%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN511-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:39:24 AM UTC 2025
% Result : Unsatisfiable 0.49s 0.68s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN511-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.18/0.32 % WCLimit : 300
% 0.18/0.32 % DateTime : Fri Jun 20 12:37:18 EDT 2025
% 0.18/0.32 % CPUTime :
% 0.49/0.68 % SZS status Unsatisfiable
% 0.49/0.68 % SZS output start Proof
% 0.49/0.68 tff(c2_1_type, type, (
% 0.49/0.68 c2_1: $i > $o)).
% 0.49/0.68 tff(a681_type, type, (
% 0.49/0.68 a681: $i)).
% 0.49/0.68 tff(hskp10_type, type, (
% 0.49/0.68 hskp10: $o)).
% 0.49/0.68 tff(c0_1_type, type, (
% 0.49/0.68 c0_1: $i > $o)).
% 0.49/0.68 tff(a680_type, type, (
% 0.49/0.68 a680: $i)).
% 0.49/0.68 tff(a678_type, type, (
% 0.49/0.68 a678: $i)).
% 0.49/0.68 tff(c3_1_type, type, (
% 0.49/0.68 c3_1: $i > $o)).
% 0.49/0.68 tff(c1_1_type, type, (
% 0.49/0.68 c1_1: $i > $o)).
% 0.49/0.68 tff(ndr1_0_type, type, (
% 0.49/0.68 ndr1_0: $o)).
% 0.49/0.68 tff(hskp28_type, type, (
% 0.49/0.68 hskp28: $o)).
% 0.49/0.68 tff(a683_type, type, (
% 0.49/0.68 a683: $i)).
% 0.49/0.68 tff(hskp11_type, type, (
% 0.49/0.68 hskp11: $o)).
% 0.49/0.68 tff(a675_type, type, (
% 0.49/0.68 a675: $i)).
% 0.49/0.68 tff(hskp7_type, type, (
% 0.49/0.68 hskp7: $o)).
% 0.49/0.68 tff(a760_type, type, (
% 0.49/0.68 a760: $i)).
% 0.49/0.68 tff(hskp25_type, type, (
% 0.49/0.68 hskp25: $o)).
% 0.49/0.68 tff(hskp5_type, type, (
% 0.49/0.68 hskp5: $o)).
% 0.49/0.68 tff(a673_type, type, (
% 0.49/0.68 a673: $i)).
% 0.49/0.68 tff(hskp30_type, type, (
% 0.49/0.68 hskp30: $o)).
% 0.49/0.68 tff(hskp8_type, type, (
% 0.49/0.68 hskp8: $o)).
% 0.49/0.68 tff(hskp9_type, type, (
% 0.49/0.68 hskp9: $o)).
% 0.49/0.68 tff(a703_type, type, (
% 0.49/0.68 a703: $i)).
% 0.49/0.68 tff(a688_type, type, (
% 0.49/0.68 a688: $i)).
% 0.49/0.68 tff(hskp13_type, type, (
% 0.49/0.68 hskp13: $o)).
% 0.49/0.68 tff(hskp17_type, type, (
% 0.49/0.68 hskp17: $o)).
% 0.49/0.68 tff(hskp14_type, type, (
% 0.49/0.68 hskp14: $o)).
% 0.49/0.68 tff(a696_type, type, (
% 0.49/0.68 a696: $i)).
% 0.49/0.68 tff(a679_type, type, (
% 0.49/0.68 a679: $i)).
% 0.49/0.68 tff(a670_type, type, (
% 0.49/0.68 a670: $i)).
% 0.49/0.68 tff(hskp2_type, type, (
% 0.49/0.68 hskp2: $o)).
% 0.49/0.68 tff(a702_type, type, (
% 0.49/0.68 a702: $i)).
% 0.49/0.68 tff(a669_type, type, (
% 0.49/0.68 a669: $i)).
% 0.49/0.68 tff(hskp1_type, type, (
% 0.49/0.68 hskp1: $o)).
% 0.49/0.68 tff(hskp16_type, type, (
% 0.49/0.68 hskp16: $o)).
% 0.49/0.68 tff(a715_type, type, (
% 0.49/0.68 a715: $i)).
% 0.49/0.68 tff(hskp21_type, type, (
% 0.49/0.68 hskp21: $o)).
% 0.49/0.68 tff(a725_type, type, (
% 0.49/0.68 a725: $i)).
% 0.49/0.68 tff(hskp29_type, type, (
% 0.49/0.68 hskp29: $o)).
% 0.49/0.68 tff(hskp0_type, type, (
% 0.49/0.68 hskp0: $o)).
% 0.49/0.68 tff(a668_type, type, (
% 0.49/0.68 a668: $i)).
% 0.49/0.68 tff(1,assumption,(c2_1(a678)), introduced(assumption)).
% 0.49/0.68 tff(2,plain,
% 0.49/0.68 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(3,plain,
% 0.49/0.68 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[2])).
% 0.49/0.68 tff(4,plain,
% 0.49/0.68 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(5,plain,
% 0.49/0.68 (^[V: $i, U: $i] : 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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(6,plain,
% 0.49/0.68 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[5])).
% 0.49/0.68 tff(7,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.49/0.68 tff(8,plain,
% 0.49/0.68 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.49/0.68 tff(9,plain,
% 0.49/0.68 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.49/0.68 tff(10,plain,(
% 0.49/0.68 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.49/0.68 inference(skolemize,[status(sab)],[9])).
% 0.49/0.68 tff(11,plain,
% 0.49/0.68 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.49/0.68 tff(12,assumption,(~hskp28), introduced(assumption)).
% 0.49/0.68 tff(13,plain,
% 0.49/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(14,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_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)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[13])).
% 0.49/0.68 tff(15,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_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)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(16,plain,
% 0.49/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(17,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[16])).
% 0.49/0.68 tff(18,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 0.49/0.68 tff(19,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.49/0.68 tff(20,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.49/0.68 tff(21,plain,(
% 0.49/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.49/0.68 inference(skolemize,[status(sab)],[20])).
% 0.49/0.68 tff(22,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.49/0.68 tff(23,plain,
% 0.49/0.68 (^[U: $i] : refl((hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(24,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[23])).
% 0.49/0.68 tff(25,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(26,plain,
% 0.49/0.68 (^[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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10) <=> (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(27,plain,
% 0.49/0.68 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10) <=> ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[26])).
% 0.49/0.68 tff(28,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.49/0.68 tff(29,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.49/0.68 tff(30,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.49/0.68 tff(31,plain,(
% 0.49/0.68 ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(skolemize,[status(sab)],[30])).
% 0.49/0.68 tff(32,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.49/0.68 tff(33,plain,
% 0.49/0.68 (^[U: $i] : refl((hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(34,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[33])).
% 0.49/0.68 tff(35,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(36,plain,
% 0.49/0.68 (^[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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(37,plain,
% 0.49/0.68 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[36])).
% 0.49/0.68 tff(38,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.49/0.68 tff(39,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.49/0.68 tff(40,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.49/0.68 tff(41,plain,(
% 0.49/0.68 ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.49/0.68 inference(skolemize,[status(sab)],[40])).
% 0.49/0.68 tff(42,plain,
% 0.49/0.68 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.49/0.68 tff(43,assumption,(~hskp7), introduced(assumption)).
% 0.49/0.68 tff(44,assumption,(hskp5), introduced(assumption)).
% 0.49/0.68 tff(45,plain,
% 0.49/0.68 (((~hskp5) | (~c3_1(a673))) <=> ((~hskp5) | (~c3_1(a673)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(46,plain,
% 0.49/0.68 (((~c3_1(a673)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a673)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(47,axiom,((~c3_1(a673)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.49/0.68 tff(48,plain,
% 0.49/0.68 ((~hskp5) | (~c3_1(a673))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.49/0.68 tff(49,plain,
% 0.49/0.68 ((~hskp5) | (~c3_1(a673))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.49/0.68 tff(50,plain,
% 0.49/0.68 (~c3_1(a673)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[49, 44])).
% 0.49/0.68 tff(51,plain,
% 0.49/0.68 (((~hskp5) | (~c2_1(a673))) <=> ((~hskp5) | (~c2_1(a673)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(52,plain,
% 0.49/0.68 (((~c2_1(a673)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a673)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(53,axiom,((~c2_1(a673)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.49/0.68 tff(54,plain,
% 0.49/0.68 ((~hskp5) | (~c2_1(a673))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.49/0.68 tff(55,plain,
% 0.49/0.68 ((~hskp5) | (~c2_1(a673))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.49/0.68 tff(56,plain,
% 0.49/0.68 (~c2_1(a673)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[55, 44])).
% 0.49/0.68 tff(57,plain,
% 0.49/0.68 (((~hskp5) | (~c0_1(a673))) <=> ((~hskp5) | (~c0_1(a673)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(58,plain,
% 0.49/0.68 (((~c0_1(a673)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a673)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(59,axiom,((~c0_1(a673)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.49/0.68 tff(60,plain,
% 0.49/0.68 ((~hskp5) | (~c0_1(a673))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.49/0.68 tff(61,plain,
% 0.49/0.68 ((~hskp5) | (~c0_1(a673))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.49/0.68 tff(62,plain,
% 0.49/0.68 (~c0_1(a673)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[61, 44])).
% 0.49/0.68 tff(63,assumption,(~ndr1_0), introduced(assumption)).
% 0.49/0.68 tff(64,plain,
% 0.49/0.68 ((ndr1_0 | (~hskp11)) <=> (ndr1_0 | (~hskp11))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(65,plain,
% 0.49/0.68 (((~hskp11) | ndr1_0) <=> (ndr1_0 | (~hskp11))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(66,axiom,((~hskp11) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 0.49/0.68 tff(67,plain,
% 0.49/0.68 (ndr1_0 | (~hskp11)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.49/0.68 tff(68,plain,
% 0.49/0.68 (ndr1_0 | (~hskp11)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.49/0.68 tff(69,plain,
% 0.49/0.68 (~hskp11),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[68, 63])).
% 0.49/0.68 tff(70,plain,
% 0.49/0.68 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(71,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.49/0.68 tff(72,plain,
% 0.49/0.68 ((~hskp30) | ndr1_0),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.49/0.68 tff(73,plain,
% 0.49/0.68 ((~hskp30) | ndr1_0),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[72, 70])).
% 0.49/0.68 tff(74,plain,
% 0.49/0.68 ((~hskp30) | ndr1_0),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.49/0.68 tff(75,plain,
% 0.49/0.68 ((~hskp30) | ndr1_0),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.49/0.68 tff(76,plain,
% 0.49/0.68 ((~hskp30) | ndr1_0),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.49/0.68 tff(77,plain,
% 0.49/0.68 (~hskp30),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[76, 63])).
% 0.49/0.68 tff(78,plain,
% 0.49/0.68 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(79,plain,
% 0.49/0.68 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(80,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.49/0.68 tff(81,plain,
% 0.49/0.68 (ndr1_0 | (~hskp28)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.49/0.68 tff(82,plain,
% 0.49/0.68 (ndr1_0 | (~hskp28)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.49/0.68 tff(83,plain,
% 0.49/0.68 (~hskp28),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[82, 63])).
% 0.49/0.68 tff(84,plain,
% 0.49/0.68 ((hskp30 | hskp28 | hskp11) <=> (hskp30 | hskp28 | hskp11)),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(85,plain,
% 0.49/0.68 (((hskp28 | hskp30) | hskp11) <=> (hskp30 | hskp28 | hskp11)),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(86,axiom,((hskp28 | hskp30) | hskp11), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.49/0.68 tff(87,plain,
% 0.49/0.68 (hskp30 | hskp28 | hskp11),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.49/0.68 tff(88,plain,
% 0.49/0.68 (hskp30 | hskp28 | hskp11),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.49/0.68 tff(89,plain,
% 0.49/0.68 (hskp30 | hskp28 | hskp11),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.49/0.68 tff(90,plain,
% 0.49/0.68 (hskp30 | hskp28 | hskp11),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[89, 84])).
% 0.49/0.68 tff(91,plain,
% 0.49/0.68 (hskp30 | hskp28 | hskp11),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[90, 84])).
% 0.49/0.68 tff(92,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[91, 83, 77, 69])).
% 0.49/0.68 tff(93,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(94,plain,
% 0.49/0.68 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(95,plain,
% 0.49/0.68 ((hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673)) <=> (hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(96,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0)))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[95])).
% 0.49/0.69 tff(97,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))),
% 0.49/0.69 inference(transitivity,[status(thm)],[96, 94])).
% 0.49/0.69 tff(98,plain,
% 0.49/0.69 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(99,plain,
% 0.49/0.69 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.49/0.69 tff(100,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[99, 93, 12, 43, 62, 56, 50, 42])).
% 0.49/0.69 tff(101,plain,((~hskp5) | hskp28 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(102,plain,
% 0.49/0.69 (~hskp5),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[101, 43, 12])).
% 0.49/0.69 tff(103,plain,
% 0.49/0.69 ((hskp25 | hskp7 | hskp5) <=> (hskp25 | hskp7 | hskp5)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(104,plain,
% 0.49/0.69 (((hskp25 | hskp7) | hskp5) <=> (hskp25 | hskp7 | hskp5)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(105,plain,
% 0.49/0.69 ((hskp7 | hskp25) <=> (hskp25 | hskp7)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(106,plain,
% 0.49/0.69 (((hskp7 | hskp25) | hskp5) <=> ((hskp25 | hskp7) | hskp5)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[105])).
% 0.49/0.69 tff(107,plain,
% 0.49/0.69 (((hskp7 | hskp25) | hskp5) <=> (hskp25 | hskp7 | hskp5)),
% 0.49/0.69 inference(transitivity,[status(thm)],[106, 104])).
% 0.49/0.69 tff(108,axiom,((hskp7 | hskp25) | hskp5), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.49/0.69 tff(109,plain,
% 0.49/0.69 (hskp25 | hskp7 | hskp5),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.49/0.69 tff(110,plain,
% 0.49/0.69 (hskp25 | hskp7 | hskp5),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[109, 103])).
% 0.49/0.69 tff(111,plain,
% 0.49/0.69 (hskp25 | hskp7 | hskp5),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.49/0.69 tff(112,plain,
% 0.49/0.69 (hskp25 | hskp7 | hskp5),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[111, 103])).
% 0.49/0.69 tff(113,plain,
% 0.49/0.69 (hskp25 | hskp7 | hskp5),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[112, 103])).
% 0.49/0.69 tff(114,plain,
% 0.49/0.69 (hskp25),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[113, 102, 43])).
% 0.49/0.69 tff(115,plain,
% 0.49/0.69 (((~hskp25) | (~c3_1(a760))) <=> ((~hskp25) | (~c3_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(116,plain,
% 0.49/0.69 (((~c3_1(a760)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(117,axiom,((~c3_1(a760)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.49/0.69 tff(118,plain,
% 0.49/0.69 ((~hskp25) | (~c3_1(a760))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.49/0.69 tff(119,plain,
% 0.49/0.69 ((~hskp25) | (~c3_1(a760))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[118, 115])).
% 0.49/0.69 tff(120,plain,
% 0.49/0.69 (~c3_1(a760)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[119, 114])).
% 0.49/0.69 tff(121,plain,
% 0.49/0.69 (((~hskp25) | (~c0_1(a760))) <=> ((~hskp25) | (~c0_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(122,plain,
% 0.49/0.69 (((~c0_1(a760)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(123,axiom,((~c0_1(a760)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.49/0.69 tff(124,plain,
% 0.49/0.69 ((~hskp25) | (~c0_1(a760))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.49/0.69 tff(125,plain,
% 0.49/0.69 ((~hskp25) | (~c0_1(a760))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.49/0.69 tff(126,plain,
% 0.49/0.69 (~c0_1(a760)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[125, 114])).
% 0.49/0.69 tff(127,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(128,plain,
% 0.49/0.69 ((hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760)) <=> (hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(129,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760)))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[128])).
% 0.49/0.69 tff(130,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))),
% 0.49/0.69 inference(transitivity,[status(thm)],[129, 127])).
% 0.49/0.69 tff(131,plain,
% 0.49/0.69 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(132,plain,
% 0.49/0.69 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.49/0.69 tff(133,plain,
% 0.49/0.69 (c2_1(a760)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[132, 93, 12, 43, 126, 120, 42])).
% 0.49/0.69 tff(134,plain,
% 0.49/0.69 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(135,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[134])).
% 0.49/0.69 tff(136,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(137,plain,
% 0.49/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(138,plain,
% 0.49/0.69 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[137])).
% 0.49/0.69 tff(139,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.49/0.69 tff(140,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.49/0.69 tff(141,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.49/0.69 tff(142,plain,(
% 0.49/0.69 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.69 inference(skolemize,[status(sab)],[141])).
% 0.49/0.69 tff(143,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.49/0.69 tff(144,plain,
% 0.49/0.69 (((~hskp25) | (~c1_1(a760))) <=> ((~hskp25) | (~c1_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(145,plain,
% 0.49/0.69 (((~c1_1(a760)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(146,axiom,((~c1_1(a760)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.49/0.69 tff(147,plain,
% 0.49/0.69 ((~hskp25) | (~c1_1(a760))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.49/0.69 tff(148,plain,
% 0.49/0.69 ((~hskp25) | (~c1_1(a760))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.49/0.69 tff(149,plain,
% 0.49/0.69 (~c1_1(a760)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[148, 114])).
% 0.49/0.69 tff(150,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(151,plain,
% 0.49/0.69 ((hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760)) <=> (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(152,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[151])).
% 0.49/0.69 tff(153,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[152, 150])).
% 0.49/0.69 tff(154,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(155,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.49/0.69 tff(156,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[155, 93, 102, 126, 149, 120, 143, 133])).
% 0.49/0.69 tff(157,plain,(hskp7 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(158,plain,
% 0.49/0.69 (hskp7),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[157, 12])).
% 0.49/0.69 tff(159,plain,
% 0.49/0.69 (((~hskp7) | (~c2_1(a675))) <=> ((~hskp7) | (~c2_1(a675)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(160,plain,
% 0.49/0.69 (((~c2_1(a675)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a675)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(161,axiom,((~c2_1(a675)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.49/0.69 tff(162,plain,
% 0.49/0.69 ((~hskp7) | (~c2_1(a675))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.49/0.69 tff(163,plain,
% 0.49/0.69 ((~hskp7) | (~c2_1(a675))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.49/0.69 tff(164,plain,
% 0.49/0.69 (~c2_1(a675)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[163, 158])).
% 0.49/0.69 tff(165,plain,
% 0.49/0.69 (((~hskp7) | c3_1(a675)) <=> ((~hskp7) | c3_1(a675))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(166,axiom,((~hskp7) | c3_1(a675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.49/0.69 tff(167,plain,
% 0.49/0.69 ((~hskp7) | c3_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.49/0.69 tff(168,plain,
% 0.49/0.69 ((~hskp7) | c3_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[167, 165])).
% 0.49/0.69 tff(169,plain,
% 0.49/0.69 ((~hskp7) | c3_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[168, 165])).
% 0.49/0.69 tff(170,plain,
% 0.49/0.69 ((~hskp7) | c3_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.49/0.69 tff(171,plain,
% 0.49/0.69 ((~hskp7) | c3_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[170, 165])).
% 0.49/0.69 tff(172,plain,
% 0.49/0.69 (c3_1(a675)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[171, 158])).
% 0.49/0.69 tff(173,plain,
% 0.49/0.69 (((~hskp7) | c1_1(a675)) <=> ((~hskp7) | c1_1(a675))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(174,axiom,((~hskp7) | c1_1(a675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.49/0.69 tff(175,plain,
% 0.49/0.69 ((~hskp7) | c1_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.49/0.69 tff(176,plain,
% 0.49/0.69 ((~hskp7) | c1_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[175, 173])).
% 0.49/0.69 tff(177,plain,
% 0.49/0.69 ((~hskp7) | c1_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.49/0.69 tff(178,plain,
% 0.49/0.69 ((~hskp7) | c1_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.49/0.69 tff(179,plain,
% 0.49/0.69 ((~hskp7) | c1_1(a675)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[178, 173])).
% 0.49/0.69 tff(180,plain,
% 0.49/0.69 (c1_1(a675)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[179, 158])).
% 0.49/0.69 tff(181,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(182,plain,
% 0.49/0.69 ((hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675))) <=> (hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(183,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[182])).
% 0.49/0.69 tff(184,plain,
% 0.49/0.69 (((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[183, 181])).
% 0.49/0.69 tff(185,plain,
% 0.49/0.69 ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(186,plain,
% 0.49/0.69 ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.49/0.69 tff(187,plain,
% 0.49/0.69 (hskp10),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[186, 93, 12, 180, 172, 164, 32])).
% 0.49/0.69 tff(188,plain,
% 0.49/0.69 (((~hskp10) | (~c0_1(a681))) <=> ((~hskp10) | (~c0_1(a681)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(189,plain,
% 0.49/0.69 (((~c0_1(a681)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a681)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(190,axiom,((~c0_1(a681)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.49/0.69 tff(191,plain,
% 0.49/0.69 ((~hskp10) | (~c0_1(a681))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.49/0.69 tff(192,plain,
% 0.49/0.69 ((~hskp10) | (~c0_1(a681))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[191, 188])).
% 0.49/0.69 tff(193,plain,
% 0.49/0.69 (~c0_1(a681)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[192, 187])).
% 0.49/0.69 tff(194,plain,
% 0.49/0.69 (((~hskp10) | c3_1(a681)) <=> ((~hskp10) | c3_1(a681))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(195,axiom,((~hskp10) | c3_1(a681)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.49/0.69 tff(196,plain,
% 0.49/0.69 ((~hskp10) | c3_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.49/0.69 tff(197,plain,
% 0.49/0.69 ((~hskp10) | c3_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[196, 194])).
% 0.49/0.69 tff(198,plain,
% 0.49/0.69 ((~hskp10) | c3_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[197, 194])).
% 0.49/0.69 tff(199,plain,
% 0.49/0.69 ((~hskp10) | c3_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.49/0.69 tff(200,plain,
% 0.49/0.69 ((~hskp10) | c3_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[199, 194])).
% 0.49/0.69 tff(201,plain,
% 0.49/0.69 (c3_1(a681)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[200, 187])).
% 0.49/0.69 tff(202,plain,
% 0.49/0.69 (((~hskp10) | c2_1(a681)) <=> ((~hskp10) | c2_1(a681))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(203,axiom,((~hskp10) | c2_1(a681)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.49/0.69 tff(204,plain,
% 0.49/0.69 ((~hskp10) | c2_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.49/0.69 tff(205,plain,
% 0.49/0.69 ((~hskp10) | c2_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[204, 202])).
% 0.49/0.69 tff(206,plain,
% 0.49/0.69 ((~hskp10) | c2_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[205, 202])).
% 0.49/0.69 tff(207,plain,
% 0.49/0.69 ((~hskp10) | c2_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.49/0.69 tff(208,plain,
% 0.49/0.69 ((~hskp10) | c2_1(a681)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[207, 202])).
% 0.49/0.69 tff(209,plain,
% 0.49/0.69 (c2_1(a681)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[208, 187])).
% 0.49/0.69 tff(210,plain,
% 0.49/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(211,plain,
% 0.49/0.69 (((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681))) <=> (c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(212,plain,
% 0.49/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[211])).
% 0.49/0.69 tff(213,plain,
% 0.49/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[212, 210])).
% 0.49/0.69 tff(214,plain,
% 0.49/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(215,plain,
% 0.49/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.49/0.69 tff(216,plain,
% 0.49/0.69 (~c1_1(a681)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[215, 93, 209, 201, 193, 22])).
% 0.49/0.69 tff(217,plain,
% 0.49/0.69 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(218,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[217])).
% 0.49/0.69 tff(219,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(220,plain,
% 0.49/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(221,plain,
% 0.49/0.70 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[220])).
% 0.49/0.70 tff(222,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.49/0.70 tff(223,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.49/0.70 tff(224,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.49/0.70 tff(225,plain,(
% 0.49/0.70 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[224])).
% 0.49/0.70 tff(226,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.49/0.70 tff(227,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(228,plain,
% 0.49/0.70 ((hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681))) <=> (hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(229,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[228])).
% 0.49/0.70 tff(230,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[229, 227])).
% 0.49/0.70 tff(231,plain,
% 0.49/0.70 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(232,plain,
% 0.49/0.70 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.49/0.70 tff(233,plain,
% 0.49/0.70 (hskp11),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[232, 93, 209, 201, 193, 226, 216])).
% 0.49/0.70 tff(234,plain,
% 0.49/0.70 (((~hskp11) | c0_1(a683)) <=> ((~hskp11) | c0_1(a683))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(235,axiom,((~hskp11) | c0_1(a683)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.49/0.70 tff(236,plain,
% 0.49/0.70 ((~hskp11) | c0_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.49/0.70 tff(237,plain,
% 0.49/0.70 ((~hskp11) | c0_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[236, 234])).
% 0.49/0.70 tff(238,plain,
% 0.49/0.70 ((~hskp11) | c0_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[237, 234])).
% 0.49/0.70 tff(239,plain,
% 0.49/0.70 ((~hskp11) | c0_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[238, 234])).
% 0.49/0.70 tff(240,plain,
% 0.49/0.70 ((~hskp11) | c0_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[239, 234])).
% 0.49/0.70 tff(241,plain,
% 0.49/0.70 (c0_1(a683)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[240, 233])).
% 0.49/0.70 tff(242,plain,
% 0.49/0.70 (((~hskp11) | c3_1(a683)) <=> ((~hskp11) | c3_1(a683))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(243,axiom,((~hskp11) | c3_1(a683)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.49/0.70 tff(244,plain,
% 0.49/0.70 ((~hskp11) | c3_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.49/0.70 tff(245,plain,
% 0.49/0.70 ((~hskp11) | c3_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[244, 242])).
% 0.49/0.70 tff(246,plain,
% 0.49/0.70 ((~hskp11) | c3_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[245, 242])).
% 0.49/0.70 tff(247,plain,
% 0.49/0.70 ((~hskp11) | c3_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.49/0.70 tff(248,plain,
% 0.49/0.70 ((~hskp11) | c3_1(a683)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[247, 242])).
% 0.49/0.70 tff(249,plain,
% 0.49/0.70 (c3_1(a683)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[248, 233])).
% 0.49/0.70 tff(250,plain,
% 0.49/0.70 (((~hskp11) | (~c2_1(a683))) <=> ((~hskp11) | (~c2_1(a683)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(251,plain,
% 0.49/0.70 (((~c2_1(a683)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a683)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(252,axiom,((~c2_1(a683)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.49/0.70 tff(253,plain,
% 0.49/0.70 ((~hskp11) | (~c2_1(a683))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.49/0.70 tff(254,plain,
% 0.49/0.70 ((~hskp11) | (~c2_1(a683))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[253, 250])).
% 0.49/0.70 tff(255,plain,
% 0.49/0.70 (~c2_1(a683)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[254, 233])).
% 0.49/0.70 tff(256,assumption,(hskp7), introduced(assumption)).
% 0.49/0.70 tff(257,plain,
% 0.49/0.70 (~c2_1(a675)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[163, 256])).
% 0.49/0.70 tff(258,plain,
% 0.49/0.70 (c3_1(a675)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[171, 256])).
% 0.49/0.70 tff(259,plain,
% 0.49/0.70 (c1_1(a675)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[179, 256])).
% 0.49/0.70 tff(260,plain,
% 0.49/0.70 (hskp10),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[186, 93, 12, 259, 258, 257, 32])).
% 0.49/0.70 tff(261,plain,
% 0.49/0.70 (~c0_1(a681)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[192, 260])).
% 0.49/0.70 tff(262,plain,
% 0.49/0.70 (c3_1(a681)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[200, 260])).
% 0.49/0.70 tff(263,plain,
% 0.49/0.70 (c2_1(a681)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[208, 260])).
% 0.49/0.70 tff(264,plain,
% 0.49/0.70 (~c1_1(a681)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[215, 93, 263, 262, 261, 22])).
% 0.49/0.70 tff(265,assumption,(c0_1(a683)), introduced(assumption)).
% 0.49/0.70 tff(266,assumption,(~c2_1(a683)), introduced(assumption)).
% 0.49/0.70 tff(267,assumption,(c3_1(a683)), introduced(assumption)).
% 0.49/0.70 tff(268,plain,
% 0.49/0.70 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(269,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[268])).
% 0.49/0.70 tff(270,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(271,plain,
% 0.49/0.70 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(272,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[271])).
% 0.49/0.70 tff(273,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 0.49/0.70 tff(274,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.49/0.70 tff(275,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.49/0.70 tff(276,plain,(
% 0.49/0.70 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.49/0.70 inference(skolemize,[status(sab)],[275])).
% 0.49/0.70 tff(277,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.49/0.70 tff(278,assumption,(hskp9), introduced(assumption)).
% 0.49/0.70 tff(279,plain,
% 0.49/0.70 (((~hskp9) | (~c3_1(a680))) <=> ((~hskp9) | (~c3_1(a680)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(280,plain,
% 0.49/0.70 (((~c3_1(a680)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a680)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(281,axiom,((~c3_1(a680)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.49/0.70 tff(282,plain,
% 0.49/0.70 ((~hskp9) | (~c3_1(a680))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.49/0.70 tff(283,plain,
% 0.49/0.70 ((~hskp9) | (~c3_1(a680))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[282, 279])).
% 0.49/0.70 tff(284,plain,
% 0.49/0.70 (~c3_1(a680)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[283, 278])).
% 0.49/0.70 tff(285,plain,
% 0.49/0.70 (((~hskp9) | (~c1_1(a680))) <=> ((~hskp9) | (~c1_1(a680)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(286,plain,
% 0.49/0.70 (((~c1_1(a680)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a680)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(287,axiom,((~c1_1(a680)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.49/0.70 tff(288,plain,
% 0.49/0.70 ((~hskp9) | (~c1_1(a680))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.49/0.70 tff(289,plain,
% 0.49/0.70 ((~hskp9) | (~c1_1(a680))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[288, 285])).
% 0.49/0.70 tff(290,plain,
% 0.49/0.70 (~c1_1(a680)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[289, 278])).
% 0.49/0.70 tff(291,assumption,(~c0_1(a681)), introduced(assumption)).
% 0.49/0.70 tff(292,assumption,(c3_1(a681)), introduced(assumption)).
% 0.49/0.70 tff(293,assumption,(c2_1(a681)), introduced(assumption)).
% 0.49/0.70 tff(294,plain,
% 0.49/0.70 (~c1_1(a681)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[215, 93, 293, 292, 291, 22])).
% 0.49/0.70 tff(295,plain,
% 0.49/0.70 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(296,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[295])).
% 0.49/0.70 tff(297,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(298,plain,
% 0.49/0.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(299,plain,
% 0.49/0.70 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[298])).
% 0.49/0.70 tff(300,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.49/0.70 tff(301,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.49/0.70 tff(302,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.49/0.70 tff(303,plain,(
% 0.49/0.70 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[302])).
% 0.49/0.70 tff(304,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[303, 296])).
% 0.49/0.70 tff(305,plain,
% 0.49/0.70 (((~hskp9) | c2_1(a680)) <=> ((~hskp9) | c2_1(a680))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(306,axiom,((~hskp9) | c2_1(a680)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.49/0.70 tff(307,plain,
% 0.49/0.70 ((~hskp9) | c2_1(a680)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.49/0.70 tff(308,plain,
% 0.49/0.70 ((~hskp9) | c2_1(a680)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[307, 305])).
% 0.49/0.70 tff(309,plain,
% 0.49/0.70 ((~hskp9) | c2_1(a680)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[308, 305])).
% 0.49/0.70 tff(310,plain,
% 0.49/0.70 ((~hskp9) | c2_1(a680)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.49/0.70 tff(311,plain,
% 0.49/0.70 ((~hskp9) | c2_1(a680)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[310, 305])).
% 0.49/0.70 tff(312,plain,
% 0.49/0.70 (c2_1(a680)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[311, 278])).
% 0.49/0.70 tff(313,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(314,plain,
% 0.49/0.70 ((hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680))) <=> (hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(315,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[314])).
% 0.49/0.70 tff(316,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[315, 313])).
% 0.49/0.70 tff(317,plain,
% 0.49/0.70 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(318,plain,
% 0.49/0.70 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.49/0.70 tff(319,plain,
% 0.49/0.70 (hskp13),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[318, 93, 293, 292, 312, 290, 284, 304, 294])).
% 0.49/0.70 tff(320,plain,
% 0.49/0.70 (((~hskp13) | (~c3_1(a688))) <=> ((~hskp13) | (~c3_1(a688)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(321,plain,
% 0.49/0.70 (((~c3_1(a688)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a688)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(322,axiom,((~c3_1(a688)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.49/0.70 tff(323,plain,
% 0.49/0.70 ((~hskp13) | (~c3_1(a688))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.49/0.70 tff(324,plain,
% 0.49/0.70 ((~hskp13) | (~c3_1(a688))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[323, 320])).
% 0.49/0.70 tff(325,plain,
% 0.49/0.70 (~c3_1(a688)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[324, 319])).
% 0.49/0.70 tff(326,plain,
% 0.49/0.70 (((~hskp13) | c0_1(a688)) <=> ((~hskp13) | c0_1(a688))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(327,axiom,((~hskp13) | c0_1(a688)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.49/0.70 tff(328,plain,
% 0.49/0.70 ((~hskp13) | c0_1(a688)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.49/0.70 tff(329,plain,
% 0.49/0.70 ((~hskp13) | c0_1(a688)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[328, 326])).
% 0.49/0.70 tff(330,plain,
% 0.49/0.70 ((~hskp13) | c0_1(a688)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[329, 326])).
% 0.49/0.70 tff(331,plain,
% 0.49/0.70 ((~hskp13) | c0_1(a688)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[330, 326])).
% 0.49/0.70 tff(332,plain,
% 0.49/0.70 ((~hskp13) | c0_1(a688)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[331, 326])).
% 0.49/0.70 tff(333,plain,
% 0.49/0.70 (c0_1(a688)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[332, 319])).
% 0.49/0.70 tff(334,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(335,plain,
% 0.49/0.70 (((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(336,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[335])).
% 0.49/0.70 tff(337,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[336, 334])).
% 0.49/0.71 tff(338,plain,
% 0.49/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(339,plain,
% 0.49/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.49/0.71 tff(340,plain,
% 0.49/0.71 (~c2_1(a688)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[339, 93, 333, 265, 267, 312, 325, 266, 290, 284, 277])).
% 0.49/0.71 tff(341,plain,
% 0.49/0.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(342,plain,
% 0.49/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[341])).
% 0.49/0.71 tff(343,plain,
% 0.49/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(344,plain,
% 0.49/0.71 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(345,plain,
% 0.49/0.71 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[344])).
% 0.49/0.71 tff(346,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.49/0.71 tff(347,plain,
% 0.49/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.49/0.71 tff(348,plain,
% 0.49/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.49/0.71 tff(349,plain,(
% 0.49/0.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.49/0.71 inference(skolemize,[status(sab)],[348])).
% 0.49/0.71 tff(350,plain,
% 0.49/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[349, 342])).
% 0.49/0.71 tff(351,assumption,(~c2_1(a675)), introduced(assumption)).
% 0.49/0.71 tff(352,assumption,(~c3_1(a680)), introduced(assumption)).
% 0.49/0.71 tff(353,assumption,(~c1_1(a680)), introduced(assumption)).
% 0.49/0.71 tff(354,assumption,(hskp14), introduced(assumption)).
% 0.49/0.71 tff(355,plain,
% 0.49/0.71 (((~hskp14) | (~c3_1(a696))) <=> ((~hskp14) | (~c3_1(a696)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(356,plain,
% 0.49/0.71 (((~c3_1(a696)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a696)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(357,axiom,((~c3_1(a696)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.49/0.71 tff(358,plain,
% 0.49/0.71 ((~hskp14) | (~c3_1(a696))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.49/0.71 tff(359,plain,
% 0.49/0.71 ((~hskp14) | (~c3_1(a696))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[358, 355])).
% 0.49/0.71 tff(360,plain,
% 0.49/0.71 (~c3_1(a696)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[359, 354])).
% 0.49/0.71 tff(361,assumption,(c2_1(a680)), introduced(assumption)).
% 0.49/0.71 tff(362,plain,
% 0.49/0.71 (((~hskp14) | c2_1(a696)) <=> ((~hskp14) | c2_1(a696))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(363,axiom,((~hskp14) | c2_1(a696)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.49/0.71 tff(364,plain,
% 0.49/0.71 ((~hskp14) | c2_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.49/0.71 tff(365,plain,
% 0.49/0.71 ((~hskp14) | c2_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[364, 362])).
% 0.49/0.71 tff(366,plain,
% 0.49/0.71 ((~hskp14) | c2_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[365, 362])).
% 0.49/0.71 tff(367,plain,
% 0.49/0.71 ((~hskp14) | c2_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[366, 362])).
% 0.49/0.71 tff(368,plain,
% 0.49/0.71 ((~hskp14) | c2_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[367, 362])).
% 0.49/0.71 tff(369,plain,
% 0.49/0.71 (c2_1(a696)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[368, 354])).
% 0.49/0.71 tff(370,plain,
% 0.49/0.71 (((~hskp14) | c0_1(a696)) <=> ((~hskp14) | c0_1(a696))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(371,axiom,((~hskp14) | c0_1(a696)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.49/0.71 tff(372,plain,
% 0.49/0.71 ((~hskp14) | c0_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.49/0.71 tff(373,plain,
% 0.49/0.71 ((~hskp14) | c0_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[372, 370])).
% 0.49/0.71 tff(374,plain,
% 0.49/0.71 ((~hskp14) | c0_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[373, 370])).
% 0.49/0.71 tff(375,plain,
% 0.49/0.71 ((~hskp14) | c0_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[374, 370])).
% 0.49/0.71 tff(376,plain,
% 0.49/0.71 ((~hskp14) | c0_1(a696)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[375, 370])).
% 0.49/0.71 tff(377,plain,
% 0.49/0.71 (c0_1(a696)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[376, 354])).
% 0.49/0.71 tff(378,plain,
% 0.49/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(379,plain,
% 0.49/0.71 (((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(380,plain,
% 0.49/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[379])).
% 0.49/0.71 tff(381,plain,
% 0.49/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[380, 378])).
% 0.49/0.71 tff(382,plain,
% 0.49/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(383,plain,
% 0.49/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.49/0.71 tff(384,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[383, 93, 377, 369, 265, 267, 361, 360, 266, 353, 352, 277])).
% 0.49/0.71 tff(385,plain,((~hskp14) | (~c0_1(a683)) | (~c3_1(a683)) | (~c2_1(a680)) | c2_1(a683) | c1_1(a680) | c3_1(a680)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(386,plain,
% 0.49/0.71 (~hskp14),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[385, 312, 267, 265, 266, 290, 284])).
% 0.49/0.71 tff(387,plain,
% 0.49/0.71 (^[U: $i] : refl((hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(388,plain,
% 0.49/0.71 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[387])).
% 0.49/0.71 tff(389,plain,
% 0.49/0.71 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(390,plain,
% 0.49/0.71 (^[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)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(391,plain,
% 0.49/0.71 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[390])).
% 0.49/0.71 tff(392,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.49/0.71 tff(393,plain,
% 0.49/0.71 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.49/0.71 tff(394,plain,
% 0.49/0.71 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[393, 389])).
% 0.49/0.71 tff(395,plain,(
% 0.49/0.71 ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.71 inference(skolemize,[status(sab)],[394])).
% 0.49/0.71 tff(396,plain,
% 0.49/0.71 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[395, 388])).
% 0.49/0.71 tff(397,assumption,(c3_1(a675)), introduced(assumption)).
% 0.49/0.71 tff(398,assumption,(c1_1(a675)), introduced(assumption)).
% 0.49/0.71 tff(399,plain,
% 0.49/0.71 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(400,plain,
% 0.49/0.71 ((hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675))) <=> (hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(401,plain,
% 0.49/0.71 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[400])).
% 0.49/0.71 tff(402,plain,
% 0.49/0.71 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[401, 399])).
% 0.49/0.71 tff(403,plain,
% 0.49/0.71 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(404,plain,
% 0.49/0.71 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.49/0.71 tff(405,plain,
% 0.49/0.71 (hskp17 | hskp14),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[404, 93, 398, 397, 351, 396])).
% 0.49/0.71 tff(406,plain,
% 0.49/0.71 (hskp17),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[405, 386])).
% 0.49/0.71 tff(407,plain,
% 0.49/0.71 (((~hskp17) | (~c0_1(a703))) <=> ((~hskp17) | (~c0_1(a703)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(408,plain,
% 0.49/0.71 (((~c0_1(a703)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a703)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(409,axiom,((~c0_1(a703)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.49/0.71 tff(410,plain,
% 0.49/0.71 ((~hskp17) | (~c0_1(a703))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.49/0.71 tff(411,plain,
% 0.49/0.71 ((~hskp17) | (~c0_1(a703))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.49/0.71 tff(412,plain,
% 0.49/0.71 (~c0_1(a703)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[411, 406])).
% 0.49/0.71 tff(413,plain,
% 0.49/0.71 (((~hskp13) | c1_1(a688)) <=> ((~hskp13) | c1_1(a688))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(414,axiom,((~hskp13) | c1_1(a688)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.49/0.71 tff(415,plain,
% 0.49/0.71 ((~hskp13) | c1_1(a688)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.49/0.71 tff(416,plain,
% 0.49/0.71 ((~hskp13) | c1_1(a688)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[415, 413])).
% 0.49/0.71 tff(417,plain,
% 0.49/0.71 ((~hskp13) | c1_1(a688)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[416, 413])).
% 0.49/0.71 tff(418,plain,
% 0.49/0.71 ((~hskp13) | c1_1(a688)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[417, 413])).
% 0.49/0.71 tff(419,plain,
% 0.49/0.71 ((~hskp13) | c1_1(a688)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[418, 413])).
% 0.49/0.71 tff(420,plain,
% 0.49/0.71 (c1_1(a688)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[419, 319])).
% 0.49/0.71 tff(421,plain,
% 0.49/0.71 (((~hskp17) | c1_1(a703)) <=> ((~hskp17) | c1_1(a703))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(422,axiom,((~hskp17) | c1_1(a703)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.49/0.71 tff(423,plain,
% 0.49/0.71 ((~hskp17) | c1_1(a703)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.49/0.71 tff(424,plain,
% 0.49/0.71 ((~hskp17) | c1_1(a703)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[423, 421])).
% 0.49/0.71 tff(425,plain,
% 0.49/0.71 ((~hskp17) | c1_1(a703)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[424, 421])).
% 0.49/0.71 tff(426,plain,
% 0.49/0.71 ((~hskp17) | c1_1(a703)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[425, 421])).
% 0.49/0.71 tff(427,plain,
% 0.49/0.71 ((~hskp17) | c1_1(a703)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[426, 421])).
% 0.49/0.71 tff(428,plain,
% 0.49/0.71 (c1_1(a703)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[427, 406])).
% 0.49/0.71 tff(429,plain,
% 0.49/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(430,plain,
% 0.49/0.71 (((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(431,plain,
% 0.49/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[430])).
% 0.49/0.71 tff(432,plain,
% 0.49/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[431, 429])).
% 0.49/0.71 tff(433,plain,
% 0.49/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(434,plain,
% 0.49/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.49/0.72 tff(435,plain,
% 0.49/0.72 (c3_1(a703)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[434, 93, 428, 333, 420, 398, 397, 412, 351, 350, 340])).
% 0.49/0.72 tff(436,plain,
% 0.49/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(437,plain,
% 0.49/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[436])).
% 0.49/0.72 tff(438,plain,
% 0.49/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(439,plain,
% 0.49/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(440,plain,
% 0.49/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[439])).
% 0.49/0.72 tff(441,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.49/0.72 tff(442,plain,
% 0.49/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.49/0.72 tff(443,plain,
% 0.49/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[442, 438])).
% 0.49/0.72 tff(444,plain,(
% 0.49/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.72 inference(skolemize,[status(sab)],[443])).
% 0.49/0.72 tff(445,plain,
% 0.49/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[444, 437])).
% 0.49/0.72 tff(446,plain,
% 0.49/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(447,plain,
% 0.49/0.72 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681))) <=> (c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(448,plain,
% 0.49/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.49/0.72 inference(monotonicity,[status(thm)],[447])).
% 0.49/0.72 tff(449,plain,
% 0.49/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.49/0.72 inference(transitivity,[status(thm)],[448, 446])).
% 0.49/0.72 tff(450,plain,
% 0.49/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))),
% 0.49/0.72 inference(quant_inst,[status(thm)],[])).
% 0.49/0.72 tff(451,plain,
% 0.49/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.49/0.72 tff(452,plain,
% 0.49/0.72 ($false),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[451, 93, 428, 265, 267, 292, 412, 266, 291, 445, 294, 435])).
% 0.49/0.72 tff(453,plain,((~hskp9) | (~c0_1(a683)) | (~c3_1(a683)) | (~c3_1(a681)) | c2_1(a683) | c0_1(a681) | (~c1_1(a675)) | (~c3_1(a675)) | c2_1(a675) | (~c2_1(a681))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.72 tff(454,plain,
% 0.49/0.72 (~hskp9),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[453, 262, 267, 265, 266, 261, 259, 258, 257, 263])).
% 0.49/0.72 tff(455,plain,
% 0.49/0.72 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(456,plain,
% 0.49/0.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[455])).
% 0.49/0.72 tff(457,plain,
% 0.49/0.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(458,plain,
% 0.49/0.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(459,plain,
% 0.49/0.72 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[458])).
% 0.49/0.72 tff(460,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.49/0.72 tff(461,plain,
% 0.49/0.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.49/0.72 tff(462,plain,
% 0.49/0.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[461, 457])).
% 0.49/0.72 tff(463,plain,(
% 0.49/0.72 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.72 inference(skolemize,[status(sab)],[462])).
% 0.49/0.72 tff(464,plain,
% 0.49/0.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[463, 456])).
% 0.49/0.72 tff(465,plain,
% 0.49/0.72 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(466,plain,
% 0.49/0.72 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681))) <=> (hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(467,plain,
% 0.49/0.72 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681)))),
% 0.49/0.72 inference(monotonicity,[status(thm)],[466])).
% 0.49/0.72 tff(468,plain,
% 0.49/0.72 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))),
% 0.49/0.72 inference(transitivity,[status(thm)],[467, 465])).
% 0.49/0.72 tff(469,plain,
% 0.49/0.72 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681)))),
% 0.49/0.72 inference(quant_inst,[status(thm)],[])).
% 0.49/0.72 tff(470,plain,
% 0.49/0.72 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.49/0.72 tff(471,plain,
% 0.49/0.72 (hskp9 | hskp8),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[470, 93, 263, 261, 464, 264])).
% 0.49/0.72 tff(472,plain,
% 0.49/0.72 (hskp8),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[471, 454])).
% 0.49/0.72 tff(473,plain,
% 0.49/0.72 (((~hskp8) | (~c0_1(a679))) <=> ((~hskp8) | (~c0_1(a679)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(474,plain,
% 0.49/0.72 (((~c0_1(a679)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a679)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(475,axiom,((~c0_1(a679)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.49/0.72 tff(476,plain,
% 0.49/0.72 ((~hskp8) | (~c0_1(a679))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.49/0.72 tff(477,plain,
% 0.49/0.72 ((~hskp8) | (~c0_1(a679))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[476, 473])).
% 0.49/0.72 tff(478,plain,
% 0.49/0.72 (~c0_1(a679)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[477, 472])).
% 0.49/0.72 tff(479,assumption,(hskp8), introduced(assumption)).
% 0.49/0.72 tff(480,plain,
% 0.49/0.72 (((~hskp8) | c1_1(a679)) <=> ((~hskp8) | c1_1(a679))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(481,axiom,((~hskp8) | c1_1(a679)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.49/0.72 tff(482,plain,
% 0.49/0.72 ((~hskp8) | c1_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.49/0.72 tff(483,plain,
% 0.49/0.72 ((~hskp8) | c1_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[482, 480])).
% 0.49/0.72 tff(484,plain,
% 0.49/0.72 ((~hskp8) | c1_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[483, 480])).
% 0.49/0.72 tff(485,plain,
% 0.49/0.72 ((~hskp8) | c1_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[484, 480])).
% 0.49/0.72 tff(486,plain,
% 0.49/0.72 ((~hskp8) | c1_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[485, 480])).
% 0.49/0.72 tff(487,plain,
% 0.49/0.72 (c1_1(a679)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[486, 479])).
% 0.49/0.72 tff(488,plain,
% 0.49/0.72 (((~hskp8) | c3_1(a679)) <=> ((~hskp8) | c3_1(a679))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(489,axiom,((~hskp8) | c3_1(a679)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.49/0.72 tff(490,plain,
% 0.49/0.72 ((~hskp8) | c3_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.49/0.72 tff(491,plain,
% 0.49/0.72 ((~hskp8) | c3_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[490, 488])).
% 0.49/0.72 tff(492,plain,
% 0.49/0.72 ((~hskp8) | c3_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[491, 488])).
% 0.49/0.72 tff(493,plain,
% 0.49/0.72 ((~hskp8) | c3_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[492, 488])).
% 0.49/0.72 tff(494,plain,
% 0.49/0.72 ((~hskp8) | c3_1(a679)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[493, 488])).
% 0.49/0.72 tff(495,plain,
% 0.49/0.72 (c3_1(a679)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[494, 479])).
% 0.49/0.72 tff(496,assumption,(~c1_1(a681)), introduced(assumption)).
% 0.49/0.72 tff(497,assumption,(~c0_1(a679)), introduced(assumption)).
% 0.49/0.72 tff(498,plain,
% 0.49/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(499,plain,
% 0.49/0.72 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681))) <=> (c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(500,plain,
% 0.49/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683))))),
% 0.49/0.72 inference(monotonicity,[status(thm)],[499])).
% 0.49/0.72 tff(501,plain,
% 0.49/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.49/0.72 inference(transitivity,[status(thm)],[500, 498])).
% 0.49/0.72 tff(502,plain,
% 0.49/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))),
% 0.49/0.72 inference(quant_inst,[status(thm)],[])).
% 0.49/0.72 tff(503,plain,
% 0.49/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.49/0.72 tff(504,plain,
% 0.49/0.72 ((~c1_1(a679)) | (~c3_1(a679))),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[503, 93, 265, 267, 292, 266, 291, 497, 445, 496])).
% 0.49/0.72 tff(505,plain,
% 0.49/0.72 ($false),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[504, 495, 487])).
% 0.49/0.72 tff(506,plain,((~hskp8) | (~c0_1(a683)) | (~c3_1(a683)) | (~c3_1(a681)) | c2_1(a683) | c0_1(a681) | c0_1(a679) | c1_1(a681)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.72 tff(507,plain,
% 0.49/0.72 ($false),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[506, 478, 472, 267, 262, 266, 261, 265, 264])).
% 0.49/0.72 tff(508,plain,((~hskp7) | (~c3_1(a683)) | c2_1(a683) | (~c0_1(a683)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.49/0.72 tff(509,plain,
% 0.49/0.72 ($false),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[508, 255, 249, 158, 241, 12])).
% 0.49/0.72 tff(510,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 0.49/0.72 tff(511,plain,
% 0.49/0.72 (((~hskp28) | c3_1(a678)) <=> ((~hskp28) | c3_1(a678))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(512,axiom,((~hskp28) | c3_1(a678)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.49/0.72 tff(513,plain,
% 0.49/0.72 ((~hskp28) | c3_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.49/0.72 tff(514,plain,
% 0.49/0.72 ((~hskp28) | c3_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[513, 511])).
% 0.49/0.72 tff(515,plain,
% 0.49/0.72 ((~hskp28) | c3_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[514, 511])).
% 0.49/0.72 tff(516,plain,
% 0.49/0.72 ((~hskp28) | c3_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[515, 511])).
% 0.49/0.72 tff(517,plain,
% 0.49/0.72 ((~hskp28) | c3_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[516, 511])).
% 0.49/0.72 tff(518,plain,
% 0.49/0.72 (c3_1(a678)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[517, 510])).
% 0.49/0.72 tff(519,plain,
% 0.49/0.72 (((~hskp28) | c1_1(a678)) <=> ((~hskp28) | c1_1(a678))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(520,axiom,((~hskp28) | c1_1(a678)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.49/0.72 tff(521,plain,
% 0.49/0.72 ((~hskp28) | c1_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.49/0.72 tff(522,plain,
% 0.49/0.72 ((~hskp28) | c1_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[521, 519])).
% 0.49/0.72 tff(523,plain,
% 0.49/0.72 ((~hskp28) | c1_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[522, 519])).
% 0.49/0.72 tff(524,plain,
% 0.49/0.72 ((~hskp28) | c1_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[523, 519])).
% 0.49/0.72 tff(525,plain,
% 0.49/0.72 ((~hskp28) | c1_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[524, 519])).
% 0.49/0.72 tff(526,plain,
% 0.49/0.72 (c1_1(a678)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[525, 510])).
% 0.49/0.72 tff(527,plain,
% 0.49/0.72 (((~hskp28) | c0_1(a678)) <=> ((~hskp28) | c0_1(a678))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(528,axiom,((~hskp28) | c0_1(a678)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.49/0.72 tff(529,plain,
% 0.49/0.72 ((~hskp28) | c0_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.49/0.72 tff(530,plain,
% 0.49/0.72 ((~hskp28) | c0_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[529, 527])).
% 0.49/0.72 tff(531,plain,
% 0.49/0.72 ((~hskp28) | c0_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[530, 527])).
% 0.49/0.72 tff(532,plain,
% 0.49/0.72 ((~hskp28) | c0_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[531, 527])).
% 0.49/0.72 tff(533,plain,
% 0.49/0.72 ((~hskp28) | c0_1(a678)),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[532, 527])).
% 0.49/0.73 tff(534,plain,
% 0.49/0.73 (c0_1(a678)),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[533, 510])).
% 0.49/0.73 tff(535,plain,
% 0.49/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(536,plain,
% 0.49/0.73 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))) <=> ((~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(537,plain,
% 0.49/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678))))),
% 0.49/0.73 inference(monotonicity,[status(thm)],[536])).
% 0.49/0.73 tff(538,plain,
% 0.49/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))),
% 0.49/0.73 inference(transitivity,[status(thm)],[537, 535])).
% 0.49/0.73 tff(539,plain,
% 0.49/0.73 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 0.49/0.73 inference(quant_inst,[status(thm)],[])).
% 0.49/0.73 tff(540,plain,
% 0.49/0.73 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.49/0.73 tff(541,plain,
% 0.49/0.73 ($false),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[540, 93, 534, 526, 518, 11, 1])).
% 0.49/0.73 tff(542,plain,(~c2_1(a678)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.73 tff(543,assumption,(~hskp9), introduced(assumption)).
% 0.49/0.73 tff(544,assumption,(~hskp2), introduced(assumption)).
% 0.49/0.73 tff(545,plain,
% 0.49/0.73 (^[U: $i] : refl((hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.49/0.73 inference(bind,[status(th)],[])).
% 0.49/0.73 tff(546,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.49/0.73 inference(quant_intro,[status(thm)],[545])).
% 0.49/0.73 tff(547,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(548,plain,
% 0.49/0.73 (^[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)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp2))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.49/0.73 inference(bind,[status(th)],[])).
% 0.49/0.73 tff(549,plain,
% 0.49/0.73 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.49/0.73 inference(quant_intro,[status(thm)],[548])).
% 0.49/0.73 tff(550,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.49/0.73 tff(551,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.49/0.73 tff(552,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[551, 547])).
% 0.49/0.73 tff(553,plain,(
% 0.49/0.73 ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.49/0.73 inference(skolemize,[status(sab)],[552])).
% 0.49/0.73 tff(554,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[553, 546])).
% 0.49/0.73 tff(555,plain,
% 0.49/0.73 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.49/0.73 inference(bind,[status(th)],[])).
% 0.49/0.73 tff(556,plain,
% 0.49/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.73 inference(quant_intro,[status(thm)],[555])).
% 0.49/0.73 tff(557,plain,
% 0.49/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(558,plain,
% 0.49/0.73 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_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(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.49/0.73 inference(bind,[status(th)],[])).
% 0.49/0.73 tff(559,plain,
% 0.49/0.73 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.73 inference(quant_intro,[status(thm)],[558])).
% 0.49/0.73 tff(560,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.49/0.73 tff(561,plain,
% 0.49/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.49/0.73 tff(562,plain,
% 0.49/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[561, 557])).
% 0.49/0.73 tff(563,plain,(
% 0.49/0.73 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.73 inference(skolemize,[status(sab)],[562])).
% 0.49/0.73 tff(564,plain,
% 0.49/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[563, 556])).
% 0.49/0.73 tff(565,assumption,(~hskp11), introduced(assumption)).
% 0.49/0.73 tff(566,assumption,(~hskp5), introduced(assumption)).
% 0.49/0.73 tff(567,plain,
% 0.49/0.73 (^[U: $i] : refl((hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 0.49/0.73 inference(bind,[status(th)],[])).
% 0.49/0.73 tff(568,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.49/0.73 inference(quant_intro,[status(thm)],[567])).
% 0.49/0.73 tff(569,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(570,plain,
% 0.49/0.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5) <=> ((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp5))), rewrite(((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp5) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.49/0.73 inference(bind,[status(th)],[])).
% 0.49/0.73 tff(571,plain,
% 0.49/0.73 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.49/0.73 inference(quant_intro,[status(thm)],[570])).
% 0.49/0.73 tff(572,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.49/0.73 tff(573,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.49/0.73 tff(574,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[573, 569])).
% 0.49/0.73 tff(575,plain,(
% 0.49/0.73 ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.49/0.73 inference(skolemize,[status(sab)],[574])).
% 0.49/0.73 tff(576,plain,
% 0.49/0.73 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[575, 568])).
% 0.49/0.73 tff(577,plain,
% 0.49/0.73 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(578,plain,
% 0.49/0.73 ((hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678))) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(579,plain,
% 0.49/0.73 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678))))),
% 0.49/0.73 inference(monotonicity,[status(thm)],[578])).
% 0.49/0.73 tff(580,plain,
% 0.49/0.73 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))),
% 0.49/0.73 inference(transitivity,[status(thm)],[579, 577])).
% 0.49/0.73 tff(581,plain,
% 0.49/0.73 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678)))),
% 0.49/0.73 inference(quant_inst,[status(thm)],[])).
% 0.49/0.73 tff(582,plain,
% 0.49/0.73 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.49/0.73 tff(583,plain,
% 0.49/0.73 (hskp9 | hskp5 | (~c2_1(a678))),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[582, 93, 534, 526, 576])).
% 0.49/0.73 tff(584,plain,
% 0.49/0.73 (~c2_1(a678)),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[583, 543, 566])).
% 0.49/0.73 tff(585,plain,
% 0.49/0.73 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(586,plain,
% 0.49/0.73 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696)))),
% 0.49/0.73 inference(quant_inst,[status(thm)],[])).
% 0.49/0.73 tff(587,plain,
% 0.49/0.73 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.49/0.73 tff(588,plain,
% 0.49/0.73 (~c1_1(a696)),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[587, 93, 543, 566, 377, 369, 576])).
% 0.49/0.73 tff(589,plain,
% 0.49/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(590,plain,
% 0.49/0.73 (((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696)) <=> (c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(591,plain,
% 0.49/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696)))),
% 0.49/0.73 inference(monotonicity,[status(thm)],[590])).
% 0.49/0.73 tff(592,plain,
% 0.49/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))),
% 0.49/0.73 inference(transitivity,[status(thm)],[591, 589])).
% 0.49/0.73 tff(593,plain,
% 0.49/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696))),
% 0.49/0.73 inference(quant_inst,[status(thm)],[])).
% 0.49/0.73 tff(594,plain,
% 0.49/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696)),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.49/0.73 tff(595,plain,
% 0.49/0.73 ($false),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[594, 93, 534, 518, 377, 369, 360, 277, 584, 588])).
% 0.49/0.73 tff(596,plain,((~hskp14) | hskp9 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.49/0.73 tff(597,plain,
% 0.49/0.73 (~hskp14),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[596, 543, 566])).
% 0.49/0.73 tff(598,plain,
% 0.49/0.73 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(599,plain,
% 0.49/0.73 ((hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678))) <=> (hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))),
% 0.49/0.73 inference(rewrite,[status(thm)],[])).
% 0.49/0.73 tff(600,plain,
% 0.49/0.73 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678))))),
% 0.49/0.73 inference(monotonicity,[status(thm)],[599])).
% 0.49/0.73 tff(601,plain,
% 0.49/0.73 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))),
% 0.49/0.73 inference(transitivity,[status(thm)],[600, 598])).
% 0.49/0.73 tff(602,plain,
% 0.49/0.73 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)))),
% 0.49/0.73 inference(quant_inst,[status(thm)],[])).
% 0.49/0.73 tff(603,plain,
% 0.49/0.73 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678))),
% 0.49/0.73 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.49/0.73 tff(604,plain,
% 0.49/0.73 (hskp17 | hskp14 | c2_1(a678)),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[603, 93, 526, 518, 396])).
% 0.49/0.73 tff(605,plain,
% 0.49/0.73 (hskp17),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[604, 597, 584])).
% 0.49/0.73 tff(606,plain,
% 0.49/0.73 (~c0_1(a703)),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[411, 605])).
% 0.49/0.73 tff(607,plain,
% 0.49/0.73 (c1_1(a703)),
% 0.49/0.73 inference(unit_resolution,[status(thm)],[427, 605])).
% 0.49/0.73 tff(608,plain,
% 0.49/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(609,plain,
% 0.58/0.74 (((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(610,plain,
% 0.58/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703))))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[609])).
% 0.58/0.74 tff(611,plain,
% 0.58/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.74 inference(transitivity,[status(thm)],[610, 608])).
% 0.58/0.74 tff(612,plain,
% 0.58/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(613,plain,
% 0.58/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.58/0.74 tff(614,plain,
% 0.58/0.74 (c3_1(a703)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[613, 93, 534, 526, 518, 607, 606, 350, 584])).
% 0.58/0.74 tff(615,plain,
% 0.58/0.74 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(616,plain,
% 0.58/0.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[615])).
% 0.58/0.74 tff(617,plain,
% 0.58/0.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(618,plain,
% 0.58/0.74 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(619,plain,
% 0.58/0.74 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[618])).
% 0.58/0.74 tff(620,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.58/0.74 tff(621,plain,
% 0.58/0.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.58/0.74 tff(622,plain,
% 0.58/0.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[621, 617])).
% 0.58/0.74 tff(623,plain,(
% 0.58/0.74 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.74 inference(skolemize,[status(sab)],[622])).
% 0.58/0.74 tff(624,plain,
% 0.58/0.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[623, 616])).
% 0.58/0.74 tff(625,plain,
% 0.58/0.74 (((~hskp17) | (~c2_1(a703))) <=> ((~hskp17) | (~c2_1(a703)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(626,plain,
% 0.58/0.74 (((~c2_1(a703)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a703)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(627,axiom,((~c2_1(a703)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.58/0.74 tff(628,plain,
% 0.58/0.74 ((~hskp17) | (~c2_1(a703))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.58/0.74 tff(629,plain,
% 0.58/0.74 ((~hskp17) | (~c2_1(a703))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[628, 625])).
% 0.58/0.74 tff(630,plain,
% 0.58/0.74 (~c2_1(a703)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[629, 605])).
% 0.58/0.74 tff(631,plain,
% 0.58/0.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(632,plain,
% 0.58/0.74 ((hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703))) <=> (hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(633,plain,
% 0.58/0.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703))))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[632])).
% 0.58/0.74 tff(634,plain,
% 0.58/0.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))),
% 0.58/0.74 inference(transitivity,[status(thm)],[633, 631])).
% 0.58/0.74 tff(635,plain,
% 0.58/0.74 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703)))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(636,plain,
% 0.58/0.74 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.58/0.74 tff(637,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[636, 93, 43, 534, 518, 606, 630, 624, 584, 614])).
% 0.58/0.74 tff(638,plain,(hskp9 | hskp7 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(639,plain,
% 0.58/0.74 (hskp9),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[638, 566, 43])).
% 0.58/0.74 tff(640,plain,
% 0.58/0.74 (~c3_1(a680)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[283, 639])).
% 0.58/0.74 tff(641,plain,
% 0.58/0.74 (~c1_1(a680)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[289, 639])).
% 0.58/0.74 tff(642,plain,
% 0.58/0.74 (hskp25),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[113, 566, 43])).
% 0.58/0.74 tff(643,plain,
% 0.58/0.74 (~c3_1(a760)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[119, 642])).
% 0.58/0.74 tff(644,plain,
% 0.58/0.74 (~c1_1(a760)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[148, 642])).
% 0.58/0.74 tff(645,plain,
% 0.58/0.74 (~c0_1(a760)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[125, 642])).
% 0.58/0.74 tff(646,plain,
% 0.58/0.74 (c2_1(a680)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[311, 639])).
% 0.58/0.74 tff(647,plain,
% 0.58/0.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(648,plain,
% 0.58/0.74 ((hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760)) <=> (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(649,plain,
% 0.58/0.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680))))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[648])).
% 0.58/0.74 tff(650,plain,
% 0.58/0.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))),
% 0.58/0.74 inference(transitivity,[status(thm)],[649, 647])).
% 0.58/0.74 tff(651,plain,
% 0.58/0.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(652,plain,
% 0.58/0.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.58/0.74 tff(653,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[652, 93, 566, 646, 645, 644, 643, 641, 640, 143])).
% 0.58/0.74 tff(654,plain,(hskp5 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(655,plain,
% 0.58/0.74 (hskp5),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[654, 43])).
% 0.58/0.74 tff(656,plain,
% 0.58/0.74 (~c3_1(a673)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[49, 655])).
% 0.58/0.74 tff(657,plain,
% 0.58/0.74 (~c0_1(a673)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[61, 655])).
% 0.58/0.74 tff(658,plain,
% 0.58/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(659,plain,
% 0.58/0.74 (((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673))) <=> (c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(660,plain,
% 0.58/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673))))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[659])).
% 0.58/0.74 tff(661,plain,
% 0.58/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))),
% 0.58/0.74 inference(transitivity,[status(thm)],[660, 658])).
% 0.58/0.74 tff(662,plain,
% 0.58/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(663,plain,
% 0.58/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.58/0.74 tff(664,plain,
% 0.58/0.74 (~c1_1(a673)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[663, 93, 534, 526, 518, 657, 656, 350, 542])).
% 0.58/0.74 tff(665,plain,
% 0.58/0.74 (~c2_1(a673)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[55, 655])).
% 0.58/0.74 tff(666,assumption,(~c1_1(a673)), introduced(assumption)).
% 0.58/0.74 tff(667,plain,
% 0.58/0.74 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(668,plain,
% 0.58/0.74 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[667])).
% 0.58/0.74 tff(669,plain,
% 0.58/0.74 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(670,plain,
% 0.58/0.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(671,plain,
% 0.58/0.74 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[670])).
% 0.58/0.74 tff(672,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.58/0.74 tff(673,plain,
% 0.58/0.74 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.58/0.74 tff(674,plain,
% 0.58/0.74 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[673, 669])).
% 0.58/0.74 tff(675,plain,(
% 0.58/0.74 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.58/0.74 inference(skolemize,[status(sab)],[674])).
% 0.58/0.74 tff(676,plain,
% 0.58/0.74 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[675, 668])).
% 0.58/0.74 tff(677,assumption,(~c2_1(a673)), introduced(assumption)).
% 0.58/0.74 tff(678,assumption,(~c0_1(a673)), introduced(assumption)).
% 0.58/0.74 tff(679,plain,
% 0.58/0.74 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(680,plain,
% 0.58/0.74 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673)) <=> (hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(681,plain,
% 0.58/0.74 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673)))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[680])).
% 0.58/0.74 tff(682,plain,
% 0.58/0.74 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))),
% 0.58/0.74 inference(transitivity,[status(thm)],[681, 679])).
% 0.58/0.74 tff(683,plain,
% 0.58/0.74 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(684,plain,
% 0.58/0.74 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.58/0.74 tff(685,plain,
% 0.58/0.74 (hskp2 | hskp1),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[684, 93, 678, 677, 676, 666])).
% 0.58/0.74 tff(686,plain,
% 0.58/0.74 (hskp1),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[685, 544])).
% 0.58/0.74 tff(687,plain,
% 0.58/0.74 (((~hskp1) | (~c2_1(a669))) <=> ((~hskp1) | (~c2_1(a669)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(688,plain,
% 0.58/0.74 (((~c2_1(a669)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a669)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(689,axiom,((~c2_1(a669)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.58/0.74 tff(690,plain,
% 0.58/0.74 ((~hskp1) | (~c2_1(a669))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.58/0.74 tff(691,plain,
% 0.58/0.74 ((~hskp1) | (~c2_1(a669))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[690, 687])).
% 0.58/0.74 tff(692,plain,
% 0.58/0.74 (~c2_1(a669)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[691, 686])).
% 0.58/0.74 tff(693,plain,
% 0.58/0.74 (((~hskp1) | (~c1_1(a669))) <=> ((~hskp1) | (~c1_1(a669)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(694,plain,
% 0.58/0.74 (((~c1_1(a669)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a669)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(695,axiom,((~c1_1(a669)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.58/0.74 tff(696,plain,
% 0.58/0.74 ((~hskp1) | (~c1_1(a669))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.58/0.74 tff(697,plain,
% 0.58/0.74 ((~hskp1) | (~c1_1(a669))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[696, 693])).
% 0.58/0.74 tff(698,plain,
% 0.58/0.74 (~c1_1(a669)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[697, 686])).
% 0.58/0.74 tff(699,plain,
% 0.58/0.74 (((~hskp1) | c0_1(a669)) <=> ((~hskp1) | c0_1(a669))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(700,axiom,((~hskp1) | c0_1(a669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.58/0.74 tff(701,plain,
% 0.58/0.74 ((~hskp1) | c0_1(a669)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.58/0.74 tff(702,plain,
% 0.58/0.74 ((~hskp1) | c0_1(a669)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[701, 699])).
% 0.58/0.74 tff(703,plain,
% 0.58/0.74 ((~hskp1) | c0_1(a669)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[702, 699])).
% 0.58/0.74 tff(704,plain,
% 0.58/0.74 ((~hskp1) | c0_1(a669)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[703, 699])).
% 0.58/0.74 tff(705,plain,
% 0.58/0.74 ((~hskp1) | c0_1(a669)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[704, 699])).
% 0.58/0.75 tff(706,plain,
% 0.58/0.75 (c0_1(a669)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[705, 686])).
% 0.58/0.75 tff(707,plain,
% 0.58/0.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(708,plain,
% 0.58/0.75 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669))) <=> (hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(709,plain,
% 0.58/0.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[708])).
% 0.58/0.75 tff(710,plain,
% 0.58/0.75 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))),
% 0.58/0.75 inference(transitivity,[status(thm)],[709, 707])).
% 0.58/0.75 tff(711,plain,
% 0.58/0.75 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669)))),
% 0.58/0.75 inference(quant_inst,[status(thm)],[])).
% 0.58/0.75 tff(712,plain,
% 0.58/0.75 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.58/0.75 tff(713,plain,
% 0.58/0.75 ($false),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[712, 93, 543, 544, 706, 698, 692, 554])).
% 0.58/0.75 tff(714,plain,(hskp2 | hskp9 | c0_1(a673) | c2_1(a673) | c1_1(a673)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.75 tff(715,plain,
% 0.58/0.75 (hskp2),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[714, 543, 657, 665, 664])).
% 0.58/0.75 tff(716,plain,
% 0.58/0.75 (((~hskp2) | (~c1_1(a670))) <=> ((~hskp2) | (~c1_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(717,plain,
% 0.58/0.75 (((~c1_1(a670)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(718,axiom,((~c1_1(a670)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.58/0.75 tff(719,plain,
% 0.58/0.75 ((~hskp2) | (~c1_1(a670))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.58/0.75 tff(720,plain,
% 0.58/0.75 ((~hskp2) | (~c1_1(a670))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[719, 716])).
% 0.58/0.75 tff(721,plain,
% 0.58/0.75 (~c1_1(a670)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[720, 715])).
% 0.58/0.75 tff(722,plain,
% 0.58/0.75 (((~hskp2) | (~c0_1(a670))) <=> ((~hskp2) | (~c0_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(723,plain,
% 0.58/0.75 (((~c0_1(a670)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(724,axiom,((~c0_1(a670)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.58/0.75 tff(725,plain,
% 0.58/0.75 ((~hskp2) | (~c0_1(a670))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.58/0.75 tff(726,plain,
% 0.58/0.75 ((~hskp2) | (~c0_1(a670))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[725, 722])).
% 0.58/0.75 tff(727,plain,
% 0.58/0.75 (~c0_1(a670)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[726, 715])).
% 0.58/0.75 tff(728,assumption,(~c2_1(a678)), introduced(assumption)).
% 0.58/0.75 tff(729,assumption,(hskp2), introduced(assumption)).
% 0.58/0.75 tff(730,plain,
% 0.58/0.75 (~c0_1(a670)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[726, 729])).
% 0.58/0.75 tff(731,plain,
% 0.58/0.75 (((~hskp2) | c3_1(a670)) <=> ((~hskp2) | c3_1(a670))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(732,axiom,((~hskp2) | c3_1(a670)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.58/0.75 tff(733,plain,
% 0.58/0.75 ((~hskp2) | c3_1(a670)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.58/0.75 tff(734,plain,
% 0.58/0.75 ((~hskp2) | c3_1(a670)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[733, 731])).
% 0.58/0.75 tff(735,plain,
% 0.58/0.75 ((~hskp2) | c3_1(a670)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[734, 731])).
% 0.58/0.75 tff(736,plain,
% 0.58/0.75 ((~hskp2) | c3_1(a670)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[735, 731])).
% 0.58/0.75 tff(737,plain,
% 0.58/0.75 ((~hskp2) | c3_1(a670)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[736, 731])).
% 0.58/0.75 tff(738,plain,
% 0.58/0.75 (c3_1(a670)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[737, 729])).
% 0.58/0.75 tff(739,plain,
% 0.58/0.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(740,plain,
% 0.58/0.75 ((hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670))) <=> (hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(741,plain,
% 0.58/0.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[740])).
% 0.58/0.75 tff(742,plain,
% 0.58/0.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.75 inference(transitivity,[status(thm)],[741, 739])).
% 0.58/0.75 tff(743,plain,
% 0.58/0.75 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.75 inference(quant_inst,[status(thm)],[])).
% 0.58/0.75 tff(744,plain,
% 0.58/0.75 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.58/0.75 tff(745,plain,
% 0.58/0.75 (c2_1(a670)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[744, 93, 43, 534, 518, 738, 730, 624, 728])).
% 0.58/0.75 tff(746,plain,
% 0.58/0.75 (~c1_1(a670)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[720, 729])).
% 0.58/0.75 tff(747,assumption,(~hskp8), introduced(assumption)).
% 0.58/0.75 tff(748,plain,
% 0.58/0.75 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(749,plain,
% 0.58/0.75 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670))) <=> (hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(750,plain,
% 0.58/0.75 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[749])).
% 0.58/0.75 tff(751,plain,
% 0.58/0.75 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))),
% 0.58/0.75 inference(transitivity,[status(thm)],[750, 748])).
% 0.58/0.75 tff(752,plain,
% 0.58/0.75 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)))),
% 0.58/0.75 inference(quant_inst,[status(thm)],[])).
% 0.58/0.75 tff(753,plain,
% 0.58/0.75 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.58/0.75 tff(754,plain,
% 0.58/0.75 ($false),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[753, 93, 543, 747, 730, 746, 464, 745])).
% 0.58/0.75 tff(755,plain,((~hskp2) | hskp9 | hskp8 | hskp7 | c2_1(a678)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.75 tff(756,plain,
% 0.58/0.75 ((~hskp2) | hskp9 | hskp8 | hskp7),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[755, 542])).
% 0.58/0.75 tff(757,plain,
% 0.58/0.75 (hskp8),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[756, 715, 543, 43])).
% 0.58/0.75 tff(758,plain,
% 0.58/0.75 (~c0_1(a679)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[477, 757])).
% 0.58/0.75 tff(759,plain,
% 0.58/0.75 (c3_1(a670)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[737, 715])).
% 0.58/0.75 tff(760,plain,
% 0.58/0.75 (c3_1(a679)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[494, 757])).
% 0.58/0.75 tff(761,plain,
% 0.58/0.75 (c1_1(a679)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[486, 757])).
% 0.58/0.75 tff(762,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(763,plain,
% 0.58/0.75 (((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(764,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[763])).
% 0.58/0.75 tff(765,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))),
% 0.58/0.75 inference(transitivity,[status(thm)],[764, 762])).
% 0.58/0.75 tff(766,plain,
% 0.58/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.58/0.75 inference(quant_inst,[status(thm)],[])).
% 0.58/0.75 tff(767,plain,
% 0.58/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.58/0.75 tff(768,plain,
% 0.58/0.75 ($false),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[767, 93, 534, 518, 761, 760, 759, 758, 727, 721, 445, 542])).
% 0.58/0.75 tff(769,plain,(hskp9 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.58/0.75 tff(770,plain,
% 0.58/0.75 (hskp9),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[769, 43])).
% 0.58/0.75 tff(771,plain,
% 0.58/0.75 (~c3_1(a680)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[283, 770])).
% 0.58/0.75 tff(772,plain,
% 0.58/0.75 (~c1_1(a680)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[289, 770])).
% 0.58/0.75 tff(773,assumption,(~hskp14), introduced(assumption)).
% 0.58/0.75 tff(774,plain,
% 0.58/0.75 (hskp17),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[604, 728, 773])).
% 0.58/0.75 tff(775,plain,
% 0.58/0.75 (~c0_1(a703)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[411, 774])).
% 0.58/0.75 tff(776,plain,
% 0.58/0.75 (c1_1(a703)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[427, 774])).
% 0.58/0.75 tff(777,plain,
% 0.58/0.75 (c3_1(a703)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[613, 93, 534, 526, 518, 776, 775, 350, 728])).
% 0.58/0.75 tff(778,plain,
% 0.58/0.75 (~c2_1(a703)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[629, 774])).
% 0.58/0.75 tff(779,plain,
% 0.58/0.75 ($false),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[636, 93, 43, 534, 518, 775, 778, 624, 728, 777])).
% 0.58/0.75 tff(780,plain,(c2_1(a678) | hskp7 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.58/0.75 tff(781,plain,
% 0.58/0.75 (hskp7 | hskp14),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[780, 542])).
% 0.58/0.75 tff(782,plain,
% 0.58/0.75 (hskp14),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[781, 43])).
% 0.58/0.75 tff(783,plain,
% 0.58/0.75 (~c3_1(a696)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[359, 782])).
% 0.58/0.75 tff(784,plain,
% 0.58/0.75 (c2_1(a680)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[311, 770])).
% 0.58/0.75 tff(785,plain,
% 0.58/0.75 (c2_1(a696)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[368, 782])).
% 0.58/0.75 tff(786,plain,
% 0.58/0.75 (c0_1(a696)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[376, 782])).
% 0.58/0.75 tff(787,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(788,plain,
% 0.58/0.75 (((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(789,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[788])).
% 0.58/0.75 tff(790,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.58/0.75 inference(transitivity,[status(thm)],[789, 787])).
% 0.58/0.75 tff(791,plain,
% 0.58/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.58/0.75 inference(quant_inst,[status(thm)],[])).
% 0.58/0.75 tff(792,plain,
% 0.58/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.58/0.75 tff(793,plain,
% 0.58/0.75 ($false),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[792, 93, 534, 518, 786, 785, 784, 783, 772, 771, 277, 542])).
% 0.58/0.75 tff(794,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 0.58/0.75 tff(795,plain,
% 0.58/0.75 (~c2_1(a675)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[163, 794])).
% 0.58/0.75 tff(796,assumption,(hskp17), introduced(assumption)).
% 0.58/0.75 tff(797,plain,
% 0.58/0.75 (~c0_1(a703)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[411, 796])).
% 0.58/0.75 tff(798,plain,
% 0.58/0.75 (c3_1(a675)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[171, 794])).
% 0.58/0.75 tff(799,plain,
% 0.58/0.75 (c1_1(a675)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[179, 794])).
% 0.58/0.75 tff(800,plain,
% 0.58/0.75 (c1_1(a703)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[427, 796])).
% 0.58/0.75 tff(801,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(802,plain,
% 0.58/0.75 (((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(803,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[802])).
% 0.58/0.75 tff(804,plain,
% 0.58/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.76 inference(transitivity,[status(thm)],[803, 801])).
% 0.58/0.76 tff(805,plain,
% 0.58/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.76 inference(quant_inst,[status(thm)],[])).
% 0.58/0.76 tff(806,plain,
% 0.58/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.58/0.76 tff(807,plain,
% 0.58/0.76 (c3_1(a703)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[806, 93, 534, 526, 800, 799, 798, 797, 795, 350, 542])).
% 0.58/0.76 tff(808,plain,
% 0.58/0.76 (~c2_1(a703)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[629, 796])).
% 0.58/0.76 tff(809,plain,
% 0.58/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(810,plain,
% 0.58/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[809])).
% 0.58/0.76 tff(811,plain,
% 0.58/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(812,plain,
% 0.58/0.76 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(813,plain,
% 0.58/0.76 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[812])).
% 0.58/0.76 tff(814,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 0.58/0.76 tff(815,plain,
% 0.58/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.58/0.76 tff(816,plain,
% 0.58/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[815, 811])).
% 0.58/0.76 tff(817,plain,(
% 0.58/0.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.76 inference(skolemize,[status(sab)],[816])).
% 0.58/0.76 tff(818,plain,
% 0.58/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[817, 810])).
% 0.58/0.76 tff(819,assumption,(hskp16), introduced(assumption)).
% 0.58/0.76 tff(820,plain,
% 0.58/0.76 (((~hskp16) | (~c1_1(a702))) <=> ((~hskp16) | (~c1_1(a702)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(821,plain,
% 0.58/0.76 (((~c1_1(a702)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a702)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(822,axiom,((~c1_1(a702)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.58/0.76 tff(823,plain,
% 0.58/0.76 ((~hskp16) | (~c1_1(a702))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.58/0.76 tff(824,plain,
% 0.58/0.76 ((~hskp16) | (~c1_1(a702))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[823, 820])).
% 0.58/0.76 tff(825,plain,
% 0.58/0.76 (~c1_1(a702)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[824, 819])).
% 0.58/0.76 tff(826,assumption,(~c2_1(a703)), introduced(assumption)).
% 0.58/0.76 tff(827,assumption,(~c0_1(a703)), introduced(assumption)).
% 0.58/0.76 tff(828,plain,
% 0.58/0.76 (((~hskp16) | c3_1(a702)) <=> ((~hskp16) | c3_1(a702))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(829,axiom,((~hskp16) | c3_1(a702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.58/0.76 tff(830,plain,
% 0.58/0.76 ((~hskp16) | c3_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.58/0.76 tff(831,plain,
% 0.58/0.76 ((~hskp16) | c3_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[830, 828])).
% 0.58/0.76 tff(832,plain,
% 0.58/0.76 ((~hskp16) | c3_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[831, 828])).
% 0.58/0.76 tff(833,plain,
% 0.58/0.76 ((~hskp16) | c3_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[832, 828])).
% 0.58/0.76 tff(834,plain,
% 0.58/0.76 ((~hskp16) | c3_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[833, 828])).
% 0.58/0.76 tff(835,plain,
% 0.58/0.76 (c3_1(a702)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[834, 819])).
% 0.58/0.76 tff(836,plain,
% 0.58/0.76 (((~hskp16) | c2_1(a702)) <=> ((~hskp16) | c2_1(a702))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(837,axiom,((~hskp16) | c2_1(a702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.58/0.76 tff(838,plain,
% 0.58/0.76 ((~hskp16) | c2_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[837, 836])).
% 0.58/0.76 tff(839,plain,
% 0.58/0.76 ((~hskp16) | c2_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[838, 836])).
% 0.58/0.76 tff(840,plain,
% 0.58/0.76 ((~hskp16) | c2_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[839, 836])).
% 0.58/0.76 tff(841,plain,
% 0.58/0.76 ((~hskp16) | c2_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[840, 836])).
% 0.58/0.76 tff(842,plain,
% 0.58/0.76 ((~hskp16) | c2_1(a702)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[841, 836])).
% 0.58/0.76 tff(843,plain,
% 0.58/0.76 (c2_1(a702)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[842, 819])).
% 0.58/0.76 tff(844,assumption,(c1_1(a703)), introduced(assumption)).
% 0.58/0.76 tff(845,plain,
% 0.58/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(846,plain,
% 0.58/0.76 (((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(847,plain,
% 0.58/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703))))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[846])).
% 0.58/0.76 tff(848,plain,
% 0.58/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))),
% 0.58/0.76 inference(transitivity,[status(thm)],[847, 845])).
% 0.58/0.76 tff(849,plain,
% 0.58/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))),
% 0.58/0.76 inference(quant_inst,[status(thm)],[])).
% 0.58/0.76 tff(850,plain,
% 0.58/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.58/0.76 tff(851,plain,
% 0.58/0.76 (~c0_1(a702)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[850, 93, 844, 843, 835, 827, 826, 825, 818])).
% 0.58/0.76 tff(852,plain,
% 0.58/0.76 (c3_1(a703)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[806, 93, 534, 526, 844, 799, 798, 827, 795, 350, 542])).
% 0.58/0.76 tff(853,plain,
% 0.58/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(854,plain,
% 0.58/0.76 (((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702))) <=> (c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(855,plain,
% 0.58/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[854])).
% 0.58/0.76 tff(856,plain,
% 0.58/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.58/0.76 inference(transitivity,[status(thm)],[855, 853])).
% 0.58/0.76 tff(857,plain,
% 0.58/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))),
% 0.58/0.76 inference(quant_inst,[status(thm)],[])).
% 0.58/0.76 tff(858,plain,
% 0.58/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[857, 856])).
% 0.58/0.76 tff(859,plain,
% 0.58/0.76 ($false),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[858, 93, 534, 518, 844, 835, 827, 825, 445, 542, 852, 851])).
% 0.58/0.76 tff(860,plain,((~hskp16) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.76 tff(861,plain,
% 0.58/0.76 (~hskp16),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[860, 800, 797, 808])).
% 0.58/0.76 tff(862,plain,
% 0.58/0.76 ((hskp21 | hskp11 | hskp2) <=> (hskp21 | hskp11 | hskp2)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(863,plain,
% 0.58/0.76 (((hskp11 | hskp21) | hskp2) <=> (hskp21 | hskp11 | hskp2)),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(864,axiom,((hskp11 | hskp21) | hskp2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.58/0.76 tff(865,plain,
% 0.58/0.76 (hskp21 | hskp11 | hskp2),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.58/0.76 tff(866,plain,
% 0.58/0.76 (hskp21 | hskp11 | hskp2),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[865, 862])).
% 0.58/0.76 tff(867,plain,
% 0.58/0.76 (hskp21 | hskp11 | hskp2),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[866, 862])).
% 0.58/0.76 tff(868,plain,
% 0.58/0.76 (hskp21 | hskp11 | hskp2),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[867, 862])).
% 0.58/0.76 tff(869,plain,
% 0.58/0.76 (hskp21 | hskp11 | hskp2),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[868, 862])).
% 0.58/0.76 tff(870,plain,
% 0.58/0.76 (hskp21),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[869, 544, 565])).
% 0.58/0.76 tff(871,plain,
% 0.58/0.76 (((~hskp21) | (~c2_1(a715))) <=> ((~hskp21) | (~c2_1(a715)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(872,plain,
% 0.58/0.76 (((~c2_1(a715)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a715)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(873,axiom,((~c2_1(a715)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.58/0.76 tff(874,plain,
% 0.58/0.76 ((~hskp21) | (~c2_1(a715))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.58/0.76 tff(875,plain,
% 0.58/0.76 ((~hskp21) | (~c2_1(a715))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[874, 871])).
% 0.58/0.76 tff(876,plain,
% 0.58/0.76 (~c2_1(a715)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[875, 870])).
% 0.58/0.76 tff(877,plain,
% 0.58/0.76 (((~hskp21) | c0_1(a715)) <=> ((~hskp21) | c0_1(a715))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(878,axiom,((~hskp21) | c0_1(a715)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.58/0.76 tff(879,plain,
% 0.58/0.76 ((~hskp21) | c0_1(a715)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[878, 877])).
% 0.58/0.76 tff(880,plain,
% 0.58/0.76 ((~hskp21) | c0_1(a715)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[879, 877])).
% 0.58/0.76 tff(881,plain,
% 0.58/0.76 ((~hskp21) | c0_1(a715)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[880, 877])).
% 0.58/0.76 tff(882,plain,
% 0.58/0.76 ((~hskp21) | c0_1(a715)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[881, 877])).
% 0.58/0.76 tff(883,plain,
% 0.58/0.76 ((~hskp21) | c0_1(a715)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[882, 877])).
% 0.58/0.76 tff(884,plain,
% 0.58/0.76 (c0_1(a715)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[883, 870])).
% 0.58/0.76 tff(885,plain,
% 0.58/0.76 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(886,plain,
% 0.58/0.76 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715))) <=> (hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(887,plain,
% 0.58/0.76 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715)))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[886])).
% 0.58/0.76 tff(888,plain,
% 0.58/0.76 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))),
% 0.58/0.76 inference(transitivity,[status(thm)],[887, 885])).
% 0.58/0.76 tff(889,plain,
% 0.58/0.76 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715)))),
% 0.58/0.76 inference(quant_inst,[status(thm)],[])).
% 0.58/0.76 tff(890,plain,
% 0.58/0.76 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.58/0.76 tff(891,plain,
% 0.58/0.76 (c1_1(a715)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[890, 93, 543, 544, 884, 876, 554])).
% 0.58/0.76 tff(892,plain,
% 0.58/0.76 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(893,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[892])).
% 0.58/0.76 tff(894,plain,
% 0.58/0.76 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(895,plain,
% 0.58/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.58/0.76 inference(bind,[status(th)],[])).
% 0.58/0.76 tff(896,plain,
% 0.58/0.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.58/0.76 inference(quant_intro,[status(thm)],[895])).
% 0.58/0.76 tff(897,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.58/0.77 tff(898,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.58/0.77 tff(899,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[898, 894])).
% 0.58/0.77 tff(900,plain,(
% 0.58/0.77 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.58/0.77 inference(skolemize,[status(sab)],[899])).
% 0.58/0.77 tff(901,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[900, 893])).
% 0.58/0.77 tff(902,plain,
% 0.58/0.77 (((~hskp21) | (~c3_1(a715))) <=> ((~hskp21) | (~c3_1(a715)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(903,plain,
% 0.58/0.77 (((~c3_1(a715)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a715)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(904,axiom,((~c3_1(a715)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.58/0.77 tff(905,plain,
% 0.58/0.77 ((~hskp21) | (~c3_1(a715))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.58/0.77 tff(906,plain,
% 0.58/0.77 ((~hskp21) | (~c3_1(a715))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[905, 902])).
% 0.58/0.77 tff(907,plain,
% 0.58/0.77 (~c3_1(a715)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[906, 870])).
% 0.58/0.77 tff(908,assumption,(~hskp16), introduced(assumption)).
% 0.58/0.77 tff(909,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(910,plain,
% 0.58/0.77 ((hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703))) <=> (hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(911,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[910])).
% 0.58/0.77 tff(912,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[911, 909])).
% 0.58/0.77 tff(913,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(914,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.58/0.77 tff(915,plain,
% 0.58/0.77 ($false),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[914, 93, 908, 884, 844, 907, 827, 901, 852, 891])).
% 0.58/0.77 tff(916,plain,(hskp2 | hskp16 | (~c1_1(a703)) | c0_1(a703) | hskp9 | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.58/0.77 tff(917,plain,
% 0.58/0.77 (hskp2),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[916, 861, 800, 797, 543, 565])).
% 0.58/0.77 tff(918,plain,
% 0.58/0.77 (~c1_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[720, 917])).
% 0.58/0.77 tff(919,plain,
% 0.58/0.77 (~c0_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[726, 917])).
% 0.58/0.77 tff(920,plain,
% 0.58/0.77 (c3_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[737, 917])).
% 0.58/0.77 tff(921,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(922,plain,
% 0.58/0.77 (((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(923,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[922])).
% 0.58/0.77 tff(924,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[923, 921])).
% 0.58/0.77 tff(925,plain,
% 0.58/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(926,plain,
% 0.58/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[925, 924])).
% 0.58/0.77 tff(927,plain,
% 0.58/0.77 ($false),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[926, 93, 534, 518, 800, 920, 797, 919, 918, 445, 542, 807])).
% 0.58/0.77 tff(928,plain,((~hskp17) | hskp9 | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.58/0.77 tff(929,plain,
% 0.58/0.77 (~hskp17),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[928, 565, 543])).
% 0.58/0.77 tff(930,plain,
% 0.58/0.77 (hskp17 | hskp14),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[604, 542])).
% 0.58/0.77 tff(931,plain,
% 0.58/0.77 (hskp14),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[930, 929])).
% 0.58/0.77 tff(932,plain,
% 0.58/0.77 (hskp5),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[596, 931, 543])).
% 0.58/0.77 tff(933,plain,
% 0.58/0.77 (~c2_1(a673)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[55, 932])).
% 0.58/0.77 tff(934,plain,
% 0.58/0.77 (~c0_1(a673)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[61, 932])).
% 0.58/0.77 tff(935,plain,
% 0.58/0.77 (~c3_1(a673)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[49, 932])).
% 0.58/0.77 tff(936,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(937,plain,
% 0.58/0.77 (((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673))) <=> (c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(938,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[937])).
% 0.58/0.77 tff(939,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[938, 936])).
% 0.58/0.77 tff(940,plain,
% 0.58/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(941,plain,
% 0.58/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.58/0.77 tff(942,plain,
% 0.58/0.77 (~c1_1(a673)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[941, 93, 534, 526, 799, 798, 795, 934, 935, 350, 542])).
% 0.58/0.77 tff(943,plain,
% 0.58/0.77 (hskp2),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[714, 942, 934, 933, 543])).
% 0.58/0.77 tff(944,plain,
% 0.58/0.77 (~c1_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[720, 943])).
% 0.58/0.77 tff(945,plain,
% 0.58/0.77 (~c0_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[726, 943])).
% 0.58/0.77 tff(946,plain,
% 0.58/0.77 (c3_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[737, 943])).
% 0.58/0.77 tff(947,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(948,plain,
% 0.58/0.77 ((hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(949,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[948])).
% 0.58/0.77 tff(950,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[949, 947])).
% 0.58/0.77 tff(951,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(952,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[951, 950])).
% 0.58/0.77 tff(953,plain,
% 0.58/0.77 (~c2_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[952, 93, 565, 946, 945, 944, 226])).
% 0.58/0.77 tff(954,plain,
% 0.58/0.77 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.58/0.77 inference(bind,[status(th)],[])).
% 0.58/0.77 tff(955,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(quant_intro,[status(thm)],[954])).
% 0.58/0.77 tff(956,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(957,plain,
% 0.58/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.58/0.77 inference(bind,[status(th)],[])).
% 0.58/0.77 tff(958,plain,
% 0.58/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(quant_intro,[status(thm)],[957])).
% 0.58/0.77 tff(959,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.58/0.77 tff(960,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.58/0.77 tff(961,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[960, 956])).
% 0.58/0.77 tff(962,plain,(
% 0.58/0.77 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(skolemize,[status(sab)],[961])).
% 0.58/0.77 tff(963,plain,
% 0.58/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[962, 955])).
% 0.58/0.77 tff(964,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(965,plain,
% 0.58/0.77 ((hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670))) <=> (hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(966,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))))),
% 0.58/0.77 inference(monotonicity,[status(thm)],[965])).
% 0.58/0.77 tff(967,plain,
% 0.58/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.77 inference(transitivity,[status(thm)],[966, 964])).
% 0.58/0.77 tff(968,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670)))),
% 0.58/0.77 inference(quant_inst,[status(thm)],[])).
% 0.58/0.77 tff(969,plain,
% 0.58/0.77 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))),
% 0.58/0.77 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.58/0.77 tff(970,plain,
% 0.58/0.77 (hskp16 | c2_1(a670)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[969, 93, 534, 526, 518, 946, 944, 963])).
% 0.58/0.77 tff(971,plain,
% 0.58/0.77 (hskp16),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[970, 953])).
% 0.58/0.77 tff(972,plain,
% 0.58/0.77 (c3_1(a702)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[834, 971])).
% 0.58/0.77 tff(973,plain,
% 0.58/0.77 (c2_1(a702)),
% 0.58/0.77 inference(unit_resolution,[status(thm)],[842, 971])).
% 0.58/0.77 tff(974,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(975,plain,
% 0.58/0.77 (((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))),
% 0.58/0.77 inference(rewrite,[status(thm)],[])).
% 0.58/0.77 tff(976,plain,
% 0.58/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702))))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[975])).
% 0.58/0.78 tff(977,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))),
% 0.58/0.78 inference(transitivity,[status(thm)],[976, 974])).
% 0.58/0.78 tff(978,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(979,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[978, 977])).
% 0.58/0.78 tff(980,plain,
% 0.58/0.78 (~c0_1(a702)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[979, 93, 534, 526, 973, 972, 946, 945, 944, 564, 542])).
% 0.58/0.78 tff(981,plain,
% 0.58/0.78 (~c1_1(a702)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[824, 971])).
% 0.58/0.78 tff(982,plain,
% 0.58/0.78 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(983,plain,
% 0.58/0.78 ((hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702))) <=> (hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(984,plain,
% 0.58/0.78 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702))))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[983])).
% 0.58/0.78 tff(985,plain,
% 0.58/0.78 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))),
% 0.58/0.78 inference(transitivity,[status(thm)],[984, 982])).
% 0.58/0.78 tff(986,plain,
% 0.58/0.78 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(987,plain,
% 0.58/0.78 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.58/0.78 tff(988,plain,
% 0.58/0.78 ($false),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[987, 93, 565, 973, 972, 981, 226, 980])).
% 0.58/0.78 tff(989,plain,(hskp11 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.58/0.78 tff(990,plain,
% 0.58/0.78 (hskp11),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[989, 543])).
% 0.58/0.78 tff(991,plain,
% 0.58/0.78 (~c2_1(a683)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[254, 990])).
% 0.58/0.78 tff(992,plain,
% 0.58/0.78 (c0_1(a683)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[240, 990])).
% 0.58/0.78 tff(993,plain,
% 0.58/0.78 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(994,plain,
% 0.58/0.78 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683))) <=> (hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(995,plain,
% 0.58/0.78 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683)))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[994])).
% 0.58/0.78 tff(996,plain,
% 0.58/0.78 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))),
% 0.58/0.78 inference(transitivity,[status(thm)],[995, 993])).
% 0.58/0.78 tff(997,plain,
% 0.58/0.78 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(998,plain,
% 0.58/0.78 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683)),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.58/0.78 tff(999,plain,
% 0.58/0.78 (hskp2 | c1_1(a683)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[998, 93, 543, 992, 991, 554])).
% 0.58/0.78 tff(1000,plain,
% 0.58/0.78 (c1_1(a683)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[999, 544])).
% 0.58/0.78 tff(1001,plain,
% 0.58/0.78 (c1_1(a673)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[714, 62, 544, 56, 543])).
% 0.58/0.78 tff(1002,plain,
% 0.58/0.78 (c3_1(a683)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[248, 990])).
% 0.58/0.78 tff(1003,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(1004,plain,
% 0.58/0.78 (((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673))) <=> (c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(1005,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683))))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[1004])).
% 0.58/0.78 tff(1006,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))),
% 0.58/0.78 inference(transitivity,[status(thm)],[1005, 1003])).
% 0.58/0.78 tff(1007,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(1008,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.58/0.78 tff(1009,plain,
% 0.58/0.78 ($false),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[1008, 93, 992, 1002, 991, 62, 50, 350, 1000, 1001])).
% 0.58/0.78 tff(1010,plain,((~hskp5) | hskp2 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.58/0.78 tff(1011,plain,
% 0.58/0.78 (~hskp5),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[1010, 544, 543])).
% 0.58/0.78 tff(1012,plain,
% 0.58/0.78 (~hskp14),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[596, 1011, 543])).
% 0.58/0.78 tff(1013,plain,
% 0.58/0.78 (hskp17),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[930, 1012])).
% 0.58/0.78 tff(1014,plain,
% 0.58/0.78 (~c0_1(a703)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[411, 1013])).
% 0.58/0.78 tff(1015,plain,
% 0.58/0.78 (c1_1(a703)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[427, 1013])).
% 0.58/0.78 tff(1016,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(1017,plain,
% 0.58/0.78 (((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(1018,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703))))),
% 0.58/0.78 inference(monotonicity,[status(thm)],[1017])).
% 0.58/0.78 tff(1019,plain,
% 0.58/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.78 inference(transitivity,[status(thm)],[1018, 1016])).
% 0.58/0.78 tff(1020,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.58/0.78 inference(quant_inst,[status(thm)],[])).
% 0.58/0.78 tff(1021,plain,
% 0.58/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.58/0.78 tff(1022,plain,
% 0.58/0.78 (c3_1(a703)),
% 0.58/0.78 inference(unit_resolution,[status(thm)],[1021, 93, 1015, 992, 1002, 1014, 991, 350, 1000])).
% 0.58/0.78 tff(1023,plain,
% 0.58/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(1024,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_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)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[1023])).
% 0.58/0.78 tff(1025,plain,
% 0.58/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_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)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(1026,plain,
% 0.58/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.63/0.78 inference(bind,[status(th)],[])).
% 0.63/0.78 tff(1027,plain,
% 0.63/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.63/0.78 inference(quant_intro,[status(thm)],[1026])).
% 0.63/0.78 tff(1028,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 0.63/0.78 tff(1029,plain,
% 0.63/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.63/0.78 tff(1030,plain,
% 0.63/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1029, 1025])).
% 0.63/0.78 tff(1031,plain,(
% 0.63/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.63/0.78 inference(skolemize,[status(sab)],[1030])).
% 0.63/0.78 tff(1032,plain,
% 0.63/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1031, 1024])).
% 0.63/0.78 tff(1033,plain,
% 0.63/0.78 (~c2_1(a703)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[629, 1013])).
% 0.63/0.78 tff(1034,plain,
% 0.63/0.78 (~hskp16),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[860, 1014, 1015, 1033])).
% 0.63/0.78 tff(1035,assumption,(c3_1(a703)), introduced(assumption)).
% 0.63/0.78 tff(1036,assumption,(hskp0), introduced(assumption)).
% 0.63/0.78 tff(1037,plain,
% 0.63/0.78 (((~hskp0) | (~c3_1(a668))) <=> ((~hskp0) | (~c3_1(a668)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1038,plain,
% 0.63/0.78 (((~c3_1(a668)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a668)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1039,axiom,((~c3_1(a668)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.63/0.78 tff(1040,plain,
% 0.63/0.78 ((~hskp0) | (~c3_1(a668))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 0.63/0.78 tff(1041,plain,
% 0.63/0.78 ((~hskp0) | (~c3_1(a668))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1040, 1037])).
% 0.63/0.78 tff(1042,plain,
% 0.63/0.78 (~c3_1(a668)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1041, 1036])).
% 0.63/0.78 tff(1043,plain,
% 0.63/0.78 (((~hskp0) | c1_1(a668)) <=> ((~hskp0) | c1_1(a668))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1044,axiom,((~hskp0) | c1_1(a668)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.63/0.78 tff(1045,plain,
% 0.63/0.78 ((~hskp0) | c1_1(a668)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.63/0.78 tff(1046,plain,
% 0.63/0.78 ((~hskp0) | c1_1(a668)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1045, 1043])).
% 0.63/0.78 tff(1047,plain,
% 0.63/0.78 ((~hskp0) | c1_1(a668)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1046, 1043])).
% 0.63/0.78 tff(1048,plain,
% 0.63/0.78 ((~hskp0) | c1_1(a668)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 0.63/0.78 tff(1049,plain,
% 0.63/0.78 ((~hskp0) | c1_1(a668)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1048, 1043])).
% 0.63/0.78 tff(1050,plain,
% 0.63/0.78 (c1_1(a668)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1049, 1036])).
% 0.63/0.78 tff(1051,plain,
% 0.63/0.78 (~hskp16),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[860, 827, 844, 826])).
% 0.63/0.78 tff(1052,plain,
% 0.63/0.78 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1053,plain,
% 0.63/0.79 ((hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703))) <=> (hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1054,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1053])).
% 0.63/0.79 tff(1055,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1054, 1052])).
% 0.63/0.79 tff(1056,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(1057,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.63/0.79 tff(1058,plain,
% 0.63/0.79 (~c0_1(a668)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1057, 93, 1051, 844, 1050, 827, 1042, 901, 1035])).
% 0.63/0.79 tff(1059,assumption,(c1_1(a683)), introduced(assumption)).
% 0.63/0.79 tff(1060,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1061,plain,
% 0.63/0.79 (((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668))) <=> (c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1062,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1061])).
% 0.63/0.79 tff(1063,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1062, 1060])).
% 0.63/0.79 tff(1064,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(1065,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.63/0.79 tff(1066,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1065, 93, 844, 265, 1050, 826, 266, 1042, 350, 1059, 1058, 1035])).
% 0.63/0.79 tff(1067,plain,((~hskp0) | (~c1_1(a703)) | (~c0_1(a683)) | c2_1(a703) | c2_1(a683) | (~c1_1(a683)) | (~c3_1(a703)) | c0_1(a703)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1068,plain,
% 0.63/0.79 (~hskp0),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1067, 1015, 992, 1033, 991, 1000, 1022, 1014])).
% 0.63/0.79 tff(1069,plain,
% 0.63/0.79 ((hskp29 | hskp16 | hskp0) <=> (hskp29 | hskp16 | hskp0)),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1070,plain,
% 0.63/0.79 (((hskp29 | hskp0) | hskp16) <=> (hskp29 | hskp16 | hskp0)),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1071,plain,
% 0.63/0.79 ((hskp29 | hskp0) <=> (hskp29 | hskp0)),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1072,plain,
% 0.63/0.79 (((hskp29 | hskp0) | hskp16) <=> ((hskp29 | hskp0) | hskp16)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1071])).
% 0.63/0.79 tff(1073,plain,
% 0.63/0.79 (((hskp29 | hskp0) | hskp16) <=> (hskp29 | hskp16 | hskp0)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1072, 1070])).
% 0.63/0.79 tff(1074,axiom,((hskp29 | hskp0) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.63/0.79 tff(1075,plain,
% 0.63/0.79 (hskp29 | hskp16 | hskp0),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 0.63/0.79 tff(1076,plain,
% 0.63/0.79 (hskp29 | hskp16 | hskp0),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1075, 1069])).
% 0.63/0.79 tff(1077,plain,
% 0.63/0.79 (hskp29 | hskp16 | hskp0),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1076, 1069])).
% 0.63/0.79 tff(1078,plain,
% 0.63/0.79 (hskp29 | hskp16 | hskp0),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1077, 1069])).
% 0.63/0.79 tff(1079,plain,
% 0.63/0.79 (hskp29 | hskp16 | hskp0),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1078, 1069])).
% 0.63/0.79 tff(1080,plain,
% 0.63/0.79 (hskp29),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1079, 1068, 1034])).
% 0.63/0.79 tff(1081,plain,
% 0.63/0.79 (((~hskp29) | c3_1(a725)) <=> ((~hskp29) | c3_1(a725))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1082,axiom,((~hskp29) | c3_1(a725)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.63/0.79 tff(1083,plain,
% 0.63/0.79 ((~hskp29) | c3_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.63/0.79 tff(1084,plain,
% 0.63/0.79 ((~hskp29) | c3_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1083, 1081])).
% 0.63/0.79 tff(1085,plain,
% 0.63/0.79 ((~hskp29) | c3_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1084, 1081])).
% 0.63/0.79 tff(1086,plain,
% 0.63/0.79 ((~hskp29) | c3_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1085, 1081])).
% 0.63/0.79 tff(1087,plain,
% 0.63/0.79 ((~hskp29) | c3_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1086, 1081])).
% 0.63/0.79 tff(1088,plain,
% 0.63/0.79 (c3_1(a725)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1087, 1080])).
% 0.63/0.79 tff(1089,plain,
% 0.63/0.79 (((~hskp29) | c2_1(a725)) <=> ((~hskp29) | c2_1(a725))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1090,axiom,((~hskp29) | c2_1(a725)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.63/0.79 tff(1091,plain,
% 0.63/0.79 ((~hskp29) | c2_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.63/0.79 tff(1092,plain,
% 0.63/0.79 ((~hskp29) | c2_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1091, 1089])).
% 0.63/0.79 tff(1093,plain,
% 0.63/0.79 ((~hskp29) | c2_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 0.63/0.79 tff(1094,plain,
% 0.63/0.79 ((~hskp29) | c2_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1093, 1089])).
% 0.63/0.79 tff(1095,plain,
% 0.63/0.79 ((~hskp29) | c2_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1094, 1089])).
% 0.63/0.79 tff(1096,plain,
% 0.63/0.79 (c2_1(a725)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1095, 1080])).
% 0.63/0.79 tff(1097,plain,
% 0.63/0.79 (((~hskp29) | c1_1(a725)) <=> ((~hskp29) | c1_1(a725))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1098,axiom,((~hskp29) | c1_1(a725)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.63/0.79 tff(1099,plain,
% 0.63/0.79 ((~hskp29) | c1_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.63/0.79 tff(1100,plain,
% 0.63/0.79 ((~hskp29) | c1_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1099, 1097])).
% 0.63/0.79 tff(1101,plain,
% 0.63/0.79 ((~hskp29) | c1_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1100, 1097])).
% 0.63/0.79 tff(1102,plain,
% 0.63/0.79 ((~hskp29) | c1_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1101, 1097])).
% 0.63/0.79 tff(1103,plain,
% 0.63/0.79 ((~hskp29) | c1_1(a725)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1102, 1097])).
% 0.63/0.79 tff(1104,plain,
% 0.63/0.79 (c1_1(a725)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1103, 1080])).
% 0.63/0.79 tff(1105,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1106,plain,
% 0.63/0.79 (((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1107,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1106])).
% 0.63/0.79 tff(1108,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1107, 1105])).
% 0.63/0.79 tff(1109,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(1110,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.63/0.79 tff(1111,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1110, 93, 1104, 1096, 1088, 1015, 1014, 1033, 1032, 1022])).
% 0.63/0.79 tff(1112,plain,(hskp2 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1113,plain,
% 0.63/0.79 (hskp2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1112, 543])).
% 0.63/0.79 tff(1114,plain,
% 0.63/0.79 (~c1_1(a670)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[720, 1113])).
% 0.63/0.79 tff(1115,plain,
% 0.63/0.79 (~c0_1(a670)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[726, 1113])).
% 0.63/0.79 tff(1116,plain,
% 0.63/0.79 (c3_1(a670)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[737, 1113])).
% 0.63/0.79 tff(1117,plain,
% 0.63/0.79 (~c0_1(a702)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[979, 93, 534, 526, 843, 835, 1116, 1115, 1114, 564, 542])).
% 0.63/0.79 tff(1118,plain,
% 0.63/0.79 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1119,plain,
% 0.63/0.79 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702))) <=> (hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1120,plain,
% 0.63/0.79 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702)))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1119])).
% 0.63/0.79 tff(1121,plain,
% 0.63/0.79 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.63/0.79 tff(1122,plain,
% 0.63/0.79 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(1123,plain,
% 0.63/0.79 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.63/0.79 tff(1124,plain,
% 0.63/0.79 (hskp8),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1123, 93, 543, 843, 825, 464, 1117])).
% 0.63/0.79 tff(1125,plain,
% 0.63/0.79 (~c0_1(a679)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[477, 1124])).
% 0.63/0.79 tff(1126,plain,
% 0.63/0.79 (c3_1(a679)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[494, 1124])).
% 0.63/0.79 tff(1127,plain,
% 0.63/0.79 (c1_1(a679)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[486, 1124])).
% 0.63/0.79 tff(1128,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1129,plain,
% 0.63/0.79 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702))) <=> (c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1130,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1129])).
% 0.63/0.79 tff(1131,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1130, 1128])).
% 0.63/0.79 tff(1132,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(1133,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.63/0.79 tff(1134,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1133, 93, 835, 992, 1002, 1127, 1126, 825, 991, 1125, 445, 1117])).
% 0.63/0.79 tff(1135,plain,((~hskp16) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1136,plain,
% 0.63/0.79 (~hskp16),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1135, 543])).
% 0.63/0.79 tff(1137,plain,
% 0.63/0.79 (hskp16 | c2_1(a670)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[969, 93, 534, 526, 518, 1116, 1114, 963])).
% 0.63/0.79 tff(1138,plain,
% 0.63/0.79 (c2_1(a670)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1137, 1136])).
% 0.63/0.79 tff(1139,plain,
% 0.63/0.79 (hskp8 | (~c2_1(a670))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[753, 93, 543, 1115, 1114, 464])).
% 0.63/0.79 tff(1140,plain,
% 0.63/0.79 (hskp8),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1139, 1138])).
% 0.63/0.79 tff(1141,plain,
% 0.63/0.79 (~c0_1(a679)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[477, 1140])).
% 0.63/0.79 tff(1142,plain,
% 0.63/0.79 (c3_1(a679)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[494, 1140])).
% 0.63/0.79 tff(1143,plain,
% 0.63/0.79 (c1_1(a679)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[486, 1140])).
% 0.63/0.79 tff(1144,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1145,plain,
% 0.63/0.79 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1146,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1145])).
% 0.63/0.79 tff(1147,plain,
% 0.63/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1146, 1144])).
% 0.63/0.79 tff(1148,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(1149,plain,
% 0.63/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.63/0.80 tff(1150,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1149, 93, 992, 1002, 1143, 1142, 1116, 991, 1141, 1115, 1114, 445])).
% 0.63/0.80 tff(1151,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(1152,plain,
% 0.63/0.80 (~c3_1(a680)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[283, 1151])).
% 0.63/0.80 tff(1153,plain,
% 0.63/0.80 (~c1_1(a680)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[289, 1151])).
% 0.63/0.80 tff(1154,plain,
% 0.63/0.80 (c2_1(a680)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[311, 1151])).
% 0.63/0.80 tff(1155,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1156,plain,
% 0.63/0.80 (((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1157,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1156])).
% 0.63/0.80 tff(1158,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1157, 1155])).
% 0.63/0.80 tff(1159,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1160,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.63/0.80 tff(1161,plain,
% 0.63/0.80 (~c0_1(a680)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1160, 93, 534, 518, 1154, 1153, 1152, 277, 542])).
% 0.63/0.80 tff(1162,plain,
% 0.63/0.80 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1163,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1162])).
% 0.63/0.80 tff(1164,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1165,plain,
% 0.63/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1166,plain,
% 0.63/0.80 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1165])).
% 0.63/0.80 tff(1167,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.63/0.80 tff(1168,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 0.63/0.80 tff(1169,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1168, 1164])).
% 0.63/0.80 tff(1170,plain,(
% 0.63/0.80 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[1169])).
% 0.63/0.80 tff(1171,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1170, 1163])).
% 0.63/0.80 tff(1172,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1173,plain,
% 0.63/0.80 ((hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680)) <=> (hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1174,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680)))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1173])).
% 0.63/0.80 tff(1175,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1174, 1172])).
% 0.63/0.80 tff(1176,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1177,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 0.63/0.80 tff(1178,plain,
% 0.63/0.80 (hskp5),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1177, 93, 1154, 1153, 1152, 143, 1161])).
% 0.63/0.80 tff(1179,plain,
% 0.63/0.80 (~c3_1(a673)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[49, 1178])).
% 0.63/0.80 tff(1180,plain,
% 0.63/0.80 (~c0_1(a673)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[61, 1178])).
% 0.63/0.80 tff(1181,plain,
% 0.63/0.80 (~c1_1(a673)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[941, 93, 534, 526, 799, 798, 795, 1180, 1179, 350, 542])).
% 0.63/0.80 tff(1182,plain,
% 0.63/0.80 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1183,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1182])).
% 0.63/0.80 tff(1184,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1185,plain,
% 0.63/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1186,plain,
% 0.63/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_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) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1185])).
% 0.63/0.80 tff(1187,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.63/0.80 tff(1188,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.63/0.80 tff(1189,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1188, 1184])).
% 0.63/0.80 tff(1190,plain,(
% 0.63/0.80 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.80 inference(skolemize,[status(sab)],[1189])).
% 0.63/0.80 tff(1191,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1190, 1183])).
% 0.63/0.80 tff(1192,plain,
% 0.63/0.80 (~c2_1(a673)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[55, 1178])).
% 0.63/0.80 tff(1193,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1194,plain,
% 0.63/0.80 ((hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673)) <=> (hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1195,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673)))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1194])).
% 0.63/0.80 tff(1196,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1195, 1193])).
% 0.63/0.80 tff(1197,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1198,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.63/0.80 tff(1199,plain,
% 0.63/0.80 (hskp0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1198, 93, 534, 526, 1180, 1192, 1191, 542, 1181])).
% 0.63/0.80 tff(1200,plain,
% 0.63/0.80 (~c3_1(a668)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1041, 1199])).
% 0.63/0.80 tff(1201,plain,
% 0.63/0.80 (((~hskp0) | (~c2_1(a668))) <=> ((~hskp0) | (~c2_1(a668)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1202,plain,
% 0.63/0.80 (((~c2_1(a668)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a668)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1203,axiom,((~c2_1(a668)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.63/0.80 tff(1204,plain,
% 0.63/0.80 ((~hskp0) | (~c2_1(a668))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 0.63/0.80 tff(1205,plain,
% 0.63/0.80 ((~hskp0) | (~c2_1(a668))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1204, 1201])).
% 0.63/0.80 tff(1206,plain,
% 0.63/0.80 (~c2_1(a668)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1205, 1199])).
% 0.63/0.80 tff(1207,plain,
% 0.63/0.80 (c1_1(a668)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1049, 1199])).
% 0.63/0.80 tff(1208,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1209,plain,
% 0.63/0.80 ((hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680))) <=> (hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1210,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680)))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1209])).
% 0.63/0.81 tff(1211,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.63/0.81 tff(1212,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1213,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.63/0.81 tff(1214,plain,
% 0.63/0.81 (hskp10),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1213, 93, 1154, 1207, 1152, 1206, 1200, 1171, 1161])).
% 0.63/0.81 tff(1215,plain,
% 0.63/0.81 (c2_1(a681)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[208, 1214])).
% 0.63/0.81 tff(1216,plain,
% 0.63/0.81 (~c0_1(a681)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[192, 1214])).
% 0.63/0.81 tff(1217,plain,
% 0.63/0.81 (c3_1(a681)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[200, 1214])).
% 0.63/0.81 tff(1218,plain,
% 0.63/0.81 (~c1_1(a681)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[215, 93, 1215, 1217, 1216, 22])).
% 0.63/0.81 tff(1219,plain,
% 0.63/0.81 (hskp11),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[232, 93, 1215, 1217, 1216, 226, 1218])).
% 0.63/0.81 tff(1220,plain,
% 0.63/0.81 (~c2_1(a683)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[254, 1219])).
% 0.63/0.81 tff(1221,plain,
% 0.63/0.81 (c0_1(a683)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[240, 1219])).
% 0.63/0.81 tff(1222,plain,
% 0.63/0.81 (c3_1(a683)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[248, 1219])).
% 0.63/0.81 tff(1223,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[453, 1222, 1221, 1151, 1217, 1220, 1216, 799, 798, 795, 1215])).
% 0.63/0.81 % SZS output end Proof
% 0.63/0.81 % E exiting
%------------------------------------------------------------------------------