TSTP Solution File: SYN037-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN037-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 23:53:15 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN037-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 01:12:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(p_type, type, (
% 0.20/0.40 p: $i > $o)).
% 0.20/0.40 tff(fy_type, type, (
% 0.20/0.40 fy: $i > $i)).
% 0.20/0.40 tff(cvv_type, type, (
% 0.20/0.40 cvv: $i)).
% 0.20/0.40 tff(m3_type, type, (
% 0.20/0.40 m3: $o)).
% 0.20/0.40 tff(m2_type, type, (
% 0.20/0.40 m2: $o)).
% 0.20/0.40 tff(q_type, type, (
% 0.20/0.40 q: $i > $o)).
% 0.20/0.40 tff(fz2_type, type, (
% 0.20/0.40 fz2: $i > $i)).
% 0.20/0.40 tff(cv_type, type, (
% 0.20/0.40 cv: $i)).
% 0.20/0.40 tff(m1_type, type, (
% 0.20/0.40 m1: $o)).
% 0.20/0.40 tff(cw_type, type, (
% 0.20/0.40 cw: $i)).
% 0.20/0.40 tff(fy3_type, type, (
% 0.20/0.40 fy3: $i > $i)).
% 0.20/0.40 tff(cu_type, type, (
% 0.20/0.40 cu: $i)).
% 0.20/0.40 tff(cuu_type, type, (
% 0.20/0.40 cuu: $i)).
% 0.20/0.40 tff(cx_type, type, (
% 0.20/0.40 cx: $i)).
% 0.20/0.40 tff(fz5_type, type, (
% 0.20/0.40 fz5: $i > $i)).
% 0.20/0.40 tff(1,assumption,(~p(cvv)), introduced(assumption)).
% 0.20/0.40 tff(2,assumption,(~m2), introduced(assumption)).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 ((m2 | p(cv)) <=> (m2 | p(cv))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(m2 | p(cv)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_21')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (m2 | p(cv)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (p(cv)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.20/0.40 tff(7,assumption,(~m1), introduced(assumption)).
% 0.20/0.40 tff(8,assumption,(m2), introduced(assumption)).
% 0.20/0.40 tff(9,assumption,(p(fy3(cvv))), introduced(assumption)).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[Vv1: $i, V1: $i] : refl(((~p(V1)) | (~m2) | p(Vv1)) <=> ((~p(V1)) | (~m2) | p(Vv1)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1)) <=> ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1)) <=> ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (^[Vv1: $i, V1: $i] : rewrite((((~m2) | (~p(V1))) | p(Vv1)) <=> ((~p(V1)) | (~m2) | p(Vv1)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![Vv1: $i, V1: $i] : (((~m2) | (~p(V1))) | p(Vv1)) <=> ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.40 tff(15,axiom,(![Vv1: $i, V1: $i] : (((~m2) | (~p(V1))) | p(Vv1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_18')).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.40 tff(18,plain,(
% 0.20/0.40 ![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.20/0.40 inference(skolemize,[status(sab)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy3(cvv))))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy3(cvv))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (((~p(fy3(cvv))) | (~m2) | p(cvv)) <=> ((~m2) | p(cvv) | (~p(fy3(cvv))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy3(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy3(cvv)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy3(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy3(cvv))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy3(cvv))) | (~m2) | p(cvv))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy3(cvv)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[25, 19, 8, 1, 9])).
% 0.20/0.40 tff(27,plain,((~p(fy3(cvv))) | (~m2) | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~p(fy3(cvv))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 1, 8])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (^[X2: $i] : refl((m1 | m3 | p(X2) | p(fy3(X2))) <=> (m1 | m3 | p(X2) | p(fy3(X2))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2))) <=> ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2))) <=> ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (^[X2: $i] : trans(monotonicity(rewrite(((m1 | m3) | p(X2)) <=> (m1 | m3 | p(X2))), ((((m1 | m3) | p(X2)) | p(fy3(X2))) <=> ((m1 | m3 | p(X2)) | p(fy3(X2))))), rewrite(((m1 | m3 | p(X2)) | p(fy3(X2))) <=> (m1 | m3 | p(X2) | p(fy3(X2)))), ((((m1 | m3) | p(X2)) | p(fy3(X2))) <=> (m1 | m3 | p(X2) | p(fy3(X2)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![X2: $i] : (((m1 | m3) | p(X2)) | p(fy3(X2))) <=> ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.40 tff(34,axiom,(![X2: $i] : (((m1 | m3) | p(X2)) | p(fy3(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_16')).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.40 tff(37,plain,(
% 0.20/0.40 ![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[36])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | (m1 | m3 | p(cvv) | p(fy3(cvv)))) <=> ((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | m1 | m3 | p(cvv) | p(fy3(cvv)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | (m1 | m3 | p(cvv) | p(fy3(cvv)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~![X2: $i] : (m1 | m3 | p(X2) | p(fy3(X2)))) | m1 | m3 | p(cvv) | p(fy3(cvv))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (m1 | m3 | p(cvv) | p(fy3(cvv))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (m3),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[42, 7, 1, 28])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 ((m1 | q(cu)) <=> (m1 | q(cu))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(45,axiom,(m1 | q(cu)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_22')).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (m1 | q(cu)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (q(cu)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 7])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (^[Z: $i] : refl(((~m3) | (~m2) | q(cw) | (~q(Z))) <=> ((~m3) | (~m2) | q(cw) | (~q(Z))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z))) <=> ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z))) <=> ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (^[Z: $i] : trans(monotonicity(rewrite((((~m2) | (~m3)) | (~q(Z))) <=> ((~m3) | (~m2) | (~q(Z)))), (((((~m2) | (~m3)) | (~q(Z))) | q(cw)) <=> (((~m3) | (~m2) | (~q(Z))) | q(cw)))), rewrite((((~m3) | (~m2) | (~q(Z))) | q(cw)) <=> ((~m3) | (~m2) | q(cw) | (~q(Z)))), (((((~m2) | (~m3)) | (~q(Z))) | q(cw)) <=> ((~m3) | (~m2) | q(cw) | (~q(Z)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![Z: $i] : ((((~m2) | (~m3)) | (~q(Z))) | q(cw)) <=> ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.40 tff(53,axiom,(![Z: $i] : ((((~m2) | (~m3)) | (~q(Z))) | q(cw))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.41 tff(56,plain,(
% 0.20/0.41 ![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[55])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | ((~m3) | (~m2) | q(cw) | (~q(cu)))) <=> ((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | (~m3) | (~m2) | q(cw) | (~q(cu)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | ((~m3) | (~m2) | q(cw) | (~q(cu)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![Z: $i] : ((~m3) | (~m2) | q(cw) | (~q(Z)))) | (~m3) | (~m2) | q(cw) | (~q(cu))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (q(cw)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 57, 8, 47, 43])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((m1 | (~q(cuu))) <=> (m1 | (~q(cuu)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~q(cuu)) | m1) <=> (m1 | (~q(cuu)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(64,axiom,((~q(cuu)) | m1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_20')).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (m1 | (~q(cuu))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (m1 | (~q(cuu))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 62])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (~q(cuu)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 7])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (^[Z1: $i] : refl(((~m3) | (~m2) | (~q(cw)) | q(Z1)) <=> ((~m3) | (~m2) | (~q(cw)) | q(Z1)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1)) <=> ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1)) <=> ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (^[Z1: $i] : trans(monotonicity(rewrite((((~m2) | (~m3)) | (~q(cw))) <=> ((~m3) | (~m2) | (~q(cw)))), (((((~m2) | (~m3)) | (~q(cw))) | q(Z1)) <=> (((~m3) | (~m2) | (~q(cw))) | q(Z1)))), rewrite((((~m3) | (~m2) | (~q(cw))) | q(Z1)) <=> ((~m3) | (~m2) | (~q(cw)) | q(Z1))), (((((~m2) | (~m3)) | (~q(cw))) | q(Z1)) <=> ((~m3) | (~m2) | (~q(cw)) | q(Z1))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![Z1: $i] : ((((~m2) | (~m3)) | (~q(cw))) | q(Z1)) <=> ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.41 tff(73,axiom,(![Z1: $i] : ((((~m2) | (~m3)) | (~q(cw))) | q(Z1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5')).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.41 tff(76,plain,(
% 0.20/0.41 ![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.20/0.41 inference(skolemize,[status(sab)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | ((~m3) | (~m2) | (~q(cw)) | q(cuu))) <=> ((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | (~m3) | (~m2) | (~q(cw)) | q(cuu))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | ((~m3) | (~m2) | (~q(cw)) | q(cuu))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 ((~![Z1: $i] : ((~m3) | (~m2) | (~q(cw)) | q(Z1))) | (~m3) | (~m2) | (~q(cw)) | q(cuu)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[80, 77, 8, 67, 43, 61])).
% 0.20/0.41 tff(82,plain,(m1 | (~m2) | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (~m2),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[82, 1, 7])).
% 0.20/0.41 tff(84,assumption,(m3), introduced(assumption)).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (^[Y1: $i] : refl((m1 | (~m3) | (~p(cx)) | p(Y1)) <=> (m1 | (~m3) | (~p(cx)) | p(Y1)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1)) <=> ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1)) <=> ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (^[Y1: $i] : trans(monotonicity(rewrite((((~m3) | (~p(cx))) | m1) <=> (m1 | (~m3) | (~p(cx)))), (((((~m3) | (~p(cx))) | m1) | p(Y1)) <=> ((m1 | (~m3) | (~p(cx))) | p(Y1)))), rewrite(((m1 | (~m3) | (~p(cx))) | p(Y1)) <=> (m1 | (~m3) | (~p(cx)) | p(Y1))), (((((~m3) | (~p(cx))) | m1) | p(Y1)) <=> (m1 | (~m3) | (~p(cx)) | p(Y1))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![Y1: $i] : ((((~m3) | (~p(cx))) | m1) | p(Y1)) <=> ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.41 tff(90,axiom,(![Y1: $i] : ((((~m3) | (~p(cx))) | m1) | p(Y1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_9')).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.41 tff(93,plain,(
% 0.20/0.41 ![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.20/0.41 inference(skolemize,[status(sab)],[92])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | (m1 | (~m3) | (~p(cx)) | p(cvv))) <=> ((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | m1 | (~m3) | (~p(cx)) | p(cvv))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | (m1 | (~m3) | (~p(cx)) | p(cvv))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~![Y1: $i] : (m1 | (~m3) | (~p(cx)) | p(Y1))) | m1 | (~m3) | (~p(cx)) | p(cvv)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (m1 | (~m3) | (~p(cx))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 94, 1])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (~p(cx)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 84, 7])).
% 0.20/0.41 tff(100,assumption,(p(cv)), introduced(assumption)).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (^[Y2: $i] : refl((m1 | (~m3) | p(cx) | (~p(Y2))) <=> (m1 | (~m3) | p(cx) | (~p(Y2))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2))) <=> ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2))) <=> ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (^[Y2: $i] : trans(monotonicity(rewrite((((~m3) | (~p(Y2))) | m1) <=> (m1 | (~m3) | (~p(Y2)))), (((((~m3) | (~p(Y2))) | m1) | p(cx)) <=> ((m1 | (~m3) | (~p(Y2))) | p(cx)))), rewrite(((m1 | (~m3) | (~p(Y2))) | p(cx)) <=> (m1 | (~m3) | p(cx) | (~p(Y2)))), (((((~m3) | (~p(Y2))) | m1) | p(cx)) <=> (m1 | (~m3) | p(cx) | (~p(Y2)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![Y2: $i] : ((((~m3) | (~p(Y2))) | m1) | p(cx)) <=> ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.41 tff(106,axiom,(![Y2: $i] : ((((~m3) | (~p(Y2))) | m1) | p(cx))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10')).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.41 tff(109,plain,(
% 0.20/0.41 ![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[108])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | (m1 | (~m3) | p(cx) | (~p(cv)))) <=> ((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | m1 | (~m3) | p(cx) | (~p(cv)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 ((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | (m1 | (~m3) | p(cx) | (~p(cv)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~![Y2: $i] : (m1 | (~m3) | p(cx) | (~p(Y2)))) | m1 | (~m3) | p(cx) | (~p(cv))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (m1 | (~m3) | p(cx)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[114, 99, 84, 7])).
% 0.20/0.42 tff(116,plain,((~m3) | m1 | (~p(cv)) | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (~m3),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[116, 7, 6, 1])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (^[Z3: $i] : refl((m3 | m2 | q(cw) | (~q(Z3))) <=> (m3 | m2 | q(cw) | (~q(Z3))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3))) <=> ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3))) <=> ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (^[Z3: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~q(Z3)) | m2) <=> (m2 | (~q(Z3)))), ((((~q(Z3)) | m2) | m3) <=> ((m2 | (~q(Z3))) | m3))), rewrite(((m2 | (~q(Z3))) | m3) <=> (m3 | m2 | (~q(Z3)))), ((((~q(Z3)) | m2) | m3) <=> (m3 | m2 | (~q(Z3))))), (((((~q(Z3)) | m2) | m3) | q(cw)) <=> ((m3 | m2 | (~q(Z3))) | q(cw)))), rewrite(((m3 | m2 | (~q(Z3))) | q(cw)) <=> (m3 | m2 | q(cw) | (~q(Z3)))), (((((~q(Z3)) | m2) | m3) | q(cw)) <=> (m3 | m2 | q(cw) | (~q(Z3)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (![Z3: $i] : ((((~q(Z3)) | m2) | m3) | q(cw)) <=> ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.42 tff(123,axiom,(![Z3: $i] : ((((~q(Z3)) | m2) | m3) | q(cw))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_15')).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.42 tff(126,plain,(
% 0.20/0.42 ![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[125])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | (m3 | m2 | q(cw) | (~q(cu)))) <=> ((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | m3 | m2 | q(cw) | (~q(cu)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 ((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | (m3 | m2 | q(cw) | (~q(cu)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 ((~![Z3: $i] : (m3 | m2 | q(cw) | (~q(Z3)))) | m3 | m2 | q(cw) | (~q(cu))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (m3 | q(cw)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[130, 127, 2, 47])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (q(cw)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[131, 117])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (^[Z4: $i] : refl((m3 | m2 | (~q(cw)) | q(Z4)) <=> (m3 | m2 | (~q(cw)) | q(Z4)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4)) <=> ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4)) <=> ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
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% 0.20/0.42 tff(136,plain,
% 0.20/0.42 (^[Z4: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~q(cw)) | m2) <=> (m2 | (~q(cw)))), ((((~q(cw)) | m2) | m3) <=> ((m2 | (~q(cw))) | m3))), rewrite(((m2 | (~q(cw))) | m3) <=> (m3 | m2 | (~q(cw)))), ((((~q(cw)) | m2) | m3) <=> (m3 | m2 | (~q(cw))))), (((((~q(cw)) | m2) | m3) | q(Z4)) <=> ((m3 | m2 | (~q(cw))) | q(Z4)))), rewrite(((m3 | m2 | (~q(cw))) | q(Z4)) <=> (m3 | m2 | (~q(cw)) | q(Z4))), (((((~q(cw)) | m2) | m3) | q(Z4)) <=> (m3 | m2 | (~q(cw)) | q(Z4))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (![Z4: $i] : ((((~q(cw)) | m2) | m3) | q(Z4)) <=> ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.42 tff(138,axiom,(![Z4: $i] : ((((~q(cw)) | m2) | m3) | q(Z4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_14')).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.42 tff(141,plain,(
% 0.20/0.42 ![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.20/0.42 inference(skolemize,[status(sab)],[140])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | (m3 | m2 | (~q(cw)) | q(cuu))) <=> ((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | m3 | m2 | (~q(cw)) | q(cuu))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 ((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | (m3 | m2 | (~q(cw)) | q(cuu))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ((~![Z4: $i] : (m3 | m2 | (~q(cw)) | q(Z4))) | m3 | m2 | (~q(cw)) | q(cuu)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (m3 | (~q(cw))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[145, 142, 2, 67])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[146, 132, 117])).
% 0.20/0.42 tff(148,plain,(m1 | m2 | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[148, 83, 1, 7])).
% 0.20/0.42 tff(150,plain,(p(cvv) | m1), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 (p(cvv)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[150, 7])).
% 0.20/0.42 tff(152,assumption,(~p(fy3(cvv))), introduced(assumption)).
% 0.20/0.42 tff(153,assumption,(p(cvv)), introduced(assumption)).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 ((m2 | (~p(cvv))) <=> (m2 | (~p(cvv)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 (((~p(cvv)) | m2) <=> (m2 | (~p(cvv)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(156,axiom,((~p(cvv)) | m2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_19')).
% 0.20/0.42 tff(157,plain,
% 0.20/0.42 (m2 | (~p(cvv))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 (m2 | (~p(cvv))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[157, 154])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 (m2),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[158, 153])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(fy3(cvv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy3(cvv)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 (((~p(cvv)) | (~m2) | p(fy3(cvv))) <=> ((~m2) | (~p(cvv)) | p(fy3(cvv)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy3(cvv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(fy3(cvv))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.42 tff(163,plain,
% 0.20/0.42 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy3(cvv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy3(cvv)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.42 tff(164,plain,
% 0.20/0.42 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy3(cvv)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(165,plain,
% 0.20/0.42 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy3(cvv))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.42 tff(166,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[165, 19, 159, 153, 152])).
% 0.20/0.42 tff(167,plain,(p(fy3(cvv)) | (~p(cvv))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(168,plain,
% 0.20/0.42 (p(fy3(cvv))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[167, 151])).
% 0.20/0.42 tff(169,plain,
% 0.20/0.42 (^[X2: $i] : refl((m1 | m3 | (~p(X2)) | (~p(fy3(X2)))) <=> (m1 | m3 | (~p(X2)) | (~p(fy3(X2)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(170,plain,
% 0.20/0.42 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2)))) <=> ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.42 tff(171,plain,
% 0.20/0.42 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2)))) <=> ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(172,plain,
% 0.20/0.42 (^[X2: $i] : trans(monotonicity(rewrite((((~p(X2)) | (~p(fy3(X2)))) | m1) <=> (m1 | (~p(X2)) | (~p(fy3(X2))))), (((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3) <=> ((m1 | (~p(X2)) | (~p(fy3(X2)))) | m3))), rewrite(((m1 | (~p(X2)) | (~p(fy3(X2)))) | m3) <=> (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))), (((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3) <=> (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(173,plain,
% 0.20/0.42 (![X2: $i] : ((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3) <=> ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.42 tff(174,axiom,(![X2: $i] : ((((~p(X2)) | (~p(fy3(X2)))) | m1) | m3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_13')).
% 0.20/0.42 tff(175,plain,
% 0.20/0.42 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.42 tff(176,plain,
% 0.20/0.42 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.20/0.42 tff(177,plain,(
% 0.20/0.42 ![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[176])).
% 0.20/0.42 tff(178,plain,
% 0.20/0.42 (![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.20/0.42 tff(179,plain,
% 0.20/0.42 (((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | (m1 | m3 | (~p(cvv)) | (~p(fy3(cvv))))) <=> ((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | m1 | m3 | (~p(cvv)) | (~p(fy3(cvv))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(180,plain,
% 0.20/0.42 ((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | (m1 | m3 | (~p(cvv)) | (~p(fy3(cvv))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(181,plain,
% 0.20/0.42 ((~![X2: $i] : (m1 | m3 | (~p(X2)) | (~p(fy3(X2))))) | m1 | m3 | (~p(cvv)) | (~p(fy3(cvv)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.42 tff(182,plain,
% 0.20/0.42 (m1 | m3 | (~p(cvv)) | (~p(fy3(cvv)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.20/0.42 tff(183,plain,
% 0.20/0.42 (m3),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[182, 168, 7, 151])).
% 0.20/0.42 tff(184,plain,
% 0.20/0.42 (m2),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[158, 151])).
% 0.20/0.42 tff(185,plain,
% 0.20/0.42 ((~m3) | q(cw)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 57, 184, 47])).
% 0.20/0.42 tff(186,plain,
% 0.20/0.42 (q(cw)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[185, 183])).
% 0.20/0.42 tff(187,plain,
% 0.20/0.42 ((~m3) | (~q(cw))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[80, 77, 184, 67])).
% 0.20/0.42 tff(188,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[187, 186, 183])).
% 0.20/0.42 tff(189,plain,(m1), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(190,assumption,(m1), introduced(assumption)).
% 0.20/0.42 tff(191,assumption,(~m3), introduced(assumption)).
% 0.20/0.42 tff(192,plain,
% 0.20/0.42 (^[Y5: $i] : refl(((~m1) | m3 | p(cx) | (~p(Y5))) <=> ((~m1) | m3 | p(cx) | (~p(Y5))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(193,plain,
% 0.20/0.42 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5))) <=> ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[192])).
% 0.20/0.42 tff(194,plain,
% 0.20/0.42 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5))) <=> ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(195,plain,
% 0.20/0.42 (^[Y5: $i] : trans(monotonicity(rewrite((((~m1) | (~p(Y5))) | m3) <=> ((~m1) | m3 | (~p(Y5)))), (((((~m1) | (~p(Y5))) | m3) | p(cx)) <=> (((~m1) | m3 | (~p(Y5))) | p(cx)))), rewrite((((~m1) | m3 | (~p(Y5))) | p(cx)) <=> ((~m1) | m3 | p(cx) | (~p(Y5)))), (((((~m1) | (~p(Y5))) | m3) | p(cx)) <=> ((~m1) | m3 | p(cx) | (~p(Y5)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(196,plain,
% 0.20/0.42 (![Y5: $i] : ((((~m1) | (~p(Y5))) | m3) | p(cx)) <=> ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[195])).
% 0.20/0.43 tff(197,axiom,(![Y5: $i] : ((((~m1) | (~p(Y5))) | m3) | p(cx))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.43 tff(199,plain,
% 0.20/0.43 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.20/0.43 tff(200,plain,(
% 0.20/0.43 ![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[199])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 (![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 (((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | ((~m1) | m3 | p(cx) | (~p(cv)))) <=> ((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | (~m1) | m3 | p(cx) | (~p(cv)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(203,plain,
% 0.20/0.43 ((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | ((~m1) | m3 | p(cx) | (~p(cv)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(204,plain,
% 0.20/0.43 ((~![Y5: $i] : ((~m1) | m3 | p(cx) | (~p(Y5)))) | (~m1) | m3 | p(cx) | (~p(cv))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.43 tff(205,plain,
% 0.20/0.43 ((~m1) | m3 | p(cx)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[204, 201, 100])).
% 0.20/0.43 tff(206,plain,
% 0.20/0.43 (p(cx)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[205, 191, 190])).
% 0.20/0.43 tff(207,plain,
% 0.20/0.43 (^[Y4: $i] : refl(((~m1) | m3 | (~p(cx)) | p(Y4)) <=> ((~m1) | m3 | (~p(cx)) | p(Y4)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(208,plain,
% 0.20/0.43 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4)) <=> ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[207])).
% 0.20/0.43 tff(209,plain,
% 0.20/0.43 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4)) <=> ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(210,plain,
% 0.20/0.43 (^[Y4: $i] : trans(monotonicity(rewrite((((~m1) | (~p(cx))) | m3) <=> ((~m1) | m3 | (~p(cx)))), (((((~m1) | (~p(cx))) | m3) | p(Y4)) <=> (((~m1) | m3 | (~p(cx))) | p(Y4)))), rewrite((((~m1) | m3 | (~p(cx))) | p(Y4)) <=> ((~m1) | m3 | (~p(cx)) | p(Y4))), (((((~m1) | (~p(cx))) | m3) | p(Y4)) <=> ((~m1) | m3 | (~p(cx)) | p(Y4))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(211,plain,
% 0.20/0.43 (![Y4: $i] : ((((~m1) | (~p(cx))) | m3) | p(Y4)) <=> ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[210])).
% 0.20/0.43 tff(212,axiom,(![Y4: $i] : ((((~m1) | (~p(cx))) | m3) | p(Y4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.20/0.43 tff(213,plain,
% 0.20/0.43 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.20/0.43 tff(214,plain,
% 0.20/0.43 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.20/0.43 tff(215,plain,(
% 0.20/0.43 ![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.20/0.43 inference(skolemize,[status(sab)],[214])).
% 0.20/0.43 tff(216,plain,
% 0.20/0.43 (![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.20/0.43 tff(217,plain,
% 0.20/0.43 (((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | ((~m1) | m3 | (~p(cx)) | p(cvv))) <=> ((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | (~m1) | m3 | (~p(cx)) | p(cvv))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(218,plain,
% 0.20/0.43 ((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | ((~m1) | m3 | (~p(cx)) | p(cvv))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(219,plain,
% 0.20/0.43 ((~![Y4: $i] : ((~m1) | m3 | (~p(cx)) | p(Y4))) | (~m1) | m3 | (~p(cx)) | p(cvv)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.43 tff(220,plain,
% 0.20/0.43 ((~m1) | m3 | (~p(cx))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[219, 216, 1])).
% 0.20/0.43 tff(221,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[220, 206, 191, 190])).
% 0.20/0.43 tff(222,plain,(m3 | (~m1) | p(cvv) | (~p(cv))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(223,plain,
% 0.20/0.43 (m3 | p(cvv) | (~p(cv))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[222, 189])).
% 0.20/0.43 tff(224,plain,
% 0.20/0.43 (m3),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[223, 6, 1])).
% 0.20/0.43 tff(225,assumption,(~q(cv)), introduced(assumption)).
% 0.20/0.43 tff(226,plain,
% 0.20/0.43 (^[W1: $i] : refl(((~m3) | m2 | q(W1) | q(fz2(W1))) <=> ((~m3) | m2 | q(W1) | q(fz2(W1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(227,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1))) <=> ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.43 tff(228,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1))) <=> ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(229,plain,
% 0.20/0.43 (^[W1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~m3) | m2) <=> ((~m3) | m2)), ((((~m3) | m2) | q(W1)) <=> (((~m3) | m2) | q(W1)))), rewrite((((~m3) | m2) | q(W1)) <=> ((~m3) | m2 | q(W1))), ((((~m3) | m2) | q(W1)) <=> ((~m3) | m2 | q(W1)))), (((((~m3) | m2) | q(W1)) | q(fz2(W1))) <=> (((~m3) | m2 | q(W1)) | q(fz2(W1))))), rewrite((((~m3) | m2 | q(W1)) | q(fz2(W1))) <=> ((~m3) | m2 | q(W1) | q(fz2(W1)))), (((((~m3) | m2) | q(W1)) | q(fz2(W1))) <=> ((~m3) | m2 | q(W1) | q(fz2(W1)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(230,plain,
% 0.20/0.43 (![W1: $i] : ((((~m3) | m2) | q(W1)) | q(fz2(W1))) <=> ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[229])).
% 0.20/0.43 tff(231,axiom,(![W1: $i] : ((((~m3) | m2) | q(W1)) | q(fz2(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_12')).
% 0.20/0.43 tff(232,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.43 tff(233,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.20/0.43 tff(234,plain,(
% 0.20/0.43 ![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[233])).
% 0.20/0.43 tff(235,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.20/0.43 tff(236,plain,
% 0.20/0.43 (((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | ((~m3) | m2 | q(cv) | q(fz2(cv)))) <=> ((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | (~m3) | m2 | q(cv) | q(fz2(cv)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(237,plain,
% 0.20/0.43 ((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | ((~m3) | m2 | q(cv) | q(fz2(cv)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(238,plain,
% 0.20/0.43 ((~![W1: $i] : ((~m3) | m2 | q(W1) | q(fz2(W1)))) | (~m3) | m2 | q(cv) | q(fz2(cv))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.20/0.43 tff(239,plain,
% 0.20/0.43 ((~m3) | m2 | q(cv) | q(fz2(cv))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[238, 235])).
% 0.20/0.43 tff(240,plain,
% 0.20/0.43 (q(fz2(cv))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[239, 225, 2, 84])).
% 0.20/0.43 tff(241,plain,
% 0.20/0.43 (^[Uu1: $i, U1: $i] : refl(((~m1) | (~q(U1)) | q(Uu1)) <=> ((~m1) | (~q(U1)) | q(Uu1)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(242,plain,
% 0.20/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1)) <=> ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[241])).
% 0.20/0.43 tff(243,plain,
% 0.20/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1)) <=> ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(244,plain,
% 0.20/0.43 (^[Uu1: $i, U1: $i] : rewrite((((~m1) | (~q(U1))) | q(Uu1)) <=> ((~m1) | (~q(U1)) | q(Uu1)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(245,plain,
% 0.20/0.43 (![Uu1: $i, U1: $i] : (((~m1) | (~q(U1))) | q(Uu1)) <=> ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[244])).
% 0.20/0.43 tff(246,axiom,(![Uu1: $i, U1: $i] : (((~m1) | (~q(U1))) | q(Uu1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_17')).
% 0.20/0.43 tff(247,plain,
% 0.20/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.20/0.43 tff(248,plain,
% 0.20/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.20/0.43 tff(249,plain,(
% 0.20/0.43 ![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.20/0.43 inference(skolemize,[status(sab)],[248])).
% 0.20/0.43 tff(250,plain,
% 0.20/0.43 (![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.20/0.43 tff(251,plain,
% 0.20/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | q(cv) | (~q(fz2(cv))))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cv) | (~q(fz2(cv))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(252,plain,
% 0.20/0.43 (((~m1) | (~q(fz2(cv))) | q(cv)) <=> ((~m1) | q(cv) | (~q(fz2(cv))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(253,plain,
% 0.20/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz2(cv))) | q(cv))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | q(cv) | (~q(fz2(cv)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[252])).
% 0.20/0.43 tff(254,plain,
% 0.20/0.43 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz2(cv))) | q(cv))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cv) | (~q(fz2(cv))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[253, 251])).
% 0.20/0.43 tff(255,plain,
% 0.20/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz2(cv))) | q(cv))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(256,plain,
% 0.20/0.43 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cv) | (~q(fz2(cv)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.20/0.43 tff(257,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[256, 250, 190, 225, 240])).
% 0.20/0.43 tff(258,plain,(q(cv) | (~m1) | m2 | (~m3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(259,plain,
% 0.20/0.43 (q(cv) | m2 | (~m3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[258, 189])).
% 0.20/0.43 tff(260,plain,
% 0.20/0.43 (q(cv)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[259, 224, 2])).
% 0.20/0.43 tff(261,plain,
% 0.20/0.43 (^[W1: $i] : refl(((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))) <=> ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(262,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))) <=> ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[261])).
% 0.20/0.43 tff(263,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1)))) <=> ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(264,plain,
% 0.20/0.43 (^[W1: $i] : trans(monotonicity(rewrite((((~m3) | (~q(W1))) | (~q(fz2(W1)))) <=> ((~m3) | (~q(W1)) | (~q(fz2(W1))))), (((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2) <=> (((~m3) | (~q(W1)) | (~q(fz2(W1)))) | m2))), rewrite((((~m3) | (~q(W1)) | (~q(fz2(W1)))) | m2) <=> ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))), (((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2) <=> ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(265,plain,
% 0.20/0.43 (![W1: $i] : ((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2) <=> ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[264])).
% 0.20/0.43 tff(266,axiom,(![W1: $i] : ((((~m3) | (~q(W1))) | (~q(fz2(W1)))) | m2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_11')).
% 0.20/0.43 tff(267,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.20/0.43 tff(268,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.20/0.43 tff(269,plain,(
% 0.20/0.43 ![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[268])).
% 0.20/0.43 tff(270,plain,
% 0.20/0.43 (![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[269, 262])).
% 0.20/0.43 tff(271,plain,
% 0.20/0.43 (((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(fz2(cv))) | (~q(cv)))) <=> ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | (~m3) | m2 | (~q(fz2(cv))) | (~q(cv)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(272,plain,
% 0.20/0.43 (((~m3) | m2 | (~q(cv)) | (~q(fz2(cv)))) <=> ((~m3) | m2 | (~q(fz2(cv))) | (~q(cv)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(273,plain,
% 0.20/0.43 (((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(cv)) | (~q(fz2(cv))))) <=> ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(fz2(cv))) | (~q(cv))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[272])).
% 0.20/0.43 tff(274,plain,
% 0.20/0.43 (((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(cv)) | (~q(fz2(cv))))) <=> ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | (~m3) | m2 | (~q(fz2(cv))) | (~q(cv)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[273, 271])).
% 0.20/0.44 tff(275,plain,
% 0.20/0.44 ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | ((~m3) | m2 | (~q(cv)) | (~q(fz2(cv))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(276,plain,
% 0.20/0.44 ((~![W1: $i] : ((~m3) | m2 | (~q(W1)) | (~q(fz2(W1))))) | (~m3) | m2 | (~q(fz2(cv))) | (~q(cv))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.20/0.44 tff(277,plain,
% 0.20/0.44 ((~m3) | m2 | (~q(fz2(cv))) | (~q(cv))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[276, 270])).
% 0.20/0.44 tff(278,plain,
% 0.20/0.44 (~q(fz2(cv))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[277, 260, 2, 224])).
% 0.20/0.44 tff(279,plain,
% 0.20/0.44 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cv)) | q(fz2(cv)))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cv)) | q(fz2(cv)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(280,plain,
% 0.20/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cv)) | q(fz2(cv)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(281,plain,
% 0.20/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cv)) | q(fz2(cv))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.20/0.44 tff(282,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[281, 250, 189, 260, 278])).
% 0.20/0.44 tff(283,plain,(m2 | p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(284,plain,
% 0.20/0.44 (m2),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[283, 1])).
% 0.20/0.44 tff(285,assumption,(~q(cu)), introduced(assumption)).
% 0.20/0.44 tff(286,plain,
% 0.20/0.44 (^[W2: $i] : refl((m3 | (~m2) | q(W2) | q(fz5(W2))) <=> (m3 | (~m2) | q(W2) | q(fz5(W2))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(287,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2))) <=> ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[286])).
% 0.20/0.44 tff(288,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2))) <=> ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(289,plain,
% 0.20/0.44 (^[W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~m2) | m3) <=> (m3 | (~m2))), ((((~m2) | m3) | q(W2)) <=> ((m3 | (~m2)) | q(W2)))), rewrite(((m3 | (~m2)) | q(W2)) <=> (m3 | (~m2) | q(W2))), ((((~m2) | m3) | q(W2)) <=> (m3 | (~m2) | q(W2)))), (((((~m2) | m3) | q(W2)) | q(fz5(W2))) <=> ((m3 | (~m2) | q(W2)) | q(fz5(W2))))), rewrite(((m3 | (~m2) | q(W2)) | q(fz5(W2))) <=> (m3 | (~m2) | q(W2) | q(fz5(W2)))), (((((~m2) | m3) | q(W2)) | q(fz5(W2))) <=> (m3 | (~m2) | q(W2) | q(fz5(W2)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(290,plain,
% 0.20/0.44 (![W2: $i] : ((((~m2) | m3) | q(W2)) | q(fz5(W2))) <=> ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[289])).
% 0.20/0.44 tff(291,axiom,(![W2: $i] : ((((~m2) | m3) | q(W2)) | q(fz5(W2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8')).
% 0.20/0.44 tff(292,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.44 tff(293,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.20/0.44 tff(294,plain,(
% 0.20/0.44 ![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[293])).
% 0.20/0.44 tff(295,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.20/0.44 tff(296,plain,
% 0.20/0.44 (((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | (m3 | (~m2) | q(cu) | q(fz5(cu)))) <=> ((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | m3 | (~m2) | q(cu) | q(fz5(cu)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(297,plain,
% 0.20/0.44 ((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | (m3 | (~m2) | q(cu) | q(fz5(cu)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(298,plain,
% 0.20/0.44 ((~![W2: $i] : (m3 | (~m2) | q(W2) | q(fz5(W2)))) | m3 | (~m2) | q(cu) | q(fz5(cu))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.20/0.44 tff(299,plain,
% 0.20/0.44 (m3 | (~m2) | q(cu) | q(fz5(cu))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[298, 295])).
% 0.20/0.44 tff(300,plain,
% 0.20/0.44 (q(fz5(cu))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[299, 285, 8, 191])).
% 0.20/0.44 tff(301,plain,
% 0.20/0.44 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | q(cu) | (~q(fz5(cu))))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cu) | (~q(fz5(cu))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(302,plain,
% 0.20/0.44 (((~m1) | (~q(fz5(cu))) | q(cu)) <=> ((~m1) | q(cu) | (~q(fz5(cu))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(303,plain,
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% 0.20/0.44 inference(monotonicity,[status(thm)],[302])).
% 0.20/0.44 tff(304,plain,
% 0.20/0.44 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz5(cu))) | q(cu))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cu) | (~q(fz5(cu))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[303, 301])).
% 0.20/0.44 tff(305,plain,
% 0.20/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(fz5(cu))) | q(cu))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(306,plain,
% 0.20/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | q(cu) | (~q(fz5(cu)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.20/0.44 tff(307,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[306, 250, 189, 285, 300])).
% 0.20/0.44 tff(308,plain,(q(cu) | (~m2) | m3), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(309,plain,
% 0.20/0.44 (q(cu)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[308, 191, 8])).
% 0.20/0.44 tff(310,plain,
% 0.20/0.44 (^[W2: $i] : refl((m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))) <=> (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(311,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))) <=> ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[310])).
% 0.20/0.44 tff(312,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2)))) <=> ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(313,plain,
% 0.20/0.44 (^[W2: $i] : trans(monotonicity(rewrite((((~m2) | (~q(W2))) | (~q(fz5(W2)))) <=> ((~m2) | (~q(W2)) | (~q(fz5(W2))))), (((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3) <=> (((~m2) | (~q(W2)) | (~q(fz5(W2)))) | m3))), rewrite((((~m2) | (~q(W2)) | (~q(fz5(W2)))) | m3) <=> (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))), (((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3) <=> (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(314,plain,
% 0.20/0.44 (![W2: $i] : ((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3) <=> ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[313])).
% 0.20/0.44 tff(315,axiom,(![W2: $i] : ((((~m2) | (~q(W2))) | (~q(fz5(W2)))) | m3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7')).
% 0.20/0.44 tff(316,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.44 tff(317,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[316, 312])).
% 0.20/0.44 tff(318,plain,(
% 0.20/0.44 ![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[317])).
% 0.20/0.44 tff(319,plain,
% 0.20/0.44 (![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[318, 311])).
% 0.20/0.44 tff(320,plain,
% 0.20/0.44 (((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | (m3 | (~m2) | (~q(cu)) | (~q(fz5(cu))))) <=> ((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | m3 | (~m2) | (~q(cu)) | (~q(fz5(cu))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(321,plain,
% 0.20/0.44 ((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | (m3 | (~m2) | (~q(cu)) | (~q(fz5(cu))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(322,plain,
% 0.20/0.44 ((~![W2: $i] : (m3 | (~m2) | (~q(W2)) | (~q(fz5(W2))))) | m3 | (~m2) | (~q(cu)) | (~q(fz5(cu)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.20/0.44 tff(323,plain,
% 0.20/0.44 (m3 | (~m2) | (~q(cu)) | (~q(fz5(cu)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[322, 319])).
% 0.20/0.44 tff(324,plain,
% 0.20/0.44 (~q(fz5(cu))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[323, 309, 191, 8])).
% 0.20/0.44 tff(325,plain,
% 0.20/0.44 (((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cu)) | q(fz5(cu)))) <=> ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cu)) | q(fz5(cu)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(326,plain,
% 0.20/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | ((~m1) | (~q(cu)) | q(fz5(cu)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(327,plain,
% 0.20/0.44 ((~![Uu1: $i, U1: $i] : ((~m1) | (~q(U1)) | q(Uu1))) | (~m1) | (~q(cu)) | q(fz5(cu))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.20/0.44 tff(328,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[327, 250, 189, 309, 324])).
% 0.20/0.44 tff(329,plain,(m3 | (~m2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(330,plain,
% 0.20/0.44 (m3),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[329, 284])).
% 0.20/0.44 tff(331,plain,
% 0.20/0.44 (^[X1: $i] : refl(((~m1) | (~m3) | p(fy(X1)) | p(X1)) <=> ((~m1) | (~m3) | p(fy(X1)) | p(X1)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(332,plain,
% 0.20/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1)) <=> ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[331])).
% 0.20/0.44 tff(333,plain,
% 0.20/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1)) <=> ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(334,plain,
% 0.20/0.44 (^[X1: $i] : trans(monotonicity(rewrite((((~m1) | (~m3)) | p(X1)) <=> ((~m1) | (~m3) | p(X1))), (((((~m1) | (~m3)) | p(X1)) | p(fy(X1))) <=> (((~m1) | (~m3) | p(X1)) | p(fy(X1))))), rewrite((((~m1) | (~m3) | p(X1)) | p(fy(X1))) <=> ((~m1) | (~m3) | p(fy(X1)) | p(X1))), (((((~m1) | (~m3)) | p(X1)) | p(fy(X1))) <=> ((~m1) | (~m3) | p(fy(X1)) | p(X1))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(335,plain,
% 0.20/0.44 (![X1: $i] : ((((~m1) | (~m3)) | p(X1)) | p(fy(X1))) <=> ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[334])).
% 0.20/0.44 tff(336,axiom,(![X1: $i] : ((((~m1) | (~m3)) | p(X1)) | p(fy(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.20/0.44 tff(337,plain,
% 0.20/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.20/0.44 tff(338,plain,
% 0.20/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.20/0.44 tff(339,plain,(
% 0.20/0.44 ![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.20/0.44 inference(skolemize,[status(sab)],[338])).
% 0.20/0.44 tff(340,plain,
% 0.20/0.44 (![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[339, 332])).
% 0.20/0.44 tff(341,plain,
% 0.20/0.44 (((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(cvv) | p(fy(cvv)))) <=> ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | (~m1) | (~m3) | p(cvv) | p(fy(cvv)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(342,plain,
% 0.20/0.44 (((~m1) | (~m3) | p(fy(cvv)) | p(cvv)) <=> ((~m1) | (~m3) | p(cvv) | p(fy(cvv)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(343,plain,
% 0.20/0.44 (((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(fy(cvv)) | p(cvv))) <=> ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(cvv) | p(fy(cvv))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[342])).
% 0.20/0.45 tff(344,plain,
% 0.20/0.45 (((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(fy(cvv)) | p(cvv))) <=> ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | (~m1) | (~m3) | p(cvv) | p(fy(cvv)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[343, 341])).
% 0.20/0.45 tff(345,plain,
% 0.20/0.45 ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | ((~m1) | (~m3) | p(fy(cvv)) | p(cvv))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(346,plain,
% 0.20/0.45 ((~![X1: $i] : ((~m1) | (~m3) | p(fy(X1)) | p(X1))) | (~m1) | (~m3) | p(cvv) | p(fy(cvv))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.20/0.45 tff(347,plain,
% 0.20/0.45 ((~m1) | (~m3) | p(cvv) | p(fy(cvv))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[346, 340])).
% 0.20/0.45 tff(348,plain,
% 0.20/0.45 ((~m3) | p(cvv) | p(fy(cvv))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[347, 189])).
% 0.20/0.45 tff(349,plain,
% 0.20/0.45 (p(fy(cvv))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[348, 330, 1])).
% 0.20/0.45 tff(350,plain,
% 0.20/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy(cvv))))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy(cvv))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(351,plain,
% 0.20/0.45 (((~p(fy(cvv))) | (~m2) | p(cvv)) <=> ((~m2) | p(cvv) | (~p(fy(cvv))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(352,plain,
% 0.20/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | p(cvv) | (~p(fy(cvv)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[351])).
% 0.20/0.45 tff(353,plain,
% 0.20/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy(cvv))) | (~m2) | p(cvv))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy(cvv))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[352, 350])).
% 0.20/0.45 tff(354,plain,
% 0.20/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(fy(cvv))) | (~m2) | p(cvv))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(355,plain,
% 0.20/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | p(cvv) | (~p(fy(cvv)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.20/0.45 tff(356,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[355, 19, 284, 1, 349])).
% 0.20/0.45 tff(357,plain,(p(cvv)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(358,plain,
% 0.20/0.45 (m2),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[158, 357])).
% 0.20/0.45 tff(359,plain,
% 0.20/0.45 (m3),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[329, 358])).
% 0.20/0.45 tff(360,plain,
% 0.20/0.45 (^[X1: $i] : refl(((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))) <=> ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(361,plain,
% 0.20/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))) <=> ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[360])).
% 0.20/0.45 tff(362,plain,
% 0.20/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1))) <=> ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(363,plain,
% 0.20/0.45 (^[X1: $i] : trans(monotonicity(rewrite((((~m1) | (~m3)) | (~p(X1))) <=> ((~m1) | (~m3) | (~p(X1)))), (((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1)))) <=> (((~m1) | (~m3) | (~p(X1))) | (~p(fy(X1)))))), rewrite((((~m1) | (~m3) | (~p(X1))) | (~p(fy(X1)))) <=> ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))), (((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1)))) <=> ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(364,plain,
% 0.20/0.45 (![X1: $i] : ((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1)))) <=> ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[363])).
% 0.20/0.45 tff(365,axiom,(![X1: $i] : ((((~m1) | (~m3)) | (~p(X1))) | (~p(fy(X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.20/0.45 tff(366,plain,
% 0.20/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.20/0.45 tff(367,plain,
% 0.20/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[366, 362])).
% 0.20/0.45 tff(368,plain,(
% 0.20/0.45 ![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[367])).
% 0.20/0.45 tff(369,plain,
% 0.20/0.45 (![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[368, 361])).
% 0.20/0.45 tff(370,plain,
% 0.20/0.45 (((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(cvv)) | (~p(fy(cvv))))) <=> ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | (~m1) | (~m3) | (~p(cvv)) | (~p(fy(cvv))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(371,plain,
% 0.20/0.45 (((~m1) | (~m3) | (~p(fy(cvv))) | (~p(cvv))) <=> ((~m1) | (~m3) | (~p(cvv)) | (~p(fy(cvv))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(372,plain,
% 0.20/0.45 (((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(fy(cvv))) | (~p(cvv)))) <=> ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(cvv)) | (~p(fy(cvv)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[371])).
% 0.20/0.45 tff(373,plain,
% 0.20/0.45 (((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(fy(cvv))) | (~p(cvv)))) <=> ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | (~m1) | (~m3) | (~p(cvv)) | (~p(fy(cvv))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[372, 370])).
% 0.20/0.45 tff(374,plain,
% 0.20/0.45 ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | ((~m1) | (~m3) | (~p(fy(cvv))) | (~p(cvv)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(375,plain,
% 0.20/0.45 ((~![X1: $i] : ((~m1) | (~m3) | (~p(fy(X1))) | (~p(X1)))) | (~m1) | (~m3) | (~p(cvv)) | (~p(fy(cvv)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.20/0.45 tff(376,plain,
% 0.20/0.45 (~p(fy(cvv))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[375, 369, 357, 189, 359])).
% 0.20/0.45 tff(377,plain,
% 0.20/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(fy(cvv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy(cvv)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(378,plain,
% 0.20/0.45 (((~p(cvv)) | (~m2) | p(fy(cvv))) <=> ((~m2) | (~p(cvv)) | p(fy(cvv)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(379,plain,
% 0.20/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy(cvv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~m2) | (~p(cvv)) | p(fy(cvv))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[378])).
% 0.20/0.45 tff(380,plain,
% 0.20/0.45 (((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy(cvv)))) <=> ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy(cvv)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[379, 377])).
% 0.20/0.45 tff(381,plain,
% 0.20/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | ((~p(cvv)) | (~m2) | p(fy(cvv)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(382,plain,
% 0.20/0.45 ((~![Vv1: $i, V1: $i] : ((~p(V1)) | (~m2) | p(Vv1))) | (~m2) | (~p(cvv)) | p(fy(cvv))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.20/0.45 tff(383,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[382, 19, 358, 357, 376])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------