TSTP Solution File: SYN207-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN207-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:54:12 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN207-1 : 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 : n023.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 02:30:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 tff(s2_type, type, (
% 0.21/0.51 s2: $i > $o)).
% 0.21/0.51 tff(c_type, type, (
% 0.21/0.51 c: $i)).
% 0.21/0.51 tff(q2_type, type, (
% 0.21/0.51 q2: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(b_type, type, (
% 0.21/0.51 b: $i)).
% 0.21/0.51 tff(l2_type, type, (
% 0.21/0.51 l2: ( $i * $i ) > $o)).
% 0.21/0.51 tff(p0_type, type, (
% 0.21/0.51 p0: ( $i * $i ) > $o)).
% 0.21/0.51 tff(m1_type, type, (
% 0.21/0.51 m1: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(e_type, type, (
% 0.21/0.51 e: $i)).
% 0.21/0.51 tff(m0_type, type, (
% 0.21/0.51 m0: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(l0_type, type, (
% 0.21/0.51 l0: $i > $o)).
% 0.21/0.51 tff(a_type, type, (
% 0.21/0.51 a: $i)).
% 0.21/0.51 tff(k1_type, type, (
% 0.21/0.51 k1: $i > $o)).
% 0.21/0.51 tff(n0_type, type, (
% 0.21/0.51 n0: ( $i * $i ) > $o)).
% 0.21/0.51 tff(d_type, type, (
% 0.21/0.51 d: $i)).
% 0.21/0.51 tff(s1_type, type, (
% 0.21/0.51 s1: $i > $o)).
% 0.21/0.51 tff(s3_type, type, (
% 0.21/0.51 s3: ( $i * $i ) > $o)).
% 0.21/0.51 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.21/0.51 tff(2,plain,
% 0.21/0.51 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(3,plain,
% 0.21/0.51 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.21/0.51 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.51 tff(4,plain,
% 0.21/0.51 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.21/0.51 tff(6,plain,
% 0.21/0.51 (![X: $i] : p0(b, X)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.51 tff(7,plain,(
% 0.21/0.51 ![X: $i] : p0(b, X)),
% 0.21/0.51 inference(skolemize,[status(sab)],[6])).
% 0.21/0.51 tff(8,plain,
% 0.21/0.51 (![X: $i] : p0(b, X)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.51 tff(9,plain,
% 0.21/0.51 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(10,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.51 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(12,plain,
% 0.21/0.51 (^[B: $i, D: $i, C: $i] : refl(((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(13,plain,
% 0.21/0.51 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.51 tff(14,plain,
% 0.21/0.51 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(15,plain,
% 0.21/0.51 (^[B: $i, D: $i, C: $i] : trans(monotonicity(rewrite((m1(B, C, C) | (~l0(D))) <=> ((~l0(D)) | m1(B, C, C))), (((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> (((~l0(D)) | m1(B, C, C)) | (~m0(C, C, B))))), rewrite((((~l0(D)) | m1(B, C, C)) | (~m0(C, C, B))) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))), (((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(16,plain,
% 0.21/0.51 (![B: $i, D: $i, C: $i] : ((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.51 tff(17,axiom,(![B: $i, D: $i, C: $i] : ((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_015')).
% 0.21/0.51 tff(18,plain,
% 0.21/0.51 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.51 tff(19,plain,
% 0.21/0.51 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.51 tff(20,plain,(
% 0.21/0.51 ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.21/0.51 inference(skolemize,[status(sab)],[19])).
% 0.21/0.51 tff(21,plain,
% 0.21/0.51 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.51 tff(22,plain,
% 0.21/0.51 (m0(b, b, e) <=> m0(b, b, e)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(23,axiom,(m0(b, b, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.21/0.51 tff(24,plain,
% 0.21/0.51 (m0(b, b, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.51 tff(25,plain,
% 0.21/0.51 (l0(a) <=> l0(a)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(26,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.21/0.51 tff(27,plain,
% 0.21/0.51 (l0(a)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.51 tff(28,plain,
% 0.21/0.51 (((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | ((~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))) <=> ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | (~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(29,plain,
% 0.21/0.51 ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | ((~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(30,plain,
% 0.21/0.51 ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | (~l0(a)) | (~m0(b, b, e)) | m1(e, b, b)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.51 tff(31,plain,
% 0.21/0.51 (m1(e, b, b)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[30, 27, 24, 21])).
% 0.21/0.51 tff(32,plain,
% 0.21/0.51 (^[I: $i, H: $i, G: $i] : refl(((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(33,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.51 tff(34,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(35,plain,
% 0.21/0.51 (^[I: $i, H: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(G, G) | (~m0(H, G, I))) <=> ((~m0(H, G, I)) | l2(G, G))), (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) <=> (((~m0(H, G, I)) | l2(G, G)) | (~m1(I, H, H))))), rewrite((((~m0(H, G, I)) | l2(G, G)) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H)))), (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))))), ((((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> (((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))) | (~p0(H, G))))), rewrite((((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))) | (~p0(H, G))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))), ((((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(36,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.51 tff(37,axiom,(![I: $i, H: $i, G: $i] : (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_134')).
% 0.21/0.51 tff(38,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.51 tff(39,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.51 tff(40,plain,(
% 0.21/0.51 ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[39])).
% 0.21/0.51 tff(41,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.51 tff(42,plain,
% 0.21/0.51 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(43,plain,
% 0.21/0.51 (((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b))) <=> (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(44,plain,
% 0.21/0.51 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.52 tff(45,plain,
% 0.21/0.52 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.52 tff(46,plain,
% 0.21/0.52 ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(47,plain,
% 0.21/0.52 ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.52 tff(48,plain,
% 0.21/0.52 (l2(b, b) | (~p0(b, b)) | (~m1(e, b, b))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[47, 24, 41])).
% 0.21/0.52 tff(49,plain,
% 0.21/0.52 (l2(b, b) | (~p0(b, b))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[48, 31])).
% 0.21/0.52 tff(50,plain,
% 0.21/0.52 (l2(b, b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[49, 11])).
% 0.21/0.52 tff(51,plain,
% 0.21/0.52 (^[D: $i, E: $i] : refl(((~k1(E)) | (~l2(E, D)) | q2(D, c, E)) <=> ((~k1(E)) | (~l2(E, D)) | q2(D, c, E)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(52,plain,
% 0.21/0.52 (![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E)) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.52 tff(53,plain,
% 0.21/0.52 (![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E)) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(54,plain,
% 0.21/0.52 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(l0(c)), (l0(c) <=> $true)), ((~l0(c)) <=> (~$true))), rewrite((~$true) <=> $false), ((~l0(c)) <=> $false)), (((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ((~k1(E)) | $false | (~l2(E, D)) | q2(D, c, E)))), rewrite(((~k1(E)) | $false | (~l2(E, D)) | q2(D, c, E)) <=> ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))), (((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(55,plain,
% 0.21/0.52 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.52 tff(56,plain,
% 0.21/0.52 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(D, c, E) | (~k1(E))) <=> ((~k1(E)) | q2(D, c, E))), (((q2(D, c, E) | (~k1(E))) | (~l0(c))) <=> (((~k1(E)) | q2(D, c, E)) | (~l0(c))))), rewrite((((~k1(E)) | q2(D, c, E)) | (~l0(c))) <=> ((~k1(E)) | (~l0(c)) | q2(D, c, E))), (((q2(D, c, E) | (~k1(E))) | (~l0(c))) <=> ((~k1(E)) | (~l0(c)) | q2(D, c, E)))), ((((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> (((~k1(E)) | (~l0(c)) | q2(D, c, E)) | (~l2(E, D))))), rewrite((((~k1(E)) | (~l0(c)) | q2(D, c, E)) | (~l2(E, D))) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))), ((((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(57,plain,
% 0.21/0.52 (![D: $i, E: $i] : (((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.52 tff(58,axiom,(![D: $i, E: $i] : (((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_183')).
% 0.21/0.52 tff(59,plain,
% 0.21/0.52 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.52 tff(60,plain,
% 0.21/0.52 (![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.52 tff(61,plain,
% 0.21/0.52 (![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.21/0.52 tff(62,plain,(
% 0.21/0.52 ![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(skolemize,[status(sab)],[61])).
% 0.21/0.52 tff(63,plain,
% 0.21/0.52 (![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.21/0.52 tff(64,plain,
% 0.21/0.52 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(65,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.52 tff(66,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(67,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.21/0.52 tff(68,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.52 tff(69,plain,(
% 0.21/0.52 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[68])).
% 0.21/0.52 tff(70,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.52 tff(71,plain,
% 0.21/0.52 (n0(d, b) <=> n0(d, b)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(72,axiom,(n0(d, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.21/0.52 tff(73,plain,
% 0.21/0.52 (n0(d, b)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.52 tff(74,plain,
% 0.21/0.52 (((~![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)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(75,plain,
% 0.21/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(76,plain,
% 0.21/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.52 tff(77,plain,
% 0.21/0.52 (k1(b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[76, 73, 70])).
% 0.21/0.52 tff(78,plain,
% 0.21/0.52 (((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(b)) | (~l2(b, b)) | q2(b, c, b))) <=> ((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(b)) | (~l2(b, b)) | q2(b, c, b))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(79,plain,
% 0.21/0.52 ((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(b)) | (~l2(b, b)) | q2(b, c, b))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(80,plain,
% 0.21/0.52 ((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(b)) | (~l2(b, b)) | q2(b, c, b)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.52 tff(81,plain,
% 0.21/0.52 (q2(b, c, b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[80, 77, 63, 50])).
% 0.21/0.52 tff(82,plain,
% 0.21/0.52 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(83,plain,
% 0.21/0.52 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.52 tff(84,plain,
% 0.21/0.52 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(85,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.21/0.52 tff(86,plain,
% 0.21/0.52 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.52 tff(87,plain,(
% 0.21/0.52 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[86])).
% 0.21/0.52 tff(88,plain,
% 0.21/0.52 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.52 tff(89,plain,
% 0.21/0.52 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(90,plain,
% 0.21/0.52 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(91,plain,
% 0.21/0.52 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.52 tff(92,plain,
% 0.21/0.52 (s1(b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[91, 88, 11])).
% 0.21/0.52 tff(93,plain,
% 0.21/0.52 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(94,plain,
% 0.21/0.52 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.52 tff(95,plain,
% 0.21/0.52 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(96,plain,
% 0.21/0.52 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(97,plain,
% 0.21/0.52 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.52 tff(98,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.21/0.52 tff(99,plain,
% 0.21/0.52 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.52 tff(100,plain,
% 0.21/0.52 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.52 tff(101,plain,(
% 0.21/0.52 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[100])).
% 0.21/0.52 tff(102,plain,
% 0.21/0.52 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.21/0.52 tff(103,plain,
% 0.21/0.52 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(c) | (~q2(b, c, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(c) | (~q2(b, c, b)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(104,plain,
% 0.21/0.52 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(c) | (~q2(b, c, b)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(105,plain,
% 0.21/0.52 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(c) | (~q2(b, c, b))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.52 tff(106,plain,
% 0.21/0.52 (s2(c)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[105, 102, 92, 81])).
% 0.21/0.52 tff(107,plain,
% 0.21/0.52 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(108,plain,
% 0.21/0.52 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.52 tff(109,plain,
% 0.21/0.52 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(110,plain,
% 0.21/0.52 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(111,plain,
% 0.21/0.52 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.52 tff(112,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 0.21/0.52 tff(113,plain,
% 0.21/0.52 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.52 tff(114,plain,
% 0.21/0.52 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.52 tff(115,plain,(
% 0.21/0.52 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.21/0.52 inference(skolemize,[status(sab)],[114])).
% 0.21/0.52 tff(116,plain,
% 0.21/0.52 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.21/0.52 tff(117,plain,
% 0.21/0.52 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(118,plain,
% 0.21/0.52 (((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e)) <=> ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(119,plain,
% 0.21/0.52 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.52 tff(120,plain,
% 0.21/0.52 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[119, 117])).
% 0.21/0.52 tff(121,plain,
% 0.21/0.52 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(122,plain,
% 0.21/0.52 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.52 tff(123,plain,
% 0.21/0.52 ((~s1(b)) | l2(e, e)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[122, 24, 116, 11])).
% 0.21/0.52 tff(124,plain,
% 0.21/0.52 (l2(e, e)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[123, 92])).
% 0.21/0.52 tff(125,plain,
% 0.21/0.52 (n0(d, e) <=> n0(d, e)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(126,axiom,(n0(d, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_3')).
% 0.21/0.52 tff(127,plain,
% 0.21/0.52 (n0(d, e)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.52 tff(128,plain,
% 0.21/0.52 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(129,plain,
% 0.21/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(130,plain,
% 0.21/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.52 tff(131,plain,
% 0.21/0.52 (k1(e)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[130, 127, 70])).
% 0.21/0.52 tff(132,plain,
% 0.21/0.52 (((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(e)) | (~l2(e, e)) | q2(e, c, e))) <=> ((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(e)) | (~l2(e, e)) | q2(e, c, e))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(133,plain,
% 0.21/0.52 ((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(e)) | (~l2(e, e)) | q2(e, c, e))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(134,plain,
% 0.21/0.52 ((~![D: $i, E: $i] : ((~k1(E)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(e)) | (~l2(e, e)) | q2(e, c, e)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.52 tff(135,plain,
% 0.21/0.52 (q2(e, c, e)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[134, 63, 131, 124])).
% 0.21/0.52 tff(136,plain,
% 0.21/0.52 ((~s3(c, c)) <=> (~s3(c, c))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(137,axiom,(~s3(c, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.52 tff(138,plain,
% 0.21/0.52 (~s3(c, c)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.52 tff(139,plain,
% 0.21/0.52 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.52 tff(144,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.21/0.52 tff(147,plain,(
% 0.21/0.52 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.21/0.52 inference(skolemize,[status(sab)],[146])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 (m0(e, b, c) <=> m0(e, b, c)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(150,axiom,(m0(e, b, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 (m0(e, b, c)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(c)) | (~m0(e, b, c)) | (~q2(e, c, e)) | s3(c, c))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(c)) | (~m0(e, b, c)) | (~q2(e, c, e)) | s3(c, c))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(153,plain,
% 0.21/0.52 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(c)) | (~m0(e, b, c)) | (~q2(e, c, e)) | s3(c, c))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(154,plain,
% 0.21/0.52 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(c)) | (~m0(e, b, c)) | (~q2(e, c, e)) | s3(c, c)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.54 tff(155,plain,
% 0.21/0.54 ((~s2(c)) | (~q2(e, c, e))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[154, 151, 148, 138])).
% 0.21/0.54 tff(156,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[155, 135, 106])).
% 0.21/0.54 % SZS output end Proof
%------------------------------------------------------------------------------