TSTP Solution File: SYN180-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN180-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:54:05 EDT 2022
% Result : Unsatisfiable 1.78s 1.40s
% Output : Proof 1.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN180-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 01:27:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 1.78/1.40 % SZS status Unsatisfiable
% 1.78/1.40 % SZS output start Proof
% 1.78/1.40 tff(q2_type, type, (
% 1.78/1.40 q2: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(a_type, type, (
% 1.78/1.40 a: $i)).
% 1.78/1.40 tff(e_type, type, (
% 1.78/1.40 e: $i)).
% 1.78/1.40 tff(p1_type, type, (
% 1.78/1.40 p1: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(k0_type, type, (
% 1.78/1.40 k0: $i > $o)).
% 1.78/1.40 tff(r0_type, type, (
% 1.78/1.40 r0: $i > $o)).
% 1.78/1.40 tff(m0_type, type, (
% 1.78/1.40 m0: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(d_type, type, (
% 1.78/1.40 d: $i)).
% 1.78/1.40 tff(r1_type, type, (
% 1.78/1.40 r1: $i > $o)).
% 1.78/1.40 tff(q1_type, type, (
% 1.78/1.40 q1: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(q0_type, type, (
% 1.78/1.40 q0: ( $i * $i ) > $o)).
% 1.78/1.40 tff(s0_type, type, (
% 1.78/1.40 s0: $i > $o)).
% 1.78/1.40 tff(m3_type, type, (
% 1.78/1.40 m3: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(p2_type, type, (
% 1.78/1.40 p2: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(m1_type, type, (
% 1.78/1.40 m1: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(l0_type, type, (
% 1.78/1.40 l0: $i > $o)).
% 1.78/1.40 tff(q4_type, type, (
% 1.78/1.40 q4: ( $i * $i ) > $o)).
% 1.78/1.40 tff(k3_type, type, (
% 1.78/1.40 k3: ( $i * $i * $i ) > $o)).
% 1.78/1.40 tff(r2_type, type, (
% 1.78/1.40 r2: $i > $o)).
% 1.78/1.40 tff(b_type, type, (
% 1.78/1.40 b: $i)).
% 1.78/1.40 tff(n0_type, type, (
% 1.78/1.40 n0: ( $i * $i ) > $o)).
% 1.78/1.40 tff(p0_type, type, (
% 1.78/1.40 p0: ( $i * $i ) > $o)).
% 1.78/1.40 tff(1,plain,
% 1.78/1.40 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(2,plain,
% 1.78/1.40 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[1])).
% 1.78/1.40 tff(3,plain,
% 1.78/1.40 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(4,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 1.78/1.40 tff(5,plain,
% 1.78/1.40 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.78/1.40 tff(6,plain,(
% 1.78/1.40 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.78/1.40 inference(skolemize,[status(sab)],[5])).
% 1.78/1.40 tff(7,plain,
% 1.78/1.40 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.78/1.40 tff(8,plain,
% 1.78/1.40 (p1(e, e, e) <=> p1(e, e, e)),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(9,plain,
% 1.78/1.40 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(10,plain,
% 1.78/1.40 ((~$true) <=> $false),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(11,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.78/1.40 tff(12,plain,
% 1.78/1.40 (k0(e) <=> $true),
% 1.78/1.40 inference(iff_true,[status(thm)],[11])).
% 1.78/1.40 tff(13,plain,
% 1.78/1.40 ((~k0(e)) <=> (~$true)),
% 1.78/1.40 inference(monotonicity,[status(thm)],[12])).
% 1.78/1.40 tff(14,plain,
% 1.78/1.40 ((~k0(e)) <=> $false),
% 1.78/1.40 inference(transitivity,[status(thm)],[13, 10])).
% 1.78/1.40 tff(15,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 1.78/1.40 tff(16,plain,
% 1.78/1.40 (r0(e) <=> $true),
% 1.78/1.40 inference(iff_true,[status(thm)],[15])).
% 1.78/1.40 tff(17,plain,
% 1.78/1.40 ((~r0(e)) <=> (~$true)),
% 1.78/1.40 inference(monotonicity,[status(thm)],[16])).
% 1.78/1.40 tff(18,plain,
% 1.78/1.40 ((~r0(e)) <=> $false),
% 1.78/1.40 inference(transitivity,[status(thm)],[17, 10])).
% 1.78/1.40 tff(19,plain,
% 1.78/1.40 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[18, 14])).
% 1.78/1.40 tff(20,plain,
% 1.78/1.40 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 1.78/1.40 inference(transitivity,[status(thm)],[19, 9])).
% 1.78/1.40 tff(21,plain,
% 1.78/1.40 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(22,plain,
% 1.78/1.40 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(23,plain,
% 1.78/1.40 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(24,plain,
% 1.78/1.40 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[23])).
% 1.78/1.40 tff(25,plain,
% 1.78/1.40 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.78/1.40 inference(transitivity,[status(thm)],[24, 22])).
% 1.78/1.40 tff(26,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 1.78/1.40 tff(27,plain,
% 1.78/1.40 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.78/1.40 tff(28,plain,
% 1.78/1.40 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[27, 21])).
% 1.78/1.40 tff(29,plain,
% 1.78/1.40 (p1(e, e, e)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[28, 20])).
% 1.78/1.40 tff(30,plain,
% 1.78/1.40 (p1(e, e, e)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[29, 8])).
% 1.78/1.40 tff(31,plain,
% 1.78/1.40 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(32,plain,
% 1.78/1.40 ((q2(e, e, e) | (~p1(e, e, e))) <=> ((~p1(e, e, e)) | q2(e, e, e))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(33,plain,
% 1.78/1.40 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e)))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[32])).
% 1.78/1.40 tff(34,plain,
% 1.78/1.40 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 1.78/1.40 inference(transitivity,[status(thm)],[33, 31])).
% 1.78/1.40 tff(35,plain,
% 1.78/1.40 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(36,plain,
% 1.78/1.40 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.78/1.40 tff(37,plain,
% 1.78/1.40 (q2(e, e, e)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[36, 30, 7])).
% 1.78/1.40 tff(38,assumption,(~m0(a, d, a)), introduced(assumption)).
% 1.78/1.40 tff(39,plain,
% 1.78/1.40 (^[X: $i] : refl(m0(a, X, a) <=> m0(a, X, a))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(40,plain,
% 1.78/1.40 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 1.78/1.40 inference(quant_intro,[status(thm)],[39])).
% 1.78/1.40 tff(41,plain,
% 1.78/1.40 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(42,axiom,(![X: $i] : m0(a, X, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_12')).
% 1.78/1.40 tff(43,plain,
% 1.78/1.40 (![X: $i] : m0(a, X, a)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.78/1.40 tff(44,plain,(
% 1.78/1.40 ![X: $i] : m0(a, X, a)),
% 1.78/1.40 inference(skolemize,[status(sab)],[43])).
% 1.78/1.40 tff(45,plain,
% 1.78/1.40 (![X: $i] : m0(a, X, a)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.78/1.40 tff(46,plain,
% 1.78/1.40 ((~![X: $i] : m0(a, X, a)) | m0(a, d, a)),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(47,plain,
% 1.78/1.40 ($false),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[46, 45, 38])).
% 1.78/1.40 tff(48,plain,(m0(a, d, a)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.40 tff(49,plain,
% 1.78/1.40 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(50,plain,
% 1.78/1.40 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[49])).
% 1.78/1.40 tff(51,plain,
% 1.78/1.40 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(52,plain,
% 1.78/1.40 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((q2(C, D, C) | (~r1(D))) <=> ((~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> (((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))))), rewrite((((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> (((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))))), rewrite((((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> (((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))))), rewrite((((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(53,plain,
% 1.78/1.40 (![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[52])).
% 1.78/1.40 tff(54,axiom,(![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 1.78/1.40 tff(55,plain,
% 1.78/1.40 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.78/1.40 tff(56,plain,
% 1.78/1.40 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.78/1.40 tff(57,plain,(
% 1.78/1.40 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.78/1.40 inference(skolemize,[status(sab)],[56])).
% 1.78/1.40 tff(58,plain,
% 1.78/1.40 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.78/1.40 tff(59,plain,
% 1.78/1.40 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(60,plain,
% 1.78/1.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[59])).
% 1.78/1.40 tff(61,plain,
% 1.78/1.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(62,plain,
% 1.78/1.40 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(d)), (s0(d) <=> $true)), ((~s0(d)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(d)) <=> $false)), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)))), rewrite(((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(63,plain,
% 1.78/1.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[62])).
% 1.78/1.40 tff(64,plain,
% 1.78/1.40 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(65,plain,
% 1.78/1.40 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[64])).
% 1.78/1.40 tff(66,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 1.78/1.40 tff(67,plain,
% 1.78/1.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.78/1.41 tff(68,plain,
% 1.78/1.41 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 1.78/1.41 tff(69,plain,
% 1.78/1.41 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.78/1.41 tff(70,plain,(
% 1.78/1.41 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.41 inference(skolemize,[status(sab)],[69])).
% 1.78/1.41 tff(71,plain,
% 1.78/1.41 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[70, 60])).
% 1.78/1.41 tff(72,plain,
% 1.78/1.41 (q1(d, d, d) <=> q1(d, d, d)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(73,plain,
% 1.78/1.41 (($false | $false | q1(d, d, d)) <=> q1(d, d, d)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(74,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 1.78/1.41 tff(75,plain,
% 1.78/1.41 (s0(d) <=> $true),
% 1.78/1.41 inference(iff_true,[status(thm)],[74])).
% 1.78/1.41 tff(76,plain,
% 1.78/1.41 ((~s0(d)) <=> (~$true)),
% 1.78/1.41 inference(monotonicity,[status(thm)],[75])).
% 1.78/1.41 tff(77,plain,
% 1.78/1.41 ((~s0(d)) <=> $false),
% 1.78/1.41 inference(transitivity,[status(thm)],[76, 10])).
% 1.78/1.41 tff(78,plain,
% 1.78/1.41 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ($false | $false | q1(d, d, d))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[77, 14])).
% 1.78/1.41 tff(79,plain,
% 1.78/1.41 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> q1(d, d, d)),
% 1.78/1.41 inference(transitivity,[status(thm)],[78, 73])).
% 1.78/1.41 tff(80,plain,
% 1.78/1.41 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(81,plain,
% 1.78/1.41 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(82,plain,
% 1.78/1.41 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(83,plain,
% 1.78/1.41 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[82])).
% 1.78/1.41 tff(84,plain,
% 1.78/1.41 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.78/1.41 inference(transitivity,[status(thm)],[83, 81])).
% 1.78/1.41 tff(85,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 1.78/1.41 tff(86,plain,
% 1.78/1.41 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.78/1.41 tff(87,plain,
% 1.78/1.41 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[86, 80])).
% 1.78/1.41 tff(88,plain,
% 1.78/1.41 (q1(d, d, d)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[87, 79])).
% 1.78/1.41 tff(89,plain,
% 1.78/1.41 (q1(d, d, d)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[88, 72])).
% 1.78/1.41 tff(90,plain,
% 1.78/1.41 (q0(e, d) <=> q0(e, d)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(91,axiom,(q0(e, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 1.78/1.41 tff(92,plain,
% 1.78/1.41 (q0(e, d)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.78/1.41 tff(93,plain,
% 1.78/1.41 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(e) | (~q1(d, d, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(94,plain,
% 1.78/1.41 (((~q0(e, d)) | (~q1(d, d, d)) | r1(e)) <=> (r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(95,plain,
% 1.78/1.41 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(e) | (~q1(d, d, d)) | (~q0(e, d))))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[94])).
% 1.78/1.41 tff(96,plain,
% 1.78/1.41 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 1.78/1.41 inference(transitivity,[status(thm)],[95, 93])).
% 1.78/1.41 tff(97,plain,
% 1.78/1.41 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(98,plain,
% 1.78/1.41 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.78/1.41 tff(99,plain,
% 1.78/1.41 (r1(e)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[98, 92, 89, 71])).
% 1.78/1.41 tff(100,plain,
% 1.78/1.41 (k0(e) <=> k0(e)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(101,plain,
% 1.78/1.41 (k0(e)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[11, 100])).
% 1.78/1.41 tff(102,plain,
% 1.78/1.41 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(e)) | (~r1(e)) | (~m0(a, d, a)) | (~q2(e, e, e)) | q2(a, e, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | (~m0(a, d, a)) | (~q2(e, e, e)) | q2(a, e, a))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(103,plain,
% 1.78/1.41 (((~m0(a, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a)) <=> ((~k0(e)) | (~r1(e)) | (~m0(a, d, a)) | (~q2(e, e, e)) | q2(a, e, a))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(104,plain,
% 1.78/1.41 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(a, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(e)) | (~r1(e)) | (~m0(a, d, a)) | (~q2(e, e, e)) | q2(a, e, a)))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[103])).
% 1.78/1.41 tff(105,plain,
% 1.78/1.41 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(a, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | (~m0(a, d, a)) | (~q2(e, e, e)) | q2(a, e, a))),
% 1.78/1.41 inference(transitivity,[status(thm)],[104, 102])).
% 1.78/1.41 tff(106,plain,
% 1.78/1.41 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(a, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(107,plain,
% 1.78/1.41 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | (~m0(a, d, a)) | (~q2(e, e, e)) | q2(a, e, a)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.78/1.41 tff(108,plain,
% 1.78/1.41 (q2(a, e, a)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[107, 101, 99, 58, 48, 37])).
% 1.78/1.41 tff(109,plain,
% 1.78/1.41 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(110,plain,
% 1.78/1.41 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[109])).
% 1.78/1.41 tff(111,plain,
% 1.78/1.41 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(112,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 1.78/1.41 tff(113,plain,
% 1.78/1.41 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.78/1.41 tff(114,plain,(
% 1.78/1.41 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.78/1.41 inference(skolemize,[status(sab)],[113])).
% 1.78/1.41 tff(115,plain,
% 1.78/1.41 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[114, 110])).
% 1.78/1.41 tff(116,plain,
% 1.78/1.41 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(117,plain,
% 1.78/1.41 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[116])).
% 1.78/1.41 tff(118,plain,
% 1.78/1.41 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(119,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 1.78/1.41 tff(120,plain,
% 1.78/1.41 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.78/1.41 tff(121,plain,(
% 1.78/1.41 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 1.78/1.41 inference(skolemize,[status(sab)],[120])).
% 1.78/1.41 tff(122,plain,
% 1.78/1.41 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[121, 117])).
% 1.78/1.41 tff(123,plain,
% 1.78/1.41 (m1(a, a, a) <=> m1(a, a, a)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(124,plain,
% 1.78/1.41 ((m1(a, a, a) | $false | $false) <=> m1(a, a, a)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(125,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 1.78/1.41 tff(126,plain,
% 1.78/1.41 (l0(a) <=> $true),
% 1.78/1.41 inference(iff_true,[status(thm)],[125])).
% 1.78/1.41 tff(127,plain,
% 1.78/1.41 ((~l0(a)) <=> (~$true)),
% 1.78/1.41 inference(monotonicity,[status(thm)],[126])).
% 1.78/1.41 tff(128,plain,
% 1.78/1.41 ((~l0(a)) <=> $false),
% 1.78/1.41 inference(transitivity,[status(thm)],[127, 10])).
% 1.78/1.41 tff(129,plain,
% 1.78/1.41 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | $false | $false)),
% 1.78/1.41 inference(monotonicity,[status(thm)],[77, 128])).
% 1.78/1.41 tff(130,plain,
% 1.78/1.41 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> m1(a, a, a)),
% 1.78/1.41 inference(transitivity,[status(thm)],[129, 124])).
% 1.78/1.41 tff(131,plain,
% 1.78/1.41 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(132,plain,
% 1.78/1.41 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(133,plain,
% 1.78/1.41 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(134,plain,
% 1.78/1.41 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[133])).
% 1.78/1.41 tff(135,plain,
% 1.78/1.41 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 1.78/1.41 inference(transitivity,[status(thm)],[134, 132])).
% 1.78/1.41 tff(136,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 1.78/1.41 tff(137,plain,
% 1.78/1.41 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.78/1.41 tff(138,plain,
% 1.78/1.41 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[137, 131])).
% 1.78/1.41 tff(139,plain,
% 1.78/1.41 (m1(a, a, a)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[138, 130])).
% 1.78/1.41 tff(140,plain,
% 1.78/1.41 (m1(a, a, a)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[139, 123])).
% 1.78/1.41 tff(141,plain,
% 1.78/1.41 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(142,plain,
% 1.78/1.41 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(143,plain,
% 1.78/1.41 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.78/1.41 tff(144,plain,
% 1.78/1.41 (p2(a, a, a)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[143, 140, 122])).
% 1.78/1.41 tff(145,plain,
% 1.78/1.41 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(146,plain,
% 1.78/1.41 ((m3(a, a, a) | (~p2(a, a, a))) <=> ((~p2(a, a, a)) | m3(a, a, a))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(147,plain,
% 1.78/1.41 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a)))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[146])).
% 1.78/1.41 tff(148,plain,
% 1.78/1.41 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 1.78/1.41 inference(transitivity,[status(thm)],[147, 145])).
% 1.78/1.41 tff(149,plain,
% 1.78/1.41 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(150,plain,
% 1.78/1.41 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.78/1.41 tff(151,plain,
% 1.78/1.41 (m3(a, a, a)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[150, 144, 115])).
% 1.78/1.41 tff(152,plain,
% 1.78/1.41 ((~q4(a, e)) <=> (~q4(a, e))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(153,axiom,(~q4(a, e)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 1.78/1.41 tff(154,plain,
% 1.78/1.41 (~q4(a, e)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.78/1.41 tff(155,plain,
% 1.78/1.41 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(156,plain,
% 1.78/1.41 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[155])).
% 1.78/1.41 tff(157,plain,
% 1.78/1.41 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(158,plain,
% 1.78/1.41 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((q4(B, C) | (~k3(D, D, B))) <=> ((~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> (((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))))), rewrite((((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> (((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))))), rewrite((((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(159,plain,
% 1.78/1.41 (![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[158])).
% 1.78/1.41 tff(160,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_295')).
% 1.78/1.41 tff(161,plain,
% 1.78/1.41 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.78/1.41 tff(162,plain,
% 1.78/1.41 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[161, 157])).
% 1.78/1.41 tff(163,plain,(
% 1.78/1.41 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.78/1.41 inference(skolemize,[status(sab)],[162])).
% 1.78/1.41 tff(164,plain,
% 1.78/1.41 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[163, 156])).
% 1.78/1.41 tff(165,plain,
% 1.78/1.41 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(166,plain,
% 1.78/1.41 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[165])).
% 1.78/1.41 tff(167,plain,
% 1.78/1.41 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(168,plain,
% 1.78/1.41 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(169,plain,
% 1.78/1.41 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[168])).
% 1.78/1.41 tff(170,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 1.78/1.41 tff(171,plain,
% 1.78/1.41 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.78/1.41 tff(172,plain,
% 1.78/1.41 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.78/1.41 tff(173,plain,(
% 1.78/1.41 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.78/1.41 inference(skolemize,[status(sab)],[172])).
% 1.78/1.41 tff(174,plain,
% 1.78/1.41 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[173, 166])).
% 1.78/1.41 tff(175,plain,
% 1.78/1.41 (p0(b, d) <=> p0(b, d)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(176,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 1.78/1.41 tff(177,plain,
% 1.78/1.41 (p0(b, d)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.78/1.41 tff(178,plain,
% 1.78/1.41 (n0(d, b) <=> n0(d, b)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(179,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 1.78/1.41 tff(180,plain,
% 1.78/1.41 (n0(d, b)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.78/1.41 tff(181,plain,
% 1.78/1.41 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(182,plain,
% 1.78/1.41 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(183,plain,
% 1.78/1.41 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.78/1.41 tff(184,plain,
% 1.78/1.41 (q1(d, b, d)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[183, 180, 177, 174])).
% 1.78/1.41 tff(185,plain,
% 1.78/1.41 (q0(a, b) <=> q0(a, b)),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(186,axiom,(q0(a, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 1.78/1.41 tff(187,plain,
% 1.78/1.41 (q0(a, b)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.78/1.41 tff(188,plain,
% 1.78/1.41 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(189,plain,
% 1.78/1.41 (((~q0(a, b)) | (~q1(d, b, d)) | r1(a)) <=> (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(190,plain,
% 1.78/1.41 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b))))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[189])).
% 1.78/1.41 tff(191,plain,
% 1.78/1.41 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 1.78/1.41 inference(transitivity,[status(thm)],[190, 188])).
% 1.78/1.41 tff(192,plain,
% 1.78/1.41 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(193,plain,
% 1.78/1.41 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.78/1.42 tff(194,plain,
% 1.78/1.42 (r1(a)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[193, 187, 71, 184])).
% 1.78/1.42 tff(195,plain,
% 1.78/1.42 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(196,plain,
% 1.78/1.42 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[195])).
% 1.78/1.42 tff(197,plain,
% 1.78/1.42 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(198,plain,
% 1.78/1.42 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(199,plain,
% 1.78/1.42 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[198])).
% 1.78/1.42 tff(200,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 1.78/1.42 tff(201,plain,
% 1.78/1.42 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.78/1.42 tff(202,plain,
% 1.78/1.42 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[201, 197])).
% 1.78/1.42 tff(203,plain,(
% 1.78/1.42 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 1.78/1.42 inference(skolemize,[status(sab)],[202])).
% 1.78/1.42 tff(204,plain,
% 1.78/1.42 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[203, 196])).
% 1.78/1.42 tff(205,plain,
% 1.78/1.42 (l0(a) <=> l0(a)),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(206,plain,
% 1.78/1.42 (l0(a)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[125, 205])).
% 1.78/1.42 tff(207,plain,
% 1.78/1.42 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(208,plain,
% 1.78/1.42 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(209,plain,
% 1.78/1.42 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.78/1.42 tff(210,plain,
% 1.78/1.42 (r2(a)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[209, 206, 204, 194])).
% 1.78/1.42 tff(211,plain,
% 1.78/1.42 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(212,plain,
% 1.78/1.42 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(213,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 1.78/1.42 tff(214,plain,
% 1.78/1.42 ((~r2(a)) | k3(a, a, a)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.78/1.42 tff(215,plain,
% 1.78/1.42 ((~r2(a)) | k3(a, a, a)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[214, 211])).
% 1.78/1.42 tff(216,plain,
% 1.78/1.42 (k3(a, a, a)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[215, 210])).
% 1.78/1.42 tff(217,plain,
% 1.78/1.42 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(a, e) | (~k3(a, a, a)) | (~m3(a, a, a)) | (~q2(a, e, a)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(a, e) | (~k3(a, a, a)) | (~m3(a, a, a)) | (~q2(a, e, a)))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(218,plain,
% 1.78/1.42 (((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(a, a, a)) | q4(a, e)) <=> (q4(a, e) | (~k3(a, a, a)) | (~m3(a, a, a)) | (~q2(a, e, a)))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(219,plain,
% 1.78/1.42 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(a, a, a)) | q4(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(a, e) | (~k3(a, a, a)) | (~m3(a, a, a)) | (~q2(a, e, a))))),
% 1.78/1.42 inference(monotonicity,[status(thm)],[218])).
% 1.78/1.42 tff(220,plain,
% 1.78/1.42 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(a, a, a)) | q4(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(a, e) | (~k3(a, a, a)) | (~m3(a, a, a)) | (~q2(a, e, a)))),
% 1.78/1.43 inference(transitivity,[status(thm)],[219, 217])).
% 1.78/1.43 tff(221,plain,
% 1.78/1.43 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(a, a, a)) | q4(a, e))),
% 1.78/1.43 inference(quant_inst,[status(thm)],[])).
% 1.78/1.43 tff(222,plain,
% 1.78/1.43 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(a, e) | (~k3(a, a, a)) | (~m3(a, a, a)) | (~q2(a, e, a))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.78/1.43 tff(223,plain,
% 1.78/1.43 ($false),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[222, 216, 164, 154, 151, 108])).
% 1.78/1.43 % SZS output end Proof
%------------------------------------------------------------------------------