TSTP Solution File: SYN205-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN205-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 23:54:11 EDT 2022
% Result : Unsatisfiable 1.11s 0.95s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN205-1 : TPTP v8.1.0. Released v1.1.0.
% 0.14/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 02:04:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.11/0.95 % SZS status Unsatisfiable
% 1.11/0.95 % SZS output start Proof
% 1.11/0.95 tff(q2_type, type, (
% 1.11/0.95 q2: ( $i * $i * $i ) > $o)).
% 1.11/0.95 tff(b_type, type, (
% 1.11/0.95 b: $i)).
% 1.11/0.95 tff(a_type, type, (
% 1.11/0.95 a: $i)).
% 1.11/0.95 tff(s1_type, type, (
% 1.11/0.95 s1: $i > $o)).
% 1.11/0.95 tff(p0_type, type, (
% 1.11/0.95 p0: ( $i * $i ) > $o)).
% 1.11/0.95 tff(s2_type, type, (
% 1.11/0.95 s2: $i > $o)).
% 1.11/0.95 tff(m0_type, type, (
% 1.11/0.95 m0: ( $i * $i * $i ) > $o)).
% 1.11/0.95 tff(d_type, type, (
% 1.11/0.95 d: $i)).
% 1.11/0.95 tff(e_type, type, (
% 1.11/0.95 e: $i)).
% 1.11/0.95 tff(p1_type, type, (
% 1.11/0.95 p1: ( $i * $i * $i ) > $o)).
% 1.11/0.95 tff(k0_type, type, (
% 1.11/0.95 k0: $i > $o)).
% 1.11/0.95 tff(l0_type, type, (
% 1.11/0.95 l0: $i > $o)).
% 1.11/0.95 tff(n1_type, type, (
% 1.11/0.95 n1: ( $i * $i * $i ) > $o)).
% 1.11/0.95 tff(k1_type, type, (
% 1.11/0.95 k1: $i > $o)).
% 1.11/0.95 tff(n0_type, type, (
% 1.11/0.95 n0: ( $i * $i ) > $o)).
% 1.11/0.95 tff(r0_type, type, (
% 1.11/0.95 r0: $i > $o)).
% 1.11/0.95 tff(s3_type, type, (
% 1.11/0.95 s3: ( $i * $i ) > $o)).
% 1.11/0.95 tff(s0_type, type, (
% 1.11/0.95 s0: $i > $o)).
% 1.11/0.95 tff(l1_type, type, (
% 1.11/0.95 l1: ( $i * $i ) > $o)).
% 1.11/0.95 tff(c_type, type, (
% 1.11/0.95 c: $i)).
% 1.11/0.95 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 1.11/0.95 tff(2,plain,
% 1.11/0.95 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(3,plain,
% 1.11/0.95 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.11/0.95 inference(quant_intro,[status(thm)],[2])).
% 1.11/0.95 tff(4,plain,
% 1.11/0.95 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.11/0.95 tff(6,plain,
% 1.11/0.95 (![X: $i] : p0(b, X)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.11/0.95 tff(7,plain,(
% 1.11/0.95 ![X: $i] : p0(b, X)),
% 1.11/0.95 inference(skolemize,[status(sab)],[6])).
% 1.11/0.95 tff(8,plain,
% 1.11/0.95 (![X: $i] : p0(b, X)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.11/0.95 tff(9,plain,
% 1.11/0.95 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(10,plain,
% 1.11/0.95 ($false),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.11/0.95 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.95 tff(12,plain,
% 1.11/0.95 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(13,plain,
% 1.11/0.95 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[12])).
% 1.11/0.95 tff(14,plain,
% 1.11/0.95 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.11/0.95 tff(16,plain,
% 1.11/0.95 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.11/0.95 tff(17,plain,(
% 1.11/0.95 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[16])).
% 1.11/0.95 tff(18,plain,
% 1.11/0.95 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.11/0.95 tff(19,plain,
% 1.11/0.95 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(20,plain,
% 1.11/0.95 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(21,plain,
% 1.11/0.95 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.11/0.95 tff(22,plain,
% 1.11/0.95 (s1(b)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 1.11/0.95 tff(23,assumption,(~m0(e, d, d)), introduced(assumption)).
% 1.11/0.95 tff(24,plain,
% 1.11/0.95 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(25,plain,
% 1.11/0.95 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.95 inference(quant_intro,[status(thm)],[24])).
% 1.11/0.95 tff(26,plain,
% 1.11/0.95 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(27,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 1.11/0.95 tff(28,plain,
% 1.11/0.95 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.11/0.95 tff(29,plain,(
% 1.11/0.95 ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.95 inference(skolemize,[status(sab)],[28])).
% 1.11/0.95 tff(30,plain,
% 1.11/0.95 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.11/0.95 tff(31,plain,
% 1.11/0.95 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(e, d, d)),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(32,plain,
% 1.11/0.95 ($false),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 1.11/0.95 tff(33,plain,(m0(e, d, d)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.95 tff(34,assumption,(~q2(a, e, e)), introduced(assumption)).
% 1.11/0.95 tff(35,plain,
% 1.11/0.95 (^[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)))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(36,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[35])).
% 1.11/0.95 tff(37,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(38,plain,
% 1.11/0.95 (^[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))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(39,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[38])).
% 1.11/0.95 tff(40,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')).
% 1.11/0.95 tff(41,plain,
% 1.11/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.11/0.95 tff(42,plain,
% 1.11/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.11/0.95 tff(43,plain,(
% 1.11/0.95 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.95 inference(skolemize,[status(sab)],[42])).
% 1.11/0.95 tff(44,plain,
% 1.11/0.95 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[43, 36])).
% 1.11/0.95 tff(45,plain,
% 1.11/0.95 (p1(a, a, a) <=> p1(a, a, a)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(46,plain,
% 1.11/0.95 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(47,plain,
% 1.11/0.95 ((~$true) <=> $false),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(48,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 1.11/0.95 tff(49,plain,
% 1.11/0.95 (l0(a) <=> $true),
% 1.11/0.95 inference(iff_true,[status(thm)],[48])).
% 1.11/0.95 tff(50,plain,
% 1.11/0.95 ((~l0(a)) <=> (~$true)),
% 1.11/0.95 inference(monotonicity,[status(thm)],[49])).
% 1.11/0.95 tff(51,plain,
% 1.11/0.95 ((~l0(a)) <=> $false),
% 1.11/0.95 inference(transitivity,[status(thm)],[50, 47])).
% 1.11/0.95 tff(52,plain,
% 1.11/0.95 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[51])).
% 1.11/0.95 tff(53,plain,
% 1.11/0.95 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 1.11/0.95 inference(transitivity,[status(thm)],[52, 46])).
% 1.11/0.95 tff(54,plain,
% 1.11/0.95 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(55,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 1.11/0.95 tff(56,plain,
% 1.11/0.95 ((~l0(a)) | p1(a, a, a)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.11/0.95 tff(57,plain,
% 1.11/0.95 (p1(a, a, a)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[56, 53])).
% 1.11/0.95 tff(58,plain,
% 1.11/0.95 (p1(a, a, a)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[57, 45])).
% 1.11/0.95 tff(59,plain,
% 1.11/0.95 (k0(e) <=> k0(e)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(60,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.11/0.95 tff(61,plain,
% 1.11/0.95 (k0(e)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.11/0.95 tff(62,plain,
% 1.11/0.95 (((~![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))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(63,plain,
% 1.11/0.95 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(64,plain,
% 1.11/0.95 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.11/0.95 tff(65,plain,
% 1.11/0.95 ($false),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[64, 61, 58, 44, 34])).
% 1.11/0.95 tff(66,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.95 tff(67,plain,
% 1.11/0.95 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(68,plain,
% 1.11/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[67])).
% 1.11/0.95 tff(69,plain,
% 1.11/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(70,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 1.11/0.95 tff(71,plain,
% 1.11/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.11/0.95 tff(72,plain,(
% 1.11/0.95 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[71])).
% 1.11/0.95 tff(73,plain,
% 1.11/0.95 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.11/0.95 tff(74,plain,
% 1.11/0.95 (n0(b, a) <=> n0(b, a)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(75,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 1.11/0.95 tff(76,plain,
% 1.11/0.95 (n0(b, a)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.11/0.95 tff(77,plain,
% 1.11/0.95 (((~![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)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(78,plain,
% 1.11/0.95 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(79,plain,
% 1.11/0.95 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.11/0.95 tff(80,plain,
% 1.11/0.95 (k1(a)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[79, 76, 73])).
% 1.11/0.95 tff(81,plain,
% 1.11/0.95 (^[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)))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(82,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[81])).
% 1.11/0.95 tff(83,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(84,plain,
% 1.11/0.95 (^[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))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(85,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[84])).
% 1.11/0.95 tff(86,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')).
% 1.11/0.95 tff(87,plain,
% 1.11/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.11/0.95 tff(88,plain,
% 1.11/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.11/0.95 tff(89,plain,(
% 1.11/0.95 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.95 inference(skolemize,[status(sab)],[88])).
% 1.11/0.95 tff(90,plain,
% 1.11/0.95 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[89, 82])).
% 1.11/0.95 tff(91,plain,
% 1.11/0.95 (m0(a, e, e) <=> m0(a, e, e)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(92,axiom,(m0(a, e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 1.11/0.95 tff(93,plain,
% 1.11/0.95 (m0(a, e, e)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.11/0.95 tff(94,plain,
% 1.11/0.95 (((~![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))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(95,plain,
% 1.11/0.95 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(96,plain,
% 1.11/0.95 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.11/0.95 tff(97,plain,
% 1.11/0.95 ((~k1(a)) | n1(a, e, e)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[96, 93, 90])).
% 1.11/0.95 tff(98,plain,
% 1.11/0.95 (n1(a, e, e)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[97, 80])).
% 1.11/0.95 tff(99,plain,
% 1.11/0.95 (^[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)))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(100,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[99])).
% 1.11/0.95 tff(101,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(102,plain,
% 1.11/0.95 (^[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))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(103,plain,
% 1.11/0.95 (![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))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[102])).
% 1.11/0.95 tff(104,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')).
% 1.11/0.95 tff(105,plain,
% 1.11/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.11/0.95 tff(106,plain,
% 1.11/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.11/0.95 tff(107,plain,(
% 1.11/0.95 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.95 inference(skolemize,[status(sab)],[106])).
% 1.11/0.95 tff(108,plain,
% 1.11/0.95 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[107, 100])).
% 1.11/0.95 tff(109,plain,
% 1.11/0.95 (p1(e, e, e) <=> p1(e, e, e)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(110,plain,
% 1.11/0.95 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(111,plain,
% 1.11/0.96 (k0(e) <=> $true),
% 1.11/0.96 inference(iff_true,[status(thm)],[60])).
% 1.11/0.96 tff(112,plain,
% 1.11/0.96 ((~k0(e)) <=> (~$true)),
% 1.11/0.96 inference(monotonicity,[status(thm)],[111])).
% 1.11/0.96 tff(113,plain,
% 1.11/0.96 ((~k0(e)) <=> $false),
% 1.11/0.96 inference(transitivity,[status(thm)],[112, 47])).
% 1.11/0.96 tff(114,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 1.11/0.96 tff(115,plain,
% 1.11/0.96 (r0(e) <=> $true),
% 1.11/0.96 inference(iff_true,[status(thm)],[114])).
% 1.11/0.96 tff(116,plain,
% 1.11/0.96 ((~r0(e)) <=> (~$true)),
% 1.11/0.96 inference(monotonicity,[status(thm)],[115])).
% 1.11/0.96 tff(117,plain,
% 1.11/0.96 ((~r0(e)) <=> $false),
% 1.11/0.96 inference(transitivity,[status(thm)],[116, 47])).
% 1.11/0.96 tff(118,plain,
% 1.11/0.96 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[117, 113])).
% 1.11/0.96 tff(119,plain,
% 1.11/0.96 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 1.11/0.96 inference(transitivity,[status(thm)],[118, 110])).
% 1.11/0.96 tff(120,plain,
% 1.11/0.96 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(121,plain,
% 1.11/0.96 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(122,plain,
% 1.11/0.96 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(123,plain,
% 1.11/0.96 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[122])).
% 1.11/0.96 tff(124,plain,
% 1.11/0.96 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.11/0.96 inference(transitivity,[status(thm)],[123, 121])).
% 1.11/0.96 tff(125,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 1.11/0.96 tff(126,plain,
% 1.11/0.96 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.11/0.96 tff(127,plain,
% 1.11/0.96 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[126, 120])).
% 1.11/0.96 tff(128,plain,
% 1.11/0.96 (p1(e, e, e)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[127, 119])).
% 1.11/0.96 tff(129,plain,
% 1.11/0.96 (p1(e, e, e)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[128, 109])).
% 1.11/0.96 tff(130,plain,
% 1.11/0.96 (((~![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(131,plain,
% 1.11/0.96 (((~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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(132,plain,
% 1.11/0.96 (((~![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)))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[131])).
% 1.11/0.96 tff(133,plain,
% 1.11/0.96 (((~![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))),
% 1.11/0.96 inference(transitivity,[status(thm)],[132, 130])).
% 1.11/0.96 tff(134,plain,
% 1.11/0.96 ((~![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))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(135,plain,
% 1.11/0.96 ((~![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)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.11/0.96 tff(136,plain,
% 1.11/0.96 ((~q2(a, e, e)) | q2(e, a, e)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[135, 129, 108, 98])).
% 1.11/0.96 tff(137,plain,
% 1.11/0.96 (q2(e, a, e)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[136, 66])).
% 1.11/0.96 tff(138,plain,
% 1.11/0.96 ((~s3(a, d)) <=> (~s3(a, d))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(139,axiom,(~s3(a, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 1.11/0.96 tff(140,plain,
% 1.11/0.96 (~s3(a, d)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.11/0.96 tff(141,plain,
% 1.11/0.96 (^[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)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(142,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[141])).
% 1.11/0.96 tff(143,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(144,plain,
% 1.11/0.96 (^[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))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(145,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[144])).
% 1.11/0.96 tff(146,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')).
% 1.11/0.96 tff(147,plain,
% 1.11/0.96 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.11/0.96 tff(148,plain,
% 1.11/0.96 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[147, 143])).
% 1.11/0.96 tff(149,plain,(
% 1.11/0.96 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.11/0.96 inference(skolemize,[status(sab)],[148])).
% 1.11/0.96 tff(150,plain,
% 1.11/0.96 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[149, 142])).
% 1.11/0.96 tff(151,plain,
% 1.11/0.96 (((~![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, d)) | (~q2(e, a, e)) | s3(a, d))) <=> ((~![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, d)) | (~q2(e, a, e)) | s3(a, d))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(152,plain,
% 1.11/0.96 ((~![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, d)) | (~q2(e, a, e)) | s3(a, d))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(153,plain,
% 1.11/0.96 ((~![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, d)) | (~q2(e, a, e)) | s3(a, d)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.11/0.96 tff(154,plain,
% 1.11/0.96 (~s2(a)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[153, 150, 140, 137, 33])).
% 1.11/0.96 tff(155,plain,
% 1.11/0.96 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(156,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[155])).
% 1.11/0.96 tff(157,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(158,plain,
% 1.11/0.96 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(159,plain,
% 1.11/0.96 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[158])).
% 1.11/0.96 tff(160,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 1.11/0.96 tff(161,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.11/0.96 tff(162,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[161, 157])).
% 1.11/0.96 tff(163,plain,(
% 1.11/0.96 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[162])).
% 1.11/0.96 tff(164,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[163, 156])).
% 1.11/0.96 tff(165,plain,
% 1.11/0.96 (((~![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)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(166,plain,
% 1.11/0.96 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(167,plain,
% 1.11/0.96 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.11/0.96 tff(168,plain,
% 1.11/0.96 (~q2(b, a, b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[167, 164, 154, 22])).
% 1.11/0.96 tff(169,plain,
% 1.11/0.96 (^[D: $i, E: $i] : refl(((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(170,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[169])).
% 1.11/0.96 tff(171,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(172,plain,
% 1.11/0.96 (^[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))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(173,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[172])).
% 1.11/0.96 tff(174,plain,
% 1.11/0.96 (^[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))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(175,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[174])).
% 1.11/0.96 tff(176,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')).
% 1.11/0.96 tff(177,plain,
% 1.11/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.11/0.96 tff(178,plain,
% 1.11/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[177, 173])).
% 1.11/0.96 tff(179,plain,
% 1.11/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[178, 171])).
% 1.11/0.96 tff(180,plain,(
% 1.11/0.96 ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.11/0.96 inference(skolemize,[status(sab)],[179])).
% 1.11/0.96 tff(181,plain,
% 1.11/0.96 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[180, 170])).
% 1.11/0.96 tff(182,plain,
% 1.11/0.96 (l0(a) <=> l0(a)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(183,plain,
% 1.11/0.96 (l0(a)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[48, 182])).
% 1.11/0.96 tff(184,plain,
% 1.11/0.96 (((~![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(185,plain,
% 1.11/0.96 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(186,plain,
% 1.11/0.96 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.11/0.96 tff(187,plain,
% 1.11/0.96 (n1(a, b, a)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[186, 183, 181, 11])).
% 1.11/0.96 tff(188,plain,
% 1.11/0.96 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(189,plain,
% 1.11/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[188])).
% 1.11/0.96 tff(190,plain,
% 1.11/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(191,plain,
% 1.11/0.96 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(192,plain,
% 1.11/0.96 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[191])).
% 1.11/0.96 tff(193,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 1.11/0.96 tff(194,plain,
% 1.11/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.11/0.96 tff(195,plain,
% 1.11/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.11/0.96 tff(196,plain,(
% 1.11/0.96 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.11/0.96 inference(skolemize,[status(sab)],[195])).
% 1.11/0.96 tff(197,plain,
% 1.11/0.96 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.11/0.96 tff(198,plain,
% 1.11/0.96 (((~![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(199,plain,
% 1.11/0.96 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(200,plain,
% 1.11/0.96 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.11/0.96 tff(201,plain,
% 1.11/0.96 (l1(a, a)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[200, 76, 197])).
% 1.11/0.96 tff(202,plain,
% 1.11/0.96 (^[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)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(203,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[202])).
% 1.11/0.96 tff(204,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(205,plain,
% 1.11/0.96 (^[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))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(206,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[205])).
% 1.11/0.96 tff(207,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')).
% 1.11/0.96 tff(208,plain,
% 1.11/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.11/0.96 tff(209,plain,
% 1.11/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.11/0.96 tff(210,plain,(
% 1.11/0.96 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.11/0.96 inference(skolemize,[status(sab)],[209])).
% 1.11/0.96 tff(211,plain,
% 1.11/0.96 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.11/0.96 tff(212,plain,
% 1.11/0.96 (((~![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)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(213,plain,
% 1.11/0.96 (((~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)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(214,plain,
% 1.11/0.96 (((~![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))))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[213])).
% 1.11/0.96 tff(215,plain,
% 1.11/0.96 (((~![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)))),
% 1.11/0.96 inference(transitivity,[status(thm)],[214, 212])).
% 1.11/0.96 tff(216,plain,
% 1.11/0.96 ((~![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))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(217,plain,
% 1.11/0.96 ((~![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))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.11/0.96 tff(218,plain,
% 1.11/0.96 (n1(a, b, b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[217, 183, 211, 201, 187])).
% 1.11/0.96 tff(219,plain,
% 1.11/0.96 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(220,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[219])).
% 1.11/0.96 tff(221,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(222,plain,
% 1.11/0.96 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(223,plain,
% 1.11/0.96 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[222])).
% 1.11/0.96 tff(224,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 1.11/0.96 tff(225,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.11/0.96 tff(226,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[225, 221])).
% 1.11/0.96 tff(227,plain,(
% 1.11/0.96 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(skolemize,[status(sab)],[226])).
% 1.11/0.96 tff(228,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[227, 220])).
% 1.11/0.96 tff(229,plain,
% 1.11/0.96 (p0(c, b) <=> p0(c, b)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(230,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.11/0.96 tff(231,plain,
% 1.11/0.96 (p0(c, b)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.11/0.96 tff(232,plain,
% 1.11/0.96 (((~![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(233,plain,
% 1.11/0.96 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(234,plain,
% 1.11/0.96 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.11/0.96 tff(235,plain,
% 1.11/0.96 (p1(b, b, b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[234, 231, 228])).
% 1.11/0.96 tff(236,plain,
% 1.11/0.96 (((~![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)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(237,plain,
% 1.11/0.96 (((~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)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(238,plain,
% 1.11/0.96 (((~![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))))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[237])).
% 1.11/0.96 tff(239,plain,
% 1.11/0.96 (((~![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)))),
% 1.11/0.96 inference(transitivity,[status(thm)],[238, 236])).
% 1.11/0.96 tff(240,plain,
% 1.11/0.96 ((~![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))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(241,plain,
% 1.11/0.96 ((~![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))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.11/0.97 tff(242,plain,
% 1.11/0.97 (~q2(a, b, b)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[241, 108, 235, 218, 168])).
% 1.11/0.97 tff(243,plain,
% 1.11/0.97 (k0(b) <=> k0(b)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(244,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 1.11/0.97 tff(245,plain,
% 1.11/0.97 (k0(b)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.11/0.97 tff(246,plain,
% 1.11/0.97 (((~![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))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(247,plain,
% 1.11/0.97 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(248,plain,
% 1.11/0.97 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.11/0.97 tff(249,plain,
% 1.11/0.97 ($false),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[248, 245, 58, 44, 242])).
% 1.11/0.97 % SZS output end Proof
%------------------------------------------------------------------------------