain,
% 1.38/1.58 (~c1_1(a923)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[519, 1854])).
% 1.38/1.58 tff(1856,plain,
% 1.38/1.58 (~c0_1(a923)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[525, 1854])).
% 1.38/1.58 tff(1857,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1858,plain,
% 1.38/1.58 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923)) <=> (c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1859,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923)))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[1858])).
% 1.38/1.58 tff(1860,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))),
% 1.38/1.58 inference(transitivity,[status(thm)],[1859, 1857])).
% 1.38/1.58 tff(1861,plain,
% 1.38/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(1862,plain,
% 1.38/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 1.38/1.58 tff(1863,plain,
% 1.38/1.58 (c2_1(a923)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1862, 115, 284, 285, 1856, 1855, 286, 469, 1833])).
% 1.38/1.58 tff(1864,plain,
% 1.38/1.58 (c3_1(a923)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[533, 1854])).
% 1.38/1.58 tff(1865,plain,
% 1.38/1.58 (hskp13),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1289, 115, 1853, 1864, 1856, 20, 1863])).
% 1.38/1.58 tff(1866,plain,
% 1.38/1.58 (c2_1(a921)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[218, 1865])).
% 1.38/1.58 tff(1867,plain,
% 1.38/1.58 (c2_1(a901)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[703, 115, 1866, 284, 285, 490, 286, 1852, 1851, 469, 1842])).
% 1.38/1.58 tff(1868,plain,
% 1.38/1.58 (~c3_1(a901)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[597, 1850])).
% 1.38/1.58 tff(1869,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1870,plain,
% 1.38/1.58 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1871,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[1870])).
% 1.38/1.58 tff(1872,plain,
% 1.38/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[1871, 1869])).
% 1.38/1.58 tff(1873,plain,
% 1.38/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(1874,plain,
% 1.38/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 1.38/1.58 tff(1875,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1874, 115, 1866, 1832, 1831, 491, 1830, 1851, 1868, 680, 1842, 1867])).
% 1.38/1.58 tff(1876,plain,(c0_1(a921) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a921) | c3_1(a906) | c2_1(a908) | c3_1(a908) | hskp21 | c2_1(a907) | c1_1(a902) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(1877,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1876, 1608, 211, 285, 284, 286, 1241, 490, 180, 1607, 952, 809, 821])).
% 1.38/1.58 tff(1878,plain,(hskp12 | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a906) | c3_1(a921) | hskp21 | c1_1(a902) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(1879,plain,
% 1.38/1.58 (c3_1(a921)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1878, 32, 284, 286, 285, 180, 952, 809, 821])).
% 1.38/1.58 tff(1880,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[204, 1879, 199])).
% 1.38/1.58 tff(1881,plain,(hskp12 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21 | c1_1(a902) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(1882,plain,
% 1.38/1.58 (c1_1(a902)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1881, 719, 286, 285, 180, 32, 284, 713])).
% 1.38/1.58 tff(1883,plain,
% 1.38/1.58 (((~hskp1) | (~c1_1(a902))) <=> ((~hskp1) | (~c1_1(a902)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1884,plain,
% 1.38/1.58 (((~c1_1(a902)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a902)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1885,axiom,((~c1_1(a902)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.38/1.58 tff(1886,plain,
% 1.38/1.58 ((~hskp1) | (~c1_1(a902))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 1.38/1.58 tff(1887,plain,
% 1.38/1.58 ((~hskp1) | (~c1_1(a902))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1886, 1883])).
% 1.38/1.58 tff(1888,plain,
% 1.38/1.58 (~hskp1),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1887, 1882])).
% 1.38/1.58 tff(1889,plain,
% 1.38/1.58 ($false),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1498, 115, 1888, 234, 250, 242, 951, 933, 950, 940])).
% 1.38/1.58 tff(1890,plain,(hskp12 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.38/1.58 tff(1891,plain,
% 1.38/1.58 (hskp12),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1890, 273, 265, 259, 180])).
% 1.38/1.58 tff(1892,plain,
% 1.38/1.58 (hskp10),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[567, 265, 259, 180, 273])).
% 1.38/1.58 tff(1893,plain,
% 1.38/1.58 (~c0_1(a912)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[573, 1892])).
% 1.38/1.58 tff(1894,plain,
% 1.38/1.58 (hskp6),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[967, 1891, 1893, 180])).
% 1.38/1.58 tff(1895,plain,
% 1.38/1.58 (~c2_1(a907)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[362, 1894])).
% 1.38/1.58 tff(1896,plain,
% 1.38/1.58 (~c2_1(a917)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[293, 1891])).
% 1.38/1.58 tff(1897,plain,
% 1.38/1.58 (c3_1(a917)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[309, 1891])).
% 1.38/1.58 tff(1898,plain,
% 1.38/1.58 (c1_1(a917)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[301, 1891])).
% 1.38/1.58 tff(1899,plain,
% 1.38/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1900,plain,
% 1.38/1.58 ((hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917))) <=> (hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(1901,plain,
% 1.38/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[1900])).
% 1.38/1.58 tff(1902,plain,
% 1.38/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.38/1.58 tff(1903,plain,
% 1.38/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(1904,plain,
% 1.38/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.38/1.58 tff(1905,plain,
% 1.38/1.58 (hskp25),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1904, 115, 180, 1898, 1897, 1896, 1790])).
% 1.38/1.58 tff(1906,plain,
% 1.38/1.58 (~c1_1(a960)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1803, 1905])).
% 1.38/1.58 tff(1907,plain,
% 1.38/1.58 (c1_1(a907)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[370, 1894])).
% 1.38/1.58 tff(1908,plain,
% 1.38/1.58 (c3_1(a960)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1811, 1905])).
% 1.38/1.58 tff(1909,plain,
% 1.38/1.58 (c0_1(a960)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[1819, 1905])).
% 1.38/1.58 tff(1910,plain,
% 1.38/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1911,plain,
% 1.38/1.59 ((hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1912,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[1911])).
% 1.38/1.59 tff(1913,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[1912, 1910])).
% 1.38/1.59 tff(1914,plain,
% 1.38/1.59 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(1915,plain,
% 1.38/1.59 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.38/1.59 tff(1916,plain,
% 1.38/1.59 (c3_1(a907)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1915, 115, 180, 1909, 1908, 1907, 1906, 1895, 179])).
% 1.38/1.59 tff(1917,plain,
% 1.38/1.59 (c0_1(a907)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[662, 1894])).
% 1.38/1.59 tff(1918,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1919,plain,
% 1.38/1.59 ((hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1920,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[1919])).
% 1.38/1.59 tff(1921,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[1920, 1918])).
% 1.38/1.59 tff(1922,plain,
% 1.38/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(1923,plain,
% 1.38/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.38/1.59 tff(1924,plain,
% 1.38/1.59 (hskp1),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1923, 115, 1909, 1908, 1917, 1907, 1906, 950, 1916])).
% 1.38/1.59 tff(1925,plain,
% 1.38/1.59 (~c1_1(a902)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1887, 1924])).
% 1.38/1.59 tff(1926,plain,
% 1.38/1.59 (hskp12),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[706, 611, 285, 286, 284, 180, 585])).
% 1.38/1.59 tff(1927,plain,
% 1.38/1.59 (~c2_1(a917)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[293, 1926])).
% 1.38/1.59 tff(1928,plain,
% 1.38/1.59 (hskp10),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[332, 1926, 180])).
% 1.38/1.59 tff(1929,plain,
% 1.38/1.59 (c2_1(a912)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[619, 1928])).
% 1.38/1.59 tff(1930,plain,
% 1.38/1.59 (c1_1(a912)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[627, 1928])).
% 1.38/1.59 tff(1931,plain,
% 1.38/1.59 (c3_1(a917)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[309, 1926])).
% 1.38/1.59 tff(1932,plain,
% 1.38/1.59 (c1_1(a917)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[301, 1926])).
% 1.38/1.59 tff(1933,plain,
% 1.38/1.59 (c1_1(a906)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1273, 115, 1932, 1931, 1930, 1929, 285, 1927, 611, 286, 680])).
% 1.38/1.59 tff(1934,plain,
% 1.38/1.59 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(1935,plain,
% 1.38/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[1934])).
% 1.38/1.59 tff(1936,plain,
% 1.38/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1937,plain,
% 1.38/1.59 (^[U: $i] : 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)))))),
% 1.38/1.59 inference(bind,[status(th)],[])).
% 1.38/1.59 tff(1938,plain,
% 1.38/1.59 (![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.38/1.59 inference(quant_intro,[status(thm)],[1937])).
% 1.38/1.59 tff(1939,axiom,(![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.38/1.59 tff(1940,plain,
% 1.38/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 1.38/1.59 tff(1941,plain,
% 1.38/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1940, 1936])).
% 1.38/1.59 tff(1942,plain,(
% 1.38/1.59 ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.38/1.59 inference(skolemize,[status(sab)],[1941])).
% 1.38/1.59 tff(1943,plain,
% 1.38/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1942, 1935])).
% 1.38/1.59 tff(1944,plain,
% 1.38/1.59 (hskp25),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1904, 115, 180, 1932, 1931, 1927, 1790])).
% 1.38/1.59 tff(1945,plain,
% 1.38/1.59 (~c1_1(a960)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1803, 1944])).
% 1.38/1.59 tff(1946,plain,
% 1.38/1.59 (c3_1(a960)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1811, 1944])).
% 1.38/1.59 tff(1947,plain,
% 1.38/1.59 (c0_1(a960)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1819, 1944])).
% 1.38/1.59 tff(1948,plain,
% 1.38/1.59 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1949,plain,
% 1.38/1.59 ((hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960))) <=> (hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1950,plain,
% 1.38/1.59 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[1949])).
% 1.38/1.59 tff(1951,plain,
% 1.38/1.59 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[1950, 1948])).
% 1.38/1.59 tff(1952,plain,
% 1.38/1.59 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(1953,plain,
% 1.38/1.59 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.38/1.59 tff(1954,plain,
% 1.38/1.59 (hskp28),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1953, 115, 1947, 1946, 1945, 1943])).
% 1.38/1.59 tff(1955,plain,
% 1.38/1.59 (c3_1(a916)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[241, 1954])).
% 1.38/1.59 tff(1956,plain,
% 1.38/1.59 (c1_1(a916)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[249, 1954])).
% 1.38/1.59 tff(1957,plain,
% 1.38/1.59 (c0_1(a916)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[233, 1954])).
% 1.38/1.59 tff(1958,plain,
% 1.38/1.59 (~hskp7),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[445, 1957, 1956, 1955, 284, 285, 286])).
% 1.38/1.59 tff(1959,plain,
% 1.38/1.59 (hskp14),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[647, 1958, 1930, 1929])).
% 1.38/1.59 tff(1960,plain,
% 1.38/1.59 (~c1_1(a923)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[519, 1959])).
% 1.38/1.59 tff(1961,plain,
% 1.38/1.59 (~c0_1(a923)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[525, 1959])).
% 1.38/1.59 tff(1962,plain,
% 1.38/1.59 (c2_1(a923)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1862, 115, 284, 285, 1961, 1960, 286, 469, 1933])).
% 1.38/1.59 tff(1963,plain,
% 1.38/1.59 (c3_1(a923)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[533, 1959])).
% 1.38/1.59 tff(1964,plain,
% 1.38/1.59 (hskp13 | (~c2_1(a923))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1289, 115, 1958, 1963, 1961, 20])).
% 1.38/1.59 tff(1965,plain,
% 1.38/1.59 (hskp13),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1964, 1962])).
% 1.38/1.59 tff(1966,plain,
% 1.38/1.59 (~c3_1(a921)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[204, 1965])).
% 1.38/1.59 tff(1967,plain,
% 1.38/1.59 (c2_1(a921)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[218, 1965])).
% 1.38/1.59 tff(1968,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1969,plain,
% 1.38/1.59 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1970,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[1969])).
% 1.38/1.59 tff(1971,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[1970, 1968])).
% 1.38/1.59 tff(1972,plain,
% 1.38/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(1973,plain,
% 1.38/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.38/1.59 tff(1974,plain,
% 1.38/1.59 (c1_1(a921)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1973, 115, 1967, 1932, 1931, 1930, 1929, 1966, 1927, 611, 680])).
% 1.38/1.59 tff(1975,plain,
% 1.38/1.59 (hskp6),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[967, 1926, 611, 180])).
% 1.38/1.59 tff(1976,plain,
% 1.38/1.59 (~c2_1(a907)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[362, 1975])).
% 1.38/1.59 tff(1977,plain,
% 1.38/1.59 (c1_1(a907)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[370, 1975])).
% 1.38/1.59 tff(1978,plain,
% 1.38/1.59 (c3_1(a907)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1915, 115, 180, 1947, 1946, 1977, 1945, 1976, 179])).
% 1.38/1.59 tff(1979,plain,
% 1.38/1.59 (c0_1(a907)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[662, 1975])).
% 1.38/1.59 tff(1980,plain,
% 1.38/1.59 (hskp1),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1923, 115, 1947, 1946, 1979, 1977, 1945, 950, 1978])).
% 1.38/1.59 tff(1981,plain,
% 1.38/1.59 (c2_1(a902)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1506, 1980])).
% 1.38/1.59 tff(1982,plain,
% 1.38/1.59 (c0_1(a902)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1514, 1980])).
% 1.38/1.59 tff(1983,plain,
% 1.38/1.59 (hskp0 | (~c0_1(a902)) | (~c2_1(a902))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1531, 115, 1979, 1977, 1976, 952, 1525])).
% 1.38/1.59 tff(1984,plain,
% 1.38/1.59 (hskp0),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1983, 1982, 1981])).
% 1.38/1.59 tff(1985,plain,
% 1.38/1.59 (~c1_1(a901)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[603, 1984])).
% 1.38/1.59 tff(1986,plain,
% 1.38/1.59 (~c0_1(a901)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[609, 1984])).
% 1.38/1.59 tff(1987,plain,
% 1.38/1.59 (c2_1(a901)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[703, 115, 1967, 284, 285, 1966, 286, 1986, 1985, 469, 1974])).
% 1.38/1.59 tff(1988,plain,
% 1.38/1.59 (~c3_1(a901)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[597, 1984])).
% 1.38/1.59 tff(1989,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1990,plain,
% 1.38/1.59 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(1991,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[1990])).
% 1.38/1.59 tff(1992,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[1991, 1989])).
% 1.38/1.59 tff(1993,plain,
% 1.38/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(1994,plain,
% 1.38/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.38/1.59 tff(1995,plain,
% 1.38/1.59 ($false),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1994, 115, 1932, 1931, 1930, 1929, 1927, 611, 1985, 1988, 680, 1987])).
% 1.38/1.59 tff(1996,plain,(c0_1(a912) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c1_1(a902) | hskp21 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.38/1.59 tff(1997,plain,
% 1.38/1.59 (hskp2),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1996, 1925, 259, 265, 1893, 180, 273])).
% 1.38/1.59 tff(1998,plain,
% 1.38/1.59 (~c2_1(a903)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[718, 1997])).
% 1.38/1.59 tff(1999,plain,
% 1.38/1.59 (~c3_1(a903)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[712, 1997])).
% 1.38/1.59 tff(2000,plain,
% 1.38/1.59 (c1_1(a906)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1273, 115, 302, 310, 955, 954, 285, 294, 611, 286, 680])).
% 1.38/1.59 tff(2001,plain,
% 1.38/1.59 (~c1_1(a903)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1262, 115, 302, 310, 294, 809, 821, 10])).
% 1.38/1.59 tff(2002,plain,
% 1.38/1.59 (c0_1(a903)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[1043, 115, 284, 285, 286, 809, 469, 2000, 2001])).
% 1.38/1.59 tff(2003,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2004,plain,
% 1.38/1.59 ((hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903))) <=> (hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2005,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[2004])).
% 1.38/1.59 tff(2006,plain,
% 1.38/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[2005, 2003])).
% 1.38/1.59 tff(2007,plain,
% 1.38/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(2008,plain,
% 1.38/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 1.38/1.59 tff(2009,plain,
% 1.38/1.59 (hskp0 | c2_1(a903) | (~c0_1(a903)) | (~c1_1(a906))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2008, 115, 284, 286, 821, 858])).
% 1.38/1.59 tff(2010,plain,
% 1.38/1.59 (hskp0),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2009, 2002, 809, 2000])).
% 1.38/1.59 tff(2011,plain,
% 1.38/1.59 (~c3_1(a901)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[597, 2010])).
% 1.38/1.59 tff(2012,plain,
% 1.38/1.59 (~c1_1(a901)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[603, 2010])).
% 1.38/1.59 tff(2013,plain,
% 1.38/1.59 (~c0_1(a901)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[609, 2010])).
% 1.38/1.59 tff(2014,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2015,plain,
% 1.38/1.59 (((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2016,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[2015])).
% 1.38/1.59 tff(2017,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[2016, 2014])).
% 1.38/1.59 tff(2018,plain,
% 1.38/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(2019,plain,
% 1.38/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.38/1.59 tff(2020,plain,
% 1.38/1.59 ($false),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2019, 115, 955, 954, 2002, 611, 809, 821, 2013, 2012, 2011, 283])).
% 1.38/1.59 tff(2021,plain,((~hskp12) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.38/1.59 tff(2022,plain,
% 1.38/1.59 ($false),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2021, 1999, 1998, 1893, 1891, 273, 265, 259, 180])).
% 1.38/1.59 tff(2023,plain,((~hskp5) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.38/1.59 tff(2024,plain,
% 1.38/1.59 (~hskp5),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2023, 180])).
% 1.38/1.59 tff(2025,plain,
% 1.38/1.59 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2026,plain,
% 1.38/1.59 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(2027,plain,
% 1.38/1.59 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2026, 2025])).
% 1.38/1.59 tff(2028,plain,
% 1.38/1.59 (hskp7 | c2_1(a916)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2027, 115, 43, 437, 435, 63])).
% 1.38/1.59 tff(2029,plain,
% 1.38/1.59 (c2_1(a916)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2028, 21])).
% 1.38/1.59 tff(2030,plain,
% 1.38/1.59 (hskp11 | (~c2_1(a916))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[344, 115, 32, 436, 435, 53])).
% 1.38/1.59 tff(2031,plain,
% 1.38/1.59 (hskp11),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2030, 2029])).
% 1.38/1.59 tff(2032,plain,
% 1.38/1.59 (~c2_1(a914)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[69, 2031])).
% 1.38/1.59 tff(2033,plain,
% 1.38/1.59 (c3_1(a914)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[77, 2031])).
% 1.38/1.59 tff(2034,plain,
% 1.38/1.59 (c0_1(a914)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[85, 2031])).
% 1.38/1.59 tff(2035,plain,
% 1.38/1.59 ($false),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[121, 115, 21, 43, 2034, 2033, 2032, 63])).
% 1.38/1.59 tff(2036,plain,(hskp7 | hskp5 | hskp12 | (~c1_1(a916)) | (~c3_1(a916)) | (~c0_1(a916))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.59 tff(2037,plain,
% 1.38/1.59 (hskp7),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2036, 32, 2024, 250, 242, 234])).
% 1.38/1.59 tff(2038,plain,
% 1.38/1.59 (~c3_1(a908)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[419, 2037])).
% 1.38/1.59 tff(2039,plain,
% 1.38/1.59 (~c2_1(a908)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[425, 2037])).
% 1.38/1.59 tff(2040,plain,
% 1.38/1.59 (hskp26),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[113, 2024, 180])).
% 1.38/1.59 tff(2041,plain,
% 1.38/1.59 (((~hskp26) | (~c3_1(a979))) <=> ((~hskp26) | (~c3_1(a979)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2042,plain,
% 1.38/1.59 (((~c3_1(a979)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a979)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2043,axiom,((~c3_1(a979)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.38/1.59 tff(2044,plain,
% 1.38/1.59 ((~hskp26) | (~c3_1(a979))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 1.38/1.59 tff(2045,plain,
% 1.38/1.59 ((~hskp26) | (~c3_1(a979))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2044, 2041])).
% 1.38/1.59 tff(2046,plain,
% 1.38/1.59 (~c3_1(a979)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2045, 2040])).
% 1.38/1.59 tff(2047,plain,
% 1.38/1.59 (c1_1(a908)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[433, 2037])).
% 1.38/1.59 tff(2048,plain,
% 1.38/1.59 (((~hskp26) | c0_1(a979)) <=> ((~hskp26) | c0_1(a979))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2049,axiom,((~hskp26) | c0_1(a979)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.38/1.59 tff(2050,plain,
% 1.38/1.59 ((~hskp26) | c0_1(a979)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 1.38/1.59 tff(2051,plain,
% 1.38/1.59 ((~hskp26) | c0_1(a979)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2050, 2048])).
% 1.38/1.59 tff(2052,plain,
% 1.38/1.59 ((~hskp26) | c0_1(a979)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2051, 2048])).
% 1.38/1.59 tff(2053,plain,
% 1.38/1.59 ((~hskp26) | c0_1(a979)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2052, 2048])).
% 1.38/1.59 tff(2054,plain,
% 1.38/1.59 ((~hskp26) | c0_1(a979)),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[2053, 2048])).
% 1.38/1.59 tff(2055,plain,
% 1.38/1.59 (c0_1(a979)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[2054, 2040])).
% 1.38/1.59 tff(2056,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2057,plain,
% 1.38/1.59 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(2058,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[2057])).
% 1.38/1.59 tff(2059,plain,
% 1.38/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2058, 2056])).
% 1.38/1.60 tff(2060,plain,
% 1.38/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2061,plain,
% 1.38/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 1.38/1.60 tff(2062,plain,
% 1.38/1.60 (~c2_1(a979)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2061, 115, 234, 250, 242, 2055, 2047, 2046, 2039, 2038, 31])).
% 1.38/1.60 tff(2063,assumption,(~c2_1(a979)), introduced(assumption)).
% 1.38/1.60 tff(2064,plain,
% 1.38/1.60 (((~hskp26) | c1_1(a979)) <=> ((~hskp26) | c1_1(a979))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2065,axiom,((~hskp26) | c1_1(a979)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.38/1.60 tff(2066,plain,
% 1.38/1.60 ((~hskp26) | c1_1(a979)),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 1.38/1.60 tff(2067,plain,
% 1.38/1.60 ((~hskp26) | c1_1(a979)),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2066, 2064])).
% 1.38/1.60 tff(2068,plain,
% 1.38/1.60 ((~hskp26) | c1_1(a979)),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2067, 2064])).
% 1.38/1.60 tff(2069,plain,
% 1.38/1.60 ((~hskp26) | c1_1(a979)),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2068, 2064])).
% 1.38/1.60 tff(2070,plain,
% 1.38/1.60 ((~hskp26) | c1_1(a979)),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2069, 2064])).
% 1.38/1.60 tff(2071,plain,
% 1.38/1.60 (c1_1(a979)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2070, 2040])).
% 1.38/1.60 tff(2072,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2073,plain,
% 1.38/1.60 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979))) <=> (c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2074,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979))))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2073])).
% 1.38/1.60 tff(2075,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2074, 2072])).
% 1.38/1.60 tff(2076,plain,
% 1.38/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2077,plain,
% 1.38/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 1.38/1.60 tff(2078,plain,
% 1.38/1.60 (~c1_1(a914)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2077, 115, 2071, 78, 2046, 70, 10, 2063])).
% 1.38/1.60 tff(2079,assumption,(c1_1(a908)), introduced(assumption)).
% 1.38/1.60 tff(2080,plain,
% 1.38/1.60 ($false),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1237, 115, 180, 86, 78, 2079, 1075, 1076, 179, 2078])).
% 1.38/1.60 tff(2081,plain,((~hskp11) | hskp21 | (~c1_1(a908)) | c2_1(a908) | c3_1(a908) | c2_1(a979)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.60 tff(2082,plain,
% 1.38/1.60 (~hskp11),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2081, 2047, 180, 2039, 2038, 2062])).
% 1.38/1.60 tff(2083,plain,
% 1.38/1.60 (~c2_1(a916)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[345, 2082])).
% 1.38/1.60 tff(2084,plain,
% 1.38/1.60 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2085,plain,
% 1.38/1.60 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2086,plain,
% 1.38/1.60 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 1.38/1.60 tff(2087,plain,
% 1.38/1.60 (hskp25 | c2_1(a916)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2086, 115, 180, 250, 242, 1790])).
% 1.38/1.60 tff(2088,plain,
% 1.38/1.60 (hskp25),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2087, 2083])).
% 1.38/1.60 tff(2089,plain,
% 1.38/1.60 (~c1_1(a960)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1803, 2088])).
% 1.38/1.60 tff(2090,plain,
% 1.38/1.60 (c3_1(a960)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1811, 2088])).
% 1.38/1.60 tff(2091,plain,
% 1.38/1.60 (c0_1(a960)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1819, 2088])).
% 1.38/1.60 tff(2092,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2093,plain,
% 1.38/1.60 ((hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2094,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2093])).
% 1.38/1.60 tff(2095,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2094, 2092])).
% 1.38/1.60 tff(2096,plain,
% 1.38/1.60 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2097,plain,
% 1.38/1.60 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 1.38/1.60 tff(2098,plain,
% 1.38/1.60 ($false),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2097, 115, 180, 2091, 2090, 2047, 2089, 2039, 2038, 179])).
% 1.38/1.60 tff(2099,plain,(hskp12 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.38/1.60 tff(2100,plain,
% 1.38/1.60 (hskp12),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2099, 180])).
% 1.38/1.60 tff(2101,plain,
% 1.38/1.60 (hskp10),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[332, 2100, 180])).
% 1.38/1.60 tff(2102,plain,
% 1.38/1.60 (~c0_1(a912)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[573, 2101])).
% 1.38/1.60 tff(2103,plain,
% 1.38/1.60 (hskp6),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[967, 2102, 2100, 180])).
% 1.38/1.60 tff(2104,plain,
% 1.38/1.60 (~c2_1(a907)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[362, 2103])).
% 1.38/1.60 tff(2105,plain,
% 1.38/1.60 (~c2_1(a917)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[293, 2100])).
% 1.38/1.60 tff(2106,plain,
% 1.38/1.60 (c3_1(a917)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[309, 2100])).
% 1.38/1.60 tff(2107,plain,
% 1.38/1.60 (c1_1(a917)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[301, 2100])).
% 1.38/1.60 tff(2108,plain,
% 1.38/1.60 (hskp25),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1904, 115, 180, 2107, 2106, 2105, 1790])).
% 1.38/1.60 tff(2109,plain,
% 1.38/1.60 (~c1_1(a960)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1803, 2108])).
% 1.38/1.60 tff(2110,plain,
% 1.38/1.60 (c1_1(a907)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[370, 2103])).
% 1.38/1.60 tff(2111,plain,
% 1.38/1.60 (c3_1(a960)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1811, 2108])).
% 1.38/1.60 tff(2112,plain,
% 1.38/1.60 (c0_1(a960)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1819, 2108])).
% 1.38/1.60 tff(2113,plain,
% 1.38/1.60 (c3_1(a907)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[1915, 115, 180, 2112, 2111, 2110, 2109, 2104, 179])).
% 1.38/1.60 tff(2114,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2115,plain,
% 1.38/1.60 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979))) <=> (c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2116,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979))))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2115])).
% 1.38/1.60 tff(2117,plain,
% 1.38/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.38/1.60 tff(2118,plain,
% 1.38/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2119,plain,
% 1.38/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.38/1.60 tff(2120,plain,
% 1.38/1.60 (c2_1(a979)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2119, 115, 2071, 2107, 2106, 2046, 2105, 10])).
% 1.38/1.60 tff(2121,plain,
% 1.38/1.60 (c0_1(a907)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[662, 2103])).
% 1.38/1.60 tff(2122,plain,
% 1.38/1.60 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2123,plain,
% 1.38/1.60 ((hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907))) <=> (hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2124,plain,
% 1.38/1.60 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907))))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2123])).
% 1.38/1.60 tff(2125,plain,
% 1.38/1.60 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2124, 2122])).
% 1.38/1.60 tff(2126,plain,
% 1.38/1.60 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2127,plain,
% 1.38/1.60 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 1.38/1.60 tff(2128,plain,
% 1.38/1.60 (hskp7 | (~c3_1(a907))),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2127, 115, 2024, 2121, 2104, 63])).
% 1.38/1.60 tff(2129,plain,
% 1.38/1.60 (hskp7),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2128, 2113])).
% 1.38/1.60 tff(2130,plain,
% 1.38/1.60 (~c3_1(a908)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[419, 2129])).
% 1.38/1.60 tff(2131,plain,
% 1.38/1.60 (~c2_1(a908)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[425, 2129])).
% 1.38/1.60 tff(2132,plain,
% 1.38/1.60 (c1_1(a908)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[433, 2129])).
% 1.38/1.60 tff(2133,plain,
% 1.38/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2134,plain,
% 1.38/1.60 (((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2135,plain,
% 1.38/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979))))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2134])).
% 1.38/1.60 tff(2136,plain,
% 1.38/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2135, 2133])).
% 1.38/1.60 tff(2137,plain,
% 1.38/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2138,plain,
% 1.38/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 1.38/1.60 tff(2139,plain,
% 1.38/1.60 ($false),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2138, 115, 2055, 2132, 2121, 2110, 2046, 2131, 2130, 31, 2120, 2113])).
% 1.38/1.60 tff(2140,plain,(hskp21), inference(lemma,lemma(discharge,[]))).
% 1.38/1.60 tff(2141,plain,
% 1.38/1.60 (((~hskp21) | (~c3_1(a946))) <=> ((~hskp21) | (~c3_1(a946)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2142,plain,
% 1.38/1.60 (((~c3_1(a946)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a946)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2143,axiom,((~c3_1(a946)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.38/1.60 tff(2144,plain,
% 1.38/1.60 ((~hskp21) | (~c3_1(a946))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 1.38/1.60 tff(2145,plain,
% 1.38/1.60 ((~hskp21) | (~c3_1(a946))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2144, 2141])).
% 1.38/1.60 tff(2146,plain,
% 1.38/1.60 (~c3_1(a946)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2145, 2140])).
% 1.38/1.60 tff(2147,plain,
% 1.38/1.60 (((~hskp21) | (~c2_1(a946))) <=> ((~hskp21) | (~c2_1(a946)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2148,plain,
% 1.38/1.60 (((~c2_1(a946)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a946)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2149,axiom,((~c2_1(a946)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.38/1.60 tff(2150,plain,
% 1.38/1.60 ((~hskp21) | (~c2_1(a946))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.38/1.60 tff(2151,plain,
% 1.38/1.60 ((~hskp21) | (~c2_1(a946))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2150, 2147])).
% 1.38/1.60 tff(2152,plain,
% 1.38/1.60 (~c2_1(a946)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2151, 2140])).
% 1.38/1.60 tff(2153,plain,
% 1.38/1.60 (((~hskp21) | (~c0_1(a946))) <=> ((~hskp21) | (~c0_1(a946)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2154,plain,
% 1.38/1.60 (((~c0_1(a946)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a946)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2155,axiom,((~c0_1(a946)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.38/1.60 tff(2156,plain,
% 1.38/1.60 ((~hskp21) | (~c0_1(a946))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.38/1.60 tff(2157,plain,
% 1.38/1.60 ((~hskp21) | (~c0_1(a946))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2156, 2153])).
% 1.38/1.60 tff(2158,plain,
% 1.38/1.60 (~c0_1(a946)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2157, 2140])).
% 1.38/1.60 tff(2159,plain,
% 1.38/1.60 (((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2160,plain,
% 1.38/1.60 ((hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946)) <=> (hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2161,plain,
% 1.38/1.60 (((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0)))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2160])).
% 1.38/1.60 tff(2162,plain,
% 1.38/1.60 (((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2161, 2159])).
% 1.38/1.60 tff(2163,plain,
% 1.38/1.60 ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2164,plain,
% 1.38/1.60 ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0)),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 1.38/1.60 tff(2165,plain,
% 1.38/1.60 (hskp27 | hskp10),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2164, 115, 2158, 2152, 2146, 169])).
% 1.38/1.60 tff(2166,plain,
% 1.38/1.60 (hskp10),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2165, 159])).
% 1.38/1.60 tff(2167,plain,
% 1.38/1.60 (c2_1(a912)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[619, 2166])).
% 1.38/1.60 tff(2168,plain,
% 1.38/1.60 (c1_1(a912)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[627, 2166])).
% 1.38/1.60 tff(2169,plain,
% 1.38/1.60 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2170,plain,
% 1.38/1.60 ((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2171,plain,
% 1.38/1.60 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912))))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2170])).
% 1.38/1.60 tff(2172,plain,
% 1.38/1.60 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.38/1.60 tff(2173,plain,
% 1.38/1.60 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2174,plain,
% 1.38/1.60 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912))),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.38/1.60 tff(2175,plain,
% 1.38/1.60 (~c3_1(a912)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2174, 115, 32, 124, 2168, 2167, 53])).
% 1.38/1.60 tff(2176,plain,
% 1.38/1.60 (~c0_1(a912)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[573, 2166])).
% 1.38/1.60 tff(2177,plain,
% 1.38/1.60 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2178,plain,
% 1.38/1.60 ((hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912))) <=> (hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.60 tff(2179,plain,
% 1.38/1.60 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912)))),
% 1.38/1.60 inference(monotonicity,[status(thm)],[2178])).
% 1.38/1.60 tff(2180,plain,
% 1.38/1.60 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))),
% 1.38/1.60 inference(transitivity,[status(thm)],[2179, 2177])).
% 1.38/1.60 tff(2181,plain,
% 1.38/1.60 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))),
% 1.38/1.60 inference(quant_inst,[status(thm)],[])).
% 1.38/1.60 tff(2182,plain,
% 1.38/1.60 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912)),
% 1.38/1.60 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.38/1.60 tff(2183,plain,
% 1.38/1.60 (hskp28),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2182, 115, 32, 2167, 2176, 190, 2175])).
% 1.38/1.60 tff(2184,plain,
% 1.38/1.60 (c0_1(a916)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[233, 2183])).
% 1.38/1.60 tff(2185,plain,
% 1.38/1.60 (c1_1(a916)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[249, 2183])).
% 1.38/1.60 tff(2186,plain,
% 1.38/1.60 (c3_1(a916)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[241, 2183])).
% 1.38/1.60 tff(2187,plain,
% 1.38/1.60 ($false),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2036, 2186, 2185, 32, 43, 21, 2184])).
% 1.38/1.60 tff(2188,plain,(hskp7 | hskp12 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.38/1.60 tff(2189,plain,
% 1.38/1.60 (hskp7),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[2188, 43, 32])).
% 1.38/1.60 tff(2190,plain,
% 1.38/1.60 (~c3_1(a908)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[419, 2189])).
% 1.38/1.60 tff(2191,plain,
% 1.38/1.60 (~c2_1(a908)),
% 1.38/1.60 inference(unit_resolution,[status(thm)],[425, 2189])).
% 1.38/1.60 tff(2192,plain,
% 1.38/1.60 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.38/1.60 inference(bind,[status(th)],[])).
% 1.38/1.60 tff(2193,plain,
% 1.38/1.60 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.38/1.60 inference(quant_intro,[status(thm)],[2192])).
% 1.38/1.60 tff(2194,plain,
% 1.38/1.60 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.38/1.60 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2195,plain,
% 1.38/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.38/1.61 inference(bind,[status(th)],[])).
% 1.38/1.61 tff(2196,plain,
% 1.38/1.61 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.38/1.61 inference(quant_intro,[status(thm)],[2195])).
% 1.38/1.61 tff(2197,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.38/1.61 tff(2198,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 1.38/1.61 tff(2199,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2198, 2194])).
% 1.38/1.61 tff(2200,plain,(
% 1.38/1.61 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.38/1.61 inference(skolemize,[status(sab)],[2199])).
% 1.38/1.61 tff(2201,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2200, 2193])).
% 1.38/1.61 tff(2202,plain,
% 1.38/1.61 (c1_1(a908)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[433, 2189])).
% 1.38/1.61 tff(2203,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2204,plain,
% 1.38/1.61 ((hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2205,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 1.38/1.61 inference(monotonicity,[status(thm)],[2204])).
% 1.38/1.61 tff(2206,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.61 inference(transitivity,[status(thm)],[2205, 2203])).
% 1.38/1.61 tff(2207,plain,
% 1.38/1.61 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.38/1.61 inference(quant_inst,[status(thm)],[])).
% 1.38/1.61 tff(2208,plain,
% 1.38/1.61 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.38/1.61 tff(2209,plain,
% 1.38/1.61 (hskp16),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2208, 115, 149, 141, 133, 2202, 2191, 2190, 2201])).
% 1.38/1.61 tff(2210,plain,
% 1.38/1.61 (((~hskp16) | (~c3_1(a926))) <=> ((~hskp16) | (~c3_1(a926)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2211,plain,
% 1.38/1.61 (((~c3_1(a926)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a926)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2212,axiom,((~c3_1(a926)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.38/1.61 tff(2213,plain,
% 1.38/1.61 ((~hskp16) | (~c3_1(a926))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 1.38/1.61 tff(2214,plain,
% 1.38/1.61 ((~hskp16) | (~c3_1(a926))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2213, 2210])).
% 1.38/1.61 tff(2215,plain,
% 1.38/1.61 (~c3_1(a926)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2214, 2209])).
% 1.38/1.61 tff(2216,plain,
% 1.38/1.61 (((~hskp16) | c2_1(a926)) <=> ((~hskp16) | c2_1(a926))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2217,axiom,((~hskp16) | c2_1(a926)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.38/1.61 tff(2218,plain,
% 1.38/1.61 ((~hskp16) | c2_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 1.38/1.61 tff(2219,plain,
% 1.38/1.61 ((~hskp16) | c2_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2218, 2216])).
% 1.38/1.61 tff(2220,plain,
% 1.38/1.61 ((~hskp16) | c2_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2219, 2216])).
% 1.38/1.61 tff(2221,plain,
% 1.38/1.61 ((~hskp16) | c2_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2220, 2216])).
% 1.38/1.61 tff(2222,plain,
% 1.38/1.61 ((~hskp16) | c2_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2221, 2216])).
% 1.38/1.61 tff(2223,plain,
% 1.38/1.61 (c2_1(a926)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2222, 2209])).
% 1.38/1.61 tff(2224,plain,
% 1.38/1.61 (hskp11),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[158, 125, 32])).
% 1.38/1.61 tff(2225,plain,
% 1.38/1.61 (~c2_1(a914)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[69, 2224])).
% 1.38/1.61 tff(2226,plain,
% 1.38/1.61 (c3_1(a914)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[77, 2224])).
% 1.38/1.61 tff(2227,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2228,plain,
% 1.38/1.61 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2229,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914))))),
% 1.38/1.61 inference(monotonicity,[status(thm)],[2228])).
% 1.38/1.61 tff(2230,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.38/1.61 inference(transitivity,[status(thm)],[2229, 2227])).
% 1.38/1.61 tff(2231,plain,
% 1.38/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.38/1.61 inference(quant_inst,[status(thm)],[])).
% 1.38/1.61 tff(2232,plain,
% 1.38/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 1.38/1.61 tff(2233,plain,
% 1.38/1.61 (~c1_1(a914)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2232, 115, 2226, 2202, 2225, 2191, 2190, 10])).
% 1.38/1.61 tff(2234,plain,
% 1.38/1.61 (c0_1(a914)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[85, 2224])).
% 1.38/1.61 tff(2235,plain,
% 1.38/1.61 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2236,plain,
% 1.38/1.61 ((hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2237,plain,
% 1.38/1.61 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.38/1.61 inference(monotonicity,[status(thm)],[2236])).
% 1.38/1.61 tff(2238,plain,
% 1.38/1.61 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.38/1.61 inference(transitivity,[status(thm)],[2237, 2235])).
% 1.38/1.61 tff(2239,plain,
% 1.38/1.61 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.38/1.61 inference(quant_inst,[status(thm)],[])).
% 1.38/1.61 tff(2240,plain,
% 1.38/1.61 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 1.38/1.61 tff(2241,plain,
% 1.38/1.61 (hskp28),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2240, 115, 2234, 2226, 1943, 2233])).
% 1.38/1.61 tff(2242,plain,
% 1.38/1.61 (c3_1(a916)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[241, 2241])).
% 1.38/1.61 tff(2243,plain,
% 1.38/1.61 (c1_1(a916)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[249, 2241])).
% 1.38/1.61 tff(2244,plain,
% 1.38/1.61 (c0_1(a916)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[233, 2241])).
% 1.38/1.61 tff(2245,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2246,plain,
% 1.38/1.61 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2247,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.38/1.61 inference(monotonicity,[status(thm)],[2246])).
% 1.38/1.61 tff(2248,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.61 inference(transitivity,[status(thm)],[2247, 2245])).
% 1.38/1.61 tff(2249,plain,
% 1.38/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.38/1.61 inference(quant_inst,[status(thm)],[])).
% 1.38/1.61 tff(2250,plain,
% 1.38/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 1.38/1.61 tff(2251,plain,
% 1.38/1.61 (~c0_1(a926)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2250, 115, 2244, 2243, 2242, 2223, 2202, 2215, 2191, 2190, 31])).
% 1.38/1.61 tff(2252,plain,
% 1.38/1.61 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.38/1.61 inference(bind,[status(th)],[])).
% 1.38/1.61 tff(2253,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.38/1.61 inference(quant_intro,[status(thm)],[2252])).
% 1.38/1.61 tff(2254,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2255,plain,
% 1.38/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(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)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | 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)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.38/1.61 inference(bind,[status(th)],[])).
% 1.38/1.61 tff(2256,plain,
% 1.38/1.61 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.38/1.61 inference(quant_intro,[status(thm)],[2255])).
% 1.38/1.61 tff(2257,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.38/1.61 tff(2258,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 1.38/1.61 tff(2259,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2258, 2254])).
% 1.38/1.61 tff(2260,plain,(
% 1.38/1.61 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.38/1.61 inference(skolemize,[status(sab)],[2259])).
% 1.38/1.61 tff(2261,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2260, 2253])).
% 1.38/1.61 tff(2262,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2263,plain,
% 1.38/1.61 ((hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946)) <=> (hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2264,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))))),
% 1.38/1.61 inference(monotonicity,[status(thm)],[2263])).
% 1.38/1.61 tff(2265,plain,
% 1.38/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.38/1.61 inference(transitivity,[status(thm)],[2264, 2262])).
% 1.38/1.61 tff(2266,plain,
% 1.38/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946))),
% 1.38/1.61 inference(quant_inst,[status(thm)],[])).
% 1.38/1.61 tff(2267,plain,
% 1.38/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 1.38/1.61 tff(2268,plain,
% 1.38/1.61 (hskp9),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2267, 115, 2234, 2158, 2152, 2146, 2225, 2261, 2233])).
% 1.38/1.61 tff(2269,plain,
% 1.38/1.61 (~c3_1(a910)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[884, 2268])).
% 1.38/1.61 tff(2270,plain,
% 1.38/1.61 (c2_1(a910)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[931, 2268])).
% 1.38/1.61 tff(2271,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2272,plain,
% 1.38/1.61 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2273,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.38/1.61 inference(monotonicity,[status(thm)],[2272])).
% 1.38/1.61 tff(2274,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.38/1.61 inference(transitivity,[status(thm)],[2273, 2271])).
% 1.38/1.61 tff(2275,plain,
% 1.38/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.38/1.61 inference(quant_inst,[status(thm)],[])).
% 1.38/1.61 tff(2276,plain,
% 1.38/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 1.38/1.61 tff(2277,plain,
% 1.38/1.61 (~c0_1(a910)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2276, 115, 2244, 2243, 2242, 2270, 2202, 2269, 2191, 2190, 31])).
% 1.38/1.61 tff(2278,plain,
% 1.38/1.61 (~c1_1(a910)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[890, 2268])).
% 1.38/1.61 tff(2279,plain,
% 1.38/1.61 (hskp17),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[406, 115, 32, 2234, 2225, 400, 2233])).
% 1.38/1.61 tff(2280,plain,
% 1.38/1.61 (~c3_1(a936)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[412, 2279])).
% 1.38/1.61 tff(2281,plain,
% 1.38/1.61 (~c2_1(a936)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[451, 2279])).
% 1.38/1.61 tff(2282,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2283,plain,
% 1.38/1.61 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2284,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936))))),
% 1.38/1.61 inference(monotonicity,[status(thm)],[2283])).
% 1.38/1.61 tff(2285,plain,
% 1.38/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))),
% 1.38/1.61 inference(transitivity,[status(thm)],[2284, 2282])).
% 1.38/1.61 tff(2286,plain,
% 1.38/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910))),
% 1.38/1.61 inference(quant_inst,[status(thm)],[])).
% 1.38/1.61 tff(2287,plain,
% 1.38/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936))),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 1.38/1.61 tff(2288,plain,
% 1.38/1.61 (c0_1(a910) | (~c0_1(a936))),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2287, 115, 2158, 2152, 2146, 2281, 2280, 2278, 2269, 1029])).
% 1.38/1.61 tff(2289,plain,
% 1.38/1.61 (~c0_1(a936)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2288, 2277])).
% 1.38/1.61 tff(2290,plain,
% 1.38/1.61 (~c1_1(a936)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[457, 2279])).
% 1.38/1.61 tff(2291,plain,
% 1.38/1.61 (((~hskp16) | c1_1(a926)) <=> ((~hskp16) | c1_1(a926))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2292,axiom,((~hskp16) | c1_1(a926)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.38/1.61 tff(2293,plain,
% 1.38/1.61 ((~hskp16) | c1_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.38/1.61 tff(2294,plain,
% 1.38/1.61 ((~hskp16) | c1_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2293, 2291])).
% 1.38/1.61 tff(2295,plain,
% 1.38/1.61 ((~hskp16) | c1_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2294, 2291])).
% 1.38/1.61 tff(2296,plain,
% 1.38/1.61 ((~hskp16) | c1_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2295, 2291])).
% 1.38/1.61 tff(2297,plain,
% 1.38/1.61 ((~hskp16) | c1_1(a926)),
% 1.38/1.61 inference(modus_ponens,[status(thm)],[2296, 2291])).
% 1.38/1.61 tff(2298,plain,
% 1.38/1.61 (c1_1(a926)),
% 1.38/1.61 inference(unit_resolution,[status(thm)],[2297, 2209])).
% 1.38/1.61 tff(2299,plain,
% 1.38/1.61 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.38/1.61 inference(bind,[status(th)],[])).
% 1.38/1.61 tff(2300,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.38/1.61 inference(quant_intro,[status(thm)],[2299])).
% 1.38/1.61 tff(2301,plain,
% 1.38/1.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.38/1.61 inference(rewrite,[status(thm)],[])).
% 1.38/1.61 tff(2302,plain,
% 1.38/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.38/1.62 inference(bind,[status(th)],[])).
% 1.38/1.62 tff(2303,plain,
% 1.38/1.62 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.38/1.62 inference(quant_intro,[status(thm)],[2302])).
% 1.38/1.62 tff(2304,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.38/1.62 tff(2305,plain,
% 1.38/1.62 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2304, 2303])).
% 1.38/1.62 tff(2306,plain,
% 1.38/1.62 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2305, 2301])).
% 1.38/1.62 tff(2307,plain,(
% 1.38/1.62 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.38/1.62 inference(skolemize,[status(sab)],[2306])).
% 1.38/1.62 tff(2308,plain,
% 1.38/1.62 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2307, 2300])).
% 1.38/1.62 tff(2309,assumption,(hskp4), introduced(assumption)).
% 1.38/1.62 tff(2310,plain,
% 1.38/1.62 (((~hskp4) | (~c0_1(a905))) <=> ((~hskp4) | (~c0_1(a905)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2311,plain,
% 1.38/1.62 (((~c0_1(a905)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a905)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2312,axiom,((~c0_1(a905)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.38/1.62 tff(2313,plain,
% 1.38/1.62 ((~hskp4) | (~c0_1(a905))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 1.38/1.62 tff(2314,plain,
% 1.38/1.62 ((~hskp4) | (~c0_1(a905))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2313, 2310])).
% 1.38/1.62 tff(2315,plain,
% 1.38/1.62 (~c0_1(a905)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2314, 2309])).
% 1.38/1.62 tff(2316,plain,
% 1.38/1.62 (((~hskp4) | c3_1(a905)) <=> ((~hskp4) | c3_1(a905))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2317,axiom,((~hskp4) | c3_1(a905)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.38/1.62 tff(2318,plain,
% 1.38/1.62 ((~hskp4) | c3_1(a905)),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 1.38/1.62 tff(2319,plain,
% 1.38/1.62 ((~hskp4) | c3_1(a905)),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2318, 2316])).
% 1.38/1.62 tff(2320,plain,
% 1.38/1.62 ((~hskp4) | c3_1(a905)),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2319, 2316])).
% 1.38/1.62 tff(2321,plain,
% 1.38/1.62 ((~hskp4) | c3_1(a905)),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2320, 2316])).
% 1.38/1.62 tff(2322,plain,
% 1.38/1.62 ((~hskp4) | c3_1(a905)),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2321, 2316])).
% 1.38/1.62 tff(2323,plain,
% 1.38/1.62 (c3_1(a905)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2322, 2309])).
% 1.38/1.62 tff(2324,assumption,(c3_1(a900)), introduced(assumption)).
% 1.38/1.62 tff(2325,assumption,(c2_1(a900)), introduced(assumption)).
% 1.38/1.62 tff(2326,assumption,(c1_1(a900)), introduced(assumption)).
% 1.38/1.62 tff(2327,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2328,plain,
% 1.38/1.62 ((hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905))) <=> (hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2329,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2328])).
% 1.38/1.62 tff(2330,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.62 inference(transitivity,[status(thm)],[2329, 2327])).
% 1.38/1.62 tff(2331,plain,
% 1.38/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905)))),
% 1.38/1.62 inference(quant_inst,[status(thm)],[])).
% 1.38/1.62 tff(2332,plain,
% 1.38/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 1.38/1.62 tff(2333,plain,
% 1.38/1.62 (c1_1(a905)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2332, 115, 43, 2326, 2325, 2324, 2323, 2315, 2308])).
% 1.38/1.62 tff(2334,assumption,(~c0_1(a926)), introduced(assumption)).
% 1.38/1.62 tff(2335,plain,
% 1.38/1.62 (((~hskp4) | (~c2_1(a905))) <=> ((~hskp4) | (~c2_1(a905)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2336,plain,
% 1.38/1.62 (((~c2_1(a905)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a905)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2337,axiom,((~c2_1(a905)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.38/1.62 tff(2338,plain,
% 1.38/1.62 ((~hskp4) | (~c2_1(a905))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 1.38/1.62 tff(2339,plain,
% 1.38/1.62 ((~hskp4) | (~c2_1(a905))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2338, 2335])).
% 1.38/1.62 tff(2340,plain,
% 1.38/1.62 (~c2_1(a905)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2339, 2309])).
% 1.38/1.62 tff(2341,assumption,(c2_1(a910)), introduced(assumption)).
% 1.38/1.62 tff(2342,assumption,(c2_1(a926)), introduced(assumption)).
% 1.38/1.62 tff(2343,assumption,(c1_1(a926)), introduced(assumption)).
% 1.38/1.62 tff(2344,plain,
% 1.38/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2345,plain,
% 1.38/1.62 (((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926))) <=> (c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2346,plain,
% 1.38/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926)))),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2345])).
% 1.38/1.62 tff(2347,plain,
% 1.38/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))),
% 1.38/1.62 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.38/1.62 tff(2348,plain,
% 1.38/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926)))),
% 1.38/1.62 inference(quant_inst,[status(thm)],[])).
% 1.38/1.62 tff(2349,plain,
% 1.38/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926)),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.38/1.62 tff(2350,plain,
% 1.38/1.62 ($false),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2349, 115, 2343, 2342, 2341, 2323, 1479, 1478, 2340, 680, 2334, 2333])).
% 1.38/1.62 tff(2351,plain,((~hskp4) | (~c1_1(a926)) | (~c2_1(a926)) | (~c2_1(a910)) | c1_1(a910) | c3_1(a910) | c0_1(a926) | hskp5 | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.62 tff(2352,plain,
% 1.38/1.62 (~hskp4),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2351, 2298, 2223, 2270, 2278, 2269, 2251, 43, 149, 141, 133])).
% 1.38/1.62 tff(2353,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2354,plain,
% 1.38/1.62 ((hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923))) <=> (hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2355,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2354])).
% 1.38/1.62 tff(2356,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.38/1.62 inference(transitivity,[status(thm)],[2355, 2353])).
% 1.38/1.62 tff(2357,plain,
% 1.38/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923)))),
% 1.38/1.62 inference(quant_inst,[status(thm)],[])).
% 1.38/1.62 tff(2358,plain,
% 1.38/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 1.38/1.62 tff(2359,plain,
% 1.38/1.62 ($false),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2358, 115, 43, 2326, 2325, 2324, 534, 526, 520, 2308])).
% 1.38/1.62 tff(2360,plain,((~hskp14) | hskp5 | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))), inference(lemma,lemma(discharge,[]))).
% 1.38/1.62 tff(2361,plain,
% 1.38/1.62 (~hskp14),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2360, 149, 43, 141, 133])).
% 1.38/1.62 tff(2362,plain,
% 1.38/1.62 ((hskp20 | hskp14 | hskp4) <=> (hskp20 | hskp14 | hskp4)),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2363,plain,
% 1.38/1.62 (((hskp20 | hskp14) | hskp4) <=> (hskp20 | hskp14 | hskp4)),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2364,plain,
% 1.38/1.62 ((hskp20 | hskp14) <=> (hskp20 | hskp14)),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2365,plain,
% 1.38/1.62 (((hskp20 | hskp14) | hskp4) <=> ((hskp20 | hskp14) | hskp4)),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2364])).
% 1.38/1.62 tff(2366,plain,
% 1.38/1.62 (((hskp20 | hskp14) | hskp4) <=> (hskp20 | hskp14 | hskp4)),
% 1.38/1.62 inference(transitivity,[status(thm)],[2365, 2363])).
% 1.38/1.62 tff(2367,axiom,((hskp20 | hskp14) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.38/1.62 tff(2368,plain,
% 1.38/1.62 (hskp20 | hskp14 | hskp4),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 1.38/1.62 tff(2369,plain,
% 1.38/1.62 (hskp20 | hskp14 | hskp4),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2368, 2362])).
% 1.38/1.62 tff(2370,plain,
% 1.38/1.62 (hskp20 | hskp14 | hskp4),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2369, 2362])).
% 1.38/1.62 tff(2371,plain,
% 1.38/1.62 (hskp20 | hskp14 | hskp4),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2370, 2362])).
% 1.38/1.62 tff(2372,plain,
% 1.38/1.62 (hskp20 | hskp14 | hskp4),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2371, 2362])).
% 1.38/1.62 tff(2373,plain,
% 1.38/1.62 (hskp20),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2372, 2361, 2352])).
% 1.38/1.62 tff(2374,plain,
% 1.38/1.62 (~c3_1(a939)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[1339, 2373])).
% 1.38/1.62 tff(2375,plain,
% 1.38/1.62 (~c1_1(a939)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[1345, 2373])).
% 1.38/1.62 tff(2376,plain,
% 1.38/1.62 (c0_1(a939)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[1353, 2373])).
% 1.38/1.62 tff(2377,plain,
% 1.38/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2378,plain,
% 1.38/1.62 (((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2379,plain,
% 1.38/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939))))),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2378])).
% 1.38/1.62 tff(2380,plain,
% 1.38/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))),
% 1.38/1.62 inference(transitivity,[status(thm)],[2379, 2377])).
% 1.38/1.62 tff(2381,plain,
% 1.38/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.38/1.62 inference(quant_inst,[status(thm)],[])).
% 1.38/1.62 tff(2382,plain,
% 1.38/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2381, 2380])).
% 1.38/1.62 tff(2383,plain,
% 1.38/1.62 ($false),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2382, 115, 2376, 2223, 2375, 2374, 2290, 2281, 2215, 489, 2289, 2251])).
% 1.38/1.62 tff(2384,plain,((~hskp27) | hskp5 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.62 tff(2385,plain,
% 1.38/1.62 (~hskp27),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2384, 43, 32])).
% 1.38/1.62 tff(2386,assumption,(~hskp27), introduced(assumption)).
% 1.38/1.62 tff(2387,plain,
% 1.38/1.62 (hskp10),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2165, 2386])).
% 1.38/1.62 tff(2388,plain,
% 1.38/1.62 (c2_1(a912)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[619, 2387])).
% 1.38/1.62 tff(2389,plain,
% 1.38/1.62 (c1_1(a912)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[627, 2387])).
% 1.38/1.62 tff(2390,plain,
% 1.38/1.62 (hskp11 | (~c3_1(a912))),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2174, 115, 32, 2389, 2388, 53])).
% 1.38/1.62 tff(2391,plain,
% 1.38/1.62 (~c3_1(a912)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2390, 150])).
% 1.38/1.62 tff(2392,plain,
% 1.38/1.62 (~c0_1(a912)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[573, 2387])).
% 1.38/1.62 tff(2393,plain,
% 1.38/1.62 (hskp28 | c3_1(a912)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2182, 115, 32, 2388, 2392, 190])).
% 1.38/1.62 tff(2394,plain,
% 1.38/1.62 (hskp28),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2393, 2391])).
% 1.38/1.62 tff(2395,plain,
% 1.38/1.62 (c3_1(a916)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[241, 2394])).
% 1.38/1.62 tff(2396,plain,
% 1.38/1.62 (c1_1(a916)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[249, 2394])).
% 1.38/1.62 tff(2397,plain,
% 1.38/1.62 (~c2_1(a916)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[344, 115, 32, 150, 2396, 2395, 53])).
% 1.38/1.62 tff(2398,plain,
% 1.38/1.62 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2399,plain,
% 1.38/1.62 ((hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946)) <=> (hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2400,plain,
% 1.38/1.62 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946)))),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2399])).
% 1.38/1.62 tff(2401,plain,
% 1.38/1.62 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))),
% 1.38/1.62 inference(transitivity,[status(thm)],[2400, 2398])).
% 1.38/1.62 tff(2402,plain,
% 1.38/1.62 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946))),
% 1.38/1.62 inference(quant_inst,[status(thm)],[])).
% 1.38/1.62 tff(2403,plain,
% 1.38/1.62 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946)),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2402, 2401])).
% 1.38/1.62 tff(2404,plain,
% 1.38/1.62 (hskp27 | hskp11 | c1_1(a946)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2403, 115, 2152, 2146, 901])).
% 1.38/1.62 tff(2405,plain,
% 1.38/1.62 (c1_1(a946)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2404, 150, 2386])).
% 1.38/1.62 tff(2406,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2407,plain,
% 1.38/1.62 (((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2408,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))))),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2407])).
% 1.38/1.62 tff(2409,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 1.38/1.62 inference(transitivity,[status(thm)],[2408, 2406])).
% 1.38/1.62 tff(2410,plain,
% 1.38/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 1.38/1.62 inference(quant_inst,[status(thm)],[])).
% 1.38/1.62 tff(2411,plain,
% 1.38/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))),
% 1.38/1.62 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 1.38/1.62 tff(2412,plain,
% 1.38/1.62 ($false),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2411, 115, 2396, 2395, 2152, 2146, 10, 2405, 2397])).
% 1.38/1.62 tff(2413,plain,(hskp11 | hskp12 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.38/1.62 tff(2414,plain,
% 1.38/1.62 (hskp11),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2413, 2385, 32])).
% 1.38/1.62 tff(2415,plain,
% 1.38/1.62 (~c2_1(a914)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[69, 2414])).
% 1.38/1.62 tff(2416,plain,
% 1.38/1.62 (c3_1(a914)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[77, 2414])).
% 1.38/1.62 tff(2417,plain,
% 1.38/1.62 (~c1_1(a914)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2232, 115, 2416, 2202, 2415, 2191, 2190, 10])).
% 1.38/1.62 tff(2418,plain,
% 1.38/1.62 (c0_1(a914)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[85, 2414])).
% 1.38/1.62 tff(2419,plain,
% 1.38/1.62 (hskp28 | c1_1(a914)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2240, 115, 2418, 2416, 1943])).
% 1.38/1.62 tff(2420,plain,
% 1.38/1.62 (hskp28),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[2419, 2417])).
% 1.38/1.62 tff(2421,plain,
% 1.38/1.62 (c3_1(a916)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[241, 2420])).
% 1.38/1.62 tff(2422,plain,
% 1.38/1.62 (c1_1(a916)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[249, 2420])).
% 1.38/1.62 tff(2423,plain,
% 1.38/1.62 (c0_1(a916)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[233, 2420])).
% 1.38/1.62 tff(2424,plain,
% 1.38/1.62 (hskp1),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[1498, 115, 2423, 2422, 2421, 2418, 2416, 950, 2417])).
% 1.38/1.62 tff(2425,plain,
% 1.38/1.62 (~c1_1(a902)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[1887, 2424])).
% 1.38/1.62 tff(2426,plain,
% 1.38/1.62 (c2_1(a902)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[1506, 2424])).
% 1.38/1.62 tff(2427,plain,
% 1.38/1.62 (c0_1(a902)),
% 1.38/1.62 inference(unit_resolution,[status(thm)],[1514, 2424])).
% 1.38/1.62 tff(2428,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2429,plain,
% 1.38/1.62 ((hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902))) <=> (hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))),
% 1.38/1.62 inference(rewrite,[status(thm)],[])).
% 1.38/1.62 tff(2430,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908))))),
% 1.38/1.62 inference(monotonicity,[status(thm)],[2429])).
% 1.38/1.62 tff(2431,plain,
% 1.38/1.62 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))),
% 1.38/1.63 inference(transitivity,[status(thm)],[2430, 2428])).
% 1.38/1.63 tff(2432,plain,
% 1.38/1.63 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))),
% 1.38/1.63 inference(quant_inst,[status(thm)],[])).
% 1.38/1.63 tff(2433,plain,
% 1.38/1.63 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908))),
% 1.38/1.63 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 1.38/1.63 tff(2434,plain,
% 1.38/1.63 ($false),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[2433, 115, 2385, 2202, 2427, 2426, 2191, 2190, 2425, 42])).
% 1.38/1.63 tff(2435,plain,(hskp5 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.63 tff(2436,plain,
% 1.38/1.63 (hskp5),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[2435, 32])).
% 1.38/1.63 tff(2437,plain,
% 1.38/1.63 (~c3_1(a906)),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[264, 2436])).
% 1.38/1.63 tff(2438,plain,
% 1.38/1.63 (c2_1(a906)),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[258, 2436])).
% 1.38/1.63 tff(2439,plain,
% 1.38/1.63 (c0_1(a906)),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[272, 2436])).
% 1.38/1.63 tff(2440,plain,
% 1.38/1.63 (~hskp27),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[158, 150, 32])).
% 1.38/1.63 tff(2441,plain,
% 1.38/1.63 ($false),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[2413, 2440, 150, 32])).
% 1.38/1.63 tff(2442,plain,(hskp11 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.38/1.63 tff(2443,plain,
% 1.38/1.63 (hskp11),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[2442, 32])).
% 1.38/1.63 tff(2444,plain,
% 1.38/1.63 (~c2_1(a914)),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[69, 2443])).
% 1.38/1.63 tff(2445,plain,
% 1.38/1.63 (c3_1(a914)),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[77, 2443])).
% 1.38/1.63 tff(2446,plain,
% 1.38/1.63 (c0_1(a914)),
% 1.38/1.63 inference(unit_resolution,[status(thm)],[85, 2443])).
% 1.38/1.63 tff(2447,plain,
% 1.38/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))),
% 1.38/1.63 inference(rewrite,[status(thm)],[])).
% 1.38/1.63 tff(2448,plain,
% 1.38/1.63 (((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))),
% 1.38/1.63 inference(rewrite,[status(thm)],[])).
% 1.38/1.63 tff(2449,plain,
% 1.38/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914))))),
% 1.38/1.63 inference(monotonicity,[status(thm)],[2448])).
% 1.38/1.63 tff(2450,plain,
% 1.38/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))),
% 1.47/1.63 inference(transitivity,[status(thm)],[2449, 2447])).
% 1.47/1.63 tff(2451,plain,
% 1.47/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2452,plain,
% 1.47/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 1.47/1.63 tff(2453,plain,
% 1.47/1.63 (~c1_1(a914)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2452, 115, 381, 380, 434, 284, 285, 426, 420, 286, 31])).
% 1.47/1.63 tff(2454,plain,
% 1.47/1.63 (hskp28 | c1_1(a914)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2240, 115, 381, 380, 1943])).
% 1.47/1.63 tff(2455,plain,
% 1.47/1.63 (hskp28),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2454, 2453])).
% 1.47/1.63 tff(2456,plain,
% 1.47/1.63 (c1_1(a916)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[249, 2455])).
% 1.47/1.63 tff(2457,plain,
% 1.47/1.63 (c0_1(a916)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[233, 2455])).
% 1.47/1.63 tff(2458,plain,
% 1.47/1.63 (c3_1(a916)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[241, 2455])).
% 1.47/1.63 tff(2459,plain,
% 1.47/1.63 ($false),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[445, 2458, 2457, 284, 285, 414, 2456, 286])).
% 1.47/1.63 tff(2460,plain,((~hskp7) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | (~c0_1(a914)) | (~c3_1(a914))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.63 tff(2461,plain,
% 1.47/1.63 (~hskp7),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2460, 2439, 2438, 2437, 2446, 2445])).
% 1.47/1.63 tff(2462,assumption,(~hskp28), introduced(assumption)).
% 1.47/1.63 tff(2463,assumption,(hskp13), introduced(assumption)).
% 1.47/1.63 tff(2464,plain,
% 1.47/1.63 (~c3_1(a921)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[204, 2463])).
% 1.47/1.63 tff(2465,plain,
% 1.47/1.63 (c2_1(a921)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[218, 2463])).
% 1.47/1.63 tff(2466,plain,
% 1.47/1.63 (~c0_1(a921)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[210, 2463])).
% 1.47/1.63 tff(2467,plain,
% 1.47/1.63 ($false),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[1062, 2466, 2465, 284, 611, 977, 1046, 2464, 286, 285])).
% 1.47/1.63 tff(2468,plain,((~hskp13) | (~c0_1(a906)) | c0_1(a912) | c1_1(a912) | c2_1(a912) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.63 tff(2469,plain,
% 1.47/1.63 (~hskp13),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2468, 1046, 611, 977, 2439, 2437, 2438])).
% 1.47/1.63 tff(2470,plain,
% 1.47/1.63 (hskp27),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2165, 978])).
% 1.47/1.63 tff(2471,plain,
% 1.47/1.63 (c3_1(a900)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[132, 2470])).
% 1.47/1.63 tff(2472,plain,
% 1.47/1.63 (c2_1(a900)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[140, 2470])).
% 1.47/1.63 tff(2473,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2474,plain,
% 1.47/1.63 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900))) <=> (hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2475,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900)))),
% 1.47/1.63 inference(monotonicity,[status(thm)],[2474])).
% 1.47/1.63 tff(2476,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 1.47/1.63 inference(transitivity,[status(thm)],[2475, 2473])).
% 1.47/1.63 tff(2477,plain,
% 1.47/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2478,plain,
% 1.47/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.47/1.63 tff(2479,plain,
% 1.47/1.63 (hskp13 | c0_1(a900)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2478, 115, 21, 2472, 2471, 20])).
% 1.47/1.63 tff(2480,plain,
% 1.47/1.63 (c0_1(a900)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2479, 2469])).
% 1.47/1.63 tff(2481,assumption,(hskp15), introduced(assumption)).
% 1.47/1.63 tff(2482,plain,
% 1.47/1.63 (~c0_1(a924)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[1189, 2481])).
% 1.47/1.63 tff(2483,plain,
% 1.47/1.63 (c2_1(a924)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[1199, 2481])).
% 1.47/1.63 tff(2484,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2485,plain,
% 1.47/1.63 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924))) <=> (hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2486,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924))))),
% 1.47/1.63 inference(monotonicity,[status(thm)],[2485])).
% 1.47/1.63 tff(2487,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))),
% 1.47/1.63 inference(transitivity,[status(thm)],[2486, 2484])).
% 1.47/1.63 tff(2488,plain,
% 1.47/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924)))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2489,plain,
% 1.47/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 1.47/1.63 tff(2490,plain,
% 1.47/1.63 (~c3_1(a924)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2489, 115, 1242, 21, 2483, 2482, 20])).
% 1.47/1.63 tff(2491,plain,
% 1.47/1.63 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2492,plain,
% 1.47/1.63 ((hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924))) <=> (hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2493,plain,
% 1.47/1.63 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924))))),
% 1.47/1.63 inference(monotonicity,[status(thm)],[2492])).
% 1.47/1.63 tff(2494,plain,
% 1.47/1.63 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))),
% 1.47/1.63 inference(transitivity,[status(thm)],[2493, 2491])).
% 1.47/1.63 tff(2495,plain,
% 1.47/1.63 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924)))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2496,plain,
% 1.47/1.63 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 1.47/1.63 tff(2497,plain,
% 1.47/1.63 ($false),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2496, 115, 2462, 32, 2483, 2482, 190, 2490])).
% 1.47/1.63 tff(2498,plain,((~hskp15) | hskp28 | hskp12 | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.47/1.63 tff(2499,plain,
% 1.47/1.63 (~hskp15),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2498, 2469, 32, 2462, 21])).
% 1.47/1.63 tff(2500,plain,
% 1.47/1.63 (^[U: $i] : refl((hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(2501,plain,
% 1.47/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[2500])).
% 1.47/1.63 tff(2502,plain,
% 1.47/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2503,plain,
% 1.47/1.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15) <=> ((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite(((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15) <=> (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(2504,plain,
% 1.47/1.63 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15) <=> ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[2503])).
% 1.47/1.63 tff(2505,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.47/1.63 tff(2506,plain,
% 1.47/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 1.47/1.63 tff(2507,plain,
% 1.47/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2506, 2502])).
% 1.47/1.63 tff(2508,plain,(
% 1.47/1.63 ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(skolemize,[status(sab)],[2507])).
% 1.47/1.63 tff(2509,plain,
% 1.47/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2508, 2501])).
% 1.47/1.63 tff(2510,plain,
% 1.47/1.63 (((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2511,plain,
% 1.47/1.63 ((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2512,plain,
% 1.47/1.63 ((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2511, 2510])).
% 1.47/1.63 tff(2513,plain,
% 1.47/1.63 (hskp23 | hskp15 | (~c0_1(a900))),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2512, 115, 2472, 2471, 2509])).
% 1.47/1.63 tff(2514,plain,
% 1.47/1.63 (hskp23),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2513, 2499, 2480])).
% 1.47/1.63 tff(2515,plain,
% 1.47/1.63 (((~hskp23) | (~c0_1(a954))) <=> ((~hskp23) | (~c0_1(a954)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2516,plain,
% 1.47/1.63 (((~c0_1(a954)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a954)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2517,axiom,((~c0_1(a954)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.47/1.63 tff(2518,plain,
% 1.47/1.63 ((~hskp23) | (~c0_1(a954))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 1.47/1.63 tff(2519,plain,
% 1.47/1.63 ((~hskp23) | (~c0_1(a954))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2518, 2515])).
% 1.47/1.63 tff(2520,plain,
% 1.47/1.63 (~c0_1(a954)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2519, 2514])).
% 1.47/1.63 tff(2521,plain,
% 1.47/1.63 (((~hskp23) | c3_1(a954)) <=> ((~hskp23) | c3_1(a954))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2522,axiom,((~hskp23) | c3_1(a954)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.47/1.63 tff(2523,plain,
% 1.47/1.63 ((~hskp23) | c3_1(a954)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 1.47/1.63 tff(2524,plain,
% 1.47/1.63 ((~hskp23) | c3_1(a954)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2523, 2521])).
% 1.47/1.63 tff(2525,plain,
% 1.47/1.63 ((~hskp23) | c3_1(a954)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2524, 2521])).
% 1.47/1.63 tff(2526,plain,
% 1.47/1.63 ((~hskp23) | c3_1(a954)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2525, 2521])).
% 1.47/1.63 tff(2527,plain,
% 1.47/1.63 ((~hskp23) | c3_1(a954)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2526, 2521])).
% 1.47/1.63 tff(2528,plain,
% 1.47/1.63 (c3_1(a954)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2527, 2514])).
% 1.47/1.63 tff(2529,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2530,plain,
% 1.47/1.63 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954))) <=> (hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2531,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954))))),
% 1.47/1.63 inference(monotonicity,[status(thm)],[2530])).
% 1.47/1.63 tff(2532,plain,
% 1.47/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))),
% 1.47/1.63 inference(transitivity,[status(thm)],[2531, 2529])).
% 1.47/1.63 tff(2533,plain,
% 1.47/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954)))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2534,plain,
% 1.47/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 1.47/1.63 tff(2535,plain,
% 1.47/1.63 (~c2_1(a954)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2534, 115, 2469, 21, 2528, 2520, 20])).
% 1.47/1.63 tff(2536,plain,
% 1.47/1.63 (c1_1(a900)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[148, 2470])).
% 1.47/1.63 tff(2537,plain,
% 1.47/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2538,plain,
% 1.47/1.63 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2539,plain,
% 1.47/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))))),
% 1.47/1.63 inference(monotonicity,[status(thm)],[2538])).
% 1.47/1.63 tff(2540,plain,
% 1.47/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 1.47/1.63 inference(transitivity,[status(thm)],[2539, 2537])).
% 1.47/1.63 tff(2541,plain,
% 1.47/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2542,plain,
% 1.47/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 1.47/1.63 tff(2543,plain,
% 1.47/1.63 ($false),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2542, 115, 2536, 2471, 2528, 977, 1046, 2520, 611, 1572, 2480, 2535])).
% 1.47/1.63 tff(2544,plain,(c2_1(a912) | c1_1(a912) | c0_1(a912) | hskp7 | hskp12 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.47/1.63 tff(2545,plain,
% 1.47/1.63 (c2_1(a912)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2544, 2462, 611, 21, 32, 977])).
% 1.47/1.63 tff(2546,plain,
% 1.47/1.63 (hskp28 | (~c2_1(a912)) | c3_1(a912)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2182, 115, 32, 611, 190])).
% 1.47/1.63 tff(2547,plain,
% 1.47/1.63 (c3_1(a912)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2546, 2545, 2462])).
% 1.47/1.63 tff(2548,plain,
% 1.47/1.63 (hskp13 | hskp7 | (~c2_1(a912)) | (~c3_1(a912))),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[1252, 115, 611, 20])).
% 1.47/1.63 tff(2549,plain,
% 1.47/1.63 (hskp13),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2548, 2545, 21, 2547])).
% 1.47/1.63 tff(2550,plain,
% 1.47/1.63 (~c3_1(a921)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[204, 2549])).
% 1.47/1.63 tff(2551,plain,
% 1.47/1.63 (~c0_1(a921)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[210, 2549])).
% 1.47/1.63 tff(2552,plain,
% 1.47/1.63 (c2_1(a921)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[218, 2549])).
% 1.47/1.63 tff(2553,plain,
% 1.47/1.63 ($false),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[225, 115, 2462, 32, 2552, 2551, 2550, 190])).
% 1.47/1.63 tff(2554,plain,(hskp28 | hskp12 | hskp7 | c0_1(a912) | c1_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.63 tff(2555,plain,
% 1.47/1.63 (hskp28),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2554, 977, 21, 611, 32])).
% 1.47/1.63 tff(2556,plain,
% 1.47/1.63 (c3_1(a916)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[241, 2555])).
% 1.47/1.63 tff(2557,plain,
% 1.47/1.63 (c1_1(a916)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[249, 2555])).
% 1.47/1.63 tff(2558,plain,
% 1.47/1.63 (c0_1(a916)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[233, 2555])).
% 1.47/1.63 tff(2559,plain,
% 1.47/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2560,plain,
% 1.47/1.63 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(2561,plain,
% 1.47/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))))),
% 1.47/1.63 inference(monotonicity,[status(thm)],[2560])).
% 1.47/1.63 tff(2562,plain,
% 1.47/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 1.47/1.63 inference(transitivity,[status(thm)],[2561, 2559])).
% 1.47/1.63 tff(2563,plain,
% 1.47/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 1.47/1.63 inference(quant_inst,[status(thm)],[])).
% 1.47/1.63 tff(2564,plain,
% 1.47/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 1.47/1.63 tff(2565,plain,
% 1.47/1.63 (~c1_1(a946)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[2564, 115, 2558, 2557, 2556, 2439, 2438, 2152, 2146, 2437, 31])).
% 1.47/1.63 tff(2566,plain,
% 1.47/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2567,plain,
% 1.47/1.64 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2568,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946)))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2567])).
% 1.47/1.64 tff(2569,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2568, 2566])).
% 1.47/1.64 tff(2570,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2571,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 1.47/1.64 tff(2572,plain,
% 1.47/1.64 (~c1_1(a906)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2571, 115, 2439, 2438, 2158, 2152, 2437, 469, 2565])).
% 1.47/1.64 tff(2573,plain,
% 1.47/1.64 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)))),
% 1.47/1.64 inference(bind,[status(th)],[])).
% 1.47/1.64 tff(2574,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.47/1.64 inference(quant_intro,[status(thm)],[2573])).
% 1.47/1.64 tff(2575,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2576,plain,
% 1.47/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))))),
% 1.47/1.64 inference(bind,[status(th)],[])).
% 1.47/1.64 tff(2577,plain,
% 1.47/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.47/1.64 inference(quant_intro,[status(thm)],[2576])).
% 1.47/1.64 tff(2578,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.47/1.64 tff(2579,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.47/1.64 tff(2580,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2579, 2575])).
% 1.47/1.64 tff(2581,plain,(
% 1.47/1.64 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.47/1.64 inference(skolemize,[status(sab)],[2580])).
% 1.47/1.64 tff(2582,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2581, 2574])).
% 1.47/1.64 tff(2583,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2584,plain,
% 1.47/1.64 ((hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946)) <=> (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2585,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946)))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2584])).
% 1.47/1.64 tff(2586,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2585, 2583])).
% 1.47/1.64 tff(2587,plain,
% 1.47/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2588,plain,
% 1.47/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 1.47/1.64 tff(2589,plain,
% 1.47/1.64 (hskp0 | c1_1(a946)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2588, 115, 2446, 2445, 2158, 2152, 2444, 2582])).
% 1.47/1.64 tff(2590,plain,
% 1.47/1.64 (hskp0),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2589, 2565])).
% 1.47/1.64 tff(2591,plain,
% 1.47/1.64 (~c3_1(a901)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[597, 2590])).
% 1.47/1.64 tff(2592,plain,
% 1.47/1.64 (~c0_1(a901)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[609, 2590])).
% 1.47/1.64 tff(2593,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2594,plain,
% 1.47/1.64 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2595,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946)))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2594])).
% 1.47/1.64 tff(2596,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2595, 2593])).
% 1.47/1.64 tff(2597,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2598,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2597, 2596])).
% 1.47/1.64 tff(2599,plain,
% 1.47/1.64 (~c2_1(a901)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2598, 115, 2439, 2158, 2152, 2437, 2592, 2591, 489, 2565, 2572])).
% 1.47/1.64 tff(2600,plain,
% 1.47/1.64 (~c1_1(a901)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[603, 2590])).
% 1.47/1.64 tff(2601,plain,
% 1.47/1.64 (~hskp13),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2468, 1046, 611, 977, 284, 286, 285])).
% 1.47/1.64 tff(2602,plain,
% 1.47/1.64 (c0_1(a900)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2479, 1242])).
% 1.47/1.64 tff(2603,assumption,(~hskp14), introduced(assumption)).
% 1.47/1.64 tff(2604,assumption,(hskp23), introduced(assumption)).
% 1.47/1.64 tff(2605,plain,
% 1.47/1.64 (~c0_1(a954)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2519, 2604])).
% 1.47/1.64 tff(2606,plain,
% 1.47/1.64 (((~hskp23) | c1_1(a954)) <=> ((~hskp23) | c1_1(a954))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2607,axiom,((~hskp23) | c1_1(a954)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.47/1.64 tff(2608,plain,
% 1.47/1.64 ((~hskp23) | c1_1(a954)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 1.47/1.64 tff(2609,plain,
% 1.47/1.64 ((~hskp23) | c1_1(a954)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2608, 2606])).
% 1.47/1.64 tff(2610,plain,
% 1.47/1.64 ((~hskp23) | c1_1(a954)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2609, 2606])).
% 1.47/1.64 tff(2611,plain,
% 1.47/1.64 ((~hskp23) | c1_1(a954)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2610, 2606])).
% 1.47/1.64 tff(2612,plain,
% 1.47/1.64 ((~hskp23) | c1_1(a954)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2611, 2606])).
% 1.47/1.64 tff(2613,plain,
% 1.47/1.64 (c1_1(a954)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2612, 2604])).
% 1.47/1.64 tff(2614,plain,
% 1.47/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2615,plain,
% 1.47/1.64 ((hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954))) <=> (hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2616,plain,
% 1.47/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2615])).
% 1.47/1.64 tff(2617,plain,
% 1.47/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2616, 2614])).
% 1.47/1.64 tff(2618,plain,
% 1.47/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954)))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2619,plain,
% 1.47/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 1.47/1.64 tff(2620,plain,
% 1.47/1.64 (~c2_1(a954)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2619, 115, 2603, 21, 2613, 2605, 640])).
% 1.47/1.64 tff(2621,plain,
% 1.47/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2622,plain,
% 1.47/1.64 ((hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900))) <=> (hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2623,plain,
% 1.47/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2622])).
% 1.47/1.64 tff(2624,plain,
% 1.47/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2623, 2621])).
% 1.47/1.64 tff(2625,plain,
% 1.47/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2626,plain,
% 1.47/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 1.47/1.64 tff(2627,plain,
% 1.47/1.64 (hskp14 | c0_1(a900)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2626, 115, 21, 2536, 2472, 640])).
% 1.47/1.64 tff(2628,plain,
% 1.47/1.64 (c0_1(a900)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2627, 2603])).
% 1.47/1.64 tff(2629,plain,
% 1.47/1.64 (c3_1(a954)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2527, 2604])).
% 1.47/1.64 tff(2630,plain,
% 1.47/1.64 ($false),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2542, 115, 2536, 2471, 2629, 977, 1046, 2605, 611, 1572, 2628, 2620])).
% 1.47/1.64 tff(2631,plain,((~hskp23) | c1_1(a912) | c2_1(a912) | c0_1(a912) | hskp14 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.47/1.64 tff(2632,plain,
% 1.47/1.64 (~hskp23),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2631, 2603, 1046, 611, 977, 21])).
% 1.47/1.64 tff(2633,plain,
% 1.47/1.64 (hskp15),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2513, 2632, 2602])).
% 1.47/1.64 tff(2634,plain,
% 1.47/1.64 (~c0_1(a924)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[1189, 2633])).
% 1.47/1.64 tff(2635,plain,
% 1.47/1.64 (c2_1(a924)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[1199, 2633])).
% 1.47/1.64 tff(2636,plain,
% 1.47/1.64 (~c3_1(a924)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2489, 115, 1242, 21, 2635, 2634, 20])).
% 1.47/1.64 tff(2637,assumption,(c0_1(a900)), introduced(assumption)).
% 1.47/1.64 tff(2638,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2639,plain,
% 1.47/1.64 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2640,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2639])).
% 1.47/1.64 tff(2641,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2640, 2638])).
% 1.47/1.64 tff(2642,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2643,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 1.47/1.64 tff(2644,plain,
% 1.47/1.64 ($false),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2643, 115, 2536, 2471, 977, 1046, 2323, 611, 2315, 2340, 1572, 2637])).
% 1.47/1.64 tff(2645,plain,((~hskp4) | c1_1(a912) | c2_1(a912) | c0_1(a912) | (~c0_1(a900))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.64 tff(2646,plain,
% 1.47/1.64 (~hskp4),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2645, 2602, 1046, 611, 977])).
% 1.47/1.64 tff(2647,plain,
% 1.47/1.64 (hskp20),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2372, 2603, 2646])).
% 1.47/1.64 tff(2648,plain,
% 1.47/1.64 (~c3_1(a939)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[1339, 2647])).
% 1.47/1.64 tff(2649,plain,
% 1.47/1.64 (~c1_1(a939)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[1345, 2647])).
% 1.47/1.64 tff(2650,plain,
% 1.47/1.64 (c0_1(a939)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[1353, 2647])).
% 1.47/1.64 tff(2651,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2652,plain,
% 1.47/1.64 (((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2653,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2652])).
% 1.47/1.64 tff(2654,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2653, 2651])).
% 1.47/1.64 tff(2655,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2656,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 1.47/1.64 tff(2657,plain,
% 1.47/1.64 ($false),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2656, 115, 2650, 2635, 977, 1046, 2649, 2648, 2634, 611, 489, 2636])).
% 1.47/1.64 tff(2658,plain,(hskp14 | c1_1(a912) | c2_1(a912) | c0_1(a912) | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.47/1.64 tff(2659,plain,
% 1.47/1.64 (hskp14),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2658, 1046, 977, 611, 2601, 21])).
% 1.47/1.64 tff(2660,plain,
% 1.47/1.64 (~c0_1(a923)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[525, 2659])).
% 1.47/1.64 tff(2661,plain,
% 1.47/1.64 (c3_1(a923)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[533, 2659])).
% 1.47/1.64 tff(2662,plain,
% 1.47/1.64 (~c2_1(a923)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[1289, 115, 2601, 21, 2661, 2660, 20])).
% 1.47/1.64 tff(2663,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2664,plain,
% 1.47/1.64 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2665,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[2664])).
% 1.47/1.64 tff(2666,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[2665, 2663])).
% 1.47/1.64 tff(2667,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(2668,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 1.47/1.64 tff(2669,plain,
% 1.47/1.64 ($false),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2668, 115, 437, 436, 435, 2661, 977, 1046, 2660, 611, 1572, 2662])).
% 1.47/1.64 tff(2670,plain,(c2_1(a912) | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916)) | c1_1(a912) | c0_1(a912) | hskp7 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.64 tff(2671,plain,
% 1.47/1.64 (c2_1(a912)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[2670, 2558, 2557, 2556, 977, 611, 21, 2439, 2437, 2438])).
% 1.47/1.64 tff(2672,assumption,(~c2_1(a901)), introduced(assumption)).
% 1.47/1.64 tff(2673,assumption,(~c3_1(a912)), introduced(assumption)).
% 1.47/1.64 tff(2674,assumption,(~c1_1(a906)), introduced(assumption)).
% 1.47/1.64 tff(2675,assumption,(~c1_1(a901)), introduced(assumption)).
% 1.47/1.64 tff(2676,assumption,(~c0_1(a901)), introduced(assumption)).
% 1.47/1.64 tff(2677,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2678,plain,
% 1.47/1.64 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(2679,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912)))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[2678])).
% 1.47/1.65 tff(2680,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))),
% 1.47/1.65 inference(transitivity,[status(thm)],[2679, 2677])).
% 1.47/1.65 tff(2681,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(2682,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 1.47/1.65 tff(2683,plain,
% 1.47/1.65 ($false),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2682, 115, 629, 284, 611, 286, 2676, 2675, 489, 2674, 2673, 2672])).
% 1.47/1.65 tff(2684,plain,(c3_1(a912) | (~c2_1(a912)) | (~c0_1(a906)) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | c1_1(a906) | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.65 tff(2685,plain,
% 1.47/1.65 (c3_1(a912)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2684, 2671, 2439, 611, 2437, 2592, 2600, 2572, 2599])).
% 1.47/1.65 tff(2686,plain,
% 1.47/1.65 (hskp13),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2548, 2685, 21, 2671])).
% 1.47/1.65 tff(2687,plain,
% 1.47/1.65 (~c3_1(a921)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[204, 2686])).
% 1.47/1.65 tff(2688,plain,
% 1.47/1.65 (~c0_1(a921)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[210, 2686])).
% 1.47/1.65 tff(2689,plain,
% 1.47/1.65 (c2_1(a921)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[218, 2686])).
% 1.47/1.65 tff(2690,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2691,plain,
% 1.47/1.65 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2692,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[2691])).
% 1.47/1.65 tff(2693,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.47/1.65 inference(transitivity,[status(thm)],[2692, 2690])).
% 1.47/1.65 tff(2694,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(2695,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.47/1.65 tff(2696,plain,
% 1.47/1.65 ($false),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2695, 115, 2689, 2439, 2688, 2687, 2437, 2592, 2600, 489, 2572, 2599])).
% 1.47/1.65 tff(2697,plain,(c1_1(a912) | hskp7 | c0_1(a912) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.47/1.65 tff(2698,plain,
% 1.47/1.65 (c1_1(a912)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2697, 21, 611, 32])).
% 1.47/1.65 tff(2699,plain,
% 1.47/1.65 (hskp27),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2165, 1106])).
% 1.47/1.65 tff(2700,plain,
% 1.47/1.65 (c3_1(a900)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[132, 2699])).
% 1.47/1.65 tff(2701,plain,
% 1.47/1.65 (c1_1(a900)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[148, 2699])).
% 1.47/1.65 tff(2702,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2703,plain,
% 1.47/1.65 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2704,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946))))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[2703])).
% 1.47/1.65 tff(2705,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))),
% 1.47/1.65 inference(transitivity,[status(thm)],[2704, 2702])).
% 1.47/1.65 tff(2706,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(2707,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 1.47/1.65 tff(2708,plain,
% 1.47/1.65 ((~c0_1(a900)) | (~c1_1(a946))),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2707, 115, 2701, 2700, 284, 285, 2152, 2146, 286, 31])).
% 1.47/1.65 tff(2709,plain,
% 1.47/1.65 (~c1_1(a946)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2708, 2637])).
% 1.47/1.65 tff(2710,plain,
% 1.47/1.65 (~c1_1(a906)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2571, 115, 284, 285, 2158, 2152, 286, 469, 2709])).
% 1.47/1.65 tff(2711,plain,
% 1.47/1.65 (c2_1(a900)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[140, 2699])).
% 1.47/1.65 tff(2712,plain,
% 1.47/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2713,plain,
% 1.47/1.65 ((hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906))) <=> (hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2714,plain,
% 1.47/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[2713])).
% 1.47/1.65 tff(2715,plain,
% 1.47/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.65 inference(transitivity,[status(thm)],[2714, 2712])).
% 1.47/1.65 tff(2716,plain,
% 1.47/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906)))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(2717,plain,
% 1.47/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 1.47/1.65 tff(2718,plain,
% 1.47/1.65 (hskp9 | c1_1(a906) | (~c0_1(a900))),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2717, 115, 2711, 2700, 284, 286, 807])).
% 1.47/1.65 tff(2719,plain,
% 1.47/1.65 (hskp9),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2718, 2710, 2637])).
% 1.47/1.65 tff(2720,plain,
% 1.47/1.65 (~c3_1(a910)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[884, 2719])).
% 1.47/1.65 tff(2721,plain,
% 1.47/1.65 (c2_1(a910)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[931, 2719])).
% 1.47/1.65 tff(2722,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2723,plain,
% 1.47/1.65 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2724,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946)))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[2723])).
% 1.47/1.65 tff(2725,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))),
% 1.47/1.65 inference(transitivity,[status(thm)],[2724, 2722])).
% 1.47/1.65 tff(2726,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(2727,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.47/1.65 tff(2728,plain,
% 1.47/1.65 (c0_1(a910)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2727, 115, 2721, 284, 2158, 2152, 2720, 286, 489, 2709, 2710])).
% 1.47/1.65 tff(2729,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2730,plain,
% 1.47/1.65 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2731,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[2730])).
% 1.47/1.65 tff(2732,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 1.47/1.65 inference(transitivity,[status(thm)],[2731, 2729])).
% 1.47/1.65 tff(2733,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(2734,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 1.47/1.65 tff(2735,plain,
% 1.47/1.65 (~c3_1(a912)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2734, 115, 2701, 2700, 1046, 2158, 2152, 611, 1572, 2709, 2637])).
% 1.47/1.65 tff(2736,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2737,plain,
% 1.47/1.65 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912))) <=> (c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2738,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 1.47/1.65 inference(monotonicity,[status(thm)],[2737])).
% 1.47/1.65 tff(2739,plain,
% 1.47/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.65 inference(transitivity,[status(thm)],[2738, 2736])).
% 1.47/1.65 tff(2740,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912)))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(2741,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 1.47/1.65 tff(2742,plain,
% 1.47/1.65 ($false),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2741, 115, 2701, 2700, 630, 1046, 2721, 2720, 31, 2637, 2735, 2728])).
% 1.47/1.65 tff(2743,plain,((~c0_1(a900)) | (~c1_1(a912)) | c2_1(a912) | (~c0_1(a906)) | c3_1(a906) | c0_1(a912) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.65 tff(2744,plain,
% 1.47/1.65 (~c0_1(a900)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[2743, 1046, 2698, 2439, 2437, 611, 2438])).
% 1.47/1.65 tff(2745,plain,
% 1.47/1.65 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(2746,plain,
% 1.47/1.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[2745])).
% 1.47/1.65 tff(2747,plain,
% 1.47/1.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(2748,plain,
% 1.47/1.65 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(2749,plain,
% 1.47/1.66 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[2748])).
% 1.47/1.66 tff(2750,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.47/1.66 tff(2751,plain,
% 1.47/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2750, 2749])).
% 1.47/1.66 tff(2752,plain,
% 1.47/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2751, 2747])).
% 1.47/1.66 tff(2753,plain,(
% 1.47/1.66 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.66 inference(skolemize,[status(sab)],[2752])).
% 1.47/1.66 tff(2754,plain,
% 1.47/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2753, 2746])).
% 1.47/1.66 tff(2755,plain,
% 1.47/1.66 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2756,plain,
% 1.47/1.66 ((hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946)) <=> (hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2757,plain,
% 1.47/1.66 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900)))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[2756])).
% 1.47/1.66 tff(2758,plain,
% 1.47/1.66 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 1.47/1.66 inference(transitivity,[status(thm)],[2757, 2755])).
% 1.47/1.66 tff(2759,plain,
% 1.47/1.66 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(2760,plain,
% 1.47/1.66 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 1.47/1.66 tff(2761,plain,
% 1.47/1.66 (hskp8),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2760, 115, 2701, 2700, 2158, 2152, 2146, 2754, 2744])).
% 1.47/1.66 tff(2762,plain,
% 1.47/1.66 (((~hskp8) | (~c3_1(a909))) <=> ((~hskp8) | (~c3_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2763,plain,
% 1.47/1.66 (((~c3_1(a909)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2764,axiom,((~c3_1(a909)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.47/1.66 tff(2765,plain,
% 1.47/1.66 ((~hskp8) | (~c3_1(a909))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 1.47/1.66 tff(2766,plain,
% 1.47/1.66 ((~hskp8) | (~c3_1(a909))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2765, 2762])).
% 1.47/1.66 tff(2767,plain,
% 1.47/1.66 (~c3_1(a909)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2766, 2761])).
% 1.47/1.66 tff(2768,plain,
% 1.47/1.66 (((~hskp8) | c1_1(a909)) <=> ((~hskp8) | c1_1(a909))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2769,axiom,((~hskp8) | c1_1(a909)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.47/1.66 tff(2770,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a909)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 1.47/1.66 tff(2771,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a909)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2770, 2768])).
% 1.47/1.66 tff(2772,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a909)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2771, 2768])).
% 1.47/1.66 tff(2773,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a909)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2772, 2768])).
% 1.47/1.66 tff(2774,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a909)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2773, 2768])).
% 1.47/1.66 tff(2775,plain,
% 1.47/1.66 (c1_1(a909)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2774, 2761])).
% 1.47/1.66 tff(2776,plain,
% 1.47/1.66 (hskp13 | c0_1(a900)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2478, 115, 21, 2711, 2700, 20])).
% 1.47/1.66 tff(2777,plain,
% 1.47/1.66 (hskp13),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2776, 2744])).
% 1.47/1.66 tff(2778,plain,
% 1.47/1.66 (~c3_1(a921)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[204, 2777])).
% 1.47/1.66 tff(2779,plain,
% 1.47/1.66 (~c0_1(a921)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[210, 2777])).
% 1.47/1.66 tff(2780,plain,
% 1.47/1.66 (c2_1(a921)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[218, 2777])).
% 1.47/1.66 tff(2781,plain,
% 1.47/1.66 (hskp28),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[225, 115, 32, 2780, 2779, 2778, 190])).
% 1.47/1.66 tff(2782,plain,
% 1.47/1.66 (c3_1(a916)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[241, 2781])).
% 1.47/1.66 tff(2783,plain,
% 1.47/1.66 (c1_1(a916)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[249, 2781])).
% 1.47/1.66 tff(2784,plain,
% 1.47/1.66 (c0_1(a916)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[233, 2781])).
% 1.47/1.66 tff(2785,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2786,plain,
% 1.47/1.66 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909))) <=> (c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2787,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[2786])).
% 1.47/1.66 tff(2788,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.47/1.66 inference(transitivity,[status(thm)],[2787, 2785])).
% 1.47/1.66 tff(2789,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909)))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(2790,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2789, 2788])).
% 1.47/1.66 tff(2791,plain,
% 1.47/1.66 (c2_1(a909)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2790, 115, 2784, 2783, 2782, 2775, 2439, 2438, 2767, 2437, 31])).
% 1.47/1.66 tff(2792,plain,
% 1.47/1.66 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(2793,plain,
% 1.47/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[2792])).
% 1.47/1.66 tff(2794,plain,
% 1.47/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2795,plain,
% 1.47/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(2796,plain,
% 1.47/1.66 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[2795])).
% 1.47/1.66 tff(2797,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.47/1.66 tff(2798,plain,
% 1.47/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2797, 2796])).
% 1.47/1.66 tff(2799,plain,
% 1.47/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2798, 2794])).
% 1.47/1.66 tff(2800,plain,(
% 1.47/1.66 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(skolemize,[status(sab)],[2799])).
% 1.47/1.66 tff(2801,plain,
% 1.47/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2800, 2793])).
% 1.47/1.66 tff(2802,plain,
% 1.47/1.66 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2803,plain,
% 1.47/1.66 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2804,plain,
% 1.47/1.66 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[2803])).
% 1.47/1.66 tff(2805,plain,
% 1.47/1.66 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.47/1.66 inference(transitivity,[status(thm)],[2804, 2802])).
% 1.47/1.66 tff(2806,plain,
% 1.47/1.66 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(2807,plain,
% 1.47/1.66 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 1.47/1.66 tff(2808,plain,
% 1.47/1.66 (hskp10 | hskp1),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2807, 115, 2446, 2445, 2444, 2801])).
% 1.47/1.66 tff(2809,plain,
% 1.47/1.66 (hskp1),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2808, 1106])).
% 1.47/1.66 tff(2810,plain,
% 1.47/1.66 (~c1_1(a902)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[1887, 2809])).
% 1.47/1.66 tff(2811,plain,
% 1.47/1.66 (hskp14 | c0_1(a900)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2626, 115, 21, 2701, 2711, 640])).
% 1.47/1.66 tff(2812,plain,
% 1.47/1.66 (hskp14),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2811, 2744])).
% 1.47/1.66 tff(2813,plain,
% 1.47/1.66 (hskp6),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[542, 2812, 21])).
% 1.47/1.66 tff(2814,plain,
% 1.47/1.66 (~c2_1(a907)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[362, 2813])).
% 1.47/1.66 tff(2815,plain,
% 1.47/1.66 (c2_1(a902)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[1506, 2809])).
% 1.47/1.66 tff(2816,plain,
% 1.47/1.66 (c0_1(a902)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[1514, 2809])).
% 1.47/1.66 tff(2817,plain,
% 1.47/1.66 (c1_1(a907)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[370, 2813])).
% 1.47/1.66 tff(2818,plain,
% 1.47/1.66 (c0_1(a907)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[662, 2813])).
% 1.47/1.66 tff(2819,plain,
% 1.47/1.66 (hskp0),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[1531, 115, 2818, 2817, 2816, 2815, 2814, 2810, 1525])).
% 1.47/1.66 tff(2820,plain,
% 1.47/1.66 (~c3_1(a901)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[597, 2819])).
% 1.47/1.66 tff(2821,plain,
% 1.47/1.66 (~c1_1(a901)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[603, 2819])).
% 1.47/1.66 tff(2822,plain,
% 1.47/1.66 (~c0_1(a901)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[609, 2819])).
% 1.47/1.66 tff(2823,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2824,plain,
% 1.47/1.66 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2825,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[2824])).
% 1.47/1.66 tff(2826,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.66 inference(transitivity,[status(thm)],[2825, 2823])).
% 1.47/1.66 tff(2827,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(2828,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.47/1.66 tff(2829,plain,
% 1.47/1.66 (c3_1(a907)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2828, 115, 2701, 2711, 2818, 2814, 2822, 2821, 2820, 283, 2744])).
% 1.47/1.66 tff(2830,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2831,plain,
% 1.47/1.66 (((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2832,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909))))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[2831])).
% 1.47/1.66 tff(2833,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 1.47/1.66 inference(transitivity,[status(thm)],[2832, 2830])).
% 1.47/1.66 tff(2834,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(2835,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2834, 2833])).
% 1.47/1.66 tff(2836,plain,
% 1.47/1.66 (c2_1(a901) | (~c2_1(a909))),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2835, 115, 2775, 2439, 2438, 2767, 2437, 2822, 2821, 469])).
% 1.47/1.66 tff(2837,plain,
% 1.47/1.66 (c2_1(a901)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2836, 2791])).
% 1.47/1.66 tff(2838,plain,
% 1.47/1.66 (((~hskp8) | (~c0_1(a909))) <=> ((~hskp8) | (~c0_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2839,plain,
% 1.47/1.66 (((~c0_1(a909)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2840,axiom,((~c0_1(a909)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.47/1.66 tff(2841,plain,
% 1.47/1.66 ((~hskp8) | (~c0_1(a909))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2840, 2839])).
% 1.47/1.66 tff(2842,plain,
% 1.47/1.66 ((~hskp8) | (~c0_1(a909))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2841, 2838])).
% 1.47/1.66 tff(2843,plain,
% 1.47/1.66 (~c0_1(a909)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2842, 2761])).
% 1.47/1.66 tff(2844,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2845,plain,
% 1.47/1.66 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909))) <=> (c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2846,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909))))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[2845])).
% 1.47/1.66 tff(2847,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 1.47/1.66 inference(transitivity,[status(thm)],[2846, 2844])).
% 1.47/1.66 tff(2848,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909)))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(2849,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2848, 2847])).
% 1.47/1.66 tff(2850,plain,
% 1.47/1.66 ((~c2_1(a901)) | (~c3_1(a907)) | (~c2_1(a909))),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2849, 115, 2775, 2817, 2843, 2814, 2821, 2820, 680])).
% 1.47/1.66 tff(2851,plain,
% 1.47/1.66 ($false),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2850, 2837, 2829, 2791])).
% 1.47/1.66 tff(2852,plain,(c2_1(a912) | hskp12 | hskp7 | c0_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.66 tff(2853,plain,
% 1.47/1.66 (c2_1(a912)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2852, 21, 32, 611])).
% 1.47/1.66 tff(2854,plain,
% 1.47/1.66 (hskp14),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[647, 2853, 21, 2698])).
% 1.47/1.66 tff(2855,plain,
% 1.47/1.66 (c3_1(a923)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[533, 2854])).
% 1.47/1.66 tff(2856,plain,
% 1.47/1.66 (~c1_1(a923)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[519, 2854])).
% 1.47/1.66 tff(2857,plain,
% 1.47/1.66 (~c0_1(a923)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[525, 2854])).
% 1.47/1.66 tff(2858,assumption,(~c0_1(a923)), introduced(assumption)).
% 1.47/1.66 tff(2859,assumption,(c3_1(a923)), introduced(assumption)).
% 1.47/1.66 tff(2860,plain,
% 1.47/1.66 (hskp13 | (~c2_1(a923))),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[1289, 115, 21, 2859, 2858, 20])).
% 1.47/1.66 tff(2861,plain,
% 1.47/1.66 (~c2_1(a923)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2860, 1242])).
% 1.47/1.66 tff(2862,plain,
% 1.47/1.66 (~c3_1(a912)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2548, 1242, 21, 629])).
% 1.47/1.66 tff(2863,assumption,(~c1_1(a923)), introduced(assumption)).
% 1.47/1.66 tff(2864,plain,
% 1.47/1.66 ((~c1_1(a906)) | c2_1(a923)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[1862, 115, 284, 285, 2858, 2863, 286, 469])).
% 1.47/1.66 tff(2865,plain,
% 1.47/1.66 (~c1_1(a906)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2864, 2861])).
% 1.47/1.66 tff(2866,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2867,plain,
% 1.47/1.66 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923)) <=> (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(2868,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[2867])).
% 1.47/1.66 tff(2869,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.47/1.66 inference(transitivity,[status(thm)],[2868, 2866])).
% 1.47/1.66 tff(2870,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(2871,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 1.47/1.66 tff(2872,plain,
% 1.47/1.66 ($false),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2871, 115, 629, 284, 2858, 2863, 611, 286, 489, 2865, 2862, 2861])).
% 1.47/1.66 tff(2873,plain,(hskp13 | (~c2_1(a912)) | (~c0_1(a906)) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~c2_1(a906)) | hskp7 | (~c3_1(a923))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.66 tff(2874,plain,
% 1.47/1.66 (hskp13),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[2873, 2853, 2439, 2857, 2856, 611, 2437, 2438, 21, 2855])).
% 1.47/1.66 tff(2875,plain,
% 1.47/1.66 (~c3_1(a921)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[204, 2874])).
% 1.47/1.66 tff(2876,plain,
% 1.47/1.66 (~c0_1(a921)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[210, 2874])).
% 1.47/1.66 tff(2877,plain,
% 1.47/1.66 (c2_1(a921)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[218, 2874])).
% 1.47/1.66 tff(2878,plain,
% 1.47/1.66 (hskp28),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[225, 115, 32, 2877, 2876, 2875, 190])).
% 1.47/1.66 tff(2879,plain,
% 1.47/1.66 (c3_1(a916)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[241, 2878])).
% 1.47/1.66 tff(2880,plain,
% 1.47/1.66 (c1_1(a916)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[249, 2878])).
% 1.47/1.66 tff(2881,plain,
% 1.47/1.66 (c0_1(a916)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[233, 2878])).
% 1.47/1.66 tff(2882,plain,
% 1.47/1.66 (~c1_1(a946)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2564, 115, 2881, 2880, 2879, 2439, 2438, 2152, 2146, 2437, 31])).
% 1.47/1.67 tff(2883,plain,
% 1.47/1.67 (hskp6),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[653, 2853, 21, 2698, 611])).
% 1.47/1.67 tff(2884,plain,
% 1.47/1.67 (~c2_1(a907)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[362, 2883])).
% 1.47/1.67 tff(2885,plain,
% 1.47/1.67 (c0_1(a907)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[662, 2883])).
% 1.47/1.67 tff(2886,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2887,plain,
% 1.47/1.67 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946)) <=> (c0_1(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2888,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946)))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2887])).
% 1.47/1.67 tff(2889,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))),
% 1.47/1.67 inference(transitivity,[status(thm)],[2888, 2886])).
% 1.47/1.67 tff(2890,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(2891,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 1.47/1.67 tff(2892,plain,
% 1.47/1.67 (c3_1(a907) | c1_1(a946)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2891, 115, 2698, 2853, 2885, 2158, 2146, 611, 2884, 283])).
% 1.47/1.67 tff(2893,plain,
% 1.47/1.67 (c3_1(a907)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2892, 2882])).
% 1.47/1.67 tff(2894,plain,
% 1.47/1.67 (c1_1(a907)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[370, 2883])).
% 1.47/1.67 tff(2895,plain,
% 1.47/1.67 ((~c3_1(a907)) | c1_1(a921)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[687, 115, 2877, 2698, 2853, 2894, 2875, 611, 2884, 680])).
% 1.47/1.67 tff(2896,plain,
% 1.47/1.67 (c1_1(a921)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2895, 2893])).
% 1.47/1.67 tff(2897,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2898,plain,
% 1.47/1.67 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2899,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946)))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2898])).
% 1.47/1.67 tff(2900,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))),
% 1.47/1.67 inference(transitivity,[status(thm)],[2899, 2897])).
% 1.47/1.67 tff(2901,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(2902,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.47/1.67 tff(2903,plain,
% 1.47/1.67 ($false),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2902, 115, 2877, 2439, 2438, 2158, 2152, 2875, 2437, 469, 2882, 2896])).
% 1.47/1.67 tff(2904,plain,(hskp7 | c0_1(a912) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.47/1.67 tff(2905,plain,
% 1.47/1.67 (c0_1(a912)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2904, 2461, 32])).
% 1.47/1.67 tff(2906,plain,
% 1.47/1.67 (~hskp10),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[573, 2905])).
% 1.47/1.67 tff(2907,plain,
% 1.47/1.67 (hskp27),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2165, 2906])).
% 1.47/1.67 tff(2908,plain,
% 1.47/1.67 (c1_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[148, 2907])).
% 1.47/1.67 tff(2909,plain,
% 1.47/1.67 (c3_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[132, 2907])).
% 1.47/1.67 tff(2910,plain,
% 1.47/1.67 (c2_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[140, 2907])).
% 1.47/1.67 tff(2911,plain,
% 1.47/1.67 (~hskp7),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2460, 284, 285, 286, 381, 380])).
% 1.47/1.67 tff(2912,plain,
% 1.47/1.67 (hskp13 | c0_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2478, 115, 2911, 2325, 2324, 20])).
% 1.47/1.67 tff(2913,plain,
% 1.47/1.67 (c0_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2912, 1242])).
% 1.47/1.67 tff(2914,plain,
% 1.47/1.67 ((~c0_1(a900)) | (~c1_1(a946))),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2707, 115, 2326, 2324, 284, 285, 2152, 2146, 286, 31])).
% 1.47/1.67 tff(2915,plain,
% 1.47/1.67 (~c1_1(a946)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2914, 2913])).
% 1.47/1.67 tff(2916,plain,
% 1.47/1.67 (~c1_1(a906)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2571, 115, 284, 285, 2158, 2152, 286, 469, 2915])).
% 1.47/1.67 tff(2917,plain,
% 1.47/1.67 (hskp0 | c1_1(a946)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2588, 115, 381, 380, 2158, 2152, 1115, 2582])).
% 1.47/1.67 tff(2918,plain,
% 1.47/1.67 (hskp0),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2917, 2915])).
% 1.47/1.67 tff(2919,plain,
% 1.47/1.67 (~c3_1(a901)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[597, 2918])).
% 1.47/1.67 tff(2920,plain,
% 1.47/1.67 (~c0_1(a901)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[609, 2918])).
% 1.47/1.67 tff(2921,plain,
% 1.47/1.67 (~c2_1(a901)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2598, 115, 284, 2158, 2152, 286, 2920, 2919, 489, 2915, 2916])).
% 1.47/1.67 tff(2922,plain,
% 1.47/1.67 (~c1_1(a901)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[603, 2918])).
% 1.47/1.67 tff(2923,plain,
% 1.47/1.67 (~c2_1(a954)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2534, 115, 1242, 21, 2629, 2605, 20])).
% 1.47/1.67 tff(2924,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2925,plain,
% 1.47/1.67 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2926,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2925])).
% 1.47/1.67 tff(2927,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[2926, 2924])).
% 1.47/1.67 tff(2928,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(2929,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[2928, 2927])).
% 1.47/1.67 tff(2930,plain,
% 1.47/1.67 ($false),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2929, 115, 2326, 2324, 2629, 2605, 2676, 2675, 1572, 2637, 2672, 2923])).
% 1.47/1.67 tff(2931,plain,((~hskp23) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a901) | c1_1(a901) | (~c0_1(a900)) | c2_1(a901) | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.47/1.67 tff(2932,plain,
% 1.47/1.67 (~hskp23),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2931, 2920, 2324, 2326, 2922, 2913, 2921, 1242, 2911])).
% 1.47/1.67 tff(2933,plain,
% 1.47/1.67 (hskp23 | hskp15 | (~c0_1(a900))),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2512, 115, 2325, 2324, 2509])).
% 1.47/1.67 tff(2934,plain,
% 1.47/1.67 (hskp15),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2933, 2932, 2913])).
% 1.47/1.67 tff(2935,plain,
% 1.47/1.67 (~c0_1(a924)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[1189, 2934])).
% 1.47/1.67 tff(2936,plain,
% 1.47/1.67 (c2_1(a924)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[1199, 2934])).
% 1.47/1.67 tff(2937,plain,
% 1.47/1.67 (~c3_1(a924)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2489, 115, 1242, 2911, 2936, 2935, 20])).
% 1.47/1.67 tff(2938,plain,
% 1.47/1.67 (hskp9 | c1_1(a906) | (~c0_1(a900))),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2717, 115, 2325, 2324, 284, 286, 807])).
% 1.47/1.67 tff(2939,plain,
% 1.47/1.67 (hskp9),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2938, 2916, 2913])).
% 1.47/1.67 tff(2940,plain,
% 1.47/1.67 (~c3_1(a910)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[884, 2939])).
% 1.47/1.67 tff(2941,plain,
% 1.47/1.67 (c2_1(a910)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[931, 2939])).
% 1.47/1.67 tff(2942,plain,
% 1.47/1.67 (c0_1(a910)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2727, 115, 2941, 284, 2158, 2152, 2940, 286, 489, 2915, 2916])).
% 1.47/1.67 tff(2943,plain,
% 1.47/1.67 (~c1_1(a910)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[890, 2939])).
% 1.47/1.67 tff(2944,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2945,plain,
% 1.47/1.67 (((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2946,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2945])).
% 1.47/1.67 tff(2947,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[2946, 2944])).
% 1.47/1.67 tff(2948,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(2949,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[2948, 2947])).
% 1.47/1.67 tff(2950,plain,
% 1.47/1.67 ($false),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2949, 115, 2936, 2935, 2943, 2940, 2920, 2922, 489, 2921, 2942, 2937])).
% 1.47/1.67 tff(2951,plain,(hskp13 | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a914)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.67 tff(2952,plain,
% 1.47/1.67 (hskp13),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2951, 2910, 2909, 2908, 2439, 2437, 2438, 2446, 2445, 2444])).
% 1.47/1.67 tff(2953,plain,
% 1.47/1.67 (~c3_1(a921)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[204, 2952])).
% 1.47/1.67 tff(2954,plain,
% 1.47/1.67 (~c0_1(a921)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[210, 2952])).
% 1.47/1.67 tff(2955,plain,
% 1.47/1.67 (c2_1(a921)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[218, 2952])).
% 1.47/1.67 tff(2956,plain,
% 1.47/1.67 (hskp28),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[225, 115, 32, 2955, 2954, 2953, 190])).
% 1.47/1.67 tff(2957,plain,
% 1.47/1.67 (c3_1(a916)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[241, 2956])).
% 1.47/1.67 tff(2958,plain,
% 1.47/1.67 (c1_1(a916)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[249, 2956])).
% 1.47/1.67 tff(2959,plain,
% 1.47/1.67 (c0_1(a916)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[233, 2956])).
% 1.47/1.67 tff(2960,plain,
% 1.47/1.67 (~c1_1(a946)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2564, 115, 2959, 2958, 2957, 2439, 2438, 2152, 2146, 2437, 31])).
% 1.47/1.67 tff(2961,plain,
% 1.47/1.67 (~c1_1(a906)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2571, 115, 2439, 2438, 2158, 2152, 2437, 469, 2960])).
% 1.47/1.67 tff(2962,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2963,plain,
% 1.47/1.67 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2964,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946)))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2963])).
% 1.47/1.67 tff(2965,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))),
% 1.47/1.67 inference(transitivity,[status(thm)],[2964, 2962])).
% 1.47/1.67 tff(2966,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(2967,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[2966, 2965])).
% 1.47/1.67 tff(2968,plain,
% 1.47/1.67 ($false),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2967, 115, 2955, 2439, 2158, 2152, 2954, 2953, 2437, 489, 2960, 2961])).
% 1.47/1.67 tff(2969,plain,(hskp12), inference(lemma,lemma(discharge,[]))).
% 1.47/1.67 tff(2970,plain,
% 1.47/1.67 (~c2_1(a917)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[293, 2969])).
% 1.47/1.67 tff(2971,plain,
% 1.47/1.67 (c3_1(a917)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[309, 2969])).
% 1.47/1.67 tff(2972,plain,
% 1.47/1.67 (c1_1(a917)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[301, 2969])).
% 1.47/1.67 tff(2973,plain,
% 1.47/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2974,plain,
% 1.47/1.67 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2975,plain,
% 1.47/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2974])).
% 1.47/1.67 tff(2976,plain,
% 1.47/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[2975, 2973])).
% 1.47/1.67 tff(2977,plain,
% 1.47/1.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(2978,plain,
% 1.47/1.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 1.47/1.67 tff(2979,plain,
% 1.47/1.67 (~c1_1(a946)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2978, 115, 2972, 2971, 2152, 2146, 2970, 10])).
% 1.47/1.67 tff(2980,plain,
% 1.47/1.67 (~hskp11),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[123, 43, 21])).
% 1.47/1.67 tff(2981,plain,
% 1.47/1.67 (hskp27 | hskp11),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2404, 2979])).
% 1.47/1.67 tff(2982,plain,
% 1.47/1.67 (hskp27),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2981, 2980])).
% 1.47/1.67 tff(2983,plain,
% 1.47/1.67 (c2_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[140, 2982])).
% 1.47/1.67 tff(2984,plain,
% 1.47/1.67 (c1_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[148, 2982])).
% 1.47/1.67 tff(2985,plain,
% 1.47/1.67 (c3_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[132, 2982])).
% 1.47/1.67 tff(2986,plain,
% 1.47/1.67 (~hskp14),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2360, 2984, 43, 2983, 2985])).
% 1.47/1.67 tff(2987,plain,
% 1.47/1.67 (c0_1(a900)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2626, 115, 2986, 21, 2984, 2983, 640])).
% 1.47/1.67 tff(2988,plain,
% 1.47/1.67 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2989,plain,
% 1.47/1.67 ((hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917))) <=> (hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2990,plain,
% 1.47/1.67 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2989])).
% 1.47/1.67 tff(2991,plain,
% 1.47/1.67 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[2990, 2988])).
% 1.47/1.67 tff(2992,plain,
% 1.47/1.67 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(2993,plain,
% 1.47/1.67 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 1.47/1.67 tff(2994,plain,
% 1.47/1.67 (hskp7 | hskp5 | (~c0_1(a917))),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2993, 115, 2971, 2970, 63])).
% 1.47/1.67 tff(2995,plain,
% 1.47/1.67 (~c0_1(a917)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[2994, 43, 21])).
% 1.47/1.67 tff(2996,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2997,plain,
% 1.47/1.67 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(2998,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[2997])).
% 1.47/1.67 tff(2999,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 1.47/1.68 inference(transitivity,[status(thm)],[2998, 2996])).
% 1.47/1.68 tff(3000,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(3001,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 1.47/1.68 tff(3002,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3001, 115, 2984, 2985, 2971, 2158, 2152, 2970, 1572, 2995, 2979, 2987])).
% 1.47/1.68 tff(3003,plain,(hskp5 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(3004,plain,
% 1.47/1.68 (hskp5),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3003, 21])).
% 1.47/1.68 tff(3005,plain,
% 1.47/1.68 (~c3_1(a906)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[264, 3004])).
% 1.47/1.68 tff(3006,plain,
% 1.47/1.68 (c2_1(a906)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[258, 3004])).
% 1.47/1.68 tff(3007,plain,
% 1.47/1.68 (c0_1(a906)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[272, 3004])).
% 1.47/1.68 tff(3008,plain,
% 1.47/1.68 (~c1_1(a906)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2571, 115, 3007, 3006, 2158, 2152, 3005, 469, 2979])).
% 1.47/1.68 tff(3009,plain,
% 1.47/1.68 (c0_1(a900)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2776, 1242])).
% 1.47/1.68 tff(3010,plain,
% 1.47/1.68 (~c1_1(a912)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2743, 3009, 1046, 3007, 3005, 611, 3006])).
% 1.47/1.68 tff(3011,plain,
% 1.47/1.68 (hskp14),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2658, 3010, 611, 1046, 1242, 21])).
% 1.47/1.68 tff(3012,plain,
% 1.47/1.68 (~c0_1(a923)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[525, 3011])).
% 1.47/1.68 tff(3013,plain,
% 1.47/1.68 (c3_1(a923)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[533, 3011])).
% 1.47/1.68 tff(3014,plain,
% 1.47/1.68 (~c2_1(a923)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[1289, 115, 1242, 21, 3013, 3012, 20])).
% 1.47/1.68 tff(3015,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3016,plain,
% 1.47/1.68 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3017,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[3016])).
% 1.47/1.68 tff(3018,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.47/1.68 inference(transitivity,[status(thm)],[3017, 3015])).
% 1.47/1.68 tff(3019,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(3020,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 1.47/1.68 tff(3021,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3020, 115, 2701, 2700, 3013, 3010, 1046, 3012, 611, 1572, 3009, 3014])).
% 1.47/1.68 tff(3022,plain,(hskp13 | c2_1(a912) | c0_1(a912) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(3023,plain,
% 1.47/1.68 (hskp13),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3022, 1046, 611, 21])).
% 1.47/1.68 tff(3024,plain,
% 1.47/1.68 (c1_1(a912)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2468, 3023, 611, 1046, 3007, 3005, 3006])).
% 1.47/1.68 tff(3025,plain,
% 1.47/1.68 (~c0_1(a900)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2743, 3024, 1046, 3007, 3005, 611, 3006])).
% 1.47/1.68 tff(3026,plain,
% 1.47/1.68 (hskp14),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2811, 3025])).
% 1.47/1.68 tff(3027,plain,
% 1.47/1.68 (hskp6),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[542, 3026, 21])).
% 1.47/1.68 tff(3028,plain,
% 1.47/1.68 (~c2_1(a907)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[362, 3027])).
% 1.47/1.68 tff(3029,plain,
% 1.47/1.68 (c1_1(a907)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[370, 3027])).
% 1.47/1.68 tff(3030,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3031,plain,
% 1.47/1.68 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900))) <=> (c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3032,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[3031])).
% 1.47/1.68 tff(3033,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.47/1.68 inference(transitivity,[status(thm)],[3032, 3030])).
% 1.47/1.68 tff(3034,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(3035,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[3034, 3033])).
% 1.47/1.68 tff(3036,plain,
% 1.47/1.68 (~c3_1(a907)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3035, 115, 2701, 2711, 3029, 3006, 3028, 3005, 680, 3025, 3008])).
% 1.47/1.68 tff(3037,plain,
% 1.47/1.68 (c0_1(a907)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[662, 3027])).
% 1.47/1.68 tff(3038,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3039,plain,
% 1.47/1.68 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946)) <=> (c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3040,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946)))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[3039])).
% 1.47/1.68 tff(3041,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))),
% 1.47/1.68 inference(transitivity,[status(thm)],[3040, 3038])).
% 1.47/1.68 tff(3042,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_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(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(3043,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946)),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 1.47/1.68 tff(3044,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3043, 115, 2701, 2711, 3037, 2158, 2146, 3028, 283, 2979, 3025, 3036])).
% 1.47/1.68 tff(3045,plain,(c2_1(a912) | hskp7 | c0_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(3046,plain,
% 1.47/1.68 (c2_1(a912)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3045, 611, 21])).
% 1.47/1.68 tff(3047,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3048,plain,
% 1.47/1.68 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3049,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946)))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[3048])).
% 1.47/1.68 tff(3050,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))),
% 1.47/1.68 inference(transitivity,[status(thm)],[3049, 3047])).
% 1.47/1.68 tff(3051,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(3052,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946)),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[3051, 3050])).
% 1.47/1.68 tff(3053,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3052, 115, 629, 284, 2158, 2152, 611, 286, 489, 2979, 2673, 2674])).
% 1.47/1.68 tff(3054,plain,(c3_1(a912) | (~c2_1(a912)) | (~c0_1(a906)) | c0_1(a912) | c3_1(a906) | c1_1(a906)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(3055,plain,
% 1.47/1.68 (c3_1(a912)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3054, 3046, 3007, 611, 3005, 3008])).
% 1.47/1.68 tff(3056,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2967, 115, 2465, 284, 2158, 2152, 2466, 2464, 286, 489, 2979, 2674])).
% 1.47/1.68 tff(3057,plain,((~hskp13) | (~c0_1(a906)) | c3_1(a906) | c1_1(a906)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(3058,plain,
% 1.47/1.68 (~hskp13),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3057, 3007, 3005, 3008])).
% 1.47/1.68 tff(3059,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[1252, 115, 3058, 21, 3046, 611, 20, 3055])).
% 1.47/1.68 tff(3060,plain,(c0_1(a912) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(3061,plain,
% 1.47/1.68 (c0_1(a912)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3060, 21])).
% 1.47/1.68 tff(3062,plain,
% 1.47/1.68 (~hskp10),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[573, 3061])).
% 1.47/1.68 tff(3063,plain,
% 1.47/1.68 (hskp27),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2165, 3062])).
% 1.47/1.68 tff(3064,plain,
% 1.47/1.68 (c3_1(a900)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[132, 3063])).
% 1.47/1.68 tff(3065,plain,
% 1.47/1.68 (c2_1(a900)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[140, 3063])).
% 1.47/1.68 tff(3066,plain,
% 1.47/1.68 (c0_1(a900)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[2478, 115, 3058, 21, 3065, 3064, 20])).
% 1.47/1.68 tff(3067,plain,
% 1.47/1.68 (c1_1(a900)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[148, 3063])).
% 1.47/1.68 tff(3068,plain,
% 1.47/1.68 (c0_1(a917)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3001, 115, 3067, 3064, 2971, 2158, 2152, 2970, 1572, 2979, 3066])).
% 1.47/1.68 tff(3069,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3070,plain,
% 1.47/1.68 ((hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946)) <=> (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(3071,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946)))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[3070])).
% 1.47/1.68 tff(3072,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))),
% 1.47/1.68 inference(transitivity,[status(thm)],[3071, 3069])).
% 1.47/1.68 tff(3073,plain,
% 1.47/1.68 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(3074,plain,
% 1.47/1.68 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946)),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 1.47/1.68 tff(3075,plain,
% 1.47/1.68 (hskp0 | (~c0_1(a917))),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3074, 115, 2971, 2158, 2152, 2970, 2582, 2979])).
% 1.47/1.68 tff(3076,plain,
% 1.47/1.68 (hskp0),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[3075, 3068])).
% 1.47/1.68 tff(3077,plain,
% 1.47/1.68 (~c0_1(a901)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[609, 3076])).
% 1.53/1.69 tff(3078,plain,
% 1.53/1.69 (~c1_1(a901)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[603, 3076])).
% 1.53/1.69 tff(3079,plain,
% 1.53/1.69 (~c3_1(a901)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[597, 3076])).
% 1.53/1.69 tff(3080,plain,
% 1.53/1.69 (~c2_1(a901)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2598, 115, 3007, 2158, 2152, 3005, 3077, 3079, 489, 2979, 3008])).
% 1.53/1.69 tff(3081,plain,
% 1.53/1.69 (~hskp23),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2931, 3080, 21, 3064, 3078, 3066, 3077, 3058, 3067])).
% 1.53/1.69 tff(3082,plain,
% 1.53/1.69 (hskp23 | hskp15 | (~c0_1(a900))),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2512, 115, 3065, 3064, 2509])).
% 1.53/1.69 tff(3083,plain,
% 1.53/1.69 (hskp15),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[3082, 3081, 3066])).
% 1.53/1.69 tff(3084,plain,
% 1.53/1.69 (~c0_1(a924)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[1189, 3083])).
% 1.53/1.69 tff(3085,plain,
% 1.53/1.69 (c2_1(a924)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[1199, 3083])).
% 1.53/1.69 tff(3086,plain,
% 1.53/1.69 (~c3_1(a924)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2489, 115, 3058, 21, 3085, 3084, 20])).
% 1.53/1.69 tff(3087,plain,
% 1.53/1.69 (hskp9 | (~c0_1(a900))),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2717, 115, 3065, 3064, 3007, 3005, 807, 3008])).
% 1.53/1.69 tff(3088,plain,
% 1.53/1.69 (hskp9),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[3087, 3066])).
% 1.53/1.69 tff(3089,plain,
% 1.53/1.69 (~c3_1(a910)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[884, 3088])).
% 1.53/1.69 tff(3090,plain,
% 1.53/1.69 (c2_1(a910)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[931, 3088])).
% 1.53/1.69 tff(3091,plain,
% 1.53/1.69 (c0_1(a910)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2727, 115, 3090, 3007, 2158, 2152, 3089, 3005, 489, 2979, 3008])).
% 1.53/1.69 tff(3092,plain,
% 1.53/1.69 (~c1_1(a910)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[890, 3088])).
% 1.53/1.69 tff(3093,plain,
% 1.53/1.69 ($false),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2949, 115, 3085, 3084, 3092, 3089, 3077, 3078, 489, 3080, 3091, 3086])).
% 1.53/1.69 tff(3094,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 1.53/1.69 tff(3095,plain,
% 1.53/1.69 (~c3_1(a908)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[419, 3094])).
% 1.53/1.69 tff(3096,plain,
% 1.53/1.69 (~c2_1(a908)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[425, 3094])).
% 1.53/1.69 tff(3097,plain,
% 1.53/1.69 (c1_1(a908)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[433, 3094])).
% 1.53/1.69 tff(3098,plain,
% 1.53/1.69 ($false),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[965, 115, 2972, 2971, 3097, 2970, 3096, 3095, 10])).
% 1.53/1.69 % SZS output end Proof
% 1.53/1.69 % E exiting
%------------------------------------------------------------------------------