TSTP Solution File: SYN190-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN190-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 23:54:07 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN190-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:07:03 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(r3_type, type, (
% 0.20/0.51 r3: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(d_type, type, (
% 0.20/0.51 d: $i)).
% 0.20/0.51 tff(a_type, type, (
% 0.20/0.51 a: $i)).
% 0.20/0.51 tff(m3_type, type, (
% 0.20/0.51 m3: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(b_type, type, (
% 0.20/0.51 b: $i)).
% 0.20/0.51 tff(k3_type, type, (
% 0.20/0.51 k3: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(s1_type, type, (
% 0.20/0.51 s1: $i > $o)).
% 0.20/0.51 tff(p0_type, type, (
% 0.20/0.51 p0: ( $i * $i ) > $o)).
% 0.20/0.51 tff(q0_type, type, (
% 0.20/0.51 q0: ( $i * $i ) > $o)).
% 0.20/0.51 tff(p2_type, type, (
% 0.20/0.51 p2: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(n0_type, type, (
% 0.20/0.51 n0: ( $i * $i ) > $o)).
% 0.20/0.51 tff(m1_type, type, (
% 0.20/0.51 m1: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(l0_type, type, (
% 0.20/0.51 l0: $i > $o)).
% 0.20/0.51 tff(s0_type, type, (
% 0.20/0.51 s0: $i > $o)).
% 0.20/0.51 tff(r2_type, type, (
% 0.20/0.51 r2: $i > $o)).
% 0.20/0.51 tff(r1_type, type, (
% 0.20/0.51 r1: $i > $o)).
% 0.20/0.51 tff(q1_type, type, (
% 0.20/0.51 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(n1_type, type, (
% 0.20/0.51 n1: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(m2_type, type, (
% 0.20/0.51 m2: $i > $o)).
% 0.20/0.51 tff(l1_type, type, (
% 0.20/0.51 l1: ( $i * $i ) > $o)).
% 0.20/0.51 tff(e_type, type, (
% 0.20/0.51 e: $i)).
% 0.20/0.51 tff(r0_type, type, (
% 0.20/0.51 r0: $i > $o)).
% 0.20/0.51 tff(m0_type, type, (
% 0.20/0.51 m0: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(c_type, type, (
% 0.20/0.51 c: $i)).
% 0.20/0.51 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (![X: $i] : p0(b, X)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.51 tff(7,plain,(
% 0.20/0.51 ![X: $i] : p0(b, X)),
% 0.20/0.51 inference(skolemize,[status(sab)],[6])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 (![X: $i] : p0(b, X)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.51 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.20/0.51 tff(16,plain,
% 0.20/0.51 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.51 tff(17,plain,(
% 0.20/0.51 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[16])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (s1(b)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(24,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.51 tff(28,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')).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.51 tff(30,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.51 tff(31,plain,(
% 0.20/0.51 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.51 inference(skolemize,[status(sab)],[30])).
% 0.20/0.51 tff(32,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 (q0(a, b) <=> q0(a, b)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(34,axiom,(q0(a, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 (q0(a, b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 (((~q0(a, b)) | (~s1(b)) | s1(a)) <=> (s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (s1(a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[41, 35, 32, 22])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (^[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)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.51 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/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_192')).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.51 tff(51,plain,(
% 0.20/0.51 ![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.20/0.51 inference(skolemize,[status(sab)],[50])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~n0(J, C)) | (~s1(A)) | (~p2(B, A, C)) | k3(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(56,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.51 tff(58,plain,(
% 0.20/0.51 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[57])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 (m1(a, a, a) <=> m1(a, a, a)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 ((m1(a, a, a) | $false | $false) <=> m1(a, a, a)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 ((~$true) <=> $false),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(63,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (l0(a) <=> $true),
% 0.20/0.51 inference(iff_true,[status(thm)],[63])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 ((~l0(a)) <=> (~$true)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 ((~l0(a)) <=> $false),
% 0.20/0.51 inference(transitivity,[status(thm)],[65, 62])).
% 0.20/0.51 tff(67,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 (s0(d) <=> $true),
% 0.20/0.51 inference(iff_true,[status(thm)],[67])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 ((~s0(d)) <=> (~$true)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 ((~s0(d)) <=> $false),
% 0.20/0.51 inference(transitivity,[status(thm)],[69, 62])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | $false | $false)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[70, 66])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> m1(a, a, a)),
% 0.20/0.51 inference(transitivity,[status(thm)],[71, 61])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.51 tff(78,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[79, 73])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (m1(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[80, 72])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 (m1(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[81, 60])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (p2(a, a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[85, 82, 59])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (n0(b, a) <=> n0(b, a)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(88,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 (n0(b, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (((~![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (((~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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 (((~![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))),
% 0.20/0.51 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 ((~![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))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 ((~![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)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 ((~s1(a)) | k3(b, a, b)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[95, 89, 86, 52])).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 (k3(b, a, b)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[96, 42])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 (^[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)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.51 tff(103,axiom,(![B: $i, C: $i] : ((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_235')).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.51 tff(105,plain,
% 0.20/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.51 tff(106,plain,(
% 0.20/0.51 ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.51 inference(skolemize,[status(sab)],[105])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 (^[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)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.51 tff(113,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.51 tff(116,plain,(
% 0.20/0.51 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(skolemize,[status(sab)],[115])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 (p0(b, d) <=> p0(b, d)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(119,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (p0(b, d)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 (n0(d, b) <=> n0(d, b)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(122,axiom,(n0(d, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 (n0(d, b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 (((~![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.52 ((~![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))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 ((~![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)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 (q1(d, b, d)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[126, 123, 120, 117])).
% 0.20/0.52 tff(128,plain,
% 0.20/0.52 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(129,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(132,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.52 tff(135,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')).
% 0.20/0.52 tff(136,plain,
% 0.20/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.20/0.52 tff(139,plain,(
% 0.20/0.52 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.52 inference(skolemize,[status(sab)],[138])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (((~![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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (((~q0(a, b)) | (~q1(d, b, d)) | r1(a)) <=> (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 (((~![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))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 (((~![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)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[143, 141])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 (r1(a)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[146, 35, 140, 127])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.52 tff(153,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.52 tff(155,plain,
% 0.20/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.20/0.52 tff(156,plain,(
% 0.20/0.52 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.52 inference(skolemize,[status(sab)],[155])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.20/0.52 tff(158,plain,
% 0.20/0.52 (l0(a) <=> l0(a)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 (l0(a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[63, 158])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 (((~![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(161,plain,
% 0.20/0.52 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.52 tff(163,plain,
% 0.20/0.52 (r2(a)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[162, 159, 157, 147])).
% 0.20/0.52 tff(164,plain,
% 0.20/0.52 (((~![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(165,plain,
% 0.20/0.52 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | ((~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(166,plain,
% 0.20/0.52 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | (~r2(a)) | (~k3(b, a, b)) | m3(b, b, a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.52 tff(167,plain,
% 0.20/0.52 (m3(b, b, a)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[166, 163, 107, 97])).
% 0.20/0.52 tff(168,plain,
% 0.20/0.52 (^[B: $i, D: $i, C: $i] : refl(((~p2(B, D, C)) | r3(B, C, B)) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(169,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.52 tff(170,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(171,plain,
% 0.20/0.52 (^[B: $i, D: $i, C: $i] : rewrite((r3(B, C, B) | (~p2(B, D, C))) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(172,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.52 tff(173,axiom,(![B: $i, D: $i, C: $i] : (r3(B, C, B) | (~p2(B, D, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_267')).
% 0.20/0.52 tff(174,plain,
% 0.20/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.52 tff(175,plain,
% 0.20/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.20/0.52 tff(176,plain,(
% 0.20/0.52 ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.52 inference(skolemize,[status(sab)],[175])).
% 0.20/0.52 tff(177,plain,
% 0.20/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.20/0.52 tff(178,plain,
% 0.20/0.52 (^[B: $i] : refl((p2(B, B, B) | (~n1(d, d, B))) <=> (p2(B, B, B) | (~n1(d, d, B))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(179,plain,
% 0.20/0.52 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[178])).
% 0.20/0.52 tff(180,plain,
% 0.20/0.52 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(181,axiom,(![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_153')).
% 0.20/0.52 tff(182,plain,
% 0.20/0.52 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.52 tff(183,plain,(
% 0.20/0.52 ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[182])).
% 0.20/0.52 tff(184,plain,
% 0.20/0.52 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.20/0.52 tff(185,plain,
% 0.20/0.52 (n1(d, d, d) <=> n1(d, d, d)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(186,plain,
% 0.20/0.52 ((n1(d, d, d) | $false) <=> n1(d, d, d)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(187,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.20/0.52 tff(188,plain,
% 0.20/0.52 (q0(d, d) <=> $true),
% 0.20/0.52 inference(iff_true,[status(thm)],[187])).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 ((~q0(d, d)) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[188])).
% 0.20/0.52 tff(190,plain,
% 0.20/0.52 ((~q0(d, d)) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[189, 62])).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | $false)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[190])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 ((n1(d, d, d) | (~q0(d, d))) <=> n1(d, d, d)),
% 0.20/0.52 inference(transitivity,[status(thm)],[191, 186])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(194,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 (n1(d, d, d) | (~q0(d, d))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 (n1(d, d, d) | (~q0(d, d))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[195, 193])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 (n1(d, d, d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 (n1(d, d, d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[197, 185])).
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% 0.20/0.52 (((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))) <=> ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 (p2(d, d, d)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[201, 198, 184])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 (((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(d, d, d)) | r3(d, d, d))) <=> ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(d, d, d)) | r3(d, d, d))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(d, d, d)) | r3(d, d, d))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(d, d, d)) | r3(d, d, d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 (r3(d, d, d)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[205, 202, 177])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 (^[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)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[207])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[210])).
% 0.20/0.52 tff(212,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/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_268')).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.20/0.52 tff(215,plain,(
% 0.20/0.52 ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.52 inference(skolemize,[status(sab)],[214])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[217])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1(C, D) | (~p0(E, C))) <=> ((~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> (((~p0(E, C)) | l1(C, D)) | (~r0(F))))), rewrite((((~p0(E, C)) | l1(C, D)) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D)))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> (((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))))), rewrite((((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 (![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[220])).
% 0.20/0.52 tff(222,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_003')).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.52 tff(224,plain,
% 0.20/0.52 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.20/0.52 tff(225,plain,(
% 0.20/0.52 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.52 inference(skolemize,[status(sab)],[224])).
% 0.20/0.52 tff(226,plain,
% 0.20/0.52 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.20/0.52 tff(227,plain,
% 0.20/0.52 (m0(e, b, c) <=> m0(e, b, c)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(228,axiom,(m0(e, b, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.20/0.52 tff(229,plain,
% 0.20/0.52 (m0(e, b, c)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 (p0(c, b) <=> p0(c, b)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(231,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 (p0(c, b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 (r0(b) <=> r0(b)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(234,axiom,(r0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 (r0(b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 (((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e)) <=> ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(238,plain,
% 0.20/0.52 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[237])).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.52 inference(transitivity,[status(thm)],[238, 236])).
% 0.20/0.52 tff(240,plain,
% 0.20/0.52 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(241,plain,
% 0.20/0.52 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.53 tff(242,plain,
% 0.20/0.53 (l1(b, e)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[241, 235, 232, 229, 226])).
% 0.20/0.53 tff(243,plain,
% 0.20/0.53 (^[H: $i, F: $i, G: $i] : refl(((~s0(F)) | (~l1(G, H)) | m2(F)) <=> ((~s0(F)) | (~l1(G, H)) | m2(F)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(244,plain,
% 0.20/0.53 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F)) <=> ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[243])).
% 0.20/0.53 tff(245,plain,
% 0.20/0.53 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F)) <=> ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(246,plain,
% 0.20/0.53 (^[H: $i, F: $i, G: $i] : rewrite(((m2(F) | (~s0(F))) | (~l1(G, H))) <=> ((~s0(F)) | (~l1(G, H)) | m2(F)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(247,plain,
% 0.20/0.53 (![H: $i, F: $i, G: $i] : ((m2(F) | (~s0(F))) | (~l1(G, H))) <=> ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[246])).
% 0.20/0.53 tff(248,axiom,(![H: $i, F: $i, G: $i] : ((m2(F) | (~s0(F))) | (~l1(G, H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_135')).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.20/0.53 tff(251,plain,(
% 0.20/0.53 ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.53 inference(skolemize,[status(sab)],[250])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 (s0(d) <=> s0(d)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(254,plain,
% 0.20/0.53 (s0(d)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[67, 253])).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | m2(d) | (~l1(b, e)))) <=> ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | (~s0(d)) | m2(d) | (~l1(b, e)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(256,plain,
% 0.20/0.53 (((~s0(d)) | (~l1(b, e)) | m2(d)) <=> ((~s0(d)) | m2(d) | (~l1(b, e)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(257,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | (~l1(b, e)) | m2(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | m2(d) | (~l1(b, e))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | (~l1(b, e)) | m2(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | (~s0(d)) | m2(d) | (~l1(b, e)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[257, 255])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | (~l1(b, e)) | m2(d))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(260,plain,
% 0.20/0.53 ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | (~s0(d)) | m2(d) | (~l1(b, e))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.53 tff(261,plain,
% 0.20/0.53 (m2(d)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[260, 254, 252, 242])).
% 0.20/0.53 tff(262,plain,
% 0.20/0.53 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(263,plain,
% 0.20/0.53 (((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d)) <=> ((~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(264,plain,
% 0.20/0.53 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[263])).
% 0.20/0.54 tff(265,plain,
% 0.20/0.54 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))),
% 0.20/0.54 inference(transitivity,[status(thm)],[264, 262])).
% 0.20/0.54 tff(266,plain,
% 0.20/0.54 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(267,plain,
% 0.20/0.54 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.20/0.54 tff(268,plain,
% 0.20/0.54 (r3(a, a, d)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[267, 261, 216, 206, 167])).
% 0.20/0.54 tff(269,plain,
% 0.20/0.54 (^[X: $i] : refl((~r3(a, X, d)) <=> (~r3(a, X, d)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(270,plain,
% 0.20/0.54 (![X: $i] : (~r3(a, X, d)) <=> ![X: $i] : (~r3(a, X, d))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[269])).
% 0.20/0.54 tff(271,plain,
% 0.20/0.54 (![X: $i] : (~r3(a, X, d)) <=> ![X: $i] : (~r3(a, X, d))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(272,axiom,(![X: $i] : (~r3(a, X, d))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.54 tff(273,plain,
% 0.20/0.54 (![X: $i] : (~r3(a, X, d))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.20/0.54 tff(274,plain,(
% 0.20/0.54 ![X: $i] : (~r3(a, X, d))),
% 0.20/0.54 inference(skolemize,[status(sab)],[273])).
% 0.20/0.54 tff(275,plain,
% 0.20/0.54 (![X: $i] : (~r3(a, X, d))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.20/0.54 tff(276,plain,
% 0.20/0.54 ((~![X: $i] : (~r3(a, X, d))) | (~r3(a, a, d))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(277,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[276, 275, 268])).
% 0.20/0.54 % SZS output end Proof
%------------------------------------------------------------------------------