TSTP Solution File: SYN298-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN298-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:54:35 EDT 2022
% Result : Unsatisfiable 1.11s 0.96s
% Output : Proof 1.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN298-1 : TPTP v8.1.0. Released v1.1.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 01:48:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.11/0.96 % SZS status Unsatisfiable
% 1.11/0.96 % SZS output start Proof
% 1.11/0.96 tff(s3_type, type, (
% 1.11/0.96 s3: ( $i * $i ) > $o)).
% 1.11/0.96 tff(c_type, type, (
% 1.11/0.96 c: $i)).
% 1.11/0.96 tff(b_type, type, (
% 1.11/0.96 b: $i)).
% 1.11/0.96 tff(m0_type, type, (
% 1.11/0.96 m0: ( $i * $i * $i ) > $o)).
% 1.11/0.96 tff(d_type, type, (
% 1.11/0.96 d: $i)).
% 1.11/0.96 tff(e_type, type, (
% 1.11/0.96 e: $i)).
% 1.11/0.96 tff(s2_type, type, (
% 1.11/0.96 s2: $i > $o)).
% 1.11/0.96 tff(s1_type, type, (
% 1.11/0.96 s1: $i > $o)).
% 1.11/0.96 tff(p0_type, type, (
% 1.11/0.96 p0: ( $i * $i ) > $o)).
% 1.11/0.96 tff(q2_type, type, (
% 1.11/0.96 q2: ( $i * $i * $i ) > $o)).
% 1.11/0.96 tff(q1_type, type, (
% 1.11/0.96 q1: ( $i * $i * $i ) > $o)).
% 1.11/0.96 tff(n0_type, type, (
% 1.11/0.96 n0: ( $i * $i ) > $o)).
% 1.11/0.96 tff(p1_type, type, (
% 1.11/0.96 p1: ( $i * $i * $i ) > $o)).
% 1.11/0.96 tff(k0_type, type, (
% 1.11/0.96 k0: $i > $o)).
% 1.11/0.96 tff(n1_type, type, (
% 1.11/0.96 n1: ( $i * $i * $i ) > $o)).
% 1.11/0.96 tff(k1_type, type, (
% 1.11/0.96 k1: $i > $o)).
% 1.11/0.96 tff(r0_type, type, (
% 1.11/0.96 r0: $i > $o)).
% 1.11/0.96 tff(1,assumption,(~m0(e, d, c)), introduced(assumption)).
% 1.11/0.96 tff(2,plain,
% 1.11/0.96 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(3,plain,
% 1.11/0.96 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.96 inference(quant_intro,[status(thm)],[2])).
% 1.11/0.96 tff(4,plain,
% 1.11/0.96 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 1.11/0.96 tff(6,plain,
% 1.11/0.96 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.11/0.96 tff(7,plain,(
% 1.11/0.96 ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.96 inference(skolemize,[status(sab)],[6])).
% 1.11/0.96 tff(8,plain,
% 1.11/0.96 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.11/0.96 tff(9,plain,
% 1.11/0.96 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(e, d, c)),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(10,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.11/0.96 tff(11,plain,(m0(e, d, c)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.96 tff(12,assumption,(~p0(b, b)), introduced(assumption)).
% 1.11/0.96 tff(13,plain,
% 1.11/0.96 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(14,plain,
% 1.11/0.96 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.11/0.96 inference(quant_intro,[status(thm)],[13])).
% 1.11/0.96 tff(15,plain,
% 1.11/0.96 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(16,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.11/0.96 tff(17,plain,
% 1.11/0.96 (![X: $i] : p0(b, X)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.11/0.96 tff(18,plain,(
% 1.11/0.96 ![X: $i] : p0(b, X)),
% 1.11/0.96 inference(skolemize,[status(sab)],[17])).
% 1.11/0.96 tff(19,plain,
% 1.11/0.96 (![X: $i] : p0(b, X)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.11/0.96 tff(20,plain,
% 1.11/0.96 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(21,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 1.11/0.96 tff(22,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.96 tff(23,plain,
% 1.11/0.96 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(24,plain,
% 1.11/0.96 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[23])).
% 1.11/0.96 tff(25,plain,
% 1.11/0.96 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(26,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.11/0.96 tff(27,plain,
% 1.11/0.96 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.11/0.96 tff(28,plain,(
% 1.11/0.96 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[27])).
% 1.11/0.96 tff(29,plain,
% 1.11/0.96 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.11/0.96 tff(30,plain,
% 1.11/0.96 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(31,plain,
% 1.11/0.96 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(32,plain,
% 1.11/0.96 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.11/0.96 tff(33,plain,
% 1.11/0.96 (s1(b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 1.11/0.96 tff(34,plain,
% 1.11/0.96 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(35,plain,
% 1.11/0.96 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[34])).
% 1.11/0.96 tff(36,plain,
% 1.11/0.96 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(37,plain,
% 1.11/0.96 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(38,plain,
% 1.11/0.96 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[37])).
% 1.11/0.96 tff(39,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 1.11/0.96 tff(40,plain,
% 1.11/0.96 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.11/0.96 tff(41,plain,
% 1.11/0.96 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.11/0.96 tff(42,plain,(
% 1.11/0.96 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.11/0.96 inference(skolemize,[status(sab)],[41])).
% 1.11/0.96 tff(43,plain,
% 1.11/0.96 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.11/0.96 tff(44,plain,
% 1.11/0.96 (n0(d, c) <=> n0(d, c)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(45,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 1.11/0.96 tff(46,plain,
% 1.11/0.96 (n0(d, c)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.11/0.96 tff(47,plain,
% 1.11/0.96 (p0(c, b) <=> p0(c, b)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(48,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.11/0.96 tff(49,plain,
% 1.11/0.96 (p0(c, b)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.11/0.96 tff(50,plain,
% 1.11/0.96 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(51,plain,
% 1.11/0.96 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(52,plain,
% 1.11/0.96 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.11/0.96 tff(53,plain,
% 1.11/0.96 (q1(b, c, b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[52, 49, 46, 43])).
% 1.11/0.96 tff(54,plain,
% 1.11/0.96 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(55,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[54])).
% 1.11/0.96 tff(56,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(57,plain,
% 1.11/0.96 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(58,plain,
% 1.11/0.96 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[57])).
% 1.11/0.96 tff(59,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 1.11/0.96 tff(60,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.11/0.96 tff(61,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.11/0.96 tff(62,plain,(
% 1.11/0.96 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.11/0.96 inference(skolemize,[status(sab)],[61])).
% 1.11/0.96 tff(63,plain,
% 1.11/0.96 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.11/0.96 tff(64,plain,
% 1.11/0.96 (((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))) <=> ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(65,plain,
% 1.11/0.96 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(66,plain,
% 1.11/0.96 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.11/0.96 tff(67,plain,
% 1.11/0.96 (q2(b, b, b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[66, 63, 53])).
% 1.11/0.96 tff(68,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(69,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)],[68])).
% 1.11/0.96 tff(70,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(71,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(72,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)],[71])).
% 1.11/0.96 tff(73,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 1.11/0.96 tff(74,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.11/0.96 tff(75,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.11/0.96 tff(76,plain,(
% 1.11/0.96 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[75])).
% 1.11/0.96 tff(77,plain,
% 1.11/0.96 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.11/0.96 tff(78,plain,
% 1.11/0.96 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(b) | (~q2(b, b, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(b) | (~q2(b, b, b)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(79,plain,
% 1.11/0.96 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(b) | (~q2(b, b, b)))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(80,plain,
% 1.11/0.96 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(b) | (~q2(b, b, b))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.11/0.96 tff(81,plain,
% 1.11/0.96 ((~s1(b)) | s2(b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[80, 77, 67])).
% 1.11/0.96 tff(82,plain,
% 1.11/0.96 (s2(b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[81, 33])).
% 1.11/0.96 tff(83,assumption,(~q2(b, e, e)), introduced(assumption)).
% 1.11/0.96 tff(84,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(85,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)],[84])).
% 1.11/0.96 tff(86,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(87,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(88,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)],[87])).
% 1.11/0.96 tff(89,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 1.11/0.96 tff(90,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)],[89, 88])).
% 1.11/0.96 tff(91,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)],[90, 86])).
% 1.11/0.96 tff(92,plain,(
% 1.11/0.96 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.11/0.96 inference(skolemize,[status(sab)],[91])).
% 1.11/0.96 tff(93,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)],[92, 85])).
% 1.11/0.96 tff(94,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(95,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(96,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)],[95, 94])).
% 1.11/0.96 tff(97,plain,
% 1.11/0.96 (p1(b, b, b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[96, 49, 93])).
% 1.11/0.96 tff(98,plain,
% 1.11/0.96 (^[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)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(99,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[98])).
% 1.11/0.96 tff(100,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(101,plain,
% 1.11/0.96 (^[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))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(102,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[101])).
% 1.11/0.96 tff(103,axiom,(![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_177')).
% 1.11/0.96 tff(104,plain,
% 1.11/0.96 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.11/0.96 tff(105,plain,
% 1.11/0.96 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[104, 100])).
% 1.11/0.96 tff(106,plain,(
% 1.11/0.96 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.96 inference(skolemize,[status(sab)],[105])).
% 1.11/0.96 tff(107,plain,
% 1.11/0.96 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[106, 99])).
% 1.11/0.96 tff(108,plain,
% 1.11/0.96 (k0(e) <=> k0(e)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(109,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.11/0.96 tff(110,plain,
% 1.11/0.96 (k0(e)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.11/0.96 tff(111,plain,
% 1.11/0.96 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(b, b, b)) | q2(b, e, e))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(b, b, b)) | q2(b, e, e))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(112,plain,
% 1.11/0.96 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(b, b, b)) | q2(b, e, e))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(113,plain,
% 1.11/0.96 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(b, b, b)) | q2(b, e, e)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.11/0.96 tff(114,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[113, 110, 107, 97, 83])).
% 1.11/0.96 tff(115,plain,(q2(b, e, e)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.96 tff(116,plain,
% 1.11/0.96 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(117,plain,
% 1.11/0.96 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[116])).
% 1.11/0.96 tff(118,plain,
% 1.11/0.96 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(119,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 1.11/0.96 tff(120,plain,
% 1.11/0.96 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.11/0.96 tff(121,plain,(
% 1.11/0.96 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[120])).
% 1.11/0.96 tff(122,plain,
% 1.11/0.96 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[121, 117])).
% 1.11/0.96 tff(123,plain,
% 1.11/0.96 (n0(d, b) <=> n0(d, b)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(124,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 1.11/0.96 tff(125,plain,
% 1.11/0.96 (n0(d, b)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.11/0.96 tff(126,plain,
% 1.11/0.96 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(127,plain,
% 1.11/0.96 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(128,plain,
% 1.11/0.96 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.11/0.96 tff(129,plain,
% 1.11/0.96 (k1(b)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[128, 125, 122])).
% 1.11/0.96 tff(130,plain,
% 1.11/0.96 (^[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)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(131,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[130])).
% 1.11/0.96 tff(132,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(133,plain,
% 1.11/0.96 (^[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))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(134,plain,
% 1.11/0.96 (![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))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[133])).
% 1.11/0.96 tff(135,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 1.11/0.96 tff(136,plain,
% 1.11/0.96 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.11/0.96 tff(137,plain,
% 1.11/0.96 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[136, 132])).
% 1.11/0.96 tff(138,plain,(
% 1.11/0.96 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.96 inference(skolemize,[status(sab)],[137])).
% 1.11/0.96 tff(139,plain,
% 1.11/0.96 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[138, 131])).
% 1.11/0.97 tff(140,plain,
% 1.11/0.97 (m0(b, b, e) <=> m0(b, b, e)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(141,axiom,(m0(b, b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 1.11/0.97 tff(142,plain,
% 1.11/0.97 (m0(b, b, e)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.11/0.97 tff(143,plain,
% 1.11/0.97 (((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))) <=> ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(144,plain,
% 1.11/0.97 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(145,plain,
% 1.11/0.97 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(b)) | (~m0(b, b, e)) | n1(b, e, e)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.11/0.97 tff(146,plain,
% 1.11/0.97 ((~k1(b)) | n1(b, e, e)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[145, 142, 139])).
% 1.11/0.97 tff(147,plain,
% 1.11/0.97 (n1(b, e, e)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[146, 129])).
% 1.11/0.97 tff(148,plain,
% 1.11/0.97 (^[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)))),
% 1.11/0.97 inference(bind,[status(th)],[])).
% 1.11/0.97 tff(149,plain,
% 1.11/0.97 (![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))),
% 1.11/0.97 inference(quant_intro,[status(thm)],[148])).
% 1.11/0.97 tff(150,plain,
% 1.11/0.97 (![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))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(151,plain,
% 1.11/0.97 (^[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))))),
% 1.11/0.97 inference(bind,[status(th)],[])).
% 1.11/0.97 tff(152,plain,
% 1.11/0.97 (![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))),
% 1.11/0.97 inference(quant_intro,[status(thm)],[151])).
% 1.11/0.97 tff(153,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/sandbox/benchmark/Axioms/SYN001-0.ax','rule_182')).
% 1.11/0.97 tff(154,plain,
% 1.11/0.97 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.11/0.97 tff(155,plain,
% 1.11/0.97 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[154, 150])).
% 1.11/0.97 tff(156,plain,(
% 1.11/0.97 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.97 inference(skolemize,[status(sab)],[155])).
% 1.11/0.97 tff(157,plain,
% 1.11/0.97 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[156, 149])).
% 1.11/0.97 tff(158,plain,
% 1.11/0.97 (p1(e, e, e) <=> p1(e, e, e)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(159,plain,
% 1.11/0.97 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(160,plain,
% 1.11/0.97 ((~$true) <=> $false),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(161,plain,
% 1.11/0.97 (k0(e) <=> $true),
% 1.11/0.97 inference(iff_true,[status(thm)],[109])).
% 1.11/0.97 tff(162,plain,
% 1.11/0.97 ((~k0(e)) <=> (~$true)),
% 1.11/0.97 inference(monotonicity,[status(thm)],[161])).
% 1.11/0.97 tff(163,plain,
% 1.11/0.97 ((~k0(e)) <=> $false),
% 1.11/0.97 inference(transitivity,[status(thm)],[162, 160])).
% 1.11/0.97 tff(164,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 1.11/0.97 tff(165,plain,
% 1.11/0.97 (r0(e) <=> $true),
% 1.11/0.97 inference(iff_true,[status(thm)],[164])).
% 1.11/0.97 tff(166,plain,
% 1.11/0.97 ((~r0(e)) <=> (~$true)),
% 1.11/0.97 inference(monotonicity,[status(thm)],[165])).
% 1.11/0.97 tff(167,plain,
% 1.11/0.97 ((~r0(e)) <=> $false),
% 1.11/0.97 inference(transitivity,[status(thm)],[166, 160])).
% 1.11/0.97 tff(168,plain,
% 1.11/0.97 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[167, 163])).
% 1.11/0.97 tff(169,plain,
% 1.11/0.97 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 1.11/0.97 inference(transitivity,[status(thm)],[168, 159])).
% 1.11/0.97 tff(170,plain,
% 1.11/0.97 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(171,plain,
% 1.11/0.97 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(172,plain,
% 1.11/0.97 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(173,plain,
% 1.11/0.97 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[172])).
% 1.11/0.97 tff(174,plain,
% 1.11/0.97 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.11/0.97 inference(transitivity,[status(thm)],[173, 171])).
% 1.11/0.97 tff(175,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 1.11/0.97 tff(176,plain,
% 1.11/0.97 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.11/0.97 tff(177,plain,
% 1.11/0.97 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[176, 170])).
% 1.11/0.97 tff(178,plain,
% 1.11/0.97 (p1(e, e, e)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[177, 169])).
% 1.11/0.97 tff(179,plain,
% 1.11/0.97 (p1(e, e, e)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[178, 158])).
% 1.11/0.97 tff(180,plain,
% 1.11/0.97 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, 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(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(181,plain,
% 1.11/0.97 (((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, e)) <=> ((~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(182,plain,
% 1.11/0.97 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, 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(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e)))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[181])).
% 1.11/0.97 tff(183,plain,
% 1.11/0.97 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, 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(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e))),
% 1.11/0.97 inference(transitivity,[status(thm)],[182, 180])).
% 1.11/0.97 tff(184,plain,
% 1.11/0.97 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, e))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(185,plain,
% 1.11/0.97 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e)),
% 1.14/0.97 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.14/0.97 tff(186,plain,
% 1.14/0.97 ((~q2(b, e, e)) | q2(e, b, e)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[185, 179, 157, 147])).
% 1.14/0.97 tff(187,plain,
% 1.14/0.97 (q2(e, b, e)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[186, 115])).
% 1.14/0.97 tff(188,plain,
% 1.14/0.97 (^[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)))),
% 1.14/0.97 inference(bind,[status(th)],[])).
% 1.14/0.97 tff(189,plain,
% 1.14/0.97 (![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))),
% 1.14/0.97 inference(quant_intro,[status(thm)],[188])).
% 1.14/0.97 tff(190,plain,
% 1.14/0.97 (![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))),
% 1.14/0.97 inference(rewrite,[status(thm)],[])).
% 1.14/0.97 tff(191,plain,
% 1.14/0.97 (^[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))))),
% 1.14/0.97 inference(bind,[status(th)],[])).
% 1.14/0.97 tff(192,plain,
% 1.14/0.97 (![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))),
% 1.14/0.97 inference(quant_intro,[status(thm)],[191])).
% 1.14/0.97 tff(193,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/sandbox/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 1.14/0.97 tff(194,plain,
% 1.14/0.97 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.14/0.97 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.14/0.97 tff(195,plain,
% 1.14/0.97 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.14/0.97 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.14/0.97 tff(196,plain,(
% 1.14/0.97 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.14/0.97 inference(skolemize,[status(sab)],[195])).
% 1.14/0.97 tff(197,plain,
% 1.14/0.97 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.14/0.97 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.14/0.97 tff(198,plain,
% 1.14/0.97 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(e, d, c)) | (~q2(e, b, e)) | s3(b, c))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(e, d, c)) | (~q2(e, b, e)) | s3(b, c))),
% 1.14/0.97 inference(rewrite,[status(thm)],[])).
% 1.14/0.97 tff(199,plain,
% 1.14/0.97 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(e, d, c)) | (~q2(e, b, e)) | s3(b, c))),
% 1.14/0.97 inference(quant_inst,[status(thm)],[])).
% 1.14/0.97 tff(200,plain,
% 1.14/0.97 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(e, d, c)) | (~q2(e, b, e)) | s3(b, c)),
% 1.14/0.97 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.14/0.97 tff(201,plain,
% 1.14/0.97 (s3(b, c)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[200, 197, 187, 82, 11])).
% 1.14/0.97 tff(202,plain,
% 1.14/0.97 (^[X: $i] : refl((~s3(b, X)) <=> (~s3(b, X)))),
% 1.14/0.97 inference(bind,[status(th)],[])).
% 1.14/0.97 tff(203,plain,
% 1.14/0.97 (![X: $i] : (~s3(b, X)) <=> ![X: $i] : (~s3(b, X))),
% 1.14/0.97 inference(quant_intro,[status(thm)],[202])).
% 1.14/0.98 tff(204,plain,
% 1.14/0.98 (![X: $i] : (~s3(b, X)) <=> ![X: $i] : (~s3(b, X))),
% 1.14/0.98 inference(rewrite,[status(thm)],[])).
% 1.14/0.98 tff(205,axiom,(![X: $i] : (~s3(b, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 1.14/0.98 tff(206,plain,
% 1.14/0.98 (![X: $i] : (~s3(b, X))),
% 1.14/0.98 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.14/0.98 tff(207,plain,(
% 1.14/0.98 ![X: $i] : (~s3(b, X))),
% 1.14/0.98 inference(skolemize,[status(sab)],[206])).
% 1.14/0.98 tff(208,plain,
% 1.14/0.98 (![X: $i] : (~s3(b, X))),
% 1.14/0.98 inference(modus_ponens,[status(thm)],[207, 203])).
% 1.14/0.98 tff(209,plain,
% 1.14/0.98 ((~![X: $i] : (~s3(b, X))) | (~s3(b, c))),
% 1.14/0.98 inference(quant_inst,[status(thm)],[])).
% 1.14/0.98 tff(210,plain,
% 1.14/0.98 ($false),
% 1.14/0.98 inference(unit_resolution,[status(thm)],[209, 208, 201])).
% 1.14/0.98 % SZS output end Proof
%------------------------------------------------------------------------------