TSTP Solution File: SYN143-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN143-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 23:53:55 EDT 2022
% Result : Unsatisfiable 1.75s 1.37s
% Output : Proof 1.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN143-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:10:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.75/1.37 % SZS status Unsatisfiable
% 1.75/1.37 % SZS output start Proof
% 1.75/1.37 tff(n1_type, type, (
% 1.75/1.37 n1: ( $i * $i * $i ) > $o)).
% 1.75/1.37 tff(a_type, type, (
% 1.75/1.37 a: $i)).
% 1.75/1.37 tff(b_type, type, (
% 1.75/1.37 b: $i)).
% 1.75/1.37 tff(p0_type, type, (
% 1.75/1.37 p0: ( $i * $i ) > $o)).
% 1.75/1.37 tff(l0_type, type, (
% 1.75/1.37 l0: $i > $o)).
% 1.75/1.37 tff(s0_type, type, (
% 1.75/1.37 s0: $i > $o)).
% 1.75/1.37 tff(l1_type, type, (
% 1.75/1.37 l1: ( $i * $i ) > $o)).
% 1.75/1.37 tff(n0_type, type, (
% 1.75/1.37 n0: ( $i * $i ) > $o)).
% 1.75/1.37 tff(q2_type, type, (
% 1.75/1.37 q2: ( $i * $i * $i ) > $o)).
% 1.75/1.37 tff(p1_type, type, (
% 1.75/1.37 p1: ( $i * $i * $i ) > $o)).
% 1.75/1.37 tff(k0_type, type, (
% 1.75/1.37 k0: $i > $o)).
% 1.75/1.37 tff(s1_type, type, (
% 1.75/1.37 s1: $i > $o)).
% 1.75/1.37 tff(s2_type, type, (
% 1.75/1.37 s2: $i > $o)).
% 1.75/1.37 tff(s3_type, type, (
% 1.75/1.37 s3: ( $i * $i ) > $o)).
% 1.75/1.37 tff(e_type, type, (
% 1.75/1.37 e: $i)).
% 1.75/1.37 tff(m4_type, type, (
% 1.75/1.37 m4: ( $i * $i ) > $o)).
% 1.75/1.37 tff(s4_type, type, (
% 1.75/1.37 s4: $i > $o)).
% 1.75/1.37 tff(d_type, type, (
% 1.75/1.37 d: $i)).
% 1.75/1.37 tff(p3_type, type, (
% 1.75/1.37 p3: ( $i * $i * $i ) > $o)).
% 1.75/1.37 tff(n2_type, type, (
% 1.75/1.37 n2: $i > $o)).
% 1.75/1.37 tff(k1_type, type, (
% 1.75/1.37 k1: $i > $o)).
% 1.75/1.37 tff(c_type, type, (
% 1.75/1.37 c: $i)).
% 1.75/1.37 tff(m5_type, type, (
% 1.75/1.37 m5: ( $i * $i ) > $o)).
% 1.75/1.38 tff(l2_type, type, (
% 1.75/1.38 l2: ( $i * $i ) > $o)).
% 1.75/1.38 tff(m0_type, type, (
% 1.75/1.38 m0: ( $i * $i * $i ) > $o)).
% 1.75/1.38 tff(r0_type, type, (
% 1.75/1.38 r0: $i > $o)).
% 1.75/1.38 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 1.75/1.38 tff(2,plain,
% 1.75/1.38 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(3,plain,
% 1.75/1.38 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.75/1.38 inference(quant_intro,[status(thm)],[2])).
% 1.75/1.38 tff(4,plain,
% 1.75/1.38 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.75/1.38 tff(6,plain,
% 1.75/1.38 (![X: $i] : p0(b, X)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.75/1.38 tff(7,plain,(
% 1.75/1.38 ![X: $i] : p0(b, X)),
% 1.75/1.38 inference(skolemize,[status(sab)],[6])).
% 1.75/1.38 tff(8,plain,
% 1.75/1.38 (![X: $i] : p0(b, X)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.75/1.38 tff(9,plain,
% 1.75/1.38 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(10,plain,
% 1.75/1.38 ($false),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.75/1.38 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.38 tff(12,plain,
% 1.75/1.38 (^[D: $i, E: $i] : refl(((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(13,plain,
% 1.75/1.38 (![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))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[12])).
% 1.75/1.38 tff(14,plain,
% 1.75/1.38 (![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))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(15,plain,
% 1.75/1.38 (^[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))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(16,plain,
% 1.75/1.38 (![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))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[15])).
% 1.75/1.38 tff(17,plain,
% 1.75/1.38 (^[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))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(18,plain,
% 1.75/1.38 (![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))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[17])).
% 1.75/1.38 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')).
% 1.75/1.38 tff(20,plain,
% 1.75/1.38 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.75/1.38 tff(21,plain,
% 1.75/1.38 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.75/1.38 tff(22,plain,
% 1.75/1.38 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.75/1.38 tff(23,plain,(
% 1.75/1.38 ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.75/1.38 inference(skolemize,[status(sab)],[22])).
% 1.75/1.38 tff(24,plain,
% 1.75/1.38 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.75/1.38 tff(25,plain,
% 1.75/1.38 (l0(a) <=> l0(a)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(26,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 1.75/1.38 tff(27,plain,
% 1.75/1.38 (l0(a)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.75/1.38 tff(28,plain,
% 1.75/1.38 (((~![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))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(29,plain,
% 1.75/1.38 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(30,plain,
% 1.75/1.38 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.75/1.38 tff(31,plain,
% 1.75/1.38 (n1(a, b, a)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[30, 27, 24, 11])).
% 1.75/1.38 tff(32,plain,
% 1.75/1.38 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(33,plain,
% 1.75/1.38 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[32])).
% 1.75/1.38 tff(34,plain,
% 1.75/1.38 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(35,plain,
% 1.75/1.38 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(36,plain,
% 1.75/1.38 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[35])).
% 1.75/1.38 tff(37,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 1.75/1.38 tff(38,plain,
% 1.75/1.38 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.75/1.38 tff(39,plain,
% 1.75/1.38 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.75/1.38 tff(40,plain,(
% 1.75/1.38 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.75/1.38 inference(skolemize,[status(sab)],[39])).
% 1.75/1.38 tff(41,plain,
% 1.75/1.38 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.75/1.38 tff(42,plain,
% 1.75/1.38 (n0(b, a) <=> n0(b, a)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(43,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 1.75/1.38 tff(44,plain,
% 1.75/1.38 (n0(b, a)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.75/1.38 tff(45,plain,
% 1.75/1.38 (((~![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))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(46,plain,
% 1.75/1.38 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(47,plain,
% 1.75/1.38 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.75/1.38 tff(48,plain,
% 1.75/1.38 (l1(a, a)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 1.75/1.38 tff(49,plain,
% 1.75/1.38 (^[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)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(50,plain,
% 1.75/1.38 (![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))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[49])).
% 1.75/1.38 tff(51,plain,
% 1.75/1.38 (![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))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(52,plain,
% 1.75/1.38 (^[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))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(53,plain,
% 1.75/1.38 (![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))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[52])).
% 1.75/1.38 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')).
% 1.75/1.38 tff(55,plain,
% 1.75/1.38 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.75/1.38 tff(56,plain,
% 1.75/1.38 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.75/1.38 tff(57,plain,(
% 1.75/1.38 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.75/1.38 inference(skolemize,[status(sab)],[56])).
% 1.75/1.38 tff(58,plain,
% 1.75/1.38 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.75/1.38 tff(59,plain,
% 1.75/1.38 (p1(a, a, a) <=> p1(a, a, a)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(60,plain,
% 1.75/1.38 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(61,plain,
% 1.75/1.38 ((~$true) <=> $false),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(62,plain,
% 1.75/1.38 (l0(a) <=> $true),
% 1.75/1.38 inference(iff_true,[status(thm)],[26])).
% 1.75/1.38 tff(63,plain,
% 1.75/1.38 ((~l0(a)) <=> (~$true)),
% 1.75/1.38 inference(monotonicity,[status(thm)],[62])).
% 1.75/1.38 tff(64,plain,
% 1.75/1.38 ((~l0(a)) <=> $false),
% 1.75/1.38 inference(transitivity,[status(thm)],[63, 61])).
% 1.75/1.38 tff(65,plain,
% 1.75/1.38 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 1.75/1.38 inference(monotonicity,[status(thm)],[64])).
% 1.75/1.38 tff(66,plain,
% 1.75/1.38 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 1.75/1.38 inference(transitivity,[status(thm)],[65, 60])).
% 1.75/1.38 tff(67,plain,
% 1.75/1.38 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(68,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 1.75/1.38 tff(69,plain,
% 1.75/1.38 ((~l0(a)) | p1(a, a, a)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.75/1.38 tff(70,plain,
% 1.75/1.38 (p1(a, a, a)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.75/1.38 tff(71,plain,
% 1.75/1.38 (p1(a, a, a)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[70, 59])).
% 1.75/1.38 tff(72,plain,
% 1.75/1.38 (k0(b) <=> k0(b)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(73,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 1.75/1.38 tff(74,plain,
% 1.75/1.38 (k0(b)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.75/1.38 tff(75,plain,
% 1.75/1.38 (((~![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))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(76,plain,
% 1.75/1.38 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(77,plain,
% 1.75/1.38 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.75/1.38 tff(78,plain,
% 1.75/1.38 (q2(a, b, b)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[77, 74, 71, 58])).
% 1.75/1.38 tff(79,plain,
% 1.75/1.38 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(80,plain,
% 1.75/1.38 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[79])).
% 1.75/1.38 tff(81,plain,
% 1.75/1.38 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(82,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.75/1.38 tff(83,plain,
% 1.75/1.38 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.75/1.38 tff(84,plain,(
% 1.75/1.38 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.75/1.38 inference(skolemize,[status(sab)],[83])).
% 1.75/1.38 tff(85,plain,
% 1.75/1.38 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[84, 80])).
% 1.75/1.38 tff(86,plain,
% 1.75/1.38 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(87,plain,
% 1.75/1.38 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(88,plain,
% 1.75/1.38 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.75/1.38 tff(89,plain,
% 1.75/1.38 (s1(b)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[88, 85, 11])).
% 1.75/1.38 tff(90,plain,
% 1.75/1.38 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(91,plain,
% 1.75/1.38 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[90])).
% 1.75/1.38 tff(92,plain,
% 1.75/1.38 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(93,plain,
% 1.75/1.38 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(94,plain,
% 1.75/1.38 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[93])).
% 1.75/1.38 tff(95,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 1.75/1.38 tff(96,plain,
% 1.75/1.38 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.75/1.38 tff(97,plain,
% 1.75/1.38 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[96, 92])).
% 1.75/1.38 tff(98,plain,(
% 1.75/1.38 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.75/1.38 inference(skolemize,[status(sab)],[97])).
% 1.75/1.38 tff(99,plain,
% 1.75/1.38 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[98, 91])).
% 1.75/1.38 tff(100,plain,
% 1.75/1.38 (p0(b, d) <=> p0(b, d)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(101,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 1.75/1.38 tff(102,plain,
% 1.75/1.38 (p0(b, d)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.75/1.38 tff(103,plain,
% 1.75/1.38 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(b, d)) | p1(d, d, d))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(b, d)) | p1(d, d, d))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(104,plain,
% 1.75/1.38 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(b, d)) | p1(d, d, d))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(105,plain,
% 1.75/1.38 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(b, d)) | p1(d, d, d)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.75/1.38 tff(106,plain,
% 1.75/1.38 (p1(d, d, d)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[105, 102, 99])).
% 1.75/1.38 tff(107,plain,
% 1.75/1.38 (^[B: $i, A: $i, C: $i] : refl((n2(A) | (~p1(B, C, A))) <=> (n2(A) | (~p1(B, C, A))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(108,plain,
% 1.75/1.38 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[107])).
% 1.75/1.38 tff(109,plain,
% 1.75/1.38 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(110,axiom,(![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_137')).
% 1.75/1.38 tff(111,plain,
% 1.75/1.38 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.75/1.38 tff(112,plain,(
% 1.75/1.38 ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 1.75/1.38 inference(skolemize,[status(sab)],[111])).
% 1.75/1.38 tff(113,plain,
% 1.75/1.38 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.75/1.38 tff(114,plain,
% 1.75/1.38 (((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(d) | (~p1(d, d, d)))) <=> ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(d) | (~p1(d, d, d)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(115,plain,
% 1.75/1.38 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(d) | (~p1(d, d, d)))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(116,plain,
% 1.75/1.38 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(d) | (~p1(d, d, d))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.75/1.38 tff(117,plain,
% 1.75/1.38 (n2(d)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[116, 113, 106])).
% 1.75/1.38 tff(118,plain,
% 1.75/1.38 (^[H: $i] : refl(((~k1(H)) | (~n2(H)) | p3(H, H, H)) <=> ((~k1(H)) | (~n2(H)) | p3(H, H, H)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(119,plain,
% 1.75/1.38 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H)) <=> ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[118])).
% 1.75/1.38 tff(120,plain,
% 1.75/1.38 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H)) <=> ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(121,plain,
% 1.75/1.38 (^[H: $i] : trans(monotonicity(rewrite((p3(H, H, H) | (~k1(H))) <=> ((~k1(H)) | p3(H, H, H))), (((p3(H, H, H) | (~k1(H))) | (~n2(H))) <=> (((~k1(H)) | p3(H, H, H)) | (~n2(H))))), rewrite((((~k1(H)) | p3(H, H, H)) | (~n2(H))) <=> ((~k1(H)) | (~n2(H)) | p3(H, H, H))), (((p3(H, H, H) | (~k1(H))) | (~n2(H))) <=> ((~k1(H)) | (~n2(H)) | p3(H, H, H))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(122,plain,
% 1.75/1.38 (![H: $i] : ((p3(H, H, H) | (~k1(H))) | (~n2(H))) <=> ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[121])).
% 1.75/1.38 tff(123,axiom,(![H: $i] : ((p3(H, H, H) | (~k1(H))) | (~n2(H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_249')).
% 1.75/1.38 tff(124,plain,
% 1.75/1.38 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.75/1.38 tff(125,plain,
% 1.75/1.38 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[124, 120])).
% 1.75/1.38 tff(126,plain,(
% 1.75/1.38 ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 1.75/1.38 inference(skolemize,[status(sab)],[125])).
% 1.75/1.38 tff(127,plain,
% 1.75/1.38 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[126, 119])).
% 1.75/1.38 tff(128,plain,
% 1.75/1.38 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(129,plain,
% 1.75/1.38 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[128])).
% 1.75/1.38 tff(130,plain,
% 1.75/1.38 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(131,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 1.75/1.38 tff(132,plain,
% 1.75/1.38 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.75/1.38 tff(133,plain,(
% 1.75/1.38 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.75/1.38 inference(skolemize,[status(sab)],[132])).
% 1.75/1.38 tff(134,plain,
% 1.75/1.38 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[133, 129])).
% 1.75/1.38 tff(135,plain,
% 1.75/1.38 (n0(c, d) <=> n0(c, d)),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(136,axiom,(n0(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 1.75/1.38 tff(137,plain,
% 1.75/1.38 (n0(c, d)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.75/1.38 tff(138,plain,
% 1.75/1.38 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(139,plain,
% 1.75/1.38 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(140,plain,
% 1.75/1.38 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.75/1.38 tff(141,plain,
% 1.75/1.38 (k1(d)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[140, 137, 134])).
% 1.75/1.38 tff(142,plain,
% 1.75/1.38 (((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | ((~k1(d)) | (~n2(d)) | p3(d, d, d))) <=> ((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | (~k1(d)) | (~n2(d)) | p3(d, d, d))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(143,plain,
% 1.75/1.38 ((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | ((~k1(d)) | (~n2(d)) | p3(d, d, d))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(144,plain,
% 1.75/1.38 ((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | (~k1(d)) | (~n2(d)) | p3(d, d, d)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.75/1.38 tff(145,plain,
% 1.75/1.38 (p3(d, d, d)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[144, 141, 127, 117])).
% 1.75/1.38 tff(146,plain,
% 1.75/1.38 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(c, d)) | l1(d, d))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(c, d)) | l1(d, d))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(147,plain,
% 1.75/1.38 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(c, d)) | l1(d, d))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(148,plain,
% 1.75/1.38 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(c, d)) | l1(d, d)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.75/1.38 tff(149,plain,
% 1.75/1.38 (l1(d, d)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[148, 137, 41])).
% 1.75/1.38 tff(150,plain,
% 1.75/1.38 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~l1(A, C)) | (~p3(B, C, D)) | s4(A)) <=> ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(151,plain,
% 1.75/1.38 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[150])).
% 1.75/1.38 tff(152,plain,
% 1.75/1.38 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(153,plain,
% 1.75/1.38 (^[B: $i, D: $i, A: $i, C: $i] : rewrite(((s4(A) | (~p3(B, C, D))) | (~l1(A, C))) <=> ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(154,plain,
% 1.75/1.38 (![B: $i, D: $i, A: $i, C: $i] : ((s4(A) | (~p3(B, C, D))) | (~l1(A, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[153])).
% 1.75/1.38 tff(155,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((s4(A) | (~p3(B, C, D))) | (~l1(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_299')).
% 1.75/1.38 tff(156,plain,
% 1.75/1.38 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.75/1.38 tff(157,plain,
% 1.75/1.38 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.75/1.38 tff(158,plain,(
% 1.75/1.38 ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 1.75/1.38 inference(skolemize,[status(sab)],[157])).
% 1.75/1.38 tff(159,plain,
% 1.75/1.38 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[158, 151])).
% 1.75/1.38 tff(160,plain,
% 1.75/1.38 (((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | ((~l1(d, d)) | s4(d) | (~p3(d, d, d)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | (~l1(d, d)) | s4(d) | (~p3(d, d, d)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(161,plain,
% 1.75/1.38 (((~l1(d, d)) | (~p3(d, d, d)) | s4(d)) <=> ((~l1(d, d)) | s4(d) | (~p3(d, d, d)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(162,plain,
% 1.75/1.38 (((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | ((~l1(d, d)) | (~p3(d, d, d)) | s4(d))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | ((~l1(d, d)) | s4(d) | (~p3(d, d, d))))),
% 1.75/1.38 inference(monotonicity,[status(thm)],[161])).
% 1.75/1.38 tff(163,plain,
% 1.75/1.38 (((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | ((~l1(d, d)) | (~p3(d, d, d)) | s4(d))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | (~l1(d, d)) | s4(d) | (~p3(d, d, d)))),
% 1.75/1.38 inference(transitivity,[status(thm)],[162, 160])).
% 1.75/1.38 tff(164,plain,
% 1.75/1.38 ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | ((~l1(d, d)) | (~p3(d, d, d)) | s4(d))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(165,plain,
% 1.75/1.38 ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | (~l1(d, d)) | s4(d) | (~p3(d, d, d))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.75/1.38 tff(166,plain,
% 1.75/1.38 (s4(d)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[165, 159, 149, 145])).
% 1.75/1.38 tff(167,plain,
% 1.75/1.38 ((~m5(d, d)) <=> (~m5(d, d))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(168,axiom,(~m5(d, d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 1.75/1.38 tff(169,plain,
% 1.75/1.38 (~m5(d, d)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.75/1.38 tff(170,plain,
% 1.75/1.38 (^[B: $i] : refl((m5(B, B) | (~m4(e, e)) | (~s4(B))) <=> (m5(B, B) | (~m4(e, e)) | (~s4(B))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(171,plain,
% 1.75/1.38 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B))) <=> ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[170])).
% 1.75/1.38 tff(172,plain,
% 1.75/1.38 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B))) <=> ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(173,plain,
% 1.75/1.38 (^[B: $i] : trans(monotonicity(rewrite((m5(B, B) | (~s4(B))) <=> (m5(B, B) | (~s4(B)))), (((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> ((m5(B, B) | (~s4(B))) | (~m4(e, e))))), rewrite(((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> (m5(B, B) | (~m4(e, e)) | (~s4(B)))), (((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> (m5(B, B) | (~m4(e, e)) | (~s4(B)))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(174,plain,
% 1.75/1.38 (![B: $i] : ((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[173])).
% 1.75/1.38 tff(175,axiom,(![B: $i] : ((m5(B, B) | (~s4(B))) | (~m4(e, e)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_305')).
% 1.75/1.38 tff(176,plain,
% 1.75/1.38 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.75/1.38 tff(177,plain,
% 1.75/1.38 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.75/1.38 tff(178,plain,(
% 1.75/1.38 ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 1.75/1.38 inference(skolemize,[status(sab)],[177])).
% 1.75/1.38 tff(179,plain,
% 1.75/1.38 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[178, 171])).
% 1.75/1.38 tff(180,plain,
% 1.75/1.38 (((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | ((~m4(e, e)) | m5(d, d) | (~s4(d)))) <=> ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (~m4(e, e)) | m5(d, d) | (~s4(d)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(181,plain,
% 1.75/1.38 ((m5(d, d) | (~m4(e, e)) | (~s4(d))) <=> ((~m4(e, e)) | m5(d, d) | (~s4(d)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(182,plain,
% 1.75/1.38 (((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (m5(d, d) | (~m4(e, e)) | (~s4(d)))) <=> ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | ((~m4(e, e)) | m5(d, d) | (~s4(d))))),
% 1.75/1.38 inference(monotonicity,[status(thm)],[181])).
% 1.75/1.38 tff(183,plain,
% 1.75/1.38 (((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (m5(d, d) | (~m4(e, e)) | (~s4(d)))) <=> ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (~m4(e, e)) | m5(d, d) | (~s4(d)))),
% 1.75/1.38 inference(transitivity,[status(thm)],[182, 180])).
% 1.75/1.39 tff(184,plain,
% 1.75/1.39 ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (m5(d, d) | (~m4(e, e)) | (~s4(d)))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(185,plain,
% 1.75/1.39 ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (~m4(e, e)) | m5(d, d) | (~s4(d))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.75/1.39 tff(186,plain,
% 1.75/1.39 ((~m4(e, e)) | (~s4(d))),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[185, 179, 169])).
% 1.75/1.39 tff(187,plain,
% 1.75/1.39 (~m4(e, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[186, 166])).
% 1.75/1.39 tff(188,plain,
% 1.75/1.39 (^[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)))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(189,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[188])).
% 1.75/1.39 tff(190,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(191,plain,
% 1.75/1.39 (^[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))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(192,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[191])).
% 1.75/1.39 tff(193,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 1.75/1.39 tff(194,plain,
% 1.75/1.39 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.75/1.39 tff(195,plain,
% 1.75/1.39 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.75/1.39 tff(196,plain,(
% 1.75/1.39 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.75/1.39 inference(skolemize,[status(sab)],[195])).
% 1.75/1.39 tff(197,plain,
% 1.75/1.39 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.75/1.39 tff(198,plain,
% 1.75/1.39 (m0(b, b, e) <=> m0(b, b, e)),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(199,axiom,(m0(b, b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 1.75/1.39 tff(200,plain,
% 1.75/1.39 (m0(b, b, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.75/1.39 tff(201,plain,
% 1.75/1.39 (((~![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)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(202,plain,
% 1.75/1.39 (((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e)) <=> ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(203,plain,
% 1.75/1.39 (((~![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))))),
% 1.75/1.39 inference(monotonicity,[status(thm)],[202])).
% 1.75/1.39 tff(204,plain,
% 1.75/1.39 (((~![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)))),
% 1.75/1.39 inference(transitivity,[status(thm)],[203, 201])).
% 1.75/1.39 tff(205,plain,
% 1.75/1.39 ((~![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))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(206,plain,
% 1.75/1.39 ((~![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))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.75/1.39 tff(207,plain,
% 1.75/1.39 ((~s1(b)) | l2(e, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[206, 200, 197, 11])).
% 1.75/1.39 tff(208,plain,
% 1.75/1.39 (l2(e, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[207, 89])).
% 1.75/1.39 tff(209,plain,
% 1.75/1.39 (^[E: $i, F: $i, G: $i] : refl(((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(210,plain,
% 1.75/1.39 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[209])).
% 1.75/1.39 tff(211,plain,
% 1.75/1.39 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(212,plain,
% 1.75/1.39 (^[E: $i, F: $i, G: $i] : trans(monotonicity(rewrite((m4(E, F) | (~l2(G, F))) <=> ((~l2(G, F)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> (((~l2(G, F)) | m4(E, F)) | (~s3(a, E))))), rewrite((((~l2(G, F)) | m4(E, F)) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(213,plain,
% 1.75/1.39 (![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[212])).
% 1.75/1.39 tff(214,axiom,(![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_279')).
% 1.75/1.39 tff(215,plain,
% 1.75/1.39 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.75/1.39 tff(216,plain,
% 1.75/1.39 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.75/1.39 tff(217,plain,(
% 1.75/1.39 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.75/1.39 inference(skolemize,[status(sab)],[216])).
% 1.75/1.39 tff(218,plain,
% 1.75/1.39 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[217, 210])).
% 1.75/1.39 tff(219,plain,
% 1.75/1.39 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(220,plain,
% 1.75/1.39 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(221,plain,
% 1.75/1.39 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.75/1.39 tff(222,plain,
% 1.75/1.39 (~s3(a, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[221, 218, 208, 187])).
% 1.75/1.39 tff(223,assumption,(~q2(a, e, e)), introduced(assumption)).
% 1.75/1.39 tff(224,plain,
% 1.75/1.39 (k0(e) <=> k0(e)),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(225,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.75/1.39 tff(226,plain,
% 1.75/1.39 (k0(e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.75/1.39 tff(227,plain,
% 1.75/1.39 (((~![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))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(228,plain,
% 1.75/1.39 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(229,plain,
% 1.75/1.39 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.75/1.39 tff(230,plain,
% 1.75/1.39 ($false),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[229, 226, 71, 58, 223])).
% 1.75/1.39 tff(231,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.39 tff(232,plain,
% 1.75/1.39 (((~![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)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(233,plain,
% 1.75/1.39 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(234,plain,
% 1.75/1.39 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.75/1.39 tff(235,plain,
% 1.75/1.39 (k1(a)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[234, 44, 134])).
% 1.75/1.39 tff(236,plain,
% 1.75/1.39 (^[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)))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(237,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[236])).
% 1.75/1.39 tff(238,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(239,plain,
% 1.75/1.39 (^[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))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(240,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[239])).
% 1.75/1.39 tff(241,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')).
% 1.75/1.39 tff(242,plain,
% 1.75/1.39 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.75/1.39 tff(243,plain,
% 1.75/1.39 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[242, 238])).
% 1.75/1.39 tff(244,plain,(
% 1.75/1.39 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.75/1.39 inference(skolemize,[status(sab)],[243])).
% 1.75/1.39 tff(245,plain,
% 1.75/1.39 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[244, 237])).
% 1.75/1.39 tff(246,plain,
% 1.75/1.39 (m0(a, e, e) <=> m0(a, e, e)),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(247,axiom,(m0(a, e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 1.75/1.39 tff(248,plain,
% 1.75/1.39 (m0(a, e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.75/1.39 tff(249,plain,
% 1.75/1.39 (((~![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))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(250,plain,
% 1.75/1.39 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(251,plain,
% 1.75/1.39 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.75/1.39 tff(252,plain,
% 1.75/1.39 ((~k1(a)) | n1(a, e, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[251, 248, 245])).
% 1.75/1.39 tff(253,plain,
% 1.75/1.39 (n1(a, e, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[252, 235])).
% 1.75/1.39 tff(254,plain,
% 1.75/1.39 (^[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)))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(255,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[254])).
% 1.75/1.39 tff(256,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(257,plain,
% 1.75/1.39 (^[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))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(258,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[257])).
% 1.75/1.39 tff(259,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')).
% 1.75/1.39 tff(260,plain,
% 1.75/1.39 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.75/1.39 tff(261,plain,
% 1.75/1.39 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[260, 256])).
% 1.75/1.39 tff(262,plain,(
% 1.75/1.39 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.75/1.39 inference(skolemize,[status(sab)],[261])).
% 1.75/1.39 tff(263,plain,
% 1.75/1.39 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[262, 255])).
% 1.75/1.39 tff(264,plain,
% 1.75/1.39 (p1(e, e, e) <=> p1(e, e, e)),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(265,plain,
% 1.75/1.39 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(266,plain,
% 1.75/1.39 (k0(e) <=> $true),
% 1.75/1.39 inference(iff_true,[status(thm)],[225])).
% 1.75/1.39 tff(267,plain,
% 1.75/1.39 ((~k0(e)) <=> (~$true)),
% 1.75/1.39 inference(monotonicity,[status(thm)],[266])).
% 1.75/1.39 tff(268,plain,
% 1.75/1.39 ((~k0(e)) <=> $false),
% 1.75/1.39 inference(transitivity,[status(thm)],[267, 61])).
% 1.75/1.39 tff(269,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 1.75/1.39 tff(270,plain,
% 1.75/1.39 (r0(e) <=> $true),
% 1.75/1.39 inference(iff_true,[status(thm)],[269])).
% 1.75/1.39 tff(271,plain,
% 1.75/1.39 ((~r0(e)) <=> (~$true)),
% 1.75/1.39 inference(monotonicity,[status(thm)],[270])).
% 1.75/1.39 tff(272,plain,
% 1.75/1.39 ((~r0(e)) <=> $false),
% 1.75/1.39 inference(transitivity,[status(thm)],[271, 61])).
% 1.75/1.39 tff(273,plain,
% 1.75/1.39 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 1.75/1.39 inference(monotonicity,[status(thm)],[272, 268])).
% 1.75/1.39 tff(274,plain,
% 1.75/1.39 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 1.75/1.39 inference(transitivity,[status(thm)],[273, 265])).
% 1.75/1.39 tff(275,plain,
% 1.75/1.39 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(276,plain,
% 1.75/1.39 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(277,plain,
% 1.75/1.39 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(278,plain,
% 1.75/1.39 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 1.75/1.39 inference(monotonicity,[status(thm)],[277])).
% 1.75/1.39 tff(279,plain,
% 1.75/1.39 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.75/1.39 inference(transitivity,[status(thm)],[278, 276])).
% 1.75/1.39 tff(280,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 1.75/1.39 tff(281,plain,
% 1.75/1.39 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.75/1.39 tff(282,plain,
% 1.75/1.39 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[281, 275])).
% 1.75/1.39 tff(283,plain,
% 1.75/1.39 (p1(e, e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[282, 274])).
% 1.75/1.39 tff(284,plain,
% 1.75/1.39 (p1(e, e, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[283, 264])).
% 1.75/1.39 tff(285,plain,
% 1.75/1.39 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, 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))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(286,plain,
% 1.75/1.39 (((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e)) <=> ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(287,plain,
% 1.75/1.39 (((~![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))) | ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e)))),
% 1.75/1.39 inference(monotonicity,[status(thm)],[286])).
% 1.75/1.39 tff(288,plain,
% 1.75/1.39 (((~![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))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 1.75/1.39 inference(transitivity,[status(thm)],[287, 285])).
% 1.75/1.39 tff(289,plain,
% 1.75/1.39 ((~![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))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(290,plain,
% 1.75/1.39 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.75/1.39 tff(291,plain,
% 1.75/1.39 ((~q2(a, e, e)) | q2(e, a, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[290, 284, 263, 253])).
% 1.75/1.39 tff(292,plain,
% 1.75/1.39 (q2(e, a, e)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[291, 231])).
% 1.75/1.39 tff(293,plain,
% 1.75/1.39 (^[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)))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(294,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[293])).
% 1.75/1.39 tff(295,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(296,plain,
% 1.75/1.39 (^[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))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(297,plain,
% 1.75/1.39 (![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))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[296])).
% 1.75/1.39 tff(298,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')).
% 1.75/1.39 tff(299,plain,
% 1.75/1.39 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.75/1.39 tff(300,plain,
% 1.75/1.39 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[299, 295])).
% 1.75/1.39 tff(301,plain,(
% 1.75/1.39 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.75/1.39 inference(skolemize,[status(sab)],[300])).
% 1.75/1.39 tff(302,plain,
% 1.75/1.39 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[301, 294])).
% 1.75/1.39 tff(303,plain,
% 1.75/1.39 (m0(e, d, e) <=> m0(e, d, e)),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(304,axiom,(m0(e, d, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_8')).
% 1.75/1.39 tff(305,plain,
% 1.75/1.39 (m0(e, d, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[304, 303])).
% 1.75/1.39 tff(306,plain,
% 1.75/1.39 (((~![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, d, e)) | (~q2(e, a, e)) | s3(a, e))) <=> ((~![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, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(307,plain,
% 1.75/1.39 ((~![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, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(308,plain,
% 1.75/1.39 ((~![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, d, e)) | (~q2(e, a, e)) | s3(a, e)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[307, 306])).
% 1.75/1.39 tff(309,plain,
% 1.75/1.39 (~s2(a)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[308, 305, 302, 292, 222])).
% 1.75/1.39 tff(310,plain,
% 1.75/1.39 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(311,plain,
% 1.75/1.39 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[310])).
% 1.75/1.39 tff(312,plain,
% 1.75/1.39 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(313,plain,
% 1.75/1.39 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(314,plain,
% 1.75/1.39 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[313])).
% 1.75/1.39 tff(315,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 1.75/1.40 tff(316,plain,
% 1.75/1.40 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[315, 314])).
% 1.75/1.40 tff(317,plain,
% 1.75/1.40 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[316, 312])).
% 1.75/1.40 tff(318,plain,(
% 1.75/1.40 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.75/1.40 inference(skolemize,[status(sab)],[317])).
% 1.75/1.40 tff(319,plain,
% 1.75/1.40 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[318, 311])).
% 1.75/1.40 tff(320,plain,
% 1.75/1.40 (((~![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)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(321,plain,
% 1.75/1.40 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(322,plain,
% 1.75/1.40 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[321, 320])).
% 1.75/1.40 tff(323,plain,
% 1.75/1.40 (~q2(b, a, b)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[322, 319, 309, 89])).
% 1.75/1.40 tff(324,plain,
% 1.75/1.40 (p0(c, b) <=> p0(c, b)),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(325,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.75/1.40 tff(326,plain,
% 1.75/1.40 (p0(c, b)),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.75/1.40 tff(327,plain,
% 1.75/1.40 (((~![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))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(328,plain,
% 1.75/1.40 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(329,plain,
% 1.75/1.40 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.75/1.40 tff(330,plain,
% 1.75/1.40 (p1(b, b, b)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[329, 326, 99])).
% 1.75/1.40 tff(331,plain,
% 1.75/1.40 (((~![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) | (~n1(a, b, b)) | (~q2(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) | (~n1(a, b, b)) | (~q2(a, b, b)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(332,plain,
% 1.75/1.40 (((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b)) <=> ((~p1(b, b, b)) | q2(b, a, b) | (~n1(a, b, b)) | (~q2(a, b, b)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(333,plain,
% 1.75/1.40 (((~![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) | (~n1(a, b, b)) | (~q2(a, b, b))))),
% 1.75/1.40 inference(monotonicity,[status(thm)],[332])).
% 1.75/1.40 tff(334,plain,
% 1.75/1.40 (((~![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) | (~n1(a, b, b)) | (~q2(a, b, b)))),
% 1.75/1.40 inference(transitivity,[status(thm)],[333, 331])).
% 1.75/1.40 tff(335,plain,
% 1.75/1.40 ((~![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))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(336,plain,
% 1.75/1.40 ((~![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) | (~n1(a, b, b)) | (~q2(a, b, b))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[335, 334])).
% 1.75/1.40 tff(337,plain,
% 1.75/1.40 (~n1(a, b, b)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[336, 263, 330, 323, 78])).
% 1.75/1.40 tff(338,plain,
% 1.75/1.40 (^[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)))),
% 1.75/1.40 inference(bind,[status(th)],[])).
% 1.75/1.40 tff(339,plain,
% 1.75/1.40 (![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))),
% 1.75/1.40 inference(quant_intro,[status(thm)],[338])).
% 1.75/1.40 tff(340,plain,
% 1.75/1.40 (![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))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(341,plain,
% 1.75/1.40 (^[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))))),
% 1.75/1.40 inference(bind,[status(th)],[])).
% 1.75/1.40 tff(342,plain,
% 1.75/1.40 (![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))),
% 1.75/1.40 inference(quant_intro,[status(thm)],[341])).
% 1.75/1.40 tff(343,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')).
% 1.75/1.40 tff(344,plain,
% 1.75/1.40 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.75/1.40 tff(345,plain,
% 1.75/1.40 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[344, 340])).
% 1.75/1.40 tff(346,plain,(
% 1.75/1.40 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.75/1.40 inference(skolemize,[status(sab)],[345])).
% 1.75/1.40 tff(347,plain,
% 1.75/1.40 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[346, 339])).
% 1.75/1.40 tff(348,plain,
% 1.75/1.40 (((~![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)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(349,plain,
% 1.75/1.40 (((~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)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(350,plain,
% 1.75/1.40 (((~![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))))),
% 1.75/1.40 inference(monotonicity,[status(thm)],[349])).
% 1.75/1.40 tff(351,plain,
% 1.75/1.40 (((~![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)))),
% 1.75/1.40 inference(transitivity,[status(thm)],[350, 348])).
% 1.75/1.40 tff(352,plain,
% 1.75/1.40 ((~![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))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(353,plain,
% 1.75/1.40 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.75/1.41 tff(354,plain,
% 1.75/1.41 ($false),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[353, 27, 347, 337, 48, 31])).
% 1.75/1.41 % SZS output end Proof
%------------------------------------------------------------------------------