TSTP Solution File: SYN036-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN036-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 23:53:14 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN036-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 01:13:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 tff(p_type, type, (
% 0.21/0.48 p: $i > $o)).
% 0.21/0.48 tff(fy5_type, type, (
% 0.21/0.48 fy5: $i > $i)).
% 0.21/0.48 tff(cx_type, type, (
% 0.21/0.48 cx: $i)).
% 0.21/0.48 tff(q_type, type, (
% 0.21/0.48 q: $i > $o)).
% 0.21/0.48 tff(fz5_type, type, (
% 0.21/0.48 fz5: $i > $i)).
% 0.21/0.48 tff(cw_type, type, (
% 0.21/0.48 cw: $i)).
% 0.21/0.48 tff(fz_type, type, (
% 0.21/0.48 fz: $i > $i)).
% 0.21/0.48 tff(fy_type, type, (
% 0.21/0.48 fy: $i > $i)).
% 0.21/0.48 tff(elem_0_type, type, (
% 0.21/0.48 elem_0: $i)).
% 0.21/0.48 tff(1,assumption,(~p(fy5(cx))), introduced(assumption)).
% 0.21/0.48 tff(2,assumption,(~q(cw)), introduced(assumption)).
% 0.21/0.48 tff(3,assumption,(~p(fy(cx))), introduced(assumption)).
% 0.21/0.48 tff(4,assumption,(q(fz(fy(cx)))), introduced(assumption)).
% 0.21/0.48 tff(5,assumption,(~p(cx)), introduced(assumption)).
% 0.21/0.48 tff(6,assumption,(~q(fz5(cw))), introduced(assumption)).
% 0.21/0.48 tff(7,assumption,(q(elem!0)), introduced(assumption)).
% 0.21/0.48 tff(8,plain,
% 0.21/0.48 (^[Z2: $i, X1: $i] : refl((p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))) <=> (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(9,plain,
% 0.21/0.48 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))) <=> ![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.48 tff(10,plain,
% 0.21/0.48 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))) <=> ![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(11,plain,
% 0.21/0.48 (^[Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~q(Z2)) | p(cx)) <=> (p(cx) | (~q(Z2)))), ((((~q(Z2)) | p(cx)) | p(X1)) <=> ((p(cx) | (~q(Z2))) | p(X1)))), rewrite(((p(cx) | (~q(Z2))) | p(X1)) <=> (p(cx) | p(X1) | (~q(Z2)))), ((((~q(Z2)) | p(cx)) | p(X1)) <=> (p(cx) | p(X1) | (~q(Z2))))), (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) <=> ((p(cx) | p(X1) | (~q(Z2))) | p(fy(X1))))), rewrite(((p(cx) | p(X1) | (~q(Z2))) | p(fy(X1))) <=> (p(cx) | p(X1) | (~q(Z2)) | p(fy(X1)))), (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) <=> (p(cx) | p(X1) | (~q(Z2)) | p(fy(X1))))), ((((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw)) <=> ((p(cx) | p(X1) | (~q(Z2)) | p(fy(X1))) | q(cw)))), rewrite(((p(cx) | p(X1) | (~q(Z2)) | p(fy(X1))) | q(cw)) <=> (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))), ((((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw)) <=> (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(12,plain,
% 0.21/0.48 (![Z2: $i, X1: $i] : (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw)) <=> ![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.48 tff(13,axiom,(![Z2: $i, X1: $i] : (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_20')).
% 0.21/0.48 tff(14,plain,
% 0.21/0.48 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.48 tff(15,plain,
% 0.21/0.48 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.48 tff(16,plain,(
% 0.21/0.48 ![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[15])).
% 0.21/0.48 tff(17,plain,
% 0.21/0.48 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.21/0.48 tff(18,plain,
% 0.21/0.48 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(elem!0)) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(elem!0)) | p(fy(cx)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(19,plain,
% 0.21/0.48 ((p(cx) | q(cw) | p(cx) | (~q(elem!0)) | p(fy(cx))) <=> (p(cx) | q(cw) | (~q(elem!0)) | p(fy(cx)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(20,plain,
% 0.21/0.48 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(elem!0)) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(elem!0)) | p(fy(cx))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[19])).
% 0.21/0.48 tff(21,plain,
% 0.21/0.48 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(elem!0)) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(elem!0)) | p(fy(cx)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[20, 18])).
% 0.21/0.48 tff(22,plain,
% 0.21/0.48 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(elem!0)) | p(fy(cx)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(elem!0)) | p(fy(cx))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.48 tff(24,plain,
% 0.21/0.48 (p(cx) | q(cw) | (~q(elem!0)) | p(fy(cx))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[23, 17])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 (p(fy(cx))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[24, 7, 5, 2])).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 (^[Y4: $i, Z4: $i] : refl((p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))) <=> (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))) <=> ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))) <=> ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 (^[Y4: $i, Z4: $i] : trans(monotonicity(rewrite((((~p(Y4)) | (~q(Z4))) | p(cx)) <=> (p(cx) | (~q(Z4)) | (~p(Y4)))), (((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw)) <=> ((p(cx) | (~q(Z4)) | (~p(Y4))) | q(cw)))), rewrite(((p(cx) | (~q(Z4)) | (~p(Y4))) | q(cw)) <=> (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))), (((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw)) <=> (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(30,plain,
% 0.21/0.48 (![Y4: $i, Z4: $i] : ((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw)) <=> ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.48 tff(31,axiom,(![Y4: $i, Z4: $i] : ((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.21/0.48 tff(32,plain,
% 0.21/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.48 tff(34,plain,(
% 0.21/0.48 ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[33])).
% 0.21/0.48 tff(35,plain,
% 0.21/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 (((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(elem!0)) | (~p(fy(cx))))) <=> ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(elem!0)) | (~p(fy(cx))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(elem!0)) | (~p(fy(cx))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(elem!0)) | (~p(fy(cx)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[38, 35, 5, 2, 7, 25])).
% 0.21/0.48 tff(40,plain,((~q(elem!0)) | p(cx) | q(cw)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 (~q(elem!0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[40, 2, 5])).
% 0.21/0.48 tff(42,assumption,(q(fz5(elem!0))), introduced(assumption)).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(fz5(elem!0))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(fz5(elem!0))) | p(fy(cx)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 ((p(cx) | q(cw) | p(cx) | (~q(fz5(elem!0))) | p(fy(cx))) <=> (p(cx) | q(cw) | (~q(fz5(elem!0))) | p(fy(cx)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(elem!0))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(fz5(elem!0))) | p(fy(cx))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[44])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(elem!0))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(fz5(elem!0))) | p(fy(cx)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[45, 43])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(elem!0))) | p(fy(cx)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(fz5(elem!0))) | p(fy(cx))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (p(cx) | q(cw) | (~q(fz5(elem!0))) | p(fy(cx))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[48, 17])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (p(fy(cx))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[49, 42, 5, 2])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(fz5(elem!0))) | (~p(fy(cx))))) <=> ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(fz5(elem!0))) | (~p(fy(cx))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(fz5(elem!0))) | (~p(fy(cx))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(fz5(elem!0))) | (~p(fy(cx)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[53, 35, 5, 2, 42, 50])).
% 0.21/0.49 tff(55,plain,((~q(fz5(elem!0))) | p(cx) | q(cw)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (~q(fz5(elem!0))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[55, 2, 5])).
% 0.21/0.49 tff(57,assumption,(p(fy5(cx))), introduced(assumption)).
% 0.21/0.49 tff(58,assumption,(~q(fz5(elem!0))), introduced(assumption)).
% 0.21/0.49 tff(59,assumption,(~q(elem!0)), introduced(assumption)).
% 0.21/0.49 tff(60,assumption,(~q(fz(cw))), introduced(assumption)).
% 0.21/0.49 tff(61,assumption,(q(cw)), introduced(assumption)).
% 0.21/0.49 tff(62,assumption,(p(fz(cw))), introduced(assumption)).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (^[Y4: $i, Z3: $i] : refl((p(cx) | (~q(cw)) | q(Z3) | (~p(Y4))) <=> (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4))) <=> ![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4))) <=> ![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (^[Y4: $i, Z3: $i] : trans(monotonicity(rewrite((((~p(Y4)) | (~q(cw))) | p(cx)) <=> (p(cx) | (~q(cw)) | (~p(Y4)))), (((((~p(Y4)) | (~q(cw))) | p(cx)) | q(Z3)) <=> ((p(cx) | (~q(cw)) | (~p(Y4))) | q(Z3)))), rewrite(((p(cx) | (~q(cw)) | (~p(Y4))) | q(Z3)) <=> (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))), (((((~p(Y4)) | (~q(cw))) | p(cx)) | q(Z3)) <=> (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 (![Y4: $i, Z3: $i] : ((((~p(Y4)) | (~q(cw))) | p(cx)) | q(Z3)) <=> ![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.49 tff(68,axiom,(![Y4: $i, Z3: $i] : ((((~p(Y4)) | (~q(cw))) | p(cx)) | q(Z3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 (![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.49 tff(71,plain,(
% 0.21/0.49 ![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[70])).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 (![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fz(cw))))) <=> ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fz(cw))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(74,plain,
% 0.21/0.49 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fz(cw))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(75,plain,
% 0.21/0.49 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fz(cw)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.49 tff(76,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[75, 72, 5, 61, 60, 62])).
% 0.21/0.49 tff(77,plain,((~p(fz(cw))) | p(cx) | (~q(cw)) | q(fz(cw))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 (~p(fz(cw))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[77, 61, 5, 60])).
% 0.21/0.49 tff(79,plain,
% 0.21/0.49 (^[Z1: $i, X1: $i] : refl((p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1))) <=> (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 (![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1))) <=> ![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.49 tff(81,plain,
% 0.21/0.49 (![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1))) <=> ![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(82,plain,
% 0.21/0.49 (^[Z1: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~q(cw)) | p(cx)) <=> (p(cx) | (~q(cw)))), ((((~q(cw)) | p(cx)) | p(X1)) <=> ((p(cx) | (~q(cw))) | p(X1)))), rewrite(((p(cx) | (~q(cw))) | p(X1)) <=> (p(cx) | (~q(cw)) | p(X1))), ((((~q(cw)) | p(cx)) | p(X1)) <=> (p(cx) | (~q(cw)) | p(X1)))), (((((~q(cw)) | p(cx)) | p(X1)) | p(fy(X1))) <=> ((p(cx) | (~q(cw)) | p(X1)) | p(fy(X1))))), rewrite(((p(cx) | (~q(cw)) | p(X1)) | p(fy(X1))) <=> (p(cx) | (~q(cw)) | p(X1) | p(fy(X1)))), (((((~q(cw)) | p(cx)) | p(X1)) | p(fy(X1))) <=> (p(cx) | (~q(cw)) | p(X1) | p(fy(X1))))), ((((((~q(cw)) | p(cx)) | p(X1)) | p(fy(X1))) | q(Z1)) <=> ((p(cx) | (~q(cw)) | p(X1) | p(fy(X1))) | q(Z1)))), rewrite(((p(cx) | (~q(cw)) | p(X1) | p(fy(X1))) | q(Z1)) <=> (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))), ((((((~q(cw)) | p(cx)) | p(X1)) | p(fy(X1))) | q(Z1)) <=> (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(83,plain,
% 0.21/0.49 (![Z1: $i, X1: $i] : (((((~q(cw)) | p(cx)) | p(X1)) | p(fy(X1))) | q(Z1)) <=> ![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.49 tff(84,axiom,(![Z1: $i, X1: $i] : (((((~q(cw)) | p(cx)) | p(X1)) | p(fy(X1))) | q(Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_19')).
% 0.21/0.49 tff(85,plain,
% 0.21/0.49 (![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.49 tff(86,plain,
% 0.21/0.49 (![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.21/0.49 tff(87,plain,(
% 0.21/0.49 ![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[86])).
% 0.21/0.49 tff(88,plain,
% 0.21/0.49 (![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.21/0.49 tff(89,plain,
% 0.21/0.49 (((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | p(fy(fz(cw))) | p(fz(cw)))) <=> ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | p(cx) | (~q(cw)) | q(fz(cw)) | p(fy(fz(cw))) | p(fz(cw)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 ((p(cx) | (~q(cw)) | q(fz(cw)) | p(fz(cw)) | p(fy(fz(cw)))) <=> (p(cx) | (~q(cw)) | q(fz(cw)) | p(fy(fz(cw))) | p(fz(cw)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | p(fz(cw)) | p(fy(fz(cw))))) <=> ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | p(fy(fz(cw))) | p(fz(cw))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | p(fz(cw)) | p(fy(fz(cw))))) <=> ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | p(cx) | (~q(cw)) | q(fz(cw)) | p(fy(fz(cw))) | p(fz(cw)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | p(fz(cw)) | p(fy(fz(cw))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | p(cx) | (~q(cw)) | q(fz(cw)) | p(fy(fz(cw))) | p(fz(cw))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (p(cx) | (~q(cw)) | q(fz(cw)) | p(fy(fz(cw))) | p(fz(cw))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 (p(fy(fz(cw)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[95, 78, 60, 5, 61])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 (((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fy(fz(cw)))))) <=> ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fy(fz(cw)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fy(fz(cw)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz(cw)) | (~p(fy(fz(cw))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[99, 72, 5, 61, 60, 96])).
% 0.21/0.50 tff(101,plain,((~q(cw)) | p(cx) | q(fz(cw))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 (~q(cw)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[101, 5, 60])).
% 0.21/0.50 tff(103,assumption,(p(elem!0)), introduced(assumption)).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (^[Y2: $i, W3: $i] : refl((p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(105,plain,
% 0.21/0.50 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))) <=> ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))) <=> ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (^[Y2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~p(Y2)) | p(cx)) <=> (p(cx) | (~p(Y2)))), ((((~p(Y2)) | p(cx)) | q(cw)) <=> ((p(cx) | (~p(Y2))) | q(cw)))), rewrite(((p(cx) | (~p(Y2))) | q(cw)) <=> (p(cx) | q(cw) | (~p(Y2)))), ((((~p(Y2)) | p(cx)) | q(cw)) <=> (p(cx) | q(cw) | (~p(Y2))))), (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) <=> ((p(cx) | q(cw) | (~p(Y2))) | q(W3)))), rewrite(((p(cx) | q(cw) | (~p(Y2))) | q(W3)) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)))), (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2))))), ((((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3))) <=> ((p(cx) | q(cw) | q(W3) | (~p(Y2))) | q(fz(W3))))), rewrite(((p(cx) | q(cw) | q(W3) | (~p(Y2))) | q(fz(W3))) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))), ((((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3))) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (![Y2: $i, W3: $i] : (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3))) <=> ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.50 tff(109,axiom,(![Y2: $i, W3: $i] : (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_15')).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.21/0.50 tff(112,plain,(
% 0.21/0.50 ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[111])).
% 0.21/0.50 tff(113,plain,
% 0.21/0.50 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.21/0.50 tff(114,plain,
% 0.21/0.50 (((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(fz(cw)) | (~p(elem!0)))) <=> ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(fz(cw)) | (~p(elem!0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(115,plain,
% 0.21/0.50 ((p(cx) | q(cw) | q(cw) | (~p(elem!0)) | q(fz(cw))) <=> (p(cx) | q(cw) | q(fz(cw)) | (~p(elem!0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(116,plain,
% 0.21/0.50 (((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cw) | (~p(elem!0)) | q(fz(cw)))) <=> ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(fz(cw)) | (~p(elem!0))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[115])).
% 0.21/0.50 tff(117,plain,
% 0.21/0.50 (((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cw) | (~p(elem!0)) | q(fz(cw)))) <=> ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(fz(cw)) | (~p(elem!0)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[116, 114])).
% 0.21/0.50 tff(118,plain,
% 0.21/0.50 ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cw) | (~p(elem!0)) | q(fz(cw)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(119,plain,
% 0.21/0.50 ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(fz(cw)) | (~p(elem!0))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.50 tff(120,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[119, 113, 5, 102, 103, 60])).
% 0.21/0.50 tff(121,plain,((~p(elem!0)) | p(cx) | q(fz(cw))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 (~p(elem!0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[121, 5, 60])).
% 0.21/0.50 tff(123,plain,
% 0.21/0.50 (^[W9: $i, X7: $i] : refl((p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(124,plain,
% 0.21/0.50 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))) <=> ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.50 tff(125,plain,
% 0.21/0.50 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))) <=> ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(126,plain,
% 0.21/0.50 (^[W9: $i, X7: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((p(cx) | p(X7)) | p(fy5(X7))) <=> (p(cx) | p(X7) | p(fy5(X7)))), ((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) <=> ((p(cx) | p(X7) | p(fy5(X7))) | q(cw)))), rewrite(((p(cx) | p(X7) | p(fy5(X7))) | q(cw)) <=> (p(cx) | q(cw) | p(X7) | p(fy5(X7)))), ((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) <=> (p(cx) | q(cw) | p(X7) | p(fy5(X7))))), (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) <=> ((p(cx) | q(cw) | p(X7) | p(fy5(X7))) | q(W9)))), rewrite(((p(cx) | q(cw) | p(X7) | p(fy5(X7))) | q(W9)) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)))), (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7))))), ((((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9))) <=> ((p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7))) | q(fz5(W9))))), rewrite(((p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7))) | q(fz5(W9))) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))), ((((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9))) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 (![W9: $i, X7: $i] : (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9))) <=> ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.50 tff(128,axiom,(![W9: $i, X7: $i] : (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_32')).
% 0.21/0.50 tff(129,plain,
% 0.21/0.50 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.50 tff(130,plain,
% 0.21/0.50 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.21/0.50 tff(131,plain,(
% 0.21/0.50 ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[130])).
% 0.21/0.50 tff(132,plain,
% 0.21/0.50 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.21/0.50 tff(133,plain,
% 0.21/0.50 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | p(elem!0) | q(fz5(elem!0)) | q(elem!0) | p(fy5(elem!0)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | p(elem!0) | q(fz5(elem!0)) | q(elem!0) | p(fy5(elem!0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(134,plain,
% 0.21/0.50 ((p(cx) | q(cw) | q(elem!0) | p(elem!0) | p(fy5(elem!0)) | q(fz5(elem!0))) <=> (p(cx) | q(cw) | p(elem!0) | q(fz5(elem!0)) | q(elem!0) | p(fy5(elem!0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(135,plain,
% 0.21/0.50 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(elem!0) | p(elem!0) | p(fy5(elem!0)) | q(fz5(elem!0)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | p(elem!0) | q(fz5(elem!0)) | q(elem!0) | p(fy5(elem!0))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[134])).
% 0.21/0.50 tff(136,plain,
% 0.21/0.50 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(elem!0) | p(elem!0) | p(fy5(elem!0)) | q(fz5(elem!0)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | p(elem!0) | q(fz5(elem!0)) | q(elem!0) | p(fy5(elem!0)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[135, 133])).
% 0.21/0.50 tff(137,plain,
% 0.21/0.50 ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(elem!0) | p(elem!0) | p(fy5(elem!0)) | q(fz5(elem!0)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(138,plain,
% 0.21/0.50 ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | p(elem!0) | q(fz5(elem!0)) | q(elem!0) | p(fy5(elem!0))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.50 tff(139,plain,
% 0.21/0.50 (p(cx) | q(cw) | p(elem!0) | q(fz5(elem!0)) | q(elem!0) | p(fy5(elem!0))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.21/0.50 tff(140,plain,
% 0.21/0.50 (p(fy5(elem!0))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[139, 122, 5, 58, 59, 102])).
% 0.21/0.50 tff(141,plain,
% 0.21/0.50 (((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(fz(cw)) | (~p(fy5(elem!0))))) <=> ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(fz(cw)) | (~p(fy5(elem!0))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(142,plain,
% 0.21/0.50 ((p(cx) | q(cw) | q(cw) | (~p(fy5(elem!0))) | q(fz(cw))) <=> (p(cx) | q(cw) | q(fz(cw)) | (~p(fy5(elem!0))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(143,plain,
% 0.21/0.51 (((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cw) | (~p(fy5(elem!0))) | q(fz(cw)))) <=> ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(fz(cw)) | (~p(fy5(elem!0)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.51 tff(144,plain,
% 0.21/0.51 (((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cw) | (~p(fy5(elem!0))) | q(fz(cw)))) <=> ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(fz(cw)) | (~p(fy5(elem!0))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[143, 141])).
% 0.21/0.51 tff(145,plain,
% 0.21/0.51 ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cw) | (~p(fy5(elem!0))) | q(fz(cw)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(146,plain,
% 0.21/0.51 ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(fz(cw)) | (~p(fy5(elem!0)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.51 tff(147,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[146, 113, 5, 102, 140, 60])).
% 0.21/0.51 tff(148,plain,(p(cx) | q(fz(cw)) | q(fz5(elem!0)) | q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(149,plain,
% 0.21/0.51 (q(fz(cw))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[148, 59, 58, 5])).
% 0.21/0.51 tff(150,plain,
% 0.21/0.51 (^[Y4: $i, W9: $i, W6: $i] : refl((p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))) <=> (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(151,plain,
% 0.21/0.51 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))) <=> ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.51 tff(152,plain,
% 0.21/0.51 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))) <=> ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(153,plain,
% 0.21/0.51 (^[Y4: $i, W9: $i, W6: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p(Y4)) | (~q(W6))) | p(cx)) <=> (p(cx) | (~q(W6)) | (~p(Y4)))), (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) <=> ((p(cx) | (~q(W6)) | (~p(Y4))) | q(W9)))), rewrite(((p(cx) | (~q(W6)) | (~p(Y4))) | q(W9)) <=> (p(cx) | q(W9) | (~q(W6)) | (~p(Y4)))), (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) <=> (p(cx) | q(W9) | (~q(W6)) | (~p(Y4))))), ((((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9))) <=> ((p(cx) | q(W9) | (~q(W6)) | (~p(Y4))) | q(fz5(W9))))), rewrite(((p(cx) | q(W9) | (~q(W6)) | (~p(Y4))) | q(fz5(W9))) <=> (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))), ((((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9))) <=> (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(154,plain,
% 0.21/0.51 (![Y4: $i, W9: $i, W6: $i] : (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9))) <=> ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[153])).
% 0.21/0.51 tff(155,axiom,(![Y4: $i, W9: $i, W6: $i] : (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17')).
% 0.21/0.51 tff(156,plain,
% 0.21/0.51 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.51 tff(157,plain,
% 0.21/0.51 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.21/0.51 tff(158,plain,(
% 0.21/0.51 ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[157])).
% 0.21/0.51 tff(159,plain,
% 0.21/0.51 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.21/0.51 tff(160,plain,
% 0.21/0.51 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy5(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy5(cx))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(161,plain,
% 0.21/0.51 ((p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy5(cx)))) <=> (p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy5(cx))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(162,plain,
% 0.21/0.51 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy5(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy5(cx)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[161])).
% 0.21/0.51 tff(163,plain,
% 0.21/0.51 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy5(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy5(cx))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[162, 160])).
% 0.21/0.51 tff(164,plain,
% 0.21/0.51 ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy5(cx))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(165,plain,
% 0.21/0.51 ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy5(cx)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.51 tff(166,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[165, 159, 5, 58, 59, 149, 57])).
% 0.21/0.51 tff(167,plain,((~p(fy5(cx))) | p(cx) | q(fz5(elem!0)) | q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(168,plain,
% 0.21/0.51 (~p(fy5(cx))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[167, 56, 5, 41])).
% 0.21/0.51 tff(169,plain,
% 0.21/0.51 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(fz5(cw)) | p(fy5(cx)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | q(fz5(cw)) | p(fy5(cx)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(170,plain,
% 0.21/0.51 ((p(cx) | q(cw) | q(cw) | p(cx) | p(fy5(cx)) | q(fz5(cw))) <=> (p(cx) | q(cw) | q(fz5(cw)) | p(fy5(cx)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(171,plain,
% 0.21/0.51 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(cw) | p(cx) | p(fy5(cx)) | q(fz5(cw)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(fz5(cw)) | p(fy5(cx))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[170])).
% 0.21/0.51 tff(172,plain,
% 0.21/0.51 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(cw) | p(cx) | p(fy5(cx)) | q(fz5(cw)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | q(fz5(cw)) | p(fy5(cx)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[171, 169])).
% 0.21/0.51 tff(173,plain,
% 0.21/0.51 ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(cw) | p(cx) | p(fy5(cx)) | q(fz5(cw)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(174,plain,
% 0.21/0.51 ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | q(fz5(cw)) | p(fy5(cx))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.51 tff(175,plain,
% 0.21/0.51 (p(cx) | q(cw) | q(fz5(cw)) | p(fy5(cx))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[174, 132])).
% 0.21/0.51 tff(176,plain,
% 0.21/0.51 (q(fz5(cw))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[175, 168, 5, 2])).
% 0.21/0.51 tff(177,plain,
% 0.21/0.51 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(fy(cx)) | (~q(fz5(cw))))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | p(fy(cx)) | (~q(fz5(cw))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(178,plain,
% 0.21/0.51 ((p(cx) | q(cw) | p(cx) | (~q(fz5(cw))) | p(fy(cx))) <=> (p(cx) | q(cw) | p(fy(cx)) | (~q(fz5(cw))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(179,plain,
% 0.21/0.52 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(cw))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(fy(cx)) | (~q(fz5(cw)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[178])).
% 0.21/0.52 tff(180,plain,
% 0.21/0.52 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(cw))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | p(fy(cx)) | (~q(fz5(cw))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[179, 177])).
% 0.21/0.52 tff(181,plain,
% 0.21/0.52 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(cw))) | p(fy(cx)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(182,plain,
% 0.21/0.52 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | p(fy(cx)) | (~q(fz5(cw)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.52 tff(183,plain,
% 0.21/0.52 (p(cx) | q(cw) | p(fy(cx)) | (~q(fz5(cw)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[182, 17])).
% 0.21/0.52 tff(184,plain,
% 0.21/0.52 (p(fy(cx))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[183, 176, 5, 2])).
% 0.21/0.52 tff(185,plain,
% 0.21/0.52 (q(fz(cw))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[148, 41, 56, 5])).
% 0.21/0.52 tff(186,plain,
% 0.21/0.52 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy(cx))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(187,plain,
% 0.21/0.52 ((p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy(cx)))) <=> (p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy(cx))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(188,plain,
% 0.21/0.52 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy(cx)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[187])).
% 0.21/0.52 tff(189,plain,
% 0.21/0.52 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy(cx))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[188, 186])).
% 0.21/0.52 tff(190,plain,
% 0.21/0.52 ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(elem!0) | (~q(fz(cw))) | q(fz5(elem!0)) | (~p(fy(cx))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(191,plain,
% 0.21/0.52 ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(elem!0)) | q(elem!0) | (~q(fz(cw))) | (~p(fy(cx)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.21/0.52 tff(192,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[191, 159, 5, 56, 41, 185, 184])).
% 0.21/0.52 tff(193,plain,(q(cw) | p(cx)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(194,plain,
% 0.21/0.52 (q(cw)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[193, 5])).
% 0.21/0.52 tff(195,plain,
% 0.21/0.52 (q(fz(cw))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[101, 194, 5])).
% 0.21/0.52 tff(196,plain,
% 0.21/0.52 (^[W3: $i, X1: $i] : refl((p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(197,plain,
% 0.21/0.52 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))) <=> ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[196])).
% 0.21/0.52 tff(198,plain,
% 0.21/0.52 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))) <=> ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(199,plain,
% 0.21/0.52 (^[W3: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) <=> ((~q(cw)) | (~q(W3)) | (~q(fz(W3))))), (((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) <=> (((~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(cx)))), rewrite((((~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(cx)) <=> (p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3))))), (((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) <=> (p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3)))))), ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) <=> ((p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(X1)))), rewrite(((p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(X1)) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3))))), ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3)))))), (((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1))) <=> ((p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3)))) | p(fy(X1))))), rewrite(((p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3)))) | p(fy(X1))) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))), (((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1))) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(200,plain,
% 0.21/0.52 (![W3: $i, X1: $i] : ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1))) <=> ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[199])).
% 0.21/0.52 tff(201,axiom,(![W3: $i, X1: $i] : ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_30')).
% 0.21/0.52 tff(202,plain,
% 0.21/0.52 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.21/0.52 tff(203,plain,
% 0.21/0.52 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.21/0.52 tff(204,plain,(
% 0.21/0.52 ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[203])).
% 0.21/0.52 tff(205,plain,
% 0.21/0.52 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.21/0.52 tff(206,plain,
% 0.21/0.52 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(fy(cx)))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(fz(cw))) | p(fy(cx)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(207,plain,
% 0.21/0.52 ((p(cx) | (~q(cw)) | p(cx) | (~q(cw)) | p(fy(cx)) | (~q(fz(cw)))) <=> (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(fy(cx)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(208,plain,
% 0.21/0.52 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cx) | (~q(cw)) | p(fy(cx)) | (~q(fz(cw))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(fy(cx))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[207])).
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% 0.21/0.52 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cx) | (~q(cw)) | p(fy(cx)) | (~q(fz(cw))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(fz(cw))) | p(fy(cx)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[208, 206])).
% 0.21/0.52 tff(210,plain,
% 0.21/0.52 ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cx) | (~q(cw)) | p(fy(cx)) | (~q(fz(cw))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(211,plain,
% 0.21/0.52 ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(fz(cw))) | p(fy(cx))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.21/0.52 tff(212,plain,
% 0.21/0.52 (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(fy(cx))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[211, 205])).
% 0.21/0.52 tff(213,plain,
% 0.21/0.52 (p(fy(cx))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[212, 195, 5, 194])).
% 0.21/0.52 tff(214,plain,
% 0.21/0.52 (((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz5(cw)) | (~p(fy(cx))))) <=> ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz5(cw)) | (~p(fy(cx))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(215,plain,
% 0.21/0.52 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz5(cw)) | (~p(fy(cx))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(216,plain,
% 0.21/0.52 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz5(cw)) | (~p(fy(cx)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.21/0.52 tff(217,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[216, 72, 5, 194, 213, 6])).
% 0.21/0.52 tff(218,plain,(q(fz5(cw)) | p(cx)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(219,plain,
% 0.21/0.52 (q(fz5(cw))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[218, 5])).
% 0.21/0.52 tff(220,plain,
% 0.21/0.52 (^[Y4: $i, W9: $i] : refl((p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))) <=> (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(221,plain,
% 0.21/0.52 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))) <=> ![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[220])).
% 0.21/0.52 tff(222,plain,
% 0.21/0.52 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))) <=> ![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(223,plain,
% 0.21/0.52 (^[Y4: $i, W9: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p(Y4)) | (~q(cw))) | (~q(W9))) <=> ((~q(cw)) | (~q(W9)) | (~p(Y4)))), (((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) <=> (((~q(cw)) | (~q(W9)) | (~p(Y4))) | (~q(fz5(W9)))))), rewrite((((~q(cw)) | (~q(W9)) | (~p(Y4))) | (~q(fz5(W9)))) <=> ((~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))), (((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) <=> ((~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))))), ((((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(cx)) <=> (((~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))) | p(cx)))), rewrite((((~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))) | p(cx)) <=> (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))), ((((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(cx)) <=> (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(224,plain,
% 0.21/0.52 (![Y4: $i, W9: $i] : (((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(cx)) <=> ![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[223])).
% 0.21/0.52 tff(225,axiom,(![Y4: $i, W9: $i] : (((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(cx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_16')).
% 0.21/0.52 tff(226,plain,
% 0.21/0.52 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.52 tff(227,plain,
% 0.21/0.52 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.21/0.52 tff(228,plain,(
% 0.21/0.52 ![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[227])).
% 0.21/0.52 tff(229,plain,
% 0.21/0.52 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.21/0.52 tff(230,plain,
% 0.21/0.52 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(231,plain,
% 0.21/0.53 ((p(cx) | (~q(cw)) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw)))) <=> (p(cx) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(232,plain,
% 0.21/0.53 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw)))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[231])).
% 0.21/0.53 tff(233,plain,
% 0.21/0.53 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[232, 230])).
% 0.21/0.53 tff(234,plain,
% 0.21/0.53 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(235,plain,
% 0.21/0.53 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.21/0.53 tff(236,plain,
% 0.21/0.53 (p(cx) | (~q(cw)) | (~p(cw)) | (~q(fz5(cw)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[235, 229])).
% 0.21/0.53 tff(237,plain,
% 0.21/0.53 (~p(cw)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[236, 219, 5, 194])).
% 0.21/0.53 tff(238,plain,
% 0.21/0.53 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(cw) | p(fy(cw)))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(fz(cw))) | p(cw) | p(fy(cw)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(239,plain,
% 0.21/0.53 ((p(cx) | (~q(cw)) | p(cw) | (~q(cw)) | p(fy(cw)) | (~q(fz(cw)))) <=> (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(cw) | p(fy(cw)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(240,plain,
% 0.21/0.53 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cw) | (~q(cw)) | p(fy(cw)) | (~q(fz(cw))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(cw) | p(fy(cw))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[239])).
% 0.21/0.53 tff(241,plain,
% 0.21/0.53 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cw) | (~q(cw)) | p(fy(cw)) | (~q(fz(cw))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(fz(cw))) | p(cw) | p(fy(cw)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[240, 238])).
% 0.21/0.53 tff(242,plain,
% 0.21/0.53 ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cw) | (~q(cw)) | p(fy(cw)) | (~q(fz(cw))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(243,plain,
% 0.21/0.53 ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(fz(cw))) | p(cw) | p(fy(cw))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.21/0.53 tff(244,plain,
% 0.21/0.53 (p(cx) | (~q(cw)) | (~q(fz(cw))) | p(cw) | p(fy(cw))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[243, 205])).
% 0.21/0.53 tff(245,plain,
% 0.21/0.53 (p(fy(cw))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[244, 237, 5, 195, 194])).
% 0.21/0.53 tff(246,plain,
% 0.21/0.53 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(247,plain,
% 0.21/0.53 ((p(cx) | (~q(cw)) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw)))) <=> (p(cx) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(248,plain,
% 0.21/0.53 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw)))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[247])).
% 0.21/0.53 tff(249,plain,
% 0.21/0.53 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[248, 246])).
% 0.21/0.53 tff(250,plain,
% 0.21/0.53 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(251,plain,
% 0.21/0.53 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~p(fy(cw))) | (~q(fz5(cw)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.21/0.53 tff(252,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[251, 229, 5, 194, 245, 219])).
% 0.21/0.53 tff(253,plain,(p(cx)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(254,plain,
% 0.21/0.53 (^[Y3: $i, Z4: $i] : refl(((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))) <=> ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(255,plain,
% 0.21/0.53 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))) <=> ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[254])).
% 0.21/0.53 tff(256,plain,
% 0.21/0.53 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))) <=> ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(257,plain,
% 0.21/0.53 (^[Y3: $i, Z4: $i] : trans(monotonicity(rewrite((((~p(cx)) | (~q(Z4))) | p(Y3)) <=> ((~p(cx)) | p(Y3) | (~q(Z4)))), (((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw)) <=> (((~p(cx)) | p(Y3) | (~q(Z4))) | q(cw)))), rewrite((((~p(cx)) | p(Y3) | (~q(Z4))) | q(cw)) <=> ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))), (((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw)) <=> ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(258,plain,
% 0.21/0.53 (![Y3: $i, Z4: $i] : ((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw)) <=> ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[257])).
% 0.21/0.53 tff(259,axiom,(![Y3: $i, Z4: $i] : ((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.21/0.53 tff(260,plain,
% 0.21/0.53 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.53 tff(261,plain,
% 0.21/0.53 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.21/0.53 tff(262,plain,(
% 0.21/0.53 ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[261])).
% 0.21/0.53 tff(263,plain,
% 0.21/0.53 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.21/0.53 tff(264,plain,
% 0.21/0.53 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(fy(cx)))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(fy(cx)))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(265,plain,
% 0.21/0.53 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(fy(cx)))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(266,plain,
% 0.21/0.53 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(fy(cx))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.21/0.53 tff(267,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[266, 263, 253, 2, 3, 4])).
% 0.21/0.53 tff(268,plain,((~q(fz(fy(cx)))) | q(cw) | p(fy(cx))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(269,plain,
% 0.21/0.53 (~q(fz(fy(cx)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[268, 3, 2])).
% 0.21/0.53 tff(270,plain,
% 0.21/0.53 (^[Y1: $i, W3: $i] : refl(((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(271,plain,
% 0.21/0.53 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3))) <=> ![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[270])).
% 0.21/0.53 tff(272,plain,
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% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(273,plain,
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% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(274,plain,
% 0.21/0.53 (![Y1: $i, W3: $i] : (((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) | q(fz(W3))) <=> ![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[273])).
% 0.21/0.53 tff(275,axiom,(![Y1: $i, W3: $i] : (((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) | q(fz(W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_10')).
% 0.21/0.53 tff(276,plain,
% 0.21/0.53 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.21/0.53 tff(277,plain,
% 0.21/0.53 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.21/0.53 tff(278,plain,(
% 0.21/0.53 ![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[277])).
% 0.21/0.53 tff(279,plain,
% 0.21/0.53 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.21/0.53 tff(280,plain,
% 0.21/0.53 (((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | q(fy(cx)) | q(fz(fy(cx))))) <=> ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | (~p(cx)) | q(cw) | p(fy(cx)) | q(fy(cx)) | q(fz(fy(cx))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(281,plain,
% 0.21/0.53 ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | q(fy(cx)) | q(fz(fy(cx))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(282,plain,
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% 0.21/0.53 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.21/0.53 tff(283,plain,
% 0.21/0.53 (q(cw) | p(fy(cx)) | q(fy(cx)) | q(fz(fy(cx)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[282, 279, 253])).
% 0.21/0.53 tff(284,plain,
% 0.21/0.53 (q(fy(cx))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[283, 269, 2, 3])).
% 0.21/0.53 tff(285,plain,
% 0.21/0.53 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fy(cx))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(cx)) | (~q(fy(cx))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(286,plain,
% 0.21/0.53 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fy(cx))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(287,plain,
% 0.21/0.53 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(cx)) | (~q(fy(cx)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.21/0.54 tff(288,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[287, 263, 253, 2, 3, 284])).
% 0.21/0.54 tff(289,plain,(p(fy(cx)) | q(cw)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(290,plain,
% 0.21/0.54 (p(fy(cx))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[289, 2])).
% 0.21/0.54 tff(291,plain,
% 0.21/0.54 (^[W3: $i, X1: $i] : refl(((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(292,plain,
% 0.21/0.54 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))) <=> ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[291])).
% 0.21/0.54 tff(293,plain,
% 0.21/0.54 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))) <=> ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(294,plain,
% 0.21/0.54 (^[W3: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) <=> ((~p(cx)) | (~p(X1)) | (~p(fy(X1))))), (((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) <=> (((~p(cx)) | (~p(X1)) | (~p(fy(X1)))) | q(cw)))), rewrite((((~p(cx)) | (~p(X1)) | (~p(fy(X1)))) | q(cw)) <=> ((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1))))), (((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) <=> ((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1)))))), ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) <=> (((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1)))) | q(W3)))), rewrite((((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1)))) | q(W3)) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1))))), ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1)))))), (((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3))) <=> (((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1)))) | q(fz(W3))))), rewrite((((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1)))) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))), (((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(295,plain,
% 0.21/0.54 (![W3: $i, X1: $i] : ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3))) <=> ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[294])).
% 0.21/0.54 tff(296,axiom,(![W3: $i, X1: $i] : ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_22')).
% 0.21/0.54 tff(297,plain,
% 0.21/0.54 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.21/0.54 tff(298,plain,
% 0.21/0.54 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[297, 293])).
% 0.21/0.54 tff(299,plain,(
% 0.21/0.54 ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.21/0.54 inference(skolemize,[status(sab)],[298])).
% 0.21/0.54 tff(300,plain,
% 0.21/0.54 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[299, 292])).
% 0.21/0.54 tff(301,plain,
% 0.21/0.54 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(fz(cw)) | (~p(fy(cx))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(fz(cw)) | (~p(fy(cx))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(302,plain,
% 0.21/0.54 (((~p(cx)) | q(cw) | q(cw) | (~p(cx)) | q(fz(cw)) | (~p(fy(cx)))) <=> ((~p(cx)) | q(cw) | q(fz(cw)) | (~p(fy(cx))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(303,plain,
% 0.21/0.54 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cw) | (~p(cx)) | q(fz(cw)) | (~p(fy(cx))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(fz(cw)) | (~p(fy(cx)))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[302])).
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% 0.21/0.54 inference(transitivity,[status(thm)],[303, 301])).
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% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(306,plain,
% 0.21/0.54 ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(fz(cw)) | (~p(fy(cx)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.21/0.54 tff(307,plain,
% 0.21/0.54 ((~p(cx)) | q(cw) | q(fz(cw)) | (~p(fy(cx)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[306, 300])).
% 0.21/0.54 tff(308,plain,
% 0.21/0.54 (q(cw) | q(fz(cw)) | (~p(fy(cx)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[307, 253])).
% 0.21/0.54 tff(309,plain,
% 0.21/0.54 (q(fz(cw))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[308, 290, 2])).
% 0.21/0.54 tff(310,plain,
% 0.21/0.54 (^[X7: $i, Z4: $i] : refl(((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))) <=> ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(311,plain,
% 0.21/0.54 (![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))) <=> ![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[310])).
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% 0.21/0.54 (![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))) <=> ![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(313,plain,
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% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(314,plain,
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% 0.21/0.54 inference(quant_intro,[status(thm)],[313])).
% 0.21/0.54 tff(315,axiom,(![X7: $i, Z4: $i] : (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(Z4))) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
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% 0.21/0.54 inference(modus_ponens,[status(thm)],[315, 314])).
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% 0.21/0.54 inference(skolemize,[status(sab)],[317])).
% 0.21/0.54 tff(319,plain,
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% 0.21/0.54 inference(modus_ponens,[status(thm)],[318, 311])).
% 0.21/0.54 tff(320,plain,
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% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(321,plain,
% 0.21/0.54 (((~p(cx)) | q(cw) | (~q(fz(cw))) | (~p(cx)) | (~p(fy5(cx)))) <=> ((~p(cx)) | q(cw) | (~q(fz(cw))) | (~p(fy5(cx))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(322,plain,
% 0.21/0.54 (((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(fz(cw))) | (~p(cx)) | (~p(fy5(cx))))) <=> ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(fz(cw))) | (~p(fy5(cx)))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[321])).
% 0.21/0.54 tff(323,plain,
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% 0.21/0.55 inference(transitivity,[status(thm)],[322, 320])).
% 0.21/0.55 tff(324,plain,
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% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(325,plain,
% 0.21/0.55 ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | (~p(cx)) | q(cw) | (~q(fz(cw))) | (~p(fy5(cx)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.21/0.55 tff(326,plain,
% 0.21/0.55 (q(cw) | (~q(fz(cw))) | (~p(fy5(cx)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[325, 319, 253])).
% 0.21/0.55 tff(327,plain,
% 0.21/0.55 (~p(fy5(cx))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[326, 309, 2])).
% 0.21/0.55 tff(328,plain,
% 0.21/0.55 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | (~q(fz(cw))) | p(fy5(cx)))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(fz(cw))) | p(fy5(cx)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(329,plain,
% 0.21/0.55 (((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cw)))) <=> ((~p(cx)) | q(cw) | (~q(fz(cw))) | p(fy5(cx)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(330,plain,
% 0.21/0.55 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cw))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | (~q(fz(cw))) | p(fy5(cx))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[329])).
% 0.21/0.55 tff(331,plain,
% 0.21/0.55 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cw))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(fz(cw))) | p(fy5(cx)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[330, 328])).
% 0.21/0.55 tff(332,plain,
% 0.21/0.55 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cw))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(333,plain,
% 0.21/0.55 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(fz(cw))) | p(fy5(cx))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.21/0.55 tff(334,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[333, 263, 253, 2, 309, 327])).
% 0.21/0.55 tff(335,plain,(q(cw)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(336,plain,
% 0.21/0.55 (^[W9: $i, Y3: $i] : refl(((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9))) <=> ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(337,plain,
% 0.21/0.55 (![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9))) <=> ![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[336])).
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% 0.21/0.55 (![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9))) <=> ![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(339,plain,
% 0.21/0.55 (^[W9: $i, Y3: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p(cx)) | (~q(cw))) | (~q(W9))) <=> ((~p(cx)) | (~q(cw)) | (~q(W9)))), (((((~p(cx)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) <=> (((~p(cx)) | (~q(cw)) | (~q(W9))) | (~q(fz5(W9)))))), rewrite((((~p(cx)) | (~q(cw)) | (~q(W9))) | (~q(fz5(W9)))) <=> ((~p(cx)) | (~q(cw)) | (~q(fz5(W9))) | (~q(W9)))), (((((~p(cx)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) <=> ((~p(cx)) | (~q(cw)) | (~q(fz5(W9))) | (~q(W9))))), ((((((~p(cx)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(Y3)) <=> (((~p(cx)) | (~q(cw)) | (~q(fz5(W9))) | (~q(W9))) | p(Y3)))), rewrite((((~p(cx)) | (~q(cw)) | (~q(fz5(W9))) | (~q(W9))) | p(Y3)) <=> ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))), ((((((~p(cx)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(Y3)) <=> ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(340,plain,
% 0.21/0.55 (![W9: $i, Y3: $i] : (((((~p(cx)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(Y3)) <=> ![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[339])).
% 0.21/0.55 tff(341,axiom,(![W9: $i, Y3: $i] : (((((~p(cx)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(Y3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.21/0.55 tff(342,plain,
% 0.21/0.55 (![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.21/0.55 tff(343,plain,
% 0.21/0.55 (![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.21/0.55 tff(344,plain,(
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% 0.21/0.55 inference(skolemize,[status(sab)],[343])).
% 0.21/0.55 tff(345,plain,
% 0.21/0.55 (![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[344, 337])).
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% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(347,plain,
% 0.21/0.55 (((~p(cx)) | (~q(cw)) | p(fy5(cx)) | (~q(fz5(cw))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | p(fy5(cx)) | (~q(fz5(cw))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(348,plain,
% 0.21/0.55 (((~![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | p(fy5(cx)) | (~q(fz5(cw))) | (~q(cw)))) <=> ((~![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | p(fy5(cx)) | (~q(fz5(cw)))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[347])).
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% 0.21/0.55 inference(transitivity,[status(thm)],[348, 346])).
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% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.21/0.55 ((~![W9: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9)))) | (~p(cx)) | (~q(cw)) | p(fy5(cx)) | (~q(fz5(cw)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[350, 349])).
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% 0.21/0.55 inference(unit_resolution,[status(thm)],[351, 345, 253, 335])).
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% 0.21/0.55 (~q(fz5(cw))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[352, 1])).
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% 0.21/0.55 (^[Z3: $i, Y3: $i] : refl(((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3)) <=> ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3)))),
% 0.21/0.55 inference(bind,[status(th)],[])).
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% 0.21/0.55 (![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3)) <=> ![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[354])).
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% 0.21/0.55 inference(rewrite,[status(thm)],[])).
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% 0.21/0.55 inference(bind,[status(th)],[])).
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% 0.21/0.55 (![Z3: $i, Y3: $i] : ((((~p(cx)) | (~q(cw))) | p(Y3)) | q(Z3)) <=> ![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[357])).
% 0.21/0.55 tff(359,axiom,(![Z3: $i, Y3: $i] : ((((~p(cx)) | (~q(cw))) | p(Y3)) | q(Z3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
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% 0.21/0.55 inference(modus_ponens,[status(thm)],[359, 358])).
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% 0.21/0.55 (![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[360, 356])).
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% 0.21/0.55 inference(skolemize,[status(sab)],[361])).
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% 0.21/0.55 inference(modus_ponens,[status(thm)],[362, 355])).
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% 0.21/0.55 (((~![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | p(fy5(cx)))) <=> ((~![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3))) | (~p(cx)) | (~q(cw)) | q(fz5(cw)) | p(fy5(cx)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
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% 0.21/0.55 ((~![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | p(fy5(cx)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
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% 0.21/0.55 ((~![Z3: $i, Y3: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | p(Y3))) | (~p(cx)) | (~q(cw)) | q(fz5(cw)) | p(fy5(cx))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.21/0.55 tff(367,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[366, 363, 253, 335, 1, 353])).
% 0.21/0.55 tff(368,plain,(p(fy5(cx))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(369,plain,
% 0.21/0.55 (^[W9: $i, X7: $i] : refl(((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
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% 0.21/0.55 (![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9))) <=> ![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[369])).
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% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(372,plain,
% 0.21/0.55 (^[W9: $i, X7: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) <=> ((~p(cx)) | (~p(fy5(X7))) | (~p(X7)))), (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) <=> (((~p(cx)) | (~p(fy5(X7))) | (~p(X7))) | (~q(cw))))), rewrite((((~p(cx)) | (~p(fy5(X7))) | (~p(X7))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)))), (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))))), ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | (~q(W9))) <=> (((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))) | (~q(W9))))), rewrite((((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))) | (~q(W9))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(W9)))), ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | (~q(W9))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(W9))))), (((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) <=> (((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(W9))) | (~q(fz5(W9)))))), rewrite((((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(W9))) | (~q(fz5(W9)))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))), (((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(373,plain,
% 0.21/0.56 (![W9: $i, X7: $i] : ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) <=> ![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[372])).
% 0.21/0.56 tff(374,axiom,(![W9: $i, X7: $i] : ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_23')).
% 0.21/0.56 tff(375,plain,
% 0.21/0.56 (![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.21/0.56 tff(376,plain,
% 0.21/0.56 (![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[375, 371])).
% 0.21/0.56 tff(377,plain,(
% 0.21/0.56 ![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[376])).
% 0.21/0.56 tff(378,plain,
% 0.21/0.56 (![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[377, 370])).
% 0.21/0.56 tff(379,plain,
% 0.21/0.56 (((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~q(fz5(cw))) | (~p(fy5(cx))))) <=> ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | (~p(cx)) | (~q(cw)) | (~q(fz5(cw))) | (~p(fy5(cx))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(380,plain,
% 0.21/0.56 (((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~p(cx)) | (~q(fz5(cw))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | (~q(fz5(cw))) | (~p(fy5(cx))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(381,plain,
% 0.21/0.56 (((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~p(cx)) | (~q(fz5(cw))) | (~q(cw)))) <=> ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~q(fz5(cw))) | (~p(fy5(cx)))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[380])).
% 0.21/0.56 tff(382,plain,
% 0.21/0.56 (((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~p(cx)) | (~q(fz5(cw))) | (~q(cw)))) <=> ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | (~p(cx)) | (~q(cw)) | (~q(fz5(cw))) | (~p(fy5(cx))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[381, 379])).
% 0.21/0.56 tff(383,plain,
% 0.21/0.56 ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~p(cx)) | (~q(fz5(cw))) | (~q(cw)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(384,plain,
% 0.21/0.56 ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | (~p(cx)) | (~q(cw)) | (~q(fz5(cw))) | (~p(fy5(cx)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.21/0.56 tff(385,plain,
% 0.21/0.56 ((~q(fz5(cw))) | (~p(fy5(cx)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[384, 378, 253, 335])).
% 0.21/0.56 tff(386,plain,
% 0.21/0.56 (~q(fz5(cw))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[385, 368])).
% 0.21/0.56 tff(387,plain,
% 0.21/0.56 (^[Z3: $i, X7: $i] : refl(((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))) <=> ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(388,plain,
% 0.21/0.56 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))) <=> ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[387])).
% 0.21/0.56 tff(389,plain,
% 0.21/0.56 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))) <=> ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(390,plain,
% 0.21/0.56 (^[Z3: $i, X7: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) <=> ((~p(cx)) | (~p(fy5(X7))) | (~p(X7)))), (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) <=> (((~p(cx)) | (~p(fy5(X7))) | (~p(X7))) | (~q(cw))))), rewrite((((~p(cx)) | (~p(fy5(X7))) | (~p(X7))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)))), (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))))), ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3)) <=> (((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))) | q(Z3)))), rewrite((((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))) | q(Z3)) <=> ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))), ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3)) <=> ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(391,plain,
% 0.21/0.56 (![Z3: $i, X7: $i] : (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3)) <=> ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[390])).
% 0.21/0.56 tff(392,axiom,(![Z3: $i, X7: $i] : (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.21/0.56 tff(393,plain,
% 0.21/0.56 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.21/0.56 tff(394,plain,
% 0.21/0.56 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[393, 389])).
% 0.21/0.56 tff(395,plain,(
% 0.21/0.56 ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[394])).
% 0.21/0.56 tff(396,plain,
% 0.21/0.56 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[395, 388])).
% 0.21/0.56 tff(397,plain,
% 0.21/0.56 (((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))))) <=> ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | (~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(398,plain,
% 0.21/0.56 (((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx))) <=> ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(399,plain,
% 0.21/0.56 (((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx)))) <=> ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx)))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[398])).
% 0.21/0.56 tff(400,plain,
% 0.21/0.56 (((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx)))) <=> ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | (~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[399, 397])).
% 0.21/0.56 tff(401,plain,
% 0.21/0.56 ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(402,plain,
% 0.21/0.56 ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | (~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.21/0.56 tff(403,plain,
% 0.21/0.56 (q(fz5(cw)) | (~p(fy5(cx)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[402, 396, 253, 335])).
% 0.21/0.56 tff(404,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[403, 386, 368])).
% 0.21/0.56 % SZS output end Proof
%------------------------------------------------------------------------------