TSTP Solution File: SYN208-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN208-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 23:54:12 EDT 2022
% Result : Unsatisfiable 1.07s 0.94s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN208-1 : TPTP v8.1.0. Released v1.1.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 02:09:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 1.07/0.94 % SZS status Unsatisfiable
% 1.07/0.94 % SZS output start Proof
% 1.07/0.94 tff(m0_type, type, (
% 1.07/0.94 m0: ( $i * $i * $i ) > $o)).
% 1.07/0.94 tff(b_type, type, (
% 1.07/0.94 b: $i)).
% 1.07/0.94 tff(d_type, type, (
% 1.07/0.94 d: $i)).
% 1.07/0.94 tff(q2_type, type, (
% 1.07/0.94 q2: ( $i * $i * $i ) > $o)).
% 1.07/0.94 tff(n1_type, type, (
% 1.07/0.94 n1: ( $i * $i * $i ) > $o)).
% 1.07/0.94 tff(q0_type, type, (
% 1.07/0.94 q0: ( $i * $i ) > $o)).
% 1.07/0.94 tff(s3_type, type, (
% 1.07/0.94 s3: ( $i * $i ) > $o)).
% 1.07/0.94 tff(s2_type, type, (
% 1.07/0.94 s2: $i > $o)).
% 1.07/0.94 tff(s1_type, type, (
% 1.07/0.94 s1: $i > $o)).
% 1.07/0.94 tff(p0_type, type, (
% 1.07/0.94 p0: ( $i * $i ) > $o)).
% 1.07/0.94 tff(r1_type, type, (
% 1.07/0.94 r1: $i > $o)).
% 1.07/0.94 tff(q1_type, type, (
% 1.07/0.94 q1: ( $i * $i * $i ) > $o)).
% 1.07/0.94 tff(s0_type, type, (
% 1.07/0.94 s0: $i > $o)).
% 1.07/0.94 tff(k0_type, type, (
% 1.07/0.94 k0: $i > $o)).
% 1.07/0.94 tff(e_type, type, (
% 1.07/0.94 e: $i)).
% 1.07/0.94 tff(1,plain,
% 1.07/0.94 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 1.07/0.94 inference(bind,[status(th)],[])).
% 1.07/0.94 tff(2,plain,
% 1.07/0.94 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.07/0.94 inference(quant_intro,[status(thm)],[1])).
% 1.07/0.94 tff(3,plain,
% 1.07/0.94 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(4,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 1.07/0.94 tff(5,plain,
% 1.07/0.94 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.07/0.94 tff(6,plain,(
% 1.07/0.94 ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.07/0.94 inference(skolemize,[status(sab)],[5])).
% 1.07/0.94 tff(7,plain,
% 1.07/0.94 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.07/0.94 tff(8,plain,
% 1.07/0.94 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, b)),
% 1.07/0.94 inference(quant_inst,[status(thm)],[])).
% 1.07/0.94 tff(9,plain,
% 1.07/0.94 (m0(d, d, b)),
% 1.07/0.94 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.07/0.94 tff(10,plain,
% 1.07/0.94 (^[B: $i, D: $i, C: $i] : refl(((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)) <=> ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)))),
% 1.07/0.94 inference(bind,[status(th)],[])).
% 1.07/0.94 tff(11,plain,
% 1.07/0.94 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)) <=> ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 1.07/0.94 inference(quant_intro,[status(thm)],[10])).
% 1.07/0.94 tff(12,plain,
% 1.07/0.94 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)) <=> ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(13,plain,
% 1.07/0.94 (^[B: $i, D: $i, C: $i] : trans(monotonicity(rewrite((q2(B, B, B) | (~q0(C, B))) <=> ((~q0(C, B)) | q2(B, B, B))), (((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D))) <=> (((~q0(C, B)) | q2(B, B, B)) | (~n1(C, B, D))))), rewrite((((~q0(C, B)) | q2(B, B, B)) | (~n1(C, B, D))) <=> ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))), (((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D))) <=> ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))))),
% 1.07/0.94 inference(bind,[status(th)],[])).
% 1.07/0.94 tff(14,plain,
% 1.07/0.94 (![B: $i, D: $i, C: $i] : ((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D))) <=> ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 1.07/0.94 inference(quant_intro,[status(thm)],[13])).
% 1.07/0.94 tff(15,axiom,(![B: $i, D: $i, C: $i] : ((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_178')).
% 1.07/0.94 tff(16,plain,
% 1.07/0.94 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.07/0.94 tff(17,plain,
% 1.07/0.94 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.07/0.94 tff(18,plain,(
% 1.07/0.94 ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 1.07/0.94 inference(skolemize,[status(sab)],[17])).
% 1.07/0.94 tff(19,plain,
% 1.07/0.94 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[18, 11])).
% 1.07/0.94 tff(20,plain,
% 1.07/0.94 (n1(d, d, d) <=> n1(d, d, d)),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(21,plain,
% 1.07/0.94 ((n1(d, d, d) | $false) <=> n1(d, d, d)),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(22,plain,
% 1.07/0.94 ((~$true) <=> $false),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(23,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 1.07/0.94 tff(24,plain,
% 1.07/0.94 (q0(d, d) <=> $true),
% 1.07/0.94 inference(iff_true,[status(thm)],[23])).
% 1.07/0.94 tff(25,plain,
% 1.07/0.94 ((~q0(d, d)) <=> (~$true)),
% 1.07/0.94 inference(monotonicity,[status(thm)],[24])).
% 1.07/0.94 tff(26,plain,
% 1.07/0.94 ((~q0(d, d)) <=> $false),
% 1.07/0.94 inference(transitivity,[status(thm)],[25, 22])).
% 1.07/0.94 tff(27,plain,
% 1.07/0.94 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | $false)),
% 1.07/0.94 inference(monotonicity,[status(thm)],[26])).
% 1.07/0.94 tff(28,plain,
% 1.07/0.94 ((n1(d, d, d) | (~q0(d, d))) <=> n1(d, d, d)),
% 1.07/0.94 inference(transitivity,[status(thm)],[27, 21])).
% 1.07/0.94 tff(29,plain,
% 1.07/0.94 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(30,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 1.07/0.94 tff(31,plain,
% 1.07/0.94 (n1(d, d, d) | (~q0(d, d))),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.07/0.94 tff(32,plain,
% 1.07/0.94 (n1(d, d, d) | (~q0(d, d))),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[31, 29])).
% 1.07/0.94 tff(33,plain,
% 1.07/0.94 (n1(d, d, d)),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.07/0.94 tff(34,plain,
% 1.07/0.94 (n1(d, d, d)),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[33, 20])).
% 1.07/0.94 tff(35,plain,
% 1.07/0.94 (q0(d, d) <=> q0(d, d)),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(36,plain,
% 1.07/0.94 (q0(d, d)),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[23, 35])).
% 1.07/0.94 tff(37,plain,
% 1.07/0.94 (((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | ((~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d))) <=> ((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | (~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d))),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(38,plain,
% 1.07/0.94 ((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | ((~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d))),
% 1.07/0.94 inference(quant_inst,[status(thm)],[])).
% 1.07/0.94 tff(39,plain,
% 1.07/0.94 ((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | (~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d)),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.07/0.94 tff(40,plain,
% 1.07/0.94 (q2(d, d, d)),
% 1.07/0.94 inference(unit_resolution,[status(thm)],[39, 36, 34, 19])).
% 1.07/0.94 tff(41,plain,
% 1.07/0.94 ((~s3(d, b)) <=> (~s3(d, b))),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(42,axiom,(~s3(d, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 1.07/0.94 tff(43,plain,
% 1.07/0.94 (~s3(d, b)),
% 1.07/0.94 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.07/0.94 tff(44,plain,
% 1.07/0.94 (^[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)))),
% 1.07/0.94 inference(bind,[status(th)],[])).
% 1.07/0.94 tff(45,plain,
% 1.07/0.94 (![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))),
% 1.07/0.94 inference(quant_intro,[status(thm)],[44])).
% 1.07/0.94 tff(46,plain,
% 1.07/0.94 (![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))),
% 1.07/0.94 inference(rewrite,[status(thm)],[])).
% 1.07/0.94 tff(47,plain,
% 1.07/0.94 (^[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))))),
% 1.07/0.94 inference(bind,[status(th)],[])).
% 1.07/0.94 tff(48,plain,
% 1.07/0.94 (![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))),
% 1.07/0.95 inference(quant_intro,[status(thm)],[47])).
% 1.07/0.95 tff(49,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')).
% 1.07/0.95 tff(50,plain,
% 1.07/0.95 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.07/0.95 tff(51,plain,
% 1.07/0.95 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.07/0.95 tff(52,plain,(
% 1.07/0.95 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.07/0.95 inference(skolemize,[status(sab)],[51])).
% 1.07/0.95 tff(53,plain,
% 1.07/0.95 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.07/0.95 tff(54,assumption,(~p0(b, b)), introduced(assumption)).
% 1.07/0.95 tff(55,plain,
% 1.07/0.95 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.07/0.95 inference(bind,[status(th)],[])).
% 1.07/0.95 tff(56,plain,
% 1.07/0.95 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.07/0.95 inference(quant_intro,[status(thm)],[55])).
% 1.07/0.95 tff(57,plain,
% 1.07/0.95 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(58,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.07/0.95 tff(59,plain,
% 1.07/0.95 (![X: $i] : p0(b, X)),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.07/0.95 tff(60,plain,(
% 1.07/0.95 ![X: $i] : p0(b, X)),
% 1.07/0.95 inference(skolemize,[status(sab)],[59])).
% 1.07/0.95 tff(61,plain,
% 1.07/0.95 (![X: $i] : p0(b, X)),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.07/0.95 tff(62,plain,
% 1.07/0.95 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.07/0.95 inference(quant_inst,[status(thm)],[])).
% 1.07/0.95 tff(63,plain,
% 1.07/0.95 ($false),
% 1.07/0.95 inference(unit_resolution,[status(thm)],[62, 61, 54])).
% 1.07/0.95 tff(64,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.07/0.95 tff(65,plain,
% 1.07/0.95 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.07/0.95 inference(bind,[status(th)],[])).
% 1.07/0.95 tff(66,plain,
% 1.07/0.95 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.07/0.95 inference(quant_intro,[status(thm)],[65])).
% 1.07/0.95 tff(67,plain,
% 1.07/0.95 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(68,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.07/0.95 tff(69,plain,
% 1.07/0.95 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.07/0.95 tff(70,plain,(
% 1.07/0.95 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.07/0.95 inference(skolemize,[status(sab)],[69])).
% 1.07/0.95 tff(71,plain,
% 1.07/0.95 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.07/0.95 tff(72,plain,
% 1.07/0.95 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(73,plain,
% 1.07/0.95 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.07/0.95 inference(quant_inst,[status(thm)],[])).
% 1.07/0.95 tff(74,plain,
% 1.07/0.95 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.07/0.95 tff(75,plain,
% 1.07/0.95 (s1(b)),
% 1.07/0.95 inference(unit_resolution,[status(thm)],[74, 71, 64])).
% 1.07/0.95 tff(76,plain,
% 1.07/0.95 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 1.07/0.95 inference(bind,[status(th)],[])).
% 1.07/0.95 tff(77,plain,
% 1.07/0.95 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 1.07/0.95 inference(quant_intro,[status(thm)],[76])).
% 1.07/0.95 tff(78,plain,
% 1.07/0.95 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(79,plain,
% 1.07/0.95 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 1.07/0.95 inference(bind,[status(th)],[])).
% 1.07/0.95 tff(80,plain,
% 1.07/0.95 (![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 1.07/0.95 inference(quant_intro,[status(thm)],[79])).
% 1.07/0.95 tff(81,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 1.07/0.95 tff(82,plain,
% 1.07/0.95 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.07/0.95 tff(83,plain,
% 1.07/0.95 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[82, 78])).
% 1.07/0.95 tff(84,plain,(
% 1.07/0.95 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 1.07/0.95 inference(skolemize,[status(sab)],[83])).
% 1.07/0.95 tff(85,plain,
% 1.07/0.95 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[84, 77])).
% 1.07/0.95 tff(86,plain,
% 1.07/0.95 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(87,plain,
% 1.07/0.95 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))),
% 1.07/0.95 inference(quant_inst,[status(thm)],[])).
% 1.07/0.95 tff(88,plain,
% 1.07/0.95 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d)),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.07/0.95 tff(89,plain,
% 1.07/0.95 (s1(d)),
% 1.07/0.95 inference(unit_resolution,[status(thm)],[88, 36, 85, 75])).
% 1.07/0.95 tff(90,plain,
% 1.07/0.95 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 1.07/0.95 inference(bind,[status(th)],[])).
% 1.07/0.95 tff(91,plain,
% 1.07/0.95 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(quant_intro,[status(thm)],[90])).
% 1.07/0.95 tff(92,plain,
% 1.07/0.95 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(93,plain,
% 1.07/0.95 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(d)), (s0(d) <=> $true)), ((~s0(d)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(d)) <=> $false)), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)))), rewrite(((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))))),
% 1.07/0.95 inference(bind,[status(th)],[])).
% 1.07/0.95 tff(94,plain,
% 1.07/0.95 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(quant_intro,[status(thm)],[93])).
% 1.07/0.95 tff(95,plain,
% 1.07/0.95 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 1.07/0.95 inference(bind,[status(th)],[])).
% 1.07/0.95 tff(96,plain,
% 1.07/0.95 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(quant_intro,[status(thm)],[95])).
% 1.07/0.95 tff(97,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 1.07/0.95 tff(98,plain,
% 1.07/0.95 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.07/0.95 tff(99,plain,
% 1.07/0.95 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.07/0.95 tff(100,plain,
% 1.07/0.95 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[99, 92])).
% 1.07/0.95 tff(101,plain,(
% 1.07/0.95 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(skolemize,[status(sab)],[100])).
% 1.07/0.95 tff(102,plain,
% 1.07/0.95 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[101, 91])).
% 1.07/0.95 tff(103,plain,
% 1.07/0.95 (q1(d, d, d) <=> q1(d, d, d)),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(104,plain,
% 1.07/0.95 (($false | $false | q1(d, d, d)) <=> q1(d, d, d)),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(105,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.07/0.95 tff(106,plain,
% 1.07/0.95 (k0(e) <=> $true),
% 1.07/0.95 inference(iff_true,[status(thm)],[105])).
% 1.07/0.95 tff(107,plain,
% 1.07/0.95 ((~k0(e)) <=> (~$true)),
% 1.07/0.95 inference(monotonicity,[status(thm)],[106])).
% 1.07/0.95 tff(108,plain,
% 1.07/0.95 ((~k0(e)) <=> $false),
% 1.07/0.95 inference(transitivity,[status(thm)],[107, 22])).
% 1.07/0.95 tff(109,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 1.07/0.95 tff(110,plain,
% 1.07/0.95 (s0(d) <=> $true),
% 1.07/0.95 inference(iff_true,[status(thm)],[109])).
% 1.07/0.95 tff(111,plain,
% 1.07/0.95 ((~s0(d)) <=> (~$true)),
% 1.07/0.95 inference(monotonicity,[status(thm)],[110])).
% 1.07/0.95 tff(112,plain,
% 1.07/0.95 ((~s0(d)) <=> $false),
% 1.07/0.95 inference(transitivity,[status(thm)],[111, 22])).
% 1.07/0.95 tff(113,plain,
% 1.07/0.95 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ($false | $false | q1(d, d, d))),
% 1.07/0.95 inference(monotonicity,[status(thm)],[112, 108])).
% 1.07/0.95 tff(114,plain,
% 1.07/0.95 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> q1(d, d, d)),
% 1.07/0.95 inference(transitivity,[status(thm)],[113, 104])).
% 1.07/0.95 tff(115,plain,
% 1.07/0.95 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(116,plain,
% 1.07/0.95 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(117,plain,
% 1.07/0.95 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(118,plain,
% 1.07/0.95 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 1.07/0.95 inference(monotonicity,[status(thm)],[117])).
% 1.07/0.95 tff(119,plain,
% 1.07/0.95 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.07/0.95 inference(transitivity,[status(thm)],[118, 116])).
% 1.07/0.95 tff(120,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 1.07/0.95 tff(121,plain,
% 1.07/0.95 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.07/0.95 tff(122,plain,
% 1.07/0.95 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[121, 115])).
% 1.07/0.95 tff(123,plain,
% 1.07/0.95 (q1(d, d, d)),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[122, 114])).
% 1.07/0.95 tff(124,plain,
% 1.07/0.95 (q1(d, d, d)),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[123, 103])).
% 1.07/0.95 tff(125,plain,
% 1.07/0.95 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | r1(d) | (~q1(d, d, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(126,plain,
% 1.07/0.95 (((~q0(d, d)) | (~q1(d, d, d)) | r1(d)) <=> ((~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 1.07/0.95 inference(rewrite,[status(thm)],[])).
% 1.07/0.95 tff(127,plain,
% 1.07/0.95 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~q1(d, d, d)) | r1(d))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | r1(d) | (~q1(d, d, d))))),
% 1.07/0.95 inference(monotonicity,[status(thm)],[126])).
% 1.07/0.95 tff(128,plain,
% 1.07/0.95 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~q1(d, d, d)) | r1(d))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 1.07/0.95 inference(transitivity,[status(thm)],[127, 125])).
% 1.07/0.95 tff(129,plain,
% 1.07/0.95 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~q1(d, d, d)) | r1(d))),
% 1.07/0.95 inference(quant_inst,[status(thm)],[])).
% 1.07/0.95 tff(130,plain,
% 1.07/0.95 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(d, d)) | r1(d) | (~q1(d, d, d))),
% 1.07/0.95 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.07/0.95 tff(131,plain,
% 1.07/0.95 (r1(d)),
% 1.07/0.95 inference(unit_resolution,[status(thm)],[130, 36, 124, 102])).
% 1.07/0.95 tff(132,plain,
% 1.07/0.95 (((~r1(d)) | s2(d) | (~s1(d))) <=> ((~r1(d)) | s2(d) | (~s1(d)))),
% 1.07/0.96 inference(rewrite,[status(thm)],[])).
% 1.07/0.96 tff(133,plain,
% 1.07/0.96 (((s2(d) | (~r1(d))) | (~s1(d))) <=> ((~r1(d)) | s2(d) | (~s1(d)))),
% 1.07/0.96 inference(rewrite,[status(thm)],[])).
% 1.07/0.96 tff(134,axiom,((s2(d) | (~r1(d))) | (~s1(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_191')).
% 1.07/0.96 tff(135,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.07/0.96 tff(136,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[135, 132])).
% 1.07/0.96 tff(137,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[136, 132])).
% 1.07/0.96 tff(138,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[137, 132])).
% 1.07/0.96 tff(139,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[138, 132])).
% 1.07/0.96 tff(140,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[139, 132])).
% 1.07/0.96 tff(141,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[140, 132])).
% 1.07/0.96 tff(142,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[141, 132])).
% 1.07/0.96 tff(143,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[142, 132])).
% 1.07/0.96 tff(144,plain,
% 1.07/0.96 ((~r1(d)) | s2(d) | (~s1(d))),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[143, 132])).
% 1.07/0.96 tff(145,plain,
% 1.07/0.96 (s2(d) | (~s1(d))),
% 1.07/0.96 inference(unit_resolution,[status(thm)],[144, 131])).
% 1.07/0.96 tff(146,plain,
% 1.07/0.96 (s2(d)),
% 1.07/0.96 inference(unit_resolution,[status(thm)],[145, 89])).
% 1.07/0.96 tff(147,plain,
% 1.07/0.96 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b))),
% 1.07/0.96 inference(rewrite,[status(thm)],[])).
% 1.07/0.96 tff(148,plain,
% 1.07/0.96 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b))),
% 1.07/0.96 inference(quant_inst,[status(thm)],[])).
% 1.07/0.96 tff(149,plain,
% 1.07/0.96 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b)),
% 1.07/0.96 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.07/0.96 tff(150,plain,
% 1.07/0.96 ($false),
% 1.07/0.96 inference(unit_resolution,[status(thm)],[149, 146, 53, 43, 40, 9])).
% 1.07/0.96 % SZS output end Proof
%------------------------------------------------------------------------------