TSTP Solution File: SYN140-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN140-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 23:53:54 EDT 2022
% Result : Unsatisfiable 3.08s 2.25s
% Output : Proof 3.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN140-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:51:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 3.08/2.25 % SZS status Unsatisfiable
% 3.08/2.25 % SZS output start Proof
% 3.08/2.25 tff(m4_type, type, (
% 3.08/2.25 m4: ( $i * $i ) > $o)).
% 3.08/2.25 tff(d_type, type, (
% 3.08/2.25 d: $i)).
% 3.08/2.25 tff(b_type, type, (
% 3.08/2.25 b: $i)).
% 3.08/2.25 tff(s3_type, type, (
% 3.08/2.25 s3: ( $i * $i ) > $o)).
% 3.08/2.25 tff(a_type, type, (
% 3.08/2.25 a: $i)).
% 3.08/2.25 tff(m0_type, type, (
% 3.08/2.25 m0: ( $i * $i * $i ) > $o)).
% 3.08/2.25 tff(q2_type, type, (
% 3.08/2.25 q2: ( $i * $i * $i ) > $o)).
% 3.08/2.25 tff(l1_type, type, (
% 3.08/2.25 l1: ( $i * $i ) > $o)).
% 3.08/2.25 tff(p0_type, type, (
% 3.08/2.25 p0: ( $i * $i ) > $o)).
% 3.08/2.25 tff(r0_type, type, (
% 3.08/2.25 r0: $i > $o)).
% 3.08/2.25 tff(p1_type, type, (
% 3.08/2.25 p1: ( $i * $i * $i ) > $o)).
% 3.08/2.25 tff(l0_type, type, (
% 3.08/2.25 l0: $i > $o)).
% 3.08/2.25 tff(n1_type, type, (
% 3.08/2.25 n1: ( $i * $i * $i ) > $o)).
% 3.08/2.25 tff(s0_type, type, (
% 3.08/2.25 s0: $i > $o)).
% 3.08/2.25 tff(s2_type, type, (
% 3.08/2.25 s2: $i > $o)).
% 3.08/2.25 tff(k0_type, type, (
% 3.08/2.25 k0: $i > $o)).
% 3.08/2.25 tff(n0_type, type, (
% 3.08/2.25 n0: ( $i * $i ) > $o)).
% 3.08/2.25 tff(c_type, type, (
% 3.08/2.25 c: $i)).
% 3.08/2.25 tff(s1_type, type, (
% 3.08/2.25 s1: $i > $o)).
% 3.08/2.25 tff(l2_type, type, (
% 3.08/2.25 l2: ( $i * $i ) > $o)).
% 3.08/2.25 tff(q0_type, type, (
% 3.08/2.25 q0: ( $i * $i ) > $o)).
% 3.08/2.25 tff(1,plain,
% 3.08/2.25 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 3.08/2.25 inference(bind,[status(th)],[])).
% 3.08/2.25 tff(2,plain,
% 3.08/2.25 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 3.08/2.25 inference(quant_intro,[status(thm)],[1])).
% 3.08/2.25 tff(3,plain,
% 3.08/2.25 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(4,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 3.08/2.25 tff(5,plain,
% 3.08/2.25 (![Y: $i, X: $i] : m0(X, d, Y)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.08/2.25 tff(6,plain,(
% 3.08/2.25 ![Y: $i, X: $i] : m0(X, d, Y)),
% 3.08/2.25 inference(skolemize,[status(sab)],[5])).
% 3.08/2.25 tff(7,plain,
% 3.08/2.25 (![Y: $i, X: $i] : m0(X, d, Y)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.08/2.25 tff(8,plain,
% 3.08/2.25 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, b)),
% 3.08/2.25 inference(quant_inst,[status(thm)],[])).
% 3.08/2.25 tff(9,plain,
% 3.08/2.25 (m0(d, d, b)),
% 3.08/2.25 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.08/2.25 tff(10,plain,
% 3.08/2.25 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(a, d, b)),
% 3.08/2.25 inference(quant_inst,[status(thm)],[])).
% 3.08/2.25 tff(11,plain,
% 3.08/2.25 (m0(a, d, b)),
% 3.08/2.25 inference(unit_resolution,[status(thm)],[10, 7])).
% 3.08/2.25 tff(12,plain,
% 3.08/2.25 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)))),
% 3.08/2.25 inference(bind,[status(th)],[])).
% 3.08/2.25 tff(13,plain,
% 3.08/2.25 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 3.08/2.25 inference(quant_intro,[status(thm)],[12])).
% 3.08/2.25 tff(14,plain,
% 3.08/2.25 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(15,plain,
% 3.08/2.25 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1(C, D) | (~p0(E, C))) <=> ((~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> (((~p0(E, C)) | l1(C, D)) | (~r0(F))))), rewrite((((~p0(E, C)) | l1(C, D)) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D)))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> (((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))))), rewrite((((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))))),
% 3.08/2.25 inference(bind,[status(th)],[])).
% 3.08/2.25 tff(16,plain,
% 3.08/2.25 (![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 3.08/2.25 inference(quant_intro,[status(thm)],[15])).
% 3.08/2.25 tff(17,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_003')).
% 3.08/2.25 tff(18,plain,
% 3.08/2.25 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.08/2.25 tff(19,plain,
% 3.08/2.25 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.08/2.25 tff(20,plain,(
% 3.08/2.25 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 3.08/2.25 inference(skolemize,[status(sab)],[19])).
% 3.08/2.25 tff(21,plain,
% 3.08/2.25 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[20, 13])).
% 3.08/2.25 tff(22,plain,
% 3.08/2.25 (p0(b, d) <=> p0(b, d)),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(23,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 3.08/2.25 tff(24,plain,
% 3.08/2.25 (p0(b, d)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[23, 22])).
% 3.08/2.25 tff(25,plain,
% 3.08/2.25 (r0(b) <=> r0(b)),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(26,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 3.08/2.25 tff(27,plain,
% 3.08/2.25 (r0(b)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[26, 25])).
% 3.08/2.25 tff(28,plain,
% 3.08/2.25 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(b, d)) | l1(d, a) | (~m0(a, d, b)))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(b, d)) | l1(d, a) | (~m0(a, d, b)))),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(29,plain,
% 3.08/2.25 (((~m0(a, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, a)) <=> ((~r0(b)) | (~p0(b, d)) | l1(d, a) | (~m0(a, d, b)))),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(30,plain,
% 3.08/2.25 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(a, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(b, d)) | l1(d, a) | (~m0(a, d, b))))),
% 3.08/2.25 inference(monotonicity,[status(thm)],[29])).
% 3.08/2.25 tff(31,plain,
% 3.08/2.25 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(a, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(b, d)) | l1(d, a) | (~m0(a, d, b)))),
% 3.08/2.25 inference(transitivity,[status(thm)],[30, 28])).
% 3.08/2.25 tff(32,plain,
% 3.08/2.25 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(a, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, a))),
% 3.08/2.25 inference(quant_inst,[status(thm)],[])).
% 3.08/2.25 tff(33,plain,
% 3.08/2.25 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(b, d)) | l1(d, a) | (~m0(a, d, b))),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[32, 31])).
% 3.08/2.25 tff(34,plain,
% 3.08/2.25 (l1(d, a)),
% 3.08/2.25 inference(unit_resolution,[status(thm)],[33, 27, 24, 21, 11])).
% 3.08/2.25 tff(35,plain,
% 3.08/2.25 (^[H: $i, G: $i] : refl(((~l1(H, G)) | q2(G, G, H)) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 3.08/2.25 inference(bind,[status(th)],[])).
% 3.08/2.25 tff(36,plain,
% 3.08/2.25 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 3.08/2.25 inference(quant_intro,[status(thm)],[35])).
% 3.08/2.25 tff(37,plain,
% 3.08/2.25 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(38,plain,
% 3.08/2.25 (^[H: $i, G: $i] : rewrite((q2(G, G, H) | (~l1(H, G))) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 3.08/2.25 inference(bind,[status(th)],[])).
% 3.08/2.25 tff(39,plain,
% 3.08/2.25 (![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G))) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 3.08/2.25 inference(quant_intro,[status(thm)],[38])).
% 3.08/2.25 tff(40,axiom,(![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_186')).
% 3.08/2.25 tff(41,plain,
% 3.08/2.25 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[40, 39])).
% 3.08/2.25 tff(42,plain,
% 3.08/2.25 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[41, 37])).
% 3.08/2.25 tff(43,plain,(
% 3.08/2.25 ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 3.08/2.25 inference(skolemize,[status(sab)],[42])).
% 3.08/2.25 tff(44,plain,
% 3.08/2.25 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[43, 36])).
% 3.08/2.25 tff(45,plain,
% 3.08/2.25 (((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(d, a)) | q2(a, a, d))) <=> ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(d, a)) | q2(a, a, d))),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(46,plain,
% 3.08/2.25 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(d, a)) | q2(a, a, d))),
% 3.08/2.25 inference(quant_inst,[status(thm)],[])).
% 3.08/2.25 tff(47,plain,
% 3.08/2.25 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(d, a)) | q2(a, a, d)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.08/2.25 tff(48,plain,
% 3.08/2.25 (q2(a, a, d)),
% 3.08/2.25 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 3.08/2.25 tff(49,assumption,(~p1(a, d, a)), introduced(assumption)).
% 3.08/2.25 tff(50,assumption,(~m0(a, a, a)), introduced(assumption)).
% 3.08/2.25 tff(51,plain,
% 3.08/2.25 (^[X: $i] : refl(m0(a, X, a) <=> m0(a, X, a))),
% 3.08/2.25 inference(bind,[status(th)],[])).
% 3.08/2.25 tff(52,plain,
% 3.08/2.25 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 3.08/2.25 inference(quant_intro,[status(thm)],[51])).
% 3.08/2.25 tff(53,plain,
% 3.08/2.25 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(54,axiom,(![X: $i] : m0(a, X, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_12')).
% 3.08/2.25 tff(55,plain,
% 3.08/2.25 (![X: $i] : m0(a, X, a)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[54, 53])).
% 3.08/2.25 tff(56,plain,(
% 3.08/2.25 ![X: $i] : m0(a, X, a)),
% 3.08/2.25 inference(skolemize,[status(sab)],[55])).
% 3.08/2.25 tff(57,plain,
% 3.08/2.25 (![X: $i] : m0(a, X, a)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[56, 52])).
% 3.08/2.25 tff(58,plain,
% 3.08/2.25 ((~![X: $i] : m0(a, X, a)) | m0(a, a, a)),
% 3.08/2.25 inference(quant_inst,[status(thm)],[])).
% 3.08/2.25 tff(59,plain,
% 3.08/2.25 ($false),
% 3.08/2.25 inference(unit_resolution,[status(thm)],[58, 57, 50])).
% 3.08/2.25 tff(60,plain,(m0(a, a, a)), inference(lemma,lemma(discharge,[]))).
% 3.08/2.25 tff(61,plain,
% 3.08/2.25 (p1(a, a, a) <=> p1(a, a, a)),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(62,plain,
% 3.08/2.25 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(63,plain,
% 3.08/2.25 ((~$true) <=> $false),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(64,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 3.08/2.25 tff(65,plain,
% 3.08/2.25 (l0(a) <=> $true),
% 3.08/2.25 inference(iff_true,[status(thm)],[64])).
% 3.08/2.25 tff(66,plain,
% 3.08/2.25 ((~l0(a)) <=> (~$true)),
% 3.08/2.25 inference(monotonicity,[status(thm)],[65])).
% 3.08/2.25 tff(67,plain,
% 3.08/2.25 ((~l0(a)) <=> $false),
% 3.08/2.25 inference(transitivity,[status(thm)],[66, 63])).
% 3.08/2.25 tff(68,plain,
% 3.08/2.25 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 3.08/2.25 inference(monotonicity,[status(thm)],[67])).
% 3.08/2.25 tff(69,plain,
% 3.08/2.25 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 3.08/2.25 inference(transitivity,[status(thm)],[68, 62])).
% 3.08/2.25 tff(70,plain,
% 3.08/2.25 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(71,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 3.08/2.25 tff(72,plain,
% 3.08/2.25 ((~l0(a)) | p1(a, a, a)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[71, 70])).
% 3.08/2.25 tff(73,plain,
% 3.08/2.25 (p1(a, a, a)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[72, 69])).
% 3.08/2.25 tff(74,plain,
% 3.08/2.25 (p1(a, a, a)),
% 3.08/2.25 inference(modus_ponens,[status(thm)],[73, 61])).
% 3.08/2.25 tff(75,plain,
% 3.08/2.25 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))))),
% 3.08/2.25 inference(bind,[status(th)],[])).
% 3.08/2.25 tff(76,plain,
% 3.08/2.25 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 3.08/2.25 inference(quant_intro,[status(thm)],[75])).
% 3.08/2.25 tff(77,plain,
% 3.08/2.25 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 3.08/2.25 inference(rewrite,[status(thm)],[])).
% 3.08/2.25 tff(78,plain,
% 3.08/2.25 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(rewrite((p1(H, I, J) | (~m0(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J))), (((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A))) <=> (((~m0(J, H, A)) | p1(H, I, J)) | (~p1(J, H, A))))), rewrite((((~m0(J, H, A)) | p1(H, I, J)) | (~p1(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))), (((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(79,plain,
% 3.08/2.26 (![I: $i, A: $i, J: $i, H: $i] : ((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[78])).
% 3.08/2.26 tff(80,axiom,(![I: $i, A: $i, J: $i, H: $i] : ((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_082')).
% 3.08/2.26 tff(81,plain,
% 3.08/2.26 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[80, 79])).
% 3.08/2.26 tff(82,plain,
% 3.08/2.26 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[81, 77])).
% 3.08/2.26 tff(83,plain,(
% 3.08/2.26 ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 3.08/2.26 inference(skolemize,[status(sab)],[82])).
% 3.08/2.26 tff(84,plain,
% 3.08/2.26 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[83, 76])).
% 3.08/2.26 tff(85,plain,
% 3.08/2.26 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(86,plain,
% 3.08/2.26 (((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a))) <=> ((~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(87,plain,
% 3.08/2.26 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a)))),
% 3.08/2.26 inference(monotonicity,[status(thm)],[86])).
% 3.08/2.26 tff(88,plain,
% 3.08/2.26 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))),
% 3.08/2.26 inference(transitivity,[status(thm)],[87, 85])).
% 3.08/2.26 tff(89,plain,
% 3.08/2.26 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a)))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(90,plain,
% 3.08/2.26 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[89, 88])).
% 3.08/2.26 tff(91,plain,
% 3.08/2.26 ($false),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[90, 84, 74, 60, 49])).
% 3.08/2.26 tff(92,plain,(p1(a, d, a)), inference(lemma,lemma(discharge,[]))).
% 3.08/2.26 tff(93,assumption,(~p1(d, d, a)), introduced(assumption)).
% 3.08/2.26 tff(94,assumption,(~m0(a, d, a)), introduced(assumption)).
% 3.08/2.26 tff(95,plain,
% 3.08/2.26 ((~![X: $i] : m0(a, X, a)) | m0(a, d, a)),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(96,plain,
% 3.08/2.26 ($false),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[95, 57, 94])).
% 3.08/2.26 tff(97,plain,(m0(a, d, a)), inference(lemma,lemma(discharge,[]))).
% 3.08/2.26 tff(98,plain,
% 3.08/2.26 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a)))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(99,plain,
% 3.08/2.26 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a)))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(100,plain,
% 3.08/2.26 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[99, 98])).
% 3.08/2.26 tff(101,plain,
% 3.08/2.26 ($false),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[100, 84, 97, 93, 92])).
% 3.08/2.26 tff(102,plain,(p1(d, d, a)), inference(lemma,lemma(discharge,[]))).
% 3.08/2.26 tff(103,plain,
% 3.08/2.26 (^[D: $i, E: $i] : refl(((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(104,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[103])).
% 3.08/2.26 tff(105,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(106,plain,
% 3.08/2.26 (^[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))))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(107,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[106])).
% 3.08/2.26 tff(108,plain,
% 3.08/2.26 (^[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))))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(109,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[108])).
% 3.08/2.26 tff(110,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')).
% 3.08/2.26 tff(111,plain,
% 3.08/2.26 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[110, 109])).
% 3.08/2.26 tff(112,plain,
% 3.08/2.26 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[111, 107])).
% 3.08/2.26 tff(113,plain,
% 3.08/2.26 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[112, 105])).
% 3.08/2.26 tff(114,plain,(
% 3.08/2.26 ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 3.08/2.26 inference(skolemize,[status(sab)],[113])).
% 3.08/2.26 tff(115,plain,
% 3.08/2.26 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[114, 104])).
% 3.08/2.26 tff(116,plain,
% 3.08/2.26 (l0(a) <=> l0(a)),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(117,plain,
% 3.08/2.26 (l0(a)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[64, 116])).
% 3.08/2.26 tff(118,plain,
% 3.08/2.26 (((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, d)) | n1(a, d, a))) <=> ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, d)) | n1(a, d, a))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(119,plain,
% 3.08/2.26 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, d)) | n1(a, d, a))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(120,plain,
% 3.08/2.26 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, d)) | n1(a, d, a)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[119, 118])).
% 3.08/2.26 tff(121,plain,
% 3.08/2.26 (n1(a, d, a)),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[120, 24, 117, 115])).
% 3.08/2.26 tff(122,plain,
% 3.08/2.26 (^[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)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(123,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[122])).
% 3.08/2.26 tff(124,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(125,plain,
% 3.08/2.26 (^[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))))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(126,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[125])).
% 3.08/2.26 tff(127,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')).
% 3.08/2.26 tff(128,plain,
% 3.08/2.26 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[127, 126])).
% 3.08/2.26 tff(129,plain,
% 3.08/2.26 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[128, 124])).
% 3.08/2.26 tff(130,plain,(
% 3.08/2.26 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 3.08/2.26 inference(skolemize,[status(sab)],[129])).
% 3.08/2.26 tff(131,plain,
% 3.08/2.26 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[130, 123])).
% 3.08/2.26 tff(132,plain,
% 3.08/2.26 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (q2(d, a, d) | (~q2(a, a, d)) | (~p1(d, d, a)) | (~n1(a, d, a)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(d, a, d) | (~q2(a, a, d)) | (~p1(d, d, a)) | (~n1(a, d, a)))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(133,plain,
% 3.08/2.26 (((~q2(a, a, d)) | (~n1(a, d, a)) | (~p1(d, d, a)) | q2(d, a, d)) <=> (q2(d, a, d) | (~q2(a, a, d)) | (~p1(d, d, a)) | (~n1(a, d, a)))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(134,plain,
% 3.08/2.26 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, a, d)) | (~n1(a, d, a)) | (~p1(d, d, a)) | q2(d, a, d))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (q2(d, a, d) | (~q2(a, a, d)) | (~p1(d, d, a)) | (~n1(a, d, a))))),
% 3.08/2.26 inference(monotonicity,[status(thm)],[133])).
% 3.08/2.26 tff(135,plain,
% 3.08/2.26 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, a, d)) | (~n1(a, d, a)) | (~p1(d, d, a)) | q2(d, a, d))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(d, a, d) | (~q2(a, a, d)) | (~p1(d, d, a)) | (~n1(a, d, a)))),
% 3.08/2.26 inference(transitivity,[status(thm)],[134, 132])).
% 3.08/2.26 tff(136,plain,
% 3.08/2.26 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, a, d)) | (~n1(a, d, a)) | (~p1(d, d, a)) | q2(d, a, d))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(137,plain,
% 3.08/2.26 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(d, a, d) | (~q2(a, a, d)) | (~p1(d, d, a)) | (~n1(a, d, a))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[136, 135])).
% 3.08/2.26 tff(138,plain,
% 3.08/2.26 (q2(d, a, d) | (~q2(a, a, d)) | (~p1(d, d, a))),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[137, 131, 121])).
% 3.08/2.26 tff(139,plain,
% 3.08/2.26 (q2(d, a, d) | (~q2(a, a, d))),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[138, 102])).
% 3.08/2.26 tff(140,plain,
% 3.08/2.26 (q2(d, a, d)),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[139, 48])).
% 3.08/2.26 tff(141,plain,
% 3.08/2.26 (^[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)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(142,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[141])).
% 3.08/2.26 tff(143,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(144,plain,
% 3.08/2.26 (^[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))))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(145,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[144])).
% 3.08/2.26 tff(146,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')).
% 3.08/2.26 tff(147,plain,
% 3.08/2.26 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[146, 145])).
% 3.08/2.26 tff(148,plain,
% 3.08/2.26 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[147, 143])).
% 3.08/2.26 tff(149,plain,(
% 3.08/2.26 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 3.08/2.26 inference(skolemize,[status(sab)],[148])).
% 3.08/2.26 tff(150,plain,
% 3.08/2.26 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[149, 142])).
% 3.08/2.26 tff(151,plain,
% 3.08/2.26 (k0(b) <=> k0(b)),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(152,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 3.08/2.26 tff(153,plain,
% 3.08/2.26 (k0(b)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[152, 151])).
% 3.08/2.26 tff(154,plain,
% 3.08/2.26 (((~![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(155,plain,
% 3.08/2.26 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(156,plain,
% 3.08/2.26 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[155, 154])).
% 3.08/2.26 tff(157,plain,
% 3.08/2.26 (q2(a, b, b)),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[156, 153, 74, 150])).
% 3.08/2.26 tff(158,assumption,(~p0(b, b)), introduced(assumption)).
% 3.08/2.26 tff(159,plain,
% 3.08/2.26 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(160,plain,
% 3.08/2.26 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 3.08/2.26 inference(quant_intro,[status(thm)],[159])).
% 3.08/2.26 tff(161,plain,
% 3.08/2.26 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(162,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 3.08/2.26 tff(163,plain,
% 3.08/2.26 (![X: $i] : p0(b, X)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[162, 161])).
% 3.08/2.26 tff(164,plain,(
% 3.08/2.26 ![X: $i] : p0(b, X)),
% 3.08/2.26 inference(skolemize,[status(sab)],[163])).
% 3.08/2.26 tff(165,plain,
% 3.08/2.26 (![X: $i] : p0(b, X)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[164, 160])).
% 3.08/2.26 tff(166,plain,
% 3.08/2.26 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(167,plain,
% 3.08/2.26 ($false),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[166, 165, 158])).
% 3.08/2.26 tff(168,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 3.08/2.26 tff(169,plain,
% 3.08/2.26 (((~![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(170,plain,
% 3.08/2.26 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(171,plain,
% 3.08/2.26 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[170, 169])).
% 3.08/2.26 tff(172,plain,
% 3.08/2.26 (n1(a, b, a)),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[171, 117, 115, 168])).
% 3.08/2.26 tff(173,plain,
% 3.08/2.26 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(174,plain,
% 3.08/2.26 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[173])).
% 3.08/2.26 tff(175,plain,
% 3.08/2.26 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(176,plain,
% 3.08/2.26 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(177,plain,
% 3.08/2.26 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[176])).
% 3.08/2.26 tff(178,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 3.08/2.26 tff(179,plain,
% 3.08/2.26 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[178, 177])).
% 3.08/2.26 tff(180,plain,
% 3.08/2.26 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[179, 175])).
% 3.08/2.26 tff(181,plain,(
% 3.08/2.26 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 3.08/2.26 inference(skolemize,[status(sab)],[180])).
% 3.08/2.26 tff(182,plain,
% 3.08/2.26 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[181, 174])).
% 3.08/2.26 tff(183,plain,
% 3.08/2.26 (n0(b, a) <=> n0(b, a)),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(184,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 3.08/2.26 tff(185,plain,
% 3.08/2.26 (n0(b, a)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[184, 183])).
% 3.08/2.26 tff(186,plain,
% 3.08/2.26 (((~![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(187,plain,
% 3.08/2.26 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(188,plain,
% 3.08/2.26 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[187, 186])).
% 3.08/2.26 tff(189,plain,
% 3.08/2.26 (l1(a, a)),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[188, 185, 182])).
% 3.08/2.26 tff(190,plain,
% 3.08/2.26 (^[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)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(191,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[190])).
% 3.08/2.26 tff(192,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(193,plain,
% 3.08/2.26 (^[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))))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(194,plain,
% 3.08/2.26 (![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))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[193])).
% 3.08/2.26 tff(195,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')).
% 3.08/2.26 tff(196,plain,
% 3.08/2.26 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[195, 194])).
% 3.08/2.26 tff(197,plain,
% 3.08/2.26 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[196, 192])).
% 3.08/2.26 tff(198,plain,(
% 3.08/2.26 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 3.08/2.26 inference(skolemize,[status(sab)],[197])).
% 3.08/2.26 tff(199,plain,
% 3.08/2.26 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[198, 191])).
% 3.08/2.26 tff(200,plain,
% 3.08/2.26 (((~![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)))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(201,plain,
% 3.08/2.26 (((~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)))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(202,plain,
% 3.08/2.26 (((~![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))))),
% 3.08/2.26 inference(monotonicity,[status(thm)],[201])).
% 3.08/2.26 tff(203,plain,
% 3.08/2.26 (((~![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)))),
% 3.08/2.26 inference(transitivity,[status(thm)],[202, 200])).
% 3.08/2.26 tff(204,plain,
% 3.08/2.26 ((~![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))),
% 3.08/2.26 inference(quant_inst,[status(thm)],[])).
% 3.08/2.26 tff(205,plain,
% 3.08/2.26 ((~![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))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[204, 203])).
% 3.08/2.26 tff(206,plain,
% 3.08/2.26 (n1(a, b, b)),
% 3.08/2.26 inference(unit_resolution,[status(thm)],[205, 117, 199, 189, 172])).
% 3.08/2.26 tff(207,plain,
% 3.08/2.26 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(208,plain,
% 3.08/2.26 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[207])).
% 3.08/2.26 tff(209,plain,
% 3.08/2.26 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(210,plain,
% 3.08/2.26 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 3.08/2.26 inference(bind,[status(th)],[])).
% 3.08/2.26 tff(211,plain,
% 3.08/2.26 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 3.08/2.26 inference(quant_intro,[status(thm)],[210])).
% 3.08/2.26 tff(212,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 3.08/2.26 tff(213,plain,
% 3.08/2.26 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[212, 211])).
% 3.08/2.26 tff(214,plain,
% 3.08/2.26 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[213, 209])).
% 3.08/2.26 tff(215,plain,(
% 3.08/2.26 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 3.08/2.26 inference(skolemize,[status(sab)],[214])).
% 3.08/2.26 tff(216,plain,
% 3.08/2.26 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[215, 208])).
% 3.08/2.26 tff(217,plain,
% 3.08/2.26 (p0(c, b) <=> p0(c, b)),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(218,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 3.08/2.26 tff(219,plain,
% 3.08/2.26 (p0(c, b)),
% 3.08/2.26 inference(modus_ponens,[status(thm)],[218, 217])).
% 3.08/2.26 tff(220,plain,
% 3.08/2.26 (((~![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))),
% 3.08/2.26 inference(rewrite,[status(thm)],[])).
% 3.08/2.26 tff(221,plain,
% 3.08/2.26 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(222,plain,
% 3.08/2.27 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[221, 220])).
% 3.08/2.27 tff(223,plain,
% 3.08/2.27 (p1(b, b, b)),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[222, 219, 216])).
% 3.08/2.27 tff(224,plain,
% 3.08/2.27 (((~![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)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(225,plain,
% 3.08/2.27 (((~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)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(226,plain,
% 3.08/2.27 (((~![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))))),
% 3.08/2.27 inference(monotonicity,[status(thm)],[225])).
% 3.08/2.27 tff(227,plain,
% 3.08/2.27 (((~![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)))),
% 3.08/2.27 inference(transitivity,[status(thm)],[226, 224])).
% 3.08/2.27 tff(228,plain,
% 3.08/2.27 ((~![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))),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(229,plain,
% 3.08/2.27 ((~![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))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[228, 227])).
% 3.08/2.27 tff(230,plain,
% 3.08/2.27 (q2(b, a, b)),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[229, 131, 223, 206, 157])).
% 3.08/2.27 tff(231,plain,
% 3.08/2.27 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(232,plain,
% 3.08/2.27 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[231])).
% 3.08/2.27 tff(233,plain,
% 3.08/2.27 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(234,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 3.08/2.27 tff(235,plain,
% 3.08/2.27 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[234, 233])).
% 3.08/2.27 tff(236,plain,(
% 3.08/2.27 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 3.08/2.27 inference(skolemize,[status(sab)],[235])).
% 3.08/2.27 tff(237,plain,
% 3.08/2.27 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[236, 232])).
% 3.08/2.27 tff(238,plain,
% 3.08/2.27 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(239,plain,
% 3.08/2.27 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(240,plain,
% 3.08/2.27 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[239, 238])).
% 3.08/2.27 tff(241,plain,
% 3.08/2.27 (s1(b)),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[240, 237, 168])).
% 3.08/2.27 tff(242,plain,
% 3.08/2.27 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(243,plain,
% 3.08/2.27 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[242])).
% 3.08/2.27 tff(244,plain,
% 3.08/2.27 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(245,plain,
% 3.08/2.27 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(246,plain,
% 3.08/2.27 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[245])).
% 3.08/2.27 tff(247,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 3.08/2.27 tff(248,plain,
% 3.08/2.27 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[247, 246])).
% 3.08/2.27 tff(249,plain,
% 3.08/2.27 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[248, 244])).
% 3.08/2.27 tff(250,plain,(
% 3.08/2.27 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 3.08/2.27 inference(skolemize,[status(sab)],[249])).
% 3.08/2.27 tff(251,plain,
% 3.08/2.27 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[250, 243])).
% 3.08/2.27 tff(252,plain,
% 3.08/2.27 (((~![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)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(253,plain,
% 3.08/2.27 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(254,plain,
% 3.08/2.27 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[253, 252])).
% 3.08/2.27 tff(255,plain,
% 3.08/2.27 (s2(a)),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[254, 251, 241, 230])).
% 3.08/2.27 tff(256,plain,
% 3.08/2.27 (^[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)))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(257,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[256])).
% 3.08/2.27 tff(258,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(259,plain,
% 3.08/2.27 (^[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))))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(260,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[259])).
% 3.08/2.27 tff(261,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')).
% 3.08/2.27 tff(262,plain,
% 3.08/2.27 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[261, 260])).
% 3.08/2.27 tff(263,plain,
% 3.08/2.27 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[262, 258])).
% 3.08/2.27 tff(264,plain,(
% 3.08/2.27 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 3.08/2.27 inference(skolemize,[status(sab)],[263])).
% 3.08/2.27 tff(265,plain,
% 3.08/2.27 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[264, 257])).
% 3.08/2.27 tff(266,plain,
% 3.08/2.27 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(d, d, b)) | (~q2(d, a, d)) | s3(a, b))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(d, d, b)) | (~q2(d, a, d)) | s3(a, b))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(267,plain,
% 3.08/2.27 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(d, d, b)) | (~q2(d, a, d)) | s3(a, b))),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(268,plain,
% 3.08/2.27 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(d, d, b)) | (~q2(d, a, d)) | s3(a, b)),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[267, 266])).
% 3.08/2.27 tff(269,plain,
% 3.08/2.27 (s3(a, b)),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[268, 265, 255, 140, 9])).
% 3.08/2.27 tff(270,assumption,(~m0(b, d, d)), introduced(assumption)).
% 3.08/2.27 tff(271,plain,
% 3.08/2.27 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, d)),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(272,plain,
% 3.08/2.27 ($false),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[271, 7, 270])).
% 3.08/2.27 tff(273,plain,(m0(b, d, d)), inference(lemma,lemma(discharge,[]))).
% 3.08/2.27 tff(274,plain,
% 3.08/2.27 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(275,plain,
% 3.08/2.27 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[274])).
% 3.08/2.27 tff(276,plain,
% 3.08/2.27 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(277,plain,
% 3.08/2.27 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(278,plain,
% 3.08/2.27 (![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[277])).
% 3.08/2.27 tff(279,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 3.08/2.27 tff(280,plain,
% 3.08/2.27 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[279, 278])).
% 3.08/2.27 tff(281,plain,
% 3.08/2.27 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[280, 276])).
% 3.08/2.27 tff(282,plain,(
% 3.08/2.27 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 3.08/2.27 inference(skolemize,[status(sab)],[281])).
% 3.08/2.27 tff(283,plain,
% 3.08/2.27 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[282, 275])).
% 3.08/2.27 tff(284,plain,
% 3.08/2.27 (q0(d, d) <=> q0(d, d)),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(285,axiom,(q0(d, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 3.08/2.27 tff(286,plain,
% 3.08/2.27 (q0(d, d)),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[285, 284])).
% 3.08/2.27 tff(287,plain,
% 3.08/2.27 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(288,plain,
% 3.08/2.27 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(289,plain,
% 3.08/2.27 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d)),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[288, 287])).
% 3.08/2.27 tff(290,plain,
% 3.08/2.27 (s1(d)),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[289, 286, 283, 241])).
% 3.08/2.27 tff(291,plain,
% 3.08/2.27 (^[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)))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(292,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[291])).
% 3.08/2.27 tff(293,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(294,plain,
% 3.08/2.27 (^[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))))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(295,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[294])).
% 3.08/2.27 tff(296,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')).
% 3.08/2.27 tff(297,plain,
% 3.08/2.27 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[296, 295])).
% 3.08/2.27 tff(298,plain,
% 3.08/2.27 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[297, 293])).
% 3.08/2.27 tff(299,plain,(
% 3.08/2.27 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 3.08/2.27 inference(skolemize,[status(sab)],[298])).
% 3.08/2.27 tff(300,plain,
% 3.08/2.27 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[299, 292])).
% 3.08/2.27 tff(301,plain,
% 3.08/2.27 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(302,plain,
% 3.08/2.27 (((~p0(b, b)) | (~m0(b, d, d)) | (~s1(d)) | l2(d, d)) <=> ((~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(303,plain,
% 3.08/2.27 (((~![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, d, d)) | (~s1(d)) | l2(d, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d))))),
% 3.08/2.27 inference(monotonicity,[status(thm)],[302])).
% 3.08/2.27 tff(304,plain,
% 3.08/2.27 (((~![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, d, d)) | (~s1(d)) | l2(d, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))),
% 3.08/2.27 inference(transitivity,[status(thm)],[303, 301])).
% 3.08/2.27 tff(305,plain,
% 3.08/2.27 ((~![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, d, d)) | (~s1(d)) | l2(d, d))),
% 3.08/2.27 inference(quant_inst,[status(thm)],[])).
% 3.08/2.27 tff(306,plain,
% 3.08/2.27 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[305, 304])).
% 3.08/2.27 tff(307,plain,
% 3.08/2.27 (l2(d, d)),
% 3.08/2.27 inference(unit_resolution,[status(thm)],[306, 300, 290, 168, 273])).
% 3.08/2.27 tff(308,plain,
% 3.08/2.27 (^[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)))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(309,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[308])).
% 3.08/2.27 tff(310,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(rewrite,[status(thm)],[])).
% 3.08/2.27 tff(311,plain,
% 3.08/2.27 (^[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))))),
% 3.08/2.27 inference(bind,[status(th)],[])).
% 3.08/2.27 tff(312,plain,
% 3.08/2.27 (![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))),
% 3.08/2.27 inference(quant_intro,[status(thm)],[311])).
% 3.08/2.27 tff(313,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')).
% 3.08/2.27 tff(314,plain,
% 3.08/2.27 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[313, 312])).
% 3.08/2.27 tff(315,plain,
% 3.08/2.27 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[314, 310])).
% 3.08/2.27 tff(316,plain,(
% 3.08/2.27 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 3.08/2.27 inference(skolemize,[status(sab)],[315])).
% 3.08/2.27 tff(317,plain,
% 3.08/2.27 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 3.08/2.27 inference(modus_ponens,[status(thm)],[316, 309])).
% 3.08/2.28 tff(318,plain,
% 3.08/2.28 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(d, d)) | (~s3(a, b)) | m4(b, d))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(d, d)) | (~s3(a, b)) | m4(b, d))),
% 3.08/2.28 inference(rewrite,[status(thm)],[])).
% 3.08/2.28 tff(319,plain,
% 3.08/2.28 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(d, d)) | (~s3(a, b)) | m4(b, d))),
% 3.08/2.28 inference(quant_inst,[status(thm)],[])).
% 3.08/2.28 tff(320,plain,
% 3.08/2.28 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(d, d)) | (~s3(a, b)) | m4(b, d)),
% 3.08/2.28 inference(modus_ponens,[status(thm)],[319, 318])).
% 3.08/2.28 tff(321,plain,
% 3.08/2.28 (m4(b, d)),
% 3.08/2.28 inference(unit_resolution,[status(thm)],[320, 317, 307, 269])).
% 3.08/2.28 tff(322,plain,
% 3.08/2.28 (^[X: $i] : refl((~m4(b, X)) <=> (~m4(b, X)))),
% 3.08/2.28 inference(bind,[status(th)],[])).
% 3.08/2.28 tff(323,plain,
% 3.08/2.28 (![X: $i] : (~m4(b, X)) <=> ![X: $i] : (~m4(b, X))),
% 3.08/2.28 inference(quant_intro,[status(thm)],[322])).
% 3.08/2.28 tff(324,plain,
% 3.08/2.28 (![X: $i] : (~m4(b, X)) <=> ![X: $i] : (~m4(b, X))),
% 3.08/2.28 inference(rewrite,[status(thm)],[])).
% 3.08/2.28 tff(325,axiom,(![X: $i] : (~m4(b, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 3.08/2.28 tff(326,plain,
% 3.08/2.28 (![X: $i] : (~m4(b, X))),
% 3.08/2.28 inference(modus_ponens,[status(thm)],[325, 324])).
% 3.08/2.28 tff(327,plain,(
% 3.08/2.28 ![X: $i] : (~m4(b, X))),
% 3.08/2.28 inference(skolemize,[status(sab)],[326])).
% 3.08/2.28 tff(328,plain,
% 3.08/2.28 (![X: $i] : (~m4(b, X))),
% 3.08/2.28 inference(modus_ponens,[status(thm)],[327, 323])).
% 3.08/2.28 tff(329,plain,
% 3.08/2.28 ((~![X: $i] : (~m4(b, X))) | (~m4(b, d))),
% 3.08/2.28 inference(quant_inst,[status(thm)],[])).
% 3.08/2.28 tff(330,plain,
% 3.08/2.28 ($false),
% 3.08/2.28 inference(unit_resolution,[status(thm)],[329, 328, 321])).
% 3.08/2.28 % SZS output end Proof
%------------------------------------------------------------------------------