TSTP Solution File: SYN300-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN300-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN300-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 02:46:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.53 % SZS status Unsatisfiable
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 tff(m0_type, type, (
% 0.20/0.53 m0: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(d_type, type, (
% 0.20/0.53 d: $i)).
% 0.20/0.53 tff(b_type, type, (
% 0.20/0.53 b: $i)).
% 0.20/0.53 tff(s2_type, type, (
% 0.20/0.53 s2: $i > $o)).
% 0.20/0.53 tff(s1_type, type, (
% 0.20/0.53 s1: $i > $o)).
% 0.20/0.53 tff(p0_type, type, (
% 0.20/0.53 p0: ( $i * $i ) > $o)).
% 0.20/0.53 tff(q2_type, type, (
% 0.20/0.53 q2: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(q1_type, type, (
% 0.20/0.53 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(c_type, type, (
% 0.20/0.53 c: $i)).
% 0.20/0.53 tff(n0_type, type, (
% 0.20/0.53 n0: ( $i * $i ) > $o)).
% 0.20/0.53 tff(s3_type, type, (
% 0.20/0.53 s3: ( $i * $i ) > $o)).
% 0.20/0.53 tff(1,assumption,(~m0(b, d, d)), introduced(assumption)).
% 0.20/0.53 tff(2,plain,
% 0.20/0.53 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(3,plain,
% 0.20/0.53 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.20/0.53 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.53 tff(4,plain,
% 0.20/0.53 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.20/0.53 tff(6,plain,
% 0.20/0.53 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.53 tff(7,plain,(
% 0.20/0.53 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.20/0.53 inference(skolemize,[status(sab)],[6])).
% 0.20/0.53 tff(8,plain,
% 0.20/0.53 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.53 tff(9,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, d)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(10,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.53 tff(11,plain,(m0(b, d, d)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(12,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.53 tff(13,plain,
% 0.20/0.53 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(14,plain,
% 0.20/0.53 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.53 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.53 tff(15,plain,
% 0.20/0.53 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(16,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.53 tff(17,plain,
% 0.20/0.53 (![X: $i] : p0(b, X)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.53 tff(18,plain,(
% 0.20/0.53 ![X: $i] : p0(b, X)),
% 0.20/0.53 inference(skolemize,[status(sab)],[17])).
% 0.20/0.53 tff(19,plain,
% 0.20/0.53 (![X: $i] : p0(b, X)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.53 tff(20,plain,
% 0.20/0.53 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(21,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.20/0.53 tff(22,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(23,plain,
% 0.20/0.53 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(24,plain,
% 0.20/0.53 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.53 tff(25,plain,
% 0.20/0.53 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(26,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.20/0.53 tff(27,plain,
% 0.20/0.53 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.53 tff(28,plain,(
% 0.20/0.53 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[27])).
% 0.20/0.53 tff(29,plain,
% 0.20/0.53 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.53 tff(30,plain,
% 0.20/0.53 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(31,plain,
% 0.20/0.53 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.53 tff(33,plain,
% 0.20/0.53 (s1(b)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 0.20/0.53 tff(34,plain,
% 0.20/0.53 (^[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)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(35,plain,
% 0.20/0.54 (![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))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.54 tff(36,plain,
% 0.20/0.54 (![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))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(37,plain,
% 0.20/0.54 (^[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))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(38,plain,
% 0.20/0.54 (![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))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.54 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')).
% 0.20/0.54 tff(40,plain,
% 0.20/0.54 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.54 tff(41,plain,
% 0.20/0.54 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.54 tff(42,plain,(
% 0.20/0.54 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.54 inference(skolemize,[status(sab)],[41])).
% 0.20/0.54 tff(43,plain,
% 0.20/0.54 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.20/0.54 tff(44,plain,
% 0.20/0.54 (n0(d, c) <=> n0(d, c)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(45,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.20/0.54 tff(46,plain,
% 0.20/0.54 (n0(d, c)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.54 tff(47,plain,
% 0.20/0.54 (p0(c, b) <=> p0(c, b)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(48,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.20/0.54 tff(49,plain,
% 0.20/0.54 (p0(c, b)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.54 tff(50,plain,
% 0.20/0.54 (((~![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))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(51,plain,
% 0.20/0.54 ((~![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))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(52,plain,
% 0.20/0.54 ((~![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)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.54 tff(53,plain,
% 0.20/0.54 (q1(b, c, b)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[52, 49, 46, 43])).
% 0.20/0.54 tff(54,plain,
% 0.20/0.54 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(55,plain,
% 0.20/0.54 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.54 tff(56,plain,
% 0.20/0.54 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(57,plain,
% 0.20/0.54 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(58,plain,
% 0.20/0.54 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.54 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')).
% 0.20/0.54 tff(60,plain,
% 0.20/0.54 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.54 tff(61,plain,
% 0.20/0.54 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.54 tff(62,plain,(
% 0.20/0.54 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.20/0.54 inference(skolemize,[status(sab)],[61])).
% 0.20/0.54 tff(63,plain,
% 0.20/0.54 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.54 tff(64,plain,
% 0.20/0.54 (((~![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))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(65,plain,
% 0.20/0.54 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(66,plain,
% 0.20/0.54 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.54 tff(67,plain,
% 0.20/0.54 (q2(b, b, b)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[66, 63, 53])).
% 0.20/0.54 tff(68,plain,
% 0.20/0.54 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(69,plain,
% 0.20/0.54 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.54 tff(70,plain,
% 0.20/0.54 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(71,plain,
% 0.20/0.54 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(72,plain,
% 0.20/0.54 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.54 tff(73,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.54 tff(75,plain,
% 0.20/0.54 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.54 tff(76,plain,(
% 0.20/0.54 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[75])).
% 0.20/0.54 tff(77,plain,
% 0.20/0.54 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.54 tff(78,plain,
% 0.20/0.54 (((~![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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(79,plain,
% 0.20/0.54 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(b) | (~q2(b, b, b)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(80,plain,
% 0.20/0.54 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(b) | (~q2(b, b, b))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.54 tff(81,plain,
% 0.20/0.54 ((~s1(b)) | s2(b)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[80, 77, 67])).
% 0.20/0.54 tff(82,plain,
% 0.20/0.54 (s2(b)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[81, 33])).
% 0.20/0.54 tff(83,plain,
% 0.20/0.54 ((~s3(b, d)) <=> (~s3(b, d))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(84,axiom,(~s3(b, d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.54 tff(85,plain,
% 0.20/0.54 (~s3(b, d)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.54 tff(86,plain,
% 0.20/0.54 (^[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)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(87,plain,
% 0.20/0.54 (![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))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.55 tff(88,plain,
% 0.20/0.55 (![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))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(89,plain,
% 0.20/0.55 (^[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))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(90,plain,
% 0.20/0.55 (![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))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.55 tff(91,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')).
% 0.20/0.55 tff(92,plain,
% 0.20/0.55 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.55 tff(93,plain,
% 0.20/0.55 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.55 tff(94,plain,(
% 0.20/0.55 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.20/0.55 inference(skolemize,[status(sab)],[93])).
% 0.20/0.55 tff(95,plain,
% 0.20/0.55 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.20/0.55 tff(96,plain,
% 0.20/0.55 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(b, d, d)) | (~q2(b, b, b)) | s3(b, d))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(b, d, d)) | (~q2(b, b, b)) | s3(b, d))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(97,plain,
% 0.20/0.55 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(b, d, d)) | (~q2(b, b, b)) | s3(b, d))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(98,plain,
% 0.20/0.55 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(b, d, d)) | (~q2(b, b, b)) | s3(b, d)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.55 tff(99,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[98, 95, 85, 67, 82, 11])).
% 0.20/0.55 % SZS output end Proof
%------------------------------------------------------------------------------