TSTP Solution File: SYN269-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN269-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 23:54:28 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SYN269-1 : TPTP v8.1.0. Released v1.1.0.
% 0.00/0.08 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.27 % Computer : n002.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon Sep 5 02:32:03 EDT 2022
% 0.08/0.27 % CPUTime :
% 0.08/0.28 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.28 Usage: tptp [options] [-file:]file
% 0.08/0.28 -h, -? prints this message.
% 0.08/0.28 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.28 -m, -model generate model.
% 0.08/0.28 -p, -proof generate proof.
% 0.08/0.28 -c, -core generate unsat core of named formulas.
% 0.08/0.28 -st, -statistics display statistics.
% 0.08/0.28 -t:timeout set timeout (in second).
% 0.08/0.28 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.28 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.28 -<param>:<value> configuration parameter and value.
% 0.08/0.28 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(r3_type, type, (
% 0.12/0.39 r3: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(b_type, type, (
% 0.12/0.39 b: $i)).
% 0.12/0.39 tff(a_type, type, (
% 0.12/0.39 a: $i)).
% 0.12/0.39 tff(m3_type, type, (
% 0.12/0.39 m3: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(k3_type, type, (
% 0.12/0.39 k3: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(s1_type, type, (
% 0.12/0.39 s1: $i > $o)).
% 0.12/0.39 tff(p0_type, type, (
% 0.12/0.39 p0: ( $i * $i ) > $o)).
% 0.12/0.39 tff(q0_type, type, (
% 0.12/0.39 q0: ( $i * $i ) > $o)).
% 0.12/0.39 tff(p2_type, type, (
% 0.12/0.39 p2: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(n0_type, type, (
% 0.12/0.39 n0: ( $i * $i ) > $o)).
% 0.12/0.39 tff(m1_type, type, (
% 0.12/0.39 m1: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(l0_type, type, (
% 0.12/0.39 l0: $i > $o)).
% 0.12/0.39 tff(s0_type, type, (
% 0.12/0.39 s0: $i > $o)).
% 0.12/0.39 tff(d_type, type, (
% 0.12/0.39 d: $i)).
% 0.12/0.39 tff(r2_type, type, (
% 0.12/0.39 r2: $i > $o)).
% 0.12/0.39 tff(r1_type, type, (
% 0.12/0.39 r1: $i > $o)).
% 0.12/0.39 tff(q1_type, type, (
% 0.12/0.39 q1: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(r0_type, type, (
% 0.12/0.39 r0: $i > $o)).
% 0.12/0.39 tff(m2_type, type, (
% 0.12/0.39 m2: $i > $o)).
% 0.12/0.39 tff(k1_type, type, (
% 0.12/0.39 k1: $i > $o)).
% 0.12/0.39 tff(p4_type, type, (
% 0.12/0.39 p4: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![X: $i] : p0(b, X)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![X: $i] : p0(b, X)),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![X: $i] : p0(b, X)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.39 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,(
% 0.12/0.39 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (s1(b)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.39 tff(31,plain,(
% 0.12/0.39 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.12/0.39 inference(skolemize,[status(sab)],[30])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (q0(a, b) <=> q0(a, b)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,axiom,(q0(a, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (q0(a, b)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (s1(a) | (~s1(b)) | (~q0(a, b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (((~q0(a, b)) | (~s1(b)) | s1(a)) <=> (s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (s1(a) | (~s1(b)) | (~q0(a, b))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[38, 36])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (s1(a)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[41, 35, 32, 22])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J)) <=> ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k3(J, A, J) | (~s1(A))) <=> ((~s1(A)) | k3(J, A, J))), (((k3(J, A, J) | (~s1(A))) | (~p2(B, A, C))) <=> (((~s1(A)) | k3(J, A, J)) | (~p2(B, A, C))))), rewrite((((~s1(A)) | k3(J, A, J)) | (~p2(B, A, C))) <=> ((~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))), (((k3(J, A, J) | (~s1(A))) | (~p2(B, A, C))) <=> ((~s1(A)) | (~p2(B, A, C)) | k3(J, A, J)))), ((((k3(J, A, J) | (~s1(A))) | (~p2(B, A, C))) | (~n0(J, C))) <=> (((~s1(A)) | (~p2(B, A, C)) | k3(J, A, J)) | (~n0(J, C))))), rewrite((((~s1(A)) | (~p2(B, A, C)) | k3(J, A, J)) | (~n0(J, C))) <=> ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))), ((((k3(J, A, J) | (~s1(A))) | (~p2(B, A, C))) | (~n0(J, C))) <=> ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![B: $i, A: $i, J: $i, C: $i] : (((k3(J, A, J) | (~s1(A))) | (~p2(B, A, C))) | (~n0(J, C))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.39 tff(48,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((k3(J, A, J) | (~s1(A))) | (~p2(B, A, C))) | (~n0(J, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_192')).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.39 tff(51,plain,(
% 0.12/0.39 ![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.12/0.39 inference(skolemize,[status(sab)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(56,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.39 tff(58,plain,(
% 0.12/0.39 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[57])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (m1(a, a, a) <=> m1(a, a, a)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((m1(a, a, a) | $false | $false) <=> m1(a, a, a)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~$true) <=> $false),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(63,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (l0(a) <=> $true),
% 0.12/0.39 inference(iff_true,[status(thm)],[63])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~l0(a)) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~l0(a)) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[65, 62])).
% 0.12/0.39 tff(67,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (s0(d) <=> $true),
% 0.12/0.39 inference(iff_true,[status(thm)],[67])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~s0(d)) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~s0(d)) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[69, 62])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | $false | $false)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[70, 66])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> m1(a, a, a)),
% 0.12/0.39 inference(transitivity,[status(thm)],[71, 61])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[75])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[76, 74])).
% 0.12/0.39 tff(78,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[79, 73])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (m1(a, a, a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[80, 72])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (m1(a, a, a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[81, 60])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (p2(a, a, a)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[85, 82, 59])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (n0(b, a) <=> n0(b, a)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(88,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (n0(b, a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | ((~s1(a)) | (~n0(b, a)) | (~p2(a, a, a)) | k3(b, a, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | (~s1(a)) | (~n0(b, a)) | (~p2(a, a, a)) | k3(b, a, b))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (((~n0(b, a)) | (~s1(a)) | (~p2(a, a, a)) | k3(b, a, b)) <=> ((~s1(a)) | (~n0(b, a)) | (~p2(a, a, a)) | k3(b, a, b))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | ((~n0(b, a)) | (~s1(a)) | (~p2(a, a, a)) | k3(b, a, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | ((~s1(a)) | (~n0(b, a)) | (~p2(a, a, a)) | k3(b, a, b)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[91])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | ((~n0(b, a)) | (~s1(a)) | (~p2(a, a, a)) | k3(b, a, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | (~s1(a)) | (~n0(b, a)) | (~p2(a, a, a)) | k3(b, a, b))),
% 0.12/0.40 inference(transitivity,[status(thm)],[92, 90])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 ((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | ((~n0(b, a)) | (~s1(a)) | (~p2(a, a, a)) | k3(b, a, b))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 ((~![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))) | (~s1(a)) | (~n0(b, a)) | (~p2(a, a, a)) | k3(b, a, b)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 ((~s1(a)) | k3(b, a, b)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[95, 89, 86, 52])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (k3(b, a, b)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[96, 42])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (^[B: $i, C: $i] : refl(((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)) <=> ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)) <=> ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)) <=> ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (^[B: $i, C: $i] : trans(monotonicity(rewrite((m3(B, B, C) | (~r2(C))) <=> ((~r2(C)) | m3(B, B, C))), (((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B))) <=> (((~r2(C)) | m3(B, B, C)) | (~k3(B, C, B))))), rewrite((((~r2(C)) | m3(B, B, C)) | (~k3(B, C, B))) <=> ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))), (((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B))) <=> ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (![B: $i, C: $i] : ((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B))) <=> ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.12/0.40 tff(103,axiom,(![B: $i, C: $i] : ((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_235')).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.12/0.40 tff(106,plain,(
% 0.12/0.40 ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.12/0.40 inference(skolemize,[status(sab)],[105])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (^[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)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(112,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[111])).
% 0.12/0.40 tff(113,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')).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.12/0.40 tff(116,plain,(
% 0.12/0.40 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.12/0.40 inference(skolemize,[status(sab)],[115])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 (p0(b, d) <=> p0(b, d)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(119,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 (p0(b, d)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 (n0(d, b) <=> n0(d, b)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(122,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (n0(d, b)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 (q1(d, b, d)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[126, 123, 120, 117])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(129,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[131])).
% 0.12/0.40 tff(133,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[133])).
% 0.12/0.40 tff(135,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.12/0.40 tff(136,plain,
% 0.12/0.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.12/0.40 tff(137,plain,
% 0.12/0.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.12/0.40 tff(138,plain,
% 0.12/0.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.12/0.40 tff(139,plain,(
% 0.12/0.40 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.12/0.40 inference(skolemize,[status(sab)],[138])).
% 0.12/0.40 tff(140,plain,
% 0.12/0.40 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.12/0.40 tff(141,plain,
% 0.12/0.40 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(142,plain,
% 0.12/0.40 (((~q0(a, b)) | (~q1(d, b, d)) | r1(a)) <=> (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(143,plain,
% 0.12/0.40 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[142])).
% 0.12/0.40 tff(144,plain,
% 0.12/0.40 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[143, 141])).
% 0.12/0.40 tff(145,plain,
% 0.12/0.40 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(146,plain,
% 0.12/0.40 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.12/0.40 tff(147,plain,
% 0.12/0.40 (r1(a)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[146, 35, 140, 127])).
% 0.12/0.40 tff(148,plain,
% 0.12/0.40 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(149,plain,
% 0.12/0.40 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[148])).
% 0.12/0.40 tff(150,plain,
% 0.12/0.40 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(151,plain,
% 0.12/0.40 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(152,plain,
% 0.12/0.40 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[151])).
% 0.12/0.40 tff(153,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.12/0.40 tff(154,plain,
% 0.12/0.40 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.12/0.40 tff(155,plain,
% 0.12/0.40 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.12/0.40 tff(156,plain,(
% 0.12/0.40 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.12/0.40 inference(skolemize,[status(sab)],[155])).
% 0.12/0.40 tff(157,plain,
% 0.12/0.40 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.12/0.40 tff(158,plain,
% 0.12/0.40 (l0(a) <=> l0(a)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(159,plain,
% 0.12/0.40 (l0(a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 158])).
% 0.12/0.40 tff(160,plain,
% 0.12/0.40 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(161,plain,
% 0.12/0.40 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(162,plain,
% 0.12/0.40 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.12/0.40 tff(163,plain,
% 0.12/0.40 (r2(a)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[162, 159, 157, 147])).
% 0.12/0.40 tff(164,plain,
% 0.12/0.40 (((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | ((~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))) <=> ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | (~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(165,plain,
% 0.12/0.40 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | ((~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(166,plain,
% 0.12/0.40 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | (~r2(a)) | (~k3(b, a, b)) | m3(b, b, a)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.12/0.40 tff(167,plain,
% 0.12/0.40 (m3(b, b, a)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[166, 163, 107, 97])).
% 0.12/0.40 tff(168,plain,
% 0.12/0.40 (^[A: $i] : refl((p2(A, A, A) | (~q1(A, A, A))) <=> (p2(A, A, A) | (~q1(A, A, A))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(169,plain,
% 0.12/0.40 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[168])).
% 0.12/0.40 tff(170,plain,
% 0.12/0.40 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(171,axiom,(![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_154')).
% 0.12/0.40 tff(172,plain,
% 0.12/0.40 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.12/0.40 tff(173,plain,(
% 0.12/0.40 ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[172])).
% 0.12/0.40 tff(174,plain,
% 0.12/0.40 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.12/0.40 tff(175,plain,
% 0.12/0.40 (q1(b, b, b) <=> q1(b, b, b)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(176,plain,
% 0.12/0.40 (($false | q1(b, b, b)) <=> q1(b, b, b)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(177,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.12/0.40 tff(178,plain,
% 0.12/0.40 (r0(b) <=> $true),
% 0.12/0.40 inference(iff_true,[status(thm)],[177])).
% 0.12/0.40 tff(179,plain,
% 0.12/0.40 ((~r0(b)) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[178])).
% 0.12/0.40 tff(180,plain,
% 0.12/0.40 ((~r0(b)) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[179, 62])).
% 0.12/0.40 tff(181,plain,
% 0.12/0.40 (((~r0(b)) | q1(b, b, b)) <=> ($false | q1(b, b, b))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[180])).
% 0.12/0.40 tff(182,plain,
% 0.12/0.40 (((~r0(b)) | q1(b, b, b)) <=> q1(b, b, b)),
% 0.12/0.40 inference(transitivity,[status(thm)],[181, 176])).
% 0.12/0.40 tff(183,plain,
% 0.12/0.40 ((q1(b, b, b) | (~r0(b))) <=> ((~r0(b)) | q1(b, b, b))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(184,axiom,(q1(b, b, b) | (~r0(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_120')).
% 0.12/0.40 tff(185,plain,
% 0.12/0.40 ((~r0(b)) | q1(b, b, b)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.12/0.40 tff(186,plain,
% 0.12/0.40 (q1(b, b, b)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[185, 182])).
% 0.12/0.40 tff(187,plain,
% 0.12/0.40 (q1(b, b, b)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[186, 175])).
% 0.12/0.40 tff(188,plain,
% 0.12/0.40 (((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | (p2(b, b, b) | (~q1(b, b, b)))) <=> ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | p2(b, b, b) | (~q1(b, b, b)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(189,plain,
% 0.12/0.40 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | (p2(b, b, b) | (~q1(b, b, b)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(190,plain,
% 0.12/0.40 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | p2(b, b, b) | (~q1(b, b, b))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.12/0.40 tff(191,plain,
% 0.12/0.40 (p2(b, b, b)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[190, 187, 174])).
% 0.12/0.40 tff(192,plain,
% 0.12/0.40 (^[B: $i, D: $i, C: $i] : refl(((~p2(B, D, C)) | r3(B, C, B)) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(193,plain,
% 0.12/0.40 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B)) <=> ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[192])).
% 0.12/0.40 tff(194,plain,
% 0.12/0.40 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B)) <=> ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(195,plain,
% 0.12/0.40 (^[B: $i, D: $i, C: $i] : rewrite((r3(B, C, B) | (~p2(B, D, C))) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(196,plain,
% 0.12/0.40 (![B: $i, D: $i, C: $i] : (r3(B, C, B) | (~p2(B, D, C))) <=> ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[195])).
% 0.12/0.40 tff(197,axiom,(![B: $i, D: $i, C: $i] : (r3(B, C, B) | (~p2(B, D, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_267')).
% 0.12/0.40 tff(198,plain,
% 0.12/0.40 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.12/0.40 tff(199,plain,
% 0.12/0.40 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.12/0.40 tff(200,plain,(
% 0.12/0.40 ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.12/0.40 inference(skolemize,[status(sab)],[199])).
% 0.12/0.40 tff(201,plain,
% 0.12/0.40 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.12/0.40 tff(202,plain,
% 0.12/0.40 (((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(b, b, b)) | r3(b, b, b))) <=> ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(b, b, b)) | r3(b, b, b))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(203,plain,
% 0.12/0.40 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(b, b, b)) | r3(b, b, b))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(204,plain,
% 0.12/0.41 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(b, b, b)) | r3(b, b, b)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.12/0.41 tff(205,plain,
% 0.12/0.41 (r3(b, b, b)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[204, 201, 191])).
% 0.12/0.41 tff(206,plain,
% 0.12/0.41 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) <=> ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(207,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[206])).
% 0.12/0.41 tff(208,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(209,plain,
% 0.12/0.41 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(trans(monotonicity(rewrite((r3(H, H, I) | (~m2(I))) <=> ((~m2(I)) | r3(H, H, I))), (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) <=> (((~m2(I)) | r3(H, H, I)) | (~m3(J, b, H))))), rewrite((((~m2(I)) | r3(H, H, I)) | (~m3(J, b, H))) <=> ((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))), (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) <=> ((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)))), ((((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A))) <=> (((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) | (~r3(I, A, A))))), rewrite((((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) | (~r3(I, A, A))) <=> ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))), ((((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A))) <=> ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(210,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[209])).
% 0.12/0.41 tff(211,axiom,(![I: $i, A: $i, J: $i, H: $i] : (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_268')).
% 0.12/0.41 tff(212,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.12/0.41 tff(213,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.12/0.41 tff(214,plain,(
% 0.12/0.41 ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.12/0.41 inference(skolemize,[status(sab)],[213])).
% 0.12/0.41 tff(215,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.12/0.41 tff(216,plain,
% 0.12/0.41 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(217,plain,
% 0.12/0.41 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[216])).
% 0.12/0.41 tff(218,plain,
% 0.12/0.41 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(219,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.12/0.41 tff(220,plain,
% 0.12/0.41 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.12/0.41 tff(221,plain,(
% 0.12/0.41 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[220])).
% 0.12/0.41 tff(222,plain,
% 0.12/0.41 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.12/0.41 tff(223,plain,
% 0.12/0.41 (((~![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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(224,plain,
% 0.12/0.41 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(225,plain,
% 0.12/0.41 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.12/0.41 tff(226,plain,
% 0.12/0.41 (k1(b)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[225, 123, 222])).
% 0.12/0.41 tff(227,plain,
% 0.12/0.41 ((m2(b) | (~k1(b))) <=> (m2(b) | (~k1(b)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(228,axiom,(m2(b) | (~k1(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_136')).
% 0.12/0.41 tff(229,plain,
% 0.12/0.41 (m2(b) | (~k1(b))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.12/0.41 tff(230,plain,
% 0.12/0.41 (m2(b)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[229, 226])).
% 0.12/0.41 tff(231,plain,
% 0.12/0.41 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(232,plain,
% 0.12/0.41 (((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b)) <=> ((~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(233,plain,
% 0.12/0.41 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[232])).
% 0.12/0.41 tff(234,plain,
% 0.12/0.41 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))),
% 0.12/0.41 inference(transitivity,[status(thm)],[233, 231])).
% 0.12/0.41 tff(235,plain,
% 0.12/0.41 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(236,plain,
% 0.12/0.41 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.12/0.41 tff(237,plain,
% 0.12/0.41 (r3(a, a, b)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[236, 230, 215, 205, 167])).
% 0.12/0.41 tff(238,plain,
% 0.12/0.41 (^[B: $i, C: $i] : refl((p4(B, C, B) | (~k3(B, B, C))) <=> (p4(B, C, B) | (~k3(B, B, C))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(239,plain,
% 0.12/0.41 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[238])).
% 0.12/0.41 tff(240,plain,
% 0.12/0.41 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(241,axiom,(![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_287')).
% 0.12/0.41 tff(242,plain,
% 0.12/0.41 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.12/0.41 tff(243,plain,(
% 0.12/0.41 ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[242])).
% 0.12/0.41 tff(244,plain,
% 0.12/0.41 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.12/0.41 tff(245,plain,
% 0.12/0.41 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(246,plain,
% 0.12/0.41 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(247,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 0.12/0.41 tff(248,plain,
% 0.12/0.41 ((~r2(a)) | k3(a, a, a)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.12/0.41 tff(249,plain,
% 0.12/0.41 ((~r2(a)) | k3(a, a, a)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[248, 245])).
% 0.12/0.41 tff(250,plain,
% 0.12/0.41 (k3(a, a, a)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[249, 163])).
% 0.12/0.41 tff(251,plain,
% 0.12/0.41 (((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))) <=> ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(252,plain,
% 0.12/0.41 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(253,plain,
% 0.12/0.41 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.12/0.41 tff(254,plain,
% 0.12/0.41 (p4(a, a, a)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[253, 250, 244])).
% 0.12/0.41 tff(255,plain,
% 0.12/0.41 ((~p4(b, a, a)) <=> (~p4(b, a, a))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(256,axiom,(~p4(b, a, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.41 tff(257,plain,
% 0.12/0.41 (~p4(b, a, a)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.12/0.41 tff(258,plain,
% 0.12/0.41 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)) <=> ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(259,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[258])).
% 0.12/0.41 tff(260,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(261,plain,
% 0.12/0.41 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(rewrite((p4(H, I, I) | (~r3(I, I, H))) <=> ((~r3(I, I, H)) | p4(H, I, I))), (((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A))) <=> (((~r3(I, I, H)) | p4(H, I, I)) | (~p4(J, J, A))))), rewrite((((~r3(I, I, H)) | p4(H, I, I)) | (~p4(J, J, A))) <=> ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))), (((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A))) <=> ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(262,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[261])).
% 0.12/0.41 tff(263,axiom,(![I: $i, A: $i, J: $i, H: $i] : ((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_288')).
% 0.12/0.41 tff(264,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.12/0.41 tff(265,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.12/0.41 tff(266,plain,(
% 0.12/0.41 ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.12/0.41 inference(skolemize,[status(sab)],[265])).
% 0.12/0.41 tff(267,plain,
% 0.12/0.41 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[266, 259])).
% 0.12/0.41 tff(268,plain,
% 0.12/0.41 (((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | ((~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | (~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(269,plain,
% 0.12/0.41 ((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | ((~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(270,plain,
% 0.12/0.41 ((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | (~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.12/0.42 tff(271,plain,
% 0.12/0.42 ($false),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[270, 267, 257, 254, 237])).
% 0.12/0.42 % SZS output end Proof
%------------------------------------------------------------------------------