TSTP Solution File: SYN204-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN204-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 23:54:11 EDT 2022
% Result : Unsatisfiable 1.32s 1.13s
% Output : Proof 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN204-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 02:07:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.32/1.13 % SZS status Unsatisfiable
% 1.32/1.13 % SZS output start Proof
% 1.32/1.13 tff(n1_type, type, (
% 1.32/1.13 n1: ( $i * $i * $i ) > $o)).
% 1.32/1.13 tff(a_type, type, (
% 1.32/1.13 a: $i)).
% 1.32/1.13 tff(b_type, type, (
% 1.32/1.13 b: $i)).
% 1.32/1.13 tff(p0_type, type, (
% 1.32/1.13 p0: ( $i * $i ) > $o)).
% 1.32/1.13 tff(l0_type, type, (
% 1.32/1.13 l0: $i > $o)).
% 1.32/1.13 tff(s0_type, type, (
% 1.32/1.13 s0: $i > $o)).
% 1.32/1.13 tff(l1_type, type, (
% 1.32/1.13 l1: ( $i * $i ) > $o)).
% 1.32/1.13 tff(n0_type, type, (
% 1.32/1.13 n0: ( $i * $i ) > $o)).
% 1.32/1.13 tff(q2_type, type, (
% 1.32/1.13 q2: ( $i * $i * $i ) > $o)).
% 1.32/1.13 tff(p1_type, type, (
% 1.32/1.13 p1: ( $i * $i * $i ) > $o)).
% 1.32/1.13 tff(k0_type, type, (
% 1.32/1.13 k0: $i > $o)).
% 1.32/1.13 tff(s1_type, type, (
% 1.32/1.13 s1: $i > $o)).
% 1.32/1.13 tff(s2_type, type, (
% 1.32/1.13 s2: $i > $o)).
% 1.32/1.13 tff(e_type, type, (
% 1.32/1.13 e: $i)).
% 1.32/1.13 tff(k1_type, type, (
% 1.32/1.13 k1: $i > $o)).
% 1.32/1.13 tff(m0_type, type, (
% 1.32/1.13 m0: ( $i * $i * $i ) > $o)).
% 1.32/1.13 tff(r0_type, type, (
% 1.32/1.13 r0: $i > $o)).
% 1.32/1.13 tff(s3_type, type, (
% 1.32/1.13 s3: ( $i * $i ) > $o)).
% 1.32/1.13 tff(c_type, type, (
% 1.32/1.13 c: $i)).
% 1.32/1.13 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 1.32/1.13 tff(2,plain,
% 1.32/1.13 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.32/1.13 inference(bind,[status(th)],[])).
% 1.32/1.13 tff(3,plain,
% 1.32/1.13 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.32/1.13 inference(quant_intro,[status(thm)],[2])).
% 1.32/1.13 tff(4,plain,
% 1.32/1.13 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.32/1.13 tff(6,plain,
% 1.32/1.13 (![X: $i] : p0(b, X)),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.32/1.13 tff(7,plain,(
% 1.32/1.13 ![X: $i] : p0(b, X)),
% 1.32/1.13 inference(skolemize,[status(sab)],[6])).
% 1.32/1.13 tff(8,plain,
% 1.32/1.13 (![X: $i] : p0(b, X)),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.32/1.13 tff(9,plain,
% 1.32/1.13 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.32/1.13 inference(quant_inst,[status(thm)],[])).
% 1.32/1.13 tff(10,plain,
% 1.32/1.13 ($false),
% 1.32/1.13 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.32/1.13 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.13 tff(12,plain,
% 1.32/1.13 (^[D: $i, E: $i] : refl(((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)))),
% 1.32/1.13 inference(bind,[status(th)],[])).
% 1.32/1.13 tff(13,plain,
% 1.32/1.13 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(quant_intro,[status(thm)],[12])).
% 1.32/1.13 tff(14,plain,
% 1.32/1.13 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(15,plain,
% 1.32/1.13 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(b)), (s0(b) <=> $true)), ((~s0(b)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(b)) <=> $false)), (((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | $false | (~p0(b, E)) | n1(D, E, D)))), rewrite(((~l0(D)) | $false | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))), (((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))))),
% 1.32/1.13 inference(bind,[status(th)],[])).
% 1.32/1.13 tff(16,plain,
% 1.32/1.13 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(quant_intro,[status(thm)],[15])).
% 1.32/1.13 tff(17,plain,
% 1.32/1.13 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(D, E, D) | (~s0(b))) <=> ((~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> (((~s0(b)) | n1(D, E, D)) | (~l0(D))))), rewrite((((~s0(b)) | n1(D, E, D)) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D)))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> (((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))))), rewrite((((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))))),
% 1.32/1.13 inference(bind,[status(th)],[])).
% 1.32/1.13 tff(18,plain,
% 1.32/1.13 (![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(quant_intro,[status(thm)],[17])).
% 1.32/1.13 tff(19,axiom,(![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_050')).
% 1.32/1.13 tff(20,plain,
% 1.32/1.13 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.32/1.13 tff(21,plain,
% 1.32/1.13 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.32/1.13 tff(22,plain,
% 1.32/1.13 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.32/1.13 tff(23,plain,(
% 1.32/1.13 ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(skolemize,[status(sab)],[22])).
% 1.32/1.13 tff(24,plain,
% 1.32/1.13 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.32/1.13 tff(25,plain,
% 1.32/1.13 (l0(a) <=> l0(a)),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(26,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 1.32/1.13 tff(27,plain,
% 1.32/1.13 (l0(a)),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.32/1.13 tff(28,plain,
% 1.32/1.13 (((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))) <=> ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(29,plain,
% 1.32/1.13 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 1.32/1.13 inference(quant_inst,[status(thm)],[])).
% 1.32/1.13 tff(30,plain,
% 1.32/1.13 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a)),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.32/1.13 tff(31,plain,
% 1.32/1.13 (n1(a, b, a)),
% 1.32/1.13 inference(unit_resolution,[status(thm)],[30, 27, 24, 11])).
% 1.32/1.13 tff(32,plain,
% 1.32/1.13 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.32/1.13 inference(bind,[status(th)],[])).
% 1.32/1.13 tff(33,plain,
% 1.32/1.13 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.32/1.13 inference(quant_intro,[status(thm)],[32])).
% 1.32/1.13 tff(34,plain,
% 1.32/1.13 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(35,plain,
% 1.32/1.13 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.32/1.13 inference(bind,[status(th)],[])).
% 1.32/1.13 tff(36,plain,
% 1.32/1.13 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.32/1.13 inference(quant_intro,[status(thm)],[35])).
% 1.32/1.13 tff(37,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 1.32/1.13 tff(38,plain,
% 1.32/1.13 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.32/1.13 tff(39,plain,
% 1.32/1.13 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.32/1.13 tff(40,plain,(
% 1.32/1.13 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.32/1.13 inference(skolemize,[status(sab)],[39])).
% 1.32/1.13 tff(41,plain,
% 1.32/1.13 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.32/1.13 tff(42,plain,
% 1.32/1.13 (n0(b, a) <=> n0(b, a)),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(43,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 1.32/1.13 tff(44,plain,
% 1.32/1.13 (n0(b, a)),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.32/1.13 tff(45,plain,
% 1.32/1.13 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a))),
% 1.32/1.13 inference(rewrite,[status(thm)],[])).
% 1.32/1.13 tff(46,plain,
% 1.32/1.13 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 1.32/1.13 inference(quant_inst,[status(thm)],[])).
% 1.32/1.13 tff(47,plain,
% 1.32/1.13 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 1.32/1.13 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.32/1.13 tff(48,plain,
% 1.32/1.13 (l1(a, a)),
% 1.32/1.13 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 1.32/1.13 tff(49,plain,
% 1.32/1.13 (^[E: $i, F: $i] : refl(((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(50,plain,
% 1.32/1.14 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[49])).
% 1.32/1.14 tff(51,plain,
% 1.32/1.14 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(52,plain,
% 1.32/1.14 (^[E: $i, F: $i] : trans(monotonicity(rewrite((q2(E, F, F) | (~k0(F))) <=> ((~k0(F)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> (((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))))), rewrite((((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(53,plain,
% 1.32/1.14 (![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[52])).
% 1.32/1.14 tff(54,axiom,(![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_177')).
% 1.32/1.14 tff(55,plain,
% 1.32/1.14 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.32/1.14 tff(56,plain,
% 1.32/1.14 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.32/1.14 tff(57,plain,(
% 1.32/1.14 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.32/1.14 inference(skolemize,[status(sab)],[56])).
% 1.32/1.14 tff(58,plain,
% 1.32/1.14 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.32/1.14 tff(59,plain,
% 1.32/1.14 (p1(a, a, a) <=> p1(a, a, a)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(60,plain,
% 1.32/1.14 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(61,plain,
% 1.32/1.14 ((~$true) <=> $false),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(62,plain,
% 1.32/1.14 (l0(a) <=> $true),
% 1.32/1.14 inference(iff_true,[status(thm)],[26])).
% 1.32/1.14 tff(63,plain,
% 1.32/1.14 ((~l0(a)) <=> (~$true)),
% 1.32/1.14 inference(monotonicity,[status(thm)],[62])).
% 1.32/1.14 tff(64,plain,
% 1.32/1.14 ((~l0(a)) <=> $false),
% 1.32/1.14 inference(transitivity,[status(thm)],[63, 61])).
% 1.32/1.14 tff(65,plain,
% 1.32/1.14 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 1.32/1.14 inference(monotonicity,[status(thm)],[64])).
% 1.32/1.14 tff(66,plain,
% 1.32/1.14 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 1.32/1.14 inference(transitivity,[status(thm)],[65, 60])).
% 1.32/1.14 tff(67,plain,
% 1.32/1.14 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(68,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 1.32/1.14 tff(69,plain,
% 1.32/1.14 ((~l0(a)) | p1(a, a, a)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.32/1.14 tff(70,plain,
% 1.32/1.14 (p1(a, a, a)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.32/1.14 tff(71,plain,
% 1.32/1.14 (p1(a, a, a)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[70, 59])).
% 1.32/1.14 tff(72,plain,
% 1.32/1.14 (k0(b) <=> k0(b)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(73,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 1.32/1.14 tff(74,plain,
% 1.32/1.14 (k0(b)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.32/1.14 tff(75,plain,
% 1.32/1.14 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(76,plain,
% 1.32/1.14 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(77,plain,
% 1.32/1.14 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.32/1.14 tff(78,plain,
% 1.32/1.14 (q2(a, b, b)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[77, 74, 71, 58])).
% 1.32/1.14 tff(79,plain,
% 1.32/1.14 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(80,plain,
% 1.32/1.14 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[79])).
% 1.32/1.14 tff(81,plain,
% 1.32/1.14 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(82,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.32/1.14 tff(83,plain,
% 1.32/1.14 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.32/1.14 tff(84,plain,(
% 1.32/1.14 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.32/1.14 inference(skolemize,[status(sab)],[83])).
% 1.32/1.14 tff(85,plain,
% 1.32/1.14 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[84, 80])).
% 1.32/1.14 tff(86,plain,
% 1.32/1.14 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(87,plain,
% 1.32/1.14 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(88,plain,
% 1.32/1.14 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.32/1.14 tff(89,plain,
% 1.32/1.14 (s1(b)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[88, 85, 11])).
% 1.32/1.14 tff(90,assumption,(~q2(a, e, e)), introduced(assumption)).
% 1.32/1.14 tff(91,plain,
% 1.32/1.14 (k0(e) <=> k0(e)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(92,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.32/1.14 tff(93,plain,
% 1.32/1.14 (k0(e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.32/1.14 tff(94,plain,
% 1.32/1.14 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(95,plain,
% 1.32/1.14 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(96,plain,
% 1.32/1.14 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.32/1.14 tff(97,plain,
% 1.32/1.14 ($false),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[96, 93, 71, 58, 90])).
% 1.32/1.14 tff(98,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.14 tff(99,plain,
% 1.32/1.14 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(100,plain,
% 1.32/1.14 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[99])).
% 1.32/1.14 tff(101,plain,
% 1.32/1.14 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(102,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 1.32/1.14 tff(103,plain,
% 1.32/1.14 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.32/1.14 tff(104,plain,(
% 1.32/1.14 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.32/1.14 inference(skolemize,[status(sab)],[103])).
% 1.32/1.14 tff(105,plain,
% 1.32/1.14 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[104, 100])).
% 1.32/1.14 tff(106,plain,
% 1.32/1.14 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(107,plain,
% 1.32/1.14 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(108,plain,
% 1.32/1.14 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.32/1.14 tff(109,plain,
% 1.32/1.14 (k1(a)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[108, 44, 105])).
% 1.32/1.14 tff(110,plain,
% 1.32/1.14 (^[D: $i, C: $i] : refl(((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(111,plain,
% 1.32/1.14 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[110])).
% 1.32/1.14 tff(112,plain,
% 1.32/1.14 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(113,plain,
% 1.32/1.14 (^[D: $i, C: $i] : trans(monotonicity(rewrite((n1(C, e, e) | (~m0(C, D, e))) <=> ((~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> (((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))))), rewrite((((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(114,plain,
% 1.32/1.14 (![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[113])).
% 1.32/1.14 tff(115,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 1.32/1.14 tff(116,plain,
% 1.32/1.14 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.32/1.14 tff(117,plain,
% 1.32/1.14 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[116, 112])).
% 1.32/1.14 tff(118,plain,(
% 1.32/1.14 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.32/1.14 inference(skolemize,[status(sab)],[117])).
% 1.32/1.14 tff(119,plain,
% 1.32/1.14 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[118, 111])).
% 1.32/1.14 tff(120,plain,
% 1.32/1.14 (m0(a, e, e) <=> m0(a, e, e)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(121,axiom,(m0(a, e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 1.32/1.14 tff(122,plain,
% 1.32/1.14 (m0(a, e, e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.32/1.14 tff(123,plain,
% 1.32/1.14 (((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))) <=> ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(124,plain,
% 1.32/1.14 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(125,plain,
% 1.32/1.14 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.32/1.14 tff(126,plain,
% 1.32/1.14 ((~k1(a)) | n1(a, e, e)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[125, 122, 119])).
% 1.32/1.14 tff(127,plain,
% 1.32/1.14 (n1(a, e, e)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[126, 109])).
% 1.32/1.14 tff(128,plain,
% 1.32/1.14 (^[H: $i, F: $i, G: $i] : refl(((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(129,plain,
% 1.32/1.14 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[128])).
% 1.32/1.14 tff(130,plain,
% 1.32/1.14 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(131,plain,
% 1.32/1.14 (^[H: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(F, G, F) | (~p1(F, F, H))) <=> ((~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> (((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))))), rewrite((((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> (((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))))), rewrite((((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(132,plain,
% 1.32/1.14 (![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[131])).
% 1.32/1.14 tff(133,axiom,(![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_182')).
% 1.32/1.14 tff(134,plain,
% 1.32/1.14 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.32/1.14 tff(135,plain,
% 1.32/1.14 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[134, 130])).
% 1.32/1.14 tff(136,plain,(
% 1.32/1.14 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.32/1.14 inference(skolemize,[status(sab)],[135])).
% 1.32/1.14 tff(137,plain,
% 1.32/1.14 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[136, 129])).
% 1.32/1.14 tff(138,plain,
% 1.32/1.14 (p1(e, e, e) <=> p1(e, e, e)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(139,plain,
% 1.32/1.14 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(140,plain,
% 1.32/1.14 (k0(e) <=> $true),
% 1.32/1.14 inference(iff_true,[status(thm)],[92])).
% 1.32/1.14 tff(141,plain,
% 1.32/1.14 ((~k0(e)) <=> (~$true)),
% 1.32/1.14 inference(monotonicity,[status(thm)],[140])).
% 1.32/1.14 tff(142,plain,
% 1.32/1.14 ((~k0(e)) <=> $false),
% 1.32/1.14 inference(transitivity,[status(thm)],[141, 61])).
% 1.32/1.14 tff(143,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 1.32/1.14 tff(144,plain,
% 1.32/1.14 (r0(e) <=> $true),
% 1.32/1.14 inference(iff_true,[status(thm)],[143])).
% 1.32/1.14 tff(145,plain,
% 1.32/1.14 ((~r0(e)) <=> (~$true)),
% 1.32/1.14 inference(monotonicity,[status(thm)],[144])).
% 1.32/1.14 tff(146,plain,
% 1.32/1.14 ((~r0(e)) <=> $false),
% 1.32/1.14 inference(transitivity,[status(thm)],[145, 61])).
% 1.32/1.14 tff(147,plain,
% 1.32/1.14 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 1.32/1.14 inference(monotonicity,[status(thm)],[146, 142])).
% 1.32/1.14 tff(148,plain,
% 1.32/1.14 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 1.32/1.14 inference(transitivity,[status(thm)],[147, 139])).
% 1.32/1.14 tff(149,plain,
% 1.32/1.14 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(150,plain,
% 1.32/1.14 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(151,plain,
% 1.32/1.14 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(152,plain,
% 1.32/1.14 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 1.32/1.14 inference(monotonicity,[status(thm)],[151])).
% 1.32/1.14 tff(153,plain,
% 1.32/1.14 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.32/1.14 inference(transitivity,[status(thm)],[152, 150])).
% 1.32/1.14 tff(154,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 1.32/1.14 tff(155,plain,
% 1.32/1.14 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.32/1.14 tff(156,plain,
% 1.32/1.14 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[155, 149])).
% 1.32/1.14 tff(157,plain,
% 1.32/1.14 (p1(e, e, e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[156, 148])).
% 1.32/1.14 tff(158,plain,
% 1.32/1.14 (p1(e, e, e)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[157, 138])).
% 1.32/1.14 tff(159,plain,
% 1.32/1.14 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(160,plain,
% 1.32/1.14 (((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e)) <=> (q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(161,plain,
% 1.32/1.14 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e))))),
% 1.32/1.14 inference(monotonicity,[status(thm)],[160])).
% 1.32/1.14 tff(162,plain,
% 1.32/1.14 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))),
% 1.32/1.14 inference(transitivity,[status(thm)],[161, 159])).
% 1.32/1.14 tff(163,plain,
% 1.32/1.14 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(164,plain,
% 1.32/1.14 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.32/1.14 tff(165,plain,
% 1.32/1.14 (q2(e, a, e) | (~q2(a, e, e))),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[164, 158, 137, 127])).
% 1.32/1.14 tff(166,plain,
% 1.32/1.14 (q2(e, a, e)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[165, 98])).
% 1.32/1.14 tff(167,plain,
% 1.32/1.14 ((~s3(a, c)) <=> (~s3(a, c))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(168,axiom,(~s3(a, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 1.32/1.14 tff(169,plain,
% 1.32/1.14 (~s3(a, c)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.32/1.14 tff(170,plain,
% 1.32/1.14 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(171,plain,
% 1.32/1.14 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[170])).
% 1.32/1.14 tff(172,plain,
% 1.32/1.14 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(173,plain,
% 1.32/1.14 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(174,plain,
% 1.32/1.14 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[173])).
% 1.32/1.14 tff(175,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 1.32/1.14 tff(176,plain,
% 1.32/1.14 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.32/1.14 tff(177,plain,
% 1.32/1.14 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.32/1.14 tff(178,plain,(
% 1.32/1.14 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.32/1.14 inference(skolemize,[status(sab)],[177])).
% 1.32/1.14 tff(179,plain,
% 1.32/1.14 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[178, 171])).
% 1.32/1.14 tff(180,plain,
% 1.32/1.14 (m0(e, b, c) <=> m0(e, b, c)),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(181,axiom,(m0(e, b, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 1.32/1.14 tff(182,plain,
% 1.32/1.14 (m0(e, b, c)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.32/1.14 tff(183,plain,
% 1.32/1.14 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, b, c)) | (~q2(e, a, e)) | s3(a, c))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, b, c)) | (~q2(e, a, e)) | s3(a, c))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(184,plain,
% 1.32/1.14 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, b, c)) | (~q2(e, a, e)) | s3(a, c))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(185,plain,
% 1.32/1.14 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, b, c)) | (~q2(e, a, e)) | s3(a, c)),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.32/1.14 tff(186,plain,
% 1.32/1.14 ((~s2(a)) | (~q2(e, a, e))),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[185, 182, 179, 169])).
% 1.32/1.14 tff(187,plain,
% 1.32/1.14 (~s2(a)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[186, 166])).
% 1.32/1.14 tff(188,plain,
% 1.32/1.14 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(189,plain,
% 1.32/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[188])).
% 1.32/1.14 tff(190,plain,
% 1.32/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(191,plain,
% 1.32/1.14 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.32/1.14 inference(bind,[status(th)],[])).
% 1.32/1.14 tff(192,plain,
% 1.32/1.14 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.32/1.14 inference(quant_intro,[status(thm)],[191])).
% 1.32/1.14 tff(193,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 1.32/1.14 tff(194,plain,
% 1.32/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.32/1.14 tff(195,plain,
% 1.32/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.32/1.14 tff(196,plain,(
% 1.32/1.14 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.32/1.14 inference(skolemize,[status(sab)],[195])).
% 1.32/1.14 tff(197,plain,
% 1.32/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.32/1.14 tff(198,plain,
% 1.32/1.14 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 1.32/1.14 inference(rewrite,[status(thm)],[])).
% 1.32/1.14 tff(199,plain,
% 1.32/1.14 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 1.32/1.14 inference(quant_inst,[status(thm)],[])).
% 1.32/1.14 tff(200,plain,
% 1.32/1.14 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 1.32/1.14 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.32/1.14 tff(201,plain,
% 1.32/1.14 (~q2(b, a, b)),
% 1.32/1.14 inference(unit_resolution,[status(thm)],[200, 197, 187, 89])).
% 1.32/1.15 tff(202,plain,
% 1.32/1.15 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.32/1.15 inference(bind,[status(th)],[])).
% 1.32/1.15 tff(203,plain,
% 1.32/1.15 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.32/1.15 inference(quant_intro,[status(thm)],[202])).
% 1.32/1.15 tff(204,plain,
% 1.32/1.15 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(205,plain,
% 1.32/1.15 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.32/1.15 inference(bind,[status(th)],[])).
% 1.32/1.15 tff(206,plain,
% 1.32/1.15 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.32/1.15 inference(quant_intro,[status(thm)],[205])).
% 1.32/1.15 tff(207,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 1.32/1.15 tff(208,plain,
% 1.32/1.15 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.32/1.15 tff(209,plain,
% 1.32/1.15 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.32/1.15 tff(210,plain,(
% 1.32/1.15 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.32/1.15 inference(skolemize,[status(sab)],[209])).
% 1.32/1.15 tff(211,plain,
% 1.32/1.15 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.32/1.15 tff(212,plain,
% 1.32/1.15 (p0(c, b) <=> p0(c, b)),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(213,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.32/1.15 tff(214,plain,
% 1.32/1.15 (p0(c, b)),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.32/1.15 tff(215,plain,
% 1.32/1.15 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b))),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(216,plain,
% 1.32/1.15 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 1.32/1.15 inference(quant_inst,[status(thm)],[])).
% 1.32/1.15 tff(217,plain,
% 1.32/1.15 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.32/1.15 tff(218,plain,
% 1.32/1.15 (p1(b, b, b)),
% 1.32/1.15 inference(unit_resolution,[status(thm)],[217, 214, 211])).
% 1.32/1.15 tff(219,plain,
% 1.32/1.15 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(220,plain,
% 1.32/1.15 (((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b)) <=> ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(221,plain,
% 1.32/1.15 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))))),
% 1.32/1.15 inference(monotonicity,[status(thm)],[220])).
% 1.32/1.15 tff(222,plain,
% 1.32/1.15 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 1.32/1.15 inference(transitivity,[status(thm)],[221, 219])).
% 1.32/1.15 tff(223,plain,
% 1.32/1.15 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))),
% 1.32/1.15 inference(quant_inst,[status(thm)],[])).
% 1.32/1.15 tff(224,plain,
% 1.32/1.15 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.32/1.15 tff(225,plain,
% 1.32/1.15 (~n1(a, b, b)),
% 1.32/1.15 inference(unit_resolution,[status(thm)],[224, 137, 218, 201, 78])).
% 1.32/1.15 tff(226,plain,
% 1.32/1.15 (^[E: $i, F: $i, G: $i] : refl(((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)))),
% 1.32/1.15 inference(bind,[status(th)],[])).
% 1.32/1.15 tff(227,plain,
% 1.32/1.15 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.32/1.15 inference(quant_intro,[status(thm)],[226])).
% 1.32/1.15 tff(228,plain,
% 1.32/1.15 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(229,plain,
% 1.32/1.15 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(E, F, F) | (~l0(G))) <=> ((~l0(G)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> (((~l0(G)) | n1(E, F, F)) | (~l1(G, E))))), rewrite((((~l0(G)) | n1(E, F, F)) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F)))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> (((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))))), rewrite((((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))))),
% 1.32/1.15 inference(bind,[status(th)],[])).
% 1.32/1.15 tff(230,plain,
% 1.32/1.15 (![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.32/1.15 inference(quant_intro,[status(thm)],[229])).
% 1.32/1.15 tff(231,axiom,(![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_054')).
% 1.32/1.15 tff(232,plain,
% 1.32/1.15 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.32/1.15 tff(233,plain,
% 1.32/1.15 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[232, 228])).
% 1.32/1.15 tff(234,plain,(
% 1.32/1.15 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.32/1.15 inference(skolemize,[status(sab)],[233])).
% 1.32/1.15 tff(235,plain,
% 1.32/1.15 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[234, 227])).
% 1.32/1.15 tff(236,plain,
% 1.32/1.15 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(237,plain,
% 1.32/1.15 (((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b)) <=> ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 1.32/1.15 inference(rewrite,[status(thm)],[])).
% 1.32/1.15 tff(238,plain,
% 1.32/1.15 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))))),
% 1.32/1.15 inference(monotonicity,[status(thm)],[237])).
% 1.32/1.15 tff(239,plain,
% 1.32/1.15 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 1.32/1.15 inference(transitivity,[status(thm)],[238, 236])).
% 1.32/1.15 tff(240,plain,
% 1.32/1.15 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))),
% 1.32/1.15 inference(quant_inst,[status(thm)],[])).
% 1.32/1.15 tff(241,plain,
% 1.32/1.15 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))),
% 1.32/1.15 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.32/1.15 tff(242,plain,
% 1.32/1.15 ($false),
% 1.32/1.15 inference(unit_resolution,[status(thm)],[241, 27, 235, 225, 48, 31])).
% 1.32/1.15 % SZS output end Proof
%------------------------------------------------------------------------------