TSTP Solution File: SYN139-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN139-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:54 EDT 2022
% Result : Unsatisfiable 1.09s 0.95s
% Output : Proof 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN139-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:01:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 1.09/0.95 % SZS status Unsatisfiable
% 1.09/0.95 % SZS output start Proof
% 1.09/0.95 tff(q2_type, type, (
% 1.09/0.95 q2: ( $i * $i * $i ) > $o)).
% 1.09/0.95 tff(b_type, type, (
% 1.09/0.95 b: $i)).
% 1.09/0.95 tff(a_type, type, (
% 1.09/0.95 a: $i)).
% 1.09/0.95 tff(s1_type, type, (
% 1.09/0.95 s1: $i > $o)).
% 1.09/0.95 tff(p0_type, type, (
% 1.09/0.95 p0: ( $i * $i ) > $o)).
% 1.09/0.95 tff(s2_type, type, (
% 1.09/0.95 s2: $i > $o)).
% 1.09/0.95 tff(e_type, type, (
% 1.09/0.95 e: $i)).
% 1.09/0.95 tff(p1_type, type, (
% 1.09/0.95 p1: ( $i * $i * $i ) > $o)).
% 1.09/0.95 tff(k0_type, type, (
% 1.09/0.95 k0: $i > $o)).
% 1.09/0.95 tff(l0_type, type, (
% 1.09/0.95 l0: $i > $o)).
% 1.09/0.95 tff(n1_type, type, (
% 1.09/0.95 n1: ( $i * $i * $i ) > $o)).
% 1.09/0.95 tff(k1_type, type, (
% 1.09/0.95 k1: $i > $o)).
% 1.09/0.95 tff(n0_type, type, (
% 1.09/0.95 n0: ( $i * $i ) > $o)).
% 1.09/0.95 tff(m0_type, type, (
% 1.09/0.95 m0: ( $i * $i * $i ) > $o)).
% 1.09/0.95 tff(r0_type, type, (
% 1.09/0.95 r0: $i > $o)).
% 1.09/0.95 tff(s3_type, type, (
% 1.09/0.95 s3: ( $i * $i ) > $o)).
% 1.09/0.95 tff(l2_type, type, (
% 1.09/0.95 l2: ( $i * $i ) > $o)).
% 1.09/0.95 tff(c_type, type, (
% 1.09/0.95 c: $i)).
% 1.09/0.95 tff(m4_type, type, (
% 1.09/0.95 m4: ( $i * $i ) > $o)).
% 1.09/0.95 tff(d_type, type, (
% 1.09/0.95 d: $i)).
% 1.09/0.95 tff(s0_type, type, (
% 1.09/0.95 s0: $i > $o)).
% 1.09/0.95 tff(l1_type, type, (
% 1.09/0.95 l1: ( $i * $i ) > $o)).
% 1.09/0.95 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 1.09/0.95 tff(2,plain,
% 1.09/0.95 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(3,plain,
% 1.09/0.95 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.09/0.95 inference(quant_intro,[status(thm)],[2])).
% 1.09/0.95 tff(4,plain,
% 1.09/0.95 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.09/0.95 tff(6,plain,
% 1.09/0.95 (![X: $i] : p0(b, X)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.09/0.95 tff(7,plain,(
% 1.09/0.95 ![X: $i] : p0(b, X)),
% 1.09/0.95 inference(skolemize,[status(sab)],[6])).
% 1.09/0.95 tff(8,plain,
% 1.09/0.95 (![X: $i] : p0(b, X)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.09/0.95 tff(9,plain,
% 1.09/0.95 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(10,plain,
% 1.09/0.95 ($false),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.09/0.95 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.09/0.95 tff(12,plain,
% 1.09/0.95 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(13,plain,
% 1.09/0.95 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[12])).
% 1.09/0.95 tff(14,plain,
% 1.09/0.95 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.09/0.95 tff(16,plain,
% 1.09/0.95 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.09/0.95 tff(17,plain,(
% 1.09/0.95 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.09/0.95 inference(skolemize,[status(sab)],[16])).
% 1.09/0.95 tff(18,plain,
% 1.09/0.95 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.09/0.95 tff(19,plain,
% 1.09/0.95 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(20,plain,
% 1.09/0.95 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(21,plain,
% 1.09/0.95 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.09/0.95 tff(22,plain,
% 1.09/0.95 (s1(b)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 1.09/0.95 tff(23,assumption,(~q2(a, e, e)), introduced(assumption)).
% 1.09/0.95 tff(24,plain,
% 1.09/0.95 (^[E: $i, F: $i] : refl(((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(25,plain,
% 1.09/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[24])).
% 1.09/0.95 tff(26,plain,
% 1.09/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(27,plain,
% 1.09/0.95 (^[E: $i, F: $i] : trans(monotonicity(rewrite((q2(E, F, F) | (~k0(F))) <=> ((~k0(F)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> (((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))))), rewrite((((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(28,plain,
% 1.09/0.95 (![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[27])).
% 1.09/0.95 tff(29,axiom,(![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_177')).
% 1.09/0.95 tff(30,plain,
% 1.09/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.09/0.95 tff(31,plain,
% 1.09/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.09/0.95 tff(32,plain,(
% 1.09/0.95 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.09/0.95 inference(skolemize,[status(sab)],[31])).
% 1.09/0.95 tff(33,plain,
% 1.09/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.09/0.95 tff(34,plain,
% 1.09/0.95 (p1(a, a, a) <=> p1(a, a, a)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(35,plain,
% 1.09/0.95 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(36,plain,
% 1.09/0.95 ((~$true) <=> $false),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(37,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 1.09/0.95 tff(38,plain,
% 1.09/0.95 (l0(a) <=> $true),
% 1.09/0.95 inference(iff_true,[status(thm)],[37])).
% 1.09/0.95 tff(39,plain,
% 1.09/0.95 ((~l0(a)) <=> (~$true)),
% 1.09/0.95 inference(monotonicity,[status(thm)],[38])).
% 1.09/0.95 tff(40,plain,
% 1.09/0.95 ((~l0(a)) <=> $false),
% 1.09/0.95 inference(transitivity,[status(thm)],[39, 36])).
% 1.09/0.95 tff(41,plain,
% 1.09/0.95 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 1.09/0.95 inference(monotonicity,[status(thm)],[40])).
% 1.09/0.95 tff(42,plain,
% 1.09/0.95 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 1.09/0.95 inference(transitivity,[status(thm)],[41, 35])).
% 1.09/0.95 tff(43,plain,
% 1.09/0.95 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(44,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 1.09/0.95 tff(45,plain,
% 1.09/0.95 ((~l0(a)) | p1(a, a, a)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.09/0.95 tff(46,plain,
% 1.09/0.95 (p1(a, a, a)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[45, 42])).
% 1.09/0.95 tff(47,plain,
% 1.09/0.95 (p1(a, a, a)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[46, 34])).
% 1.09/0.95 tff(48,plain,
% 1.09/0.95 (k0(e) <=> k0(e)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(49,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.09/0.95 tff(50,plain,
% 1.09/0.95 (k0(e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.09/0.95 tff(51,plain,
% 1.09/0.95 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(52,plain,
% 1.09/0.95 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(53,plain,
% 1.09/0.95 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.09/0.95 tff(54,plain,
% 1.09/0.95 ($false),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[53, 50, 47, 33, 23])).
% 1.09/0.95 tff(55,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 1.09/0.95 tff(56,plain,
% 1.09/0.95 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(57,plain,
% 1.09/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[56])).
% 1.09/0.95 tff(58,plain,
% 1.09/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(59,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 1.09/0.95 tff(60,plain,
% 1.09/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.09/0.95 tff(61,plain,(
% 1.09/0.95 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.09/0.95 inference(skolemize,[status(sab)],[60])).
% 1.09/0.95 tff(62,plain,
% 1.09/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.09/0.95 tff(63,plain,
% 1.09/0.95 (n0(b, a) <=> n0(b, a)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(64,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 1.09/0.95 tff(65,plain,
% 1.09/0.95 (n0(b, a)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.09/0.95 tff(66,plain,
% 1.09/0.95 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a)))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(67,plain,
% 1.09/0.95 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(68,plain,
% 1.09/0.95 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.09/0.95 tff(69,plain,
% 1.09/0.95 (k1(a)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[68, 65, 62])).
% 1.09/0.95 tff(70,plain,
% 1.09/0.95 (^[D: $i, C: $i] : refl(((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(71,plain,
% 1.09/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[70])).
% 1.09/0.95 tff(72,plain,
% 1.09/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(73,plain,
% 1.09/0.95 (^[D: $i, C: $i] : trans(monotonicity(rewrite((n1(C, e, e) | (~m0(C, D, e))) <=> ((~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> (((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))))), rewrite((((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(74,plain,
% 1.09/0.95 (![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[73])).
% 1.09/0.95 tff(75,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 1.09/0.95 tff(76,plain,
% 1.09/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.09/0.95 tff(77,plain,
% 1.09/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.09/0.95 tff(78,plain,(
% 1.09/0.95 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.09/0.95 inference(skolemize,[status(sab)],[77])).
% 1.09/0.95 tff(79,plain,
% 1.09/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[78, 71])).
% 1.09/0.95 tff(80,plain,
% 1.09/0.95 (m0(a, e, e) <=> m0(a, e, e)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(81,axiom,(m0(a, e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 1.09/0.95 tff(82,plain,
% 1.09/0.95 (m0(a, e, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.09/0.95 tff(83,plain,
% 1.09/0.95 (((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))) <=> ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(84,plain,
% 1.09/0.95 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(85,plain,
% 1.09/0.95 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.09/0.95 tff(86,plain,
% 1.09/0.95 ((~k1(a)) | n1(a, e, e)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[85, 82, 79])).
% 1.09/0.95 tff(87,plain,
% 1.09/0.95 (n1(a, e, e)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[86, 69])).
% 1.09/0.95 tff(88,plain,
% 1.09/0.95 (^[H: $i, F: $i, G: $i] : refl(((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(89,plain,
% 1.09/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[88])).
% 1.09/0.95 tff(90,plain,
% 1.09/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(91,plain,
% 1.09/0.95 (^[H: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(F, G, F) | (~p1(F, F, H))) <=> ((~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> (((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))))), rewrite((((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> (((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))))), rewrite((((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(92,plain,
% 1.09/0.95 (![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[91])).
% 1.09/0.95 tff(93,axiom,(![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_182')).
% 1.09/0.95 tff(94,plain,
% 1.09/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.09/0.95 tff(95,plain,
% 1.09/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.09/0.95 tff(96,plain,(
% 1.09/0.95 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.09/0.95 inference(skolemize,[status(sab)],[95])).
% 1.09/0.95 tff(97,plain,
% 1.09/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.09/0.95 tff(98,plain,
% 1.09/0.95 (p1(e, e, e) <=> p1(e, e, e)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(99,plain,
% 1.09/0.95 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(100,plain,
% 1.09/0.95 (k0(e) <=> $true),
% 1.09/0.95 inference(iff_true,[status(thm)],[49])).
% 1.09/0.95 tff(101,plain,
% 1.09/0.95 ((~k0(e)) <=> (~$true)),
% 1.09/0.95 inference(monotonicity,[status(thm)],[100])).
% 1.09/0.95 tff(102,plain,
% 1.09/0.95 ((~k0(e)) <=> $false),
% 1.09/0.95 inference(transitivity,[status(thm)],[101, 36])).
% 1.09/0.95 tff(103,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 1.09/0.95 tff(104,plain,
% 1.09/0.95 (r0(e) <=> $true),
% 1.09/0.95 inference(iff_true,[status(thm)],[103])).
% 1.09/0.95 tff(105,plain,
% 1.09/0.95 ((~r0(e)) <=> (~$true)),
% 1.09/0.95 inference(monotonicity,[status(thm)],[104])).
% 1.09/0.95 tff(106,plain,
% 1.09/0.95 ((~r0(e)) <=> $false),
% 1.09/0.95 inference(transitivity,[status(thm)],[105, 36])).
% 1.09/0.95 tff(107,plain,
% 1.09/0.95 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 1.09/0.95 inference(monotonicity,[status(thm)],[106, 102])).
% 1.09/0.95 tff(108,plain,
% 1.09/0.95 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 1.09/0.95 inference(transitivity,[status(thm)],[107, 99])).
% 1.09/0.95 tff(109,plain,
% 1.09/0.95 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(110,plain,
% 1.09/0.95 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(111,plain,
% 1.09/0.95 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(112,plain,
% 1.09/0.95 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 1.09/0.95 inference(monotonicity,[status(thm)],[111])).
% 1.09/0.95 tff(113,plain,
% 1.09/0.95 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.09/0.95 inference(transitivity,[status(thm)],[112, 110])).
% 1.09/0.95 tff(114,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 1.09/0.95 tff(115,plain,
% 1.09/0.95 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.09/0.95 tff(116,plain,
% 1.09/0.95 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[115, 109])).
% 1.09/0.95 tff(117,plain,
% 1.09/0.95 (p1(e, e, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[116, 108])).
% 1.09/0.95 tff(118,plain,
% 1.09/0.95 (p1(e, e, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[117, 98])).
% 1.09/0.95 tff(119,plain,
% 1.09/0.95 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(120,plain,
% 1.09/0.95 (((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e)) <=> ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(121,plain,
% 1.09/0.95 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e)))),
% 1.09/0.95 inference(monotonicity,[status(thm)],[120])).
% 1.09/0.95 tff(122,plain,
% 1.09/0.95 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 1.09/0.95 inference(transitivity,[status(thm)],[121, 119])).
% 1.09/0.95 tff(123,plain,
% 1.09/0.95 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(124,plain,
% 1.09/0.95 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.09/0.95 tff(125,plain,
% 1.09/0.95 ((~q2(a, e, e)) | q2(e, a, e)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[124, 118, 97, 87])).
% 1.09/0.95 tff(126,plain,
% 1.09/0.95 (q2(e, a, e)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[125, 55])).
% 1.09/0.95 tff(127,plain,
% 1.09/0.95 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(128,plain,
% 1.09/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[127])).
% 1.09/0.95 tff(129,plain,
% 1.09/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(130,plain,
% 1.09/0.95 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(131,plain,
% 1.09/0.95 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[130])).
% 1.09/0.95 tff(132,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 1.09/0.95 tff(133,plain,
% 1.09/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.09/0.95 tff(134,plain,
% 1.09/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[133, 129])).
% 1.09/0.95 tff(135,plain,(
% 1.09/0.95 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.09/0.95 inference(skolemize,[status(sab)],[134])).
% 1.09/0.95 tff(136,plain,
% 1.09/0.95 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[135, 128])).
% 1.09/0.95 tff(137,plain,
% 1.09/0.95 (m0(c, b, a) <=> m0(c, b, a)),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(138,axiom,(m0(c, b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_16')).
% 1.09/0.95 tff(139,plain,
% 1.09/0.95 (m0(c, b, a)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.09/0.95 tff(140,plain,
% 1.09/0.95 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~m0(c, b, a)) | (~s1(b)) | l2(a, a) | (~p0(b, b)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~m0(c, b, a)) | (~s1(b)) | l2(a, a) | (~p0(b, b)))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(141,plain,
% 1.09/0.95 (((~p0(b, b)) | (~m0(c, b, a)) | (~s1(b)) | l2(a, a)) <=> ((~m0(c, b, a)) | (~s1(b)) | l2(a, a) | (~p0(b, b)))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(142,plain,
% 1.09/0.95 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(c, b, a)) | (~s1(b)) | l2(a, a))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~m0(c, b, a)) | (~s1(b)) | l2(a, a) | (~p0(b, b))))),
% 1.09/0.95 inference(monotonicity,[status(thm)],[141])).
% 1.09/0.95 tff(143,plain,
% 1.09/0.95 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(c, b, a)) | (~s1(b)) | l2(a, a))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~m0(c, b, a)) | (~s1(b)) | l2(a, a) | (~p0(b, b)))),
% 1.09/0.95 inference(transitivity,[status(thm)],[142, 140])).
% 1.09/0.95 tff(144,plain,
% 1.09/0.95 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(c, b, a)) | (~s1(b)) | l2(a, a))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(145,plain,
% 1.09/0.95 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~m0(c, b, a)) | (~s1(b)) | l2(a, a) | (~p0(b, b))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.09/0.95 tff(146,plain,
% 1.09/0.95 ((~s1(b)) | l2(a, a)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[145, 139, 136, 11])).
% 1.09/0.95 tff(147,plain,
% 1.09/0.95 (l2(a, a)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[146, 22])).
% 1.09/0.95 tff(148,plain,
% 1.09/0.95 ((~m4(a, a)) <=> (~m4(a, a))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(149,axiom,(~m4(a, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 1.09/0.95 tff(150,plain,
% 1.09/0.95 (~m4(a, a)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.09/0.95 tff(151,plain,
% 1.09/0.95 (^[E: $i, F: $i, G: $i] : refl(((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(152,plain,
% 1.09/0.95 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[151])).
% 1.09/0.95 tff(153,plain,
% 1.09/0.95 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(154,plain,
% 1.09/0.95 (^[E: $i, F: $i, G: $i] : trans(monotonicity(rewrite((m4(E, F) | (~l2(G, F))) <=> ((~l2(G, F)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> (((~l2(G, F)) | m4(E, F)) | (~s3(a, E))))), rewrite((((~l2(G, F)) | m4(E, F)) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(155,plain,
% 1.09/0.95 (![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[154])).
% 1.09/0.95 tff(156,axiom,(![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_279')).
% 1.09/0.95 tff(157,plain,
% 1.09/0.95 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.09/0.95 tff(158,plain,
% 1.09/0.95 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[157, 153])).
% 1.09/0.95 tff(159,plain,(
% 1.09/0.95 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.09/0.95 inference(skolemize,[status(sab)],[158])).
% 1.09/0.95 tff(160,plain,
% 1.09/0.95 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[159, 152])).
% 1.09/0.95 tff(161,plain,
% 1.09/0.95 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(a, a)) | (~s3(a, a)) | m4(a, a))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(a, a)) | (~s3(a, a)) | m4(a, a))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(162,plain,
% 1.09/0.95 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(a, a)) | (~s3(a, a)) | m4(a, a))),
% 1.09/0.95 inference(quant_inst,[status(thm)],[])).
% 1.09/0.95 tff(163,plain,
% 1.09/0.95 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(a, a)) | (~s3(a, a)) | m4(a, a)),
% 1.09/0.95 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.09/0.95 tff(164,plain,
% 1.09/0.95 (~s3(a, a)),
% 1.09/0.95 inference(unit_resolution,[status(thm)],[163, 160, 150, 147])).
% 1.09/0.95 tff(165,plain,
% 1.09/0.95 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 1.09/0.95 inference(bind,[status(th)],[])).
% 1.09/0.95 tff(166,plain,
% 1.09/0.95 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.09/0.95 inference(quant_intro,[status(thm)],[165])).
% 1.09/0.95 tff(167,plain,
% 1.09/0.95 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.09/0.95 inference(rewrite,[status(thm)],[])).
% 1.09/0.95 tff(168,plain,
% 1.09/0.95 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(169,plain,
% 1.09/0.96 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[168])).
% 1.09/0.96 tff(170,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 1.09/0.96 tff(171,plain,
% 1.09/0.96 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.09/0.96 tff(172,plain,
% 1.09/0.96 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.09/0.96 tff(173,plain,(
% 1.09/0.96 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.09/0.96 inference(skolemize,[status(sab)],[172])).
% 1.09/0.96 tff(174,plain,
% 1.09/0.96 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[173, 166])).
% 1.09/0.96 tff(175,plain,
% 1.09/0.96 (m0(e, d, a) <=> m0(e, d, a)),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(176,axiom,(m0(e, d, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_4')).
% 1.09/0.96 tff(177,plain,
% 1.09/0.96 (m0(e, d, a)),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.09/0.96 tff(178,plain,
% 1.09/0.96 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, a)) | (~q2(e, a, e)) | s3(a, a))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, a)) | (~q2(e, a, e)) | s3(a, a))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(179,plain,
% 1.09/0.96 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, a)) | (~q2(e, a, e)) | s3(a, a))),
% 1.09/0.96 inference(quant_inst,[status(thm)],[])).
% 1.09/0.96 tff(180,plain,
% 1.09/0.96 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, a)) | (~q2(e, a, e)) | s3(a, a)),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.09/0.96 tff(181,plain,
% 1.09/0.96 ((~s2(a)) | (~q2(e, a, e))),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[180, 177, 174, 164])).
% 1.09/0.96 tff(182,plain,
% 1.09/0.96 (~s2(a)),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[181, 126])).
% 1.09/0.96 tff(183,plain,
% 1.09/0.96 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(184,plain,
% 1.09/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[183])).
% 1.09/0.96 tff(185,plain,
% 1.09/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(186,plain,
% 1.09/0.96 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(187,plain,
% 1.09/0.96 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[186])).
% 1.09/0.96 tff(188,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 1.09/0.96 tff(189,plain,
% 1.09/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.09/0.96 tff(190,plain,
% 1.09/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[189, 185])).
% 1.09/0.96 tff(191,plain,(
% 1.09/0.96 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.09/0.96 inference(skolemize,[status(sab)],[190])).
% 1.09/0.96 tff(192,plain,
% 1.09/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[191, 184])).
% 1.09/0.96 tff(193,plain,
% 1.09/0.96 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(194,plain,
% 1.09/0.96 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 1.09/0.96 inference(quant_inst,[status(thm)],[])).
% 1.09/0.96 tff(195,plain,
% 1.09/0.96 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.09/0.96 tff(196,plain,
% 1.09/0.96 (~q2(b, a, b)),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[195, 192, 182, 22])).
% 1.09/0.96 tff(197,plain,
% 1.09/0.96 (^[D: $i, E: $i] : refl(((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(198,plain,
% 1.09/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[197])).
% 1.09/0.96 tff(199,plain,
% 1.09/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(200,plain,
% 1.09/0.96 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(b)), (s0(b) <=> $true)), ((~s0(b)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(b)) <=> $false)), (((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | $false | (~p0(b, E)) | n1(D, E, D)))), rewrite(((~l0(D)) | $false | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))), (((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(201,plain,
% 1.09/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[200])).
% 1.09/0.96 tff(202,plain,
% 1.09/0.96 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(D, E, D) | (~s0(b))) <=> ((~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> (((~s0(b)) | n1(D, E, D)) | (~l0(D))))), rewrite((((~s0(b)) | n1(D, E, D)) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D)))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> (((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))))), rewrite((((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(203,plain,
% 1.09/0.96 (![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[202])).
% 1.09/0.96 tff(204,axiom,(![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_050')).
% 1.09/0.96 tff(205,plain,
% 1.09/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.09/0.96 tff(206,plain,
% 1.09/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[205, 201])).
% 1.09/0.96 tff(207,plain,
% 1.09/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[206, 199])).
% 1.09/0.96 tff(208,plain,(
% 1.09/0.96 ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(skolemize,[status(sab)],[207])).
% 1.09/0.96 tff(209,plain,
% 1.09/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[208, 198])).
% 1.09/0.96 tff(210,plain,
% 1.09/0.96 (l0(a) <=> l0(a)),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(211,plain,
% 1.09/0.96 (l0(a)),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[37, 210])).
% 1.09/0.96 tff(212,plain,
% 1.09/0.96 (((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))) <=> ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(213,plain,
% 1.09/0.96 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 1.09/0.96 inference(quant_inst,[status(thm)],[])).
% 1.09/0.96 tff(214,plain,
% 1.09/0.96 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a)),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.09/0.96 tff(215,plain,
% 1.09/0.96 (n1(a, b, a)),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[214, 211, 209, 11])).
% 1.09/0.96 tff(216,plain,
% 1.09/0.96 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(217,plain,
% 1.09/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[216])).
% 1.09/0.96 tff(218,plain,
% 1.09/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(219,plain,
% 1.09/0.96 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(220,plain,
% 1.09/0.96 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[219])).
% 1.09/0.96 tff(221,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 1.09/0.96 tff(222,plain,
% 1.09/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.09/0.96 tff(223,plain,
% 1.09/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[222, 218])).
% 1.09/0.96 tff(224,plain,(
% 1.09/0.96 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.09/0.96 inference(skolemize,[status(sab)],[223])).
% 1.09/0.96 tff(225,plain,
% 1.09/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[224, 217])).
% 1.09/0.96 tff(226,plain,
% 1.09/0.96 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(227,plain,
% 1.09/0.96 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 1.09/0.96 inference(quant_inst,[status(thm)],[])).
% 1.09/0.96 tff(228,plain,
% 1.09/0.96 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.09/0.96 tff(229,plain,
% 1.09/0.96 (l1(a, a)),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[228, 65, 225])).
% 1.09/0.96 tff(230,plain,
% 1.09/0.96 (^[E: $i, F: $i, G: $i] : refl(((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(231,plain,
% 1.09/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[230])).
% 1.09/0.96 tff(232,plain,
% 1.09/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(233,plain,
% 1.09/0.96 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(E, F, F) | (~l0(G))) <=> ((~l0(G)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> (((~l0(G)) | n1(E, F, F)) | (~l1(G, E))))), rewrite((((~l0(G)) | n1(E, F, F)) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F)))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> (((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))))), rewrite((((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(234,plain,
% 1.09/0.96 (![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[233])).
% 1.09/0.96 tff(235,axiom,(![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_054')).
% 1.09/0.96 tff(236,plain,
% 1.09/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.09/0.96 tff(237,plain,
% 1.09/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[236, 232])).
% 1.09/0.96 tff(238,plain,(
% 1.09/0.96 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.09/0.96 inference(skolemize,[status(sab)],[237])).
% 1.09/0.96 tff(239,plain,
% 1.09/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[238, 231])).
% 1.09/0.96 tff(240,plain,
% 1.09/0.96 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(241,plain,
% 1.09/0.96 (((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b)) <=> ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(242,plain,
% 1.09/0.96 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))))),
% 1.09/0.96 inference(monotonicity,[status(thm)],[241])).
% 1.09/0.96 tff(243,plain,
% 1.09/0.96 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 1.09/0.96 inference(transitivity,[status(thm)],[242, 240])).
% 1.09/0.96 tff(244,plain,
% 1.09/0.96 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))),
% 1.09/0.96 inference(quant_inst,[status(thm)],[])).
% 1.09/0.96 tff(245,plain,
% 1.09/0.96 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.09/0.96 tff(246,plain,
% 1.09/0.96 (n1(a, b, b)),
% 1.09/0.96 inference(unit_resolution,[status(thm)],[245, 211, 239, 229, 215])).
% 1.09/0.96 tff(247,plain,
% 1.09/0.96 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(248,plain,
% 1.09/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[247])).
% 1.09/0.96 tff(249,plain,
% 1.09/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.09/0.96 inference(rewrite,[status(thm)],[])).
% 1.09/0.96 tff(250,plain,
% 1.09/0.96 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.09/0.96 inference(bind,[status(th)],[])).
% 1.09/0.96 tff(251,plain,
% 1.09/0.96 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.09/0.96 inference(quant_intro,[status(thm)],[250])).
% 1.09/0.96 tff(252,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 1.09/0.96 tff(253,plain,
% 1.09/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.09/0.96 tff(254,plain,
% 1.09/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[253, 249])).
% 1.09/0.96 tff(255,plain,(
% 1.09/0.96 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.09/0.96 inference(skolemize,[status(sab)],[254])).
% 1.09/0.96 tff(256,plain,
% 1.09/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.09/0.96 inference(modus_ponens,[status(thm)],[255, 248])).
% 1.09/0.97 tff(257,plain,
% 1.09/0.97 (p0(c, b) <=> p0(c, b)),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(258,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.09/0.97 tff(259,plain,
% 1.09/0.97 (p0(c, b)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.09/0.97 tff(260,plain,
% 1.09/0.97 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(261,plain,
% 1.09/0.97 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(262,plain,
% 1.09/0.97 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[261, 260])).
% 1.09/0.97 tff(263,plain,
% 1.09/0.97 (p1(b, b, b)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[262, 259, 256])).
% 1.09/0.97 tff(264,plain,
% 1.09/0.97 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(265,plain,
% 1.09/0.97 (((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b)) <=> ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(266,plain,
% 1.09/0.97 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))))),
% 1.09/0.97 inference(monotonicity,[status(thm)],[265])).
% 1.09/0.97 tff(267,plain,
% 1.09/0.97 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 1.09/0.97 inference(transitivity,[status(thm)],[266, 264])).
% 1.09/0.97 tff(268,plain,
% 1.09/0.97 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(269,plain,
% 1.09/0.97 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.09/0.97 tff(270,plain,
% 1.09/0.97 (~q2(a, b, b)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[269, 97, 263, 246, 196])).
% 1.09/0.97 tff(271,plain,
% 1.09/0.97 (k0(b) <=> k0(b)),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(272,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 1.09/0.97 tff(273,plain,
% 1.09/0.97 (k0(b)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.09/0.97 tff(274,plain,
% 1.09/0.97 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(275,plain,
% 1.09/0.97 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(276,plain,
% 1.09/0.97 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[275, 274])).
% 1.09/0.97 tff(277,plain,
% 1.09/0.97 ($false),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[276, 273, 47, 33, 270])).
% 1.09/0.97 % SZS output end Proof
%------------------------------------------------------------------------------