TSTP Solution File: SYN252-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN252-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:54:23 EDT 2022
% Result : Unsatisfiable 2.02s 1.53s
% Output : Proof 2.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN252-1 : TPTP v8.1.0. Released v1.1.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 02:38:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 2.02/1.53 % SZS status Unsatisfiable
% 2.02/1.53 % SZS output start Proof
% 2.02/1.53 tff(m4_type, type, (
% 2.02/1.53 m4: ( $i * $i ) > $o)).
% 2.02/1.53 tff(d_type, type, (
% 2.02/1.53 d: $i)).
% 2.02/1.53 tff(c_type, type, (
% 2.02/1.53 c: $i)).
% 2.02/1.53 tff(s3_type, type, (
% 2.02/1.53 s3: ( $i * $i ) > $o)).
% 2.02/1.53 tff(a_type, type, (
% 2.02/1.53 a: $i)).
% 2.02/1.53 tff(m0_type, type, (
% 2.02/1.53 m0: ( $i * $i * $i ) > $o)).
% 2.02/1.53 tff(e_type, type, (
% 2.02/1.53 e: $i)).
% 2.02/1.53 tff(q2_type, type, (
% 2.02/1.53 q2: ( $i * $i * $i ) > $o)).
% 2.02/1.53 tff(p1_type, type, (
% 2.02/1.53 p1: ( $i * $i * $i ) > $o)).
% 2.02/1.53 tff(k0_type, type, (
% 2.02/1.53 k0: $i > $o)).
% 2.02/1.53 tff(l0_type, type, (
% 2.02/1.53 l0: $i > $o)).
% 2.02/1.53 tff(n1_type, type, (
% 2.02/1.53 n1: ( $i * $i * $i ) > $o)).
% 2.02/1.53 tff(k1_type, type, (
% 2.02/1.53 k1: $i > $o)).
% 2.02/1.53 tff(n0_type, type, (
% 2.02/1.53 n0: ( $i * $i ) > $o)).
% 2.02/1.53 tff(b_type, type, (
% 2.02/1.53 b: $i)).
% 2.02/1.53 tff(r0_type, type, (
% 2.02/1.53 r0: $i > $o)).
% 2.02/1.53 tff(s2_type, type, (
% 2.02/1.53 s2: $i > $o)).
% 2.02/1.53 tff(p0_type, type, (
% 2.02/1.53 p0: ( $i * $i ) > $o)).
% 2.02/1.53 tff(s0_type, type, (
% 2.02/1.53 s0: $i > $o)).
% 2.02/1.53 tff(l1_type, type, (
% 2.02/1.53 l1: ( $i * $i ) > $o)).
% 2.02/1.53 tff(s1_type, type, (
% 2.02/1.53 s1: $i > $o)).
% 2.02/1.53 tff(l2_type, type, (
% 2.02/1.53 l2: ( $i * $i ) > $o)).
% 2.02/1.53 tff(q0_type, type, (
% 2.02/1.53 q0: ( $i * $i ) > $o)).
% 2.02/1.53 tff(1,assumption,(~m0(e, d, c)), introduced(assumption)).
% 2.02/1.53 tff(2,plain,
% 2.02/1.53 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 2.02/1.53 inference(bind,[status(th)],[])).
% 2.02/1.53 tff(3,plain,
% 2.02/1.53 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 2.02/1.53 inference(quant_intro,[status(thm)],[2])).
% 2.02/1.53 tff(4,plain,
% 2.02/1.53 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 2.02/1.53 tff(6,plain,
% 2.02/1.53 (![Y: $i, X: $i] : m0(X, d, Y)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.02/1.53 tff(7,plain,(
% 2.02/1.53 ![Y: $i, X: $i] : m0(X, d, Y)),
% 2.02/1.53 inference(skolemize,[status(sab)],[6])).
% 2.02/1.53 tff(8,plain,
% 2.02/1.53 (![Y: $i, X: $i] : m0(X, d, Y)),
% 2.02/1.53 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.02/1.53 tff(9,plain,
% 2.02/1.53 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(e, d, c)),
% 2.02/1.53 inference(quant_inst,[status(thm)],[])).
% 2.02/1.53 tff(10,plain,
% 2.02/1.53 ($false),
% 2.02/1.53 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 2.02/1.53 tff(11,plain,(m0(e, d, c)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.53 tff(12,assumption,(~q2(a, e, e)), introduced(assumption)).
% 2.02/1.53 tff(13,plain,
% 2.02/1.53 (^[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)))),
% 2.02/1.53 inference(bind,[status(th)],[])).
% 2.02/1.53 tff(14,plain,
% 2.02/1.53 (![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))),
% 2.02/1.53 inference(quant_intro,[status(thm)],[13])).
% 2.02/1.53 tff(15,plain,
% 2.02/1.53 (![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))),
% 2.02/1.53 inference(rewrite,[status(thm)],[])).
% 2.02/1.53 tff(16,plain,
% 2.02/1.53 (^[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))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(17,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[16])).
% 2.02/1.54 tff(18,axiom,(![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_177')).
% 2.02/1.54 tff(19,plain,
% 2.02/1.54 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[18, 17])).
% 2.02/1.54 tff(20,plain,
% 2.02/1.54 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[19, 15])).
% 2.02/1.54 tff(21,plain,(
% 2.02/1.54 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 2.02/1.54 inference(skolemize,[status(sab)],[20])).
% 2.02/1.54 tff(22,plain,
% 2.02/1.54 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[21, 14])).
% 2.02/1.54 tff(23,plain,
% 2.02/1.54 (p1(a, a, a) <=> p1(a, a, a)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(24,plain,
% 2.02/1.54 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(25,plain,
% 2.02/1.54 ((~$true) <=> $false),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(26,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 2.02/1.54 tff(27,plain,
% 2.02/1.54 (l0(a) <=> $true),
% 2.02/1.54 inference(iff_true,[status(thm)],[26])).
% 2.02/1.54 tff(28,plain,
% 2.02/1.54 ((~l0(a)) <=> (~$true)),
% 2.02/1.54 inference(monotonicity,[status(thm)],[27])).
% 2.02/1.54 tff(29,plain,
% 2.02/1.54 ((~l0(a)) <=> $false),
% 2.02/1.54 inference(transitivity,[status(thm)],[28, 25])).
% 2.02/1.54 tff(30,plain,
% 2.02/1.54 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[29])).
% 2.02/1.54 tff(31,plain,
% 2.02/1.54 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 2.02/1.54 inference(transitivity,[status(thm)],[30, 24])).
% 2.02/1.54 tff(32,plain,
% 2.02/1.54 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(33,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 2.02/1.54 tff(34,plain,
% 2.02/1.54 ((~l0(a)) | p1(a, a, a)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[33, 32])).
% 2.02/1.54 tff(35,plain,
% 2.02/1.54 (p1(a, a, a)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[34, 31])).
% 2.02/1.54 tff(36,plain,
% 2.02/1.54 (p1(a, a, a)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[35, 23])).
% 2.02/1.54 tff(37,plain,
% 2.02/1.54 (k0(e) <=> k0(e)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(38,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 2.02/1.54 tff(39,plain,
% 2.02/1.54 (k0(e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[38, 37])).
% 2.02/1.54 tff(40,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(41,plain,
% 2.02/1.54 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(42,plain,
% 2.02/1.54 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[41, 40])).
% 2.02/1.54 tff(43,plain,
% 2.02/1.54 ($false),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[42, 39, 36, 22, 12])).
% 2.02/1.54 tff(44,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.54 tff(45,plain,
% 2.02/1.54 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(46,plain,
% 2.02/1.54 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[45])).
% 2.02/1.54 tff(47,plain,
% 2.02/1.54 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(48,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 2.02/1.54 tff(49,plain,
% 2.02/1.54 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[48, 47])).
% 2.02/1.54 tff(50,plain,(
% 2.02/1.54 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 2.02/1.54 inference(skolemize,[status(sab)],[49])).
% 2.02/1.54 tff(51,plain,
% 2.02/1.54 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[50, 46])).
% 2.02/1.54 tff(52,plain,
% 2.02/1.54 (n0(b, a) <=> n0(b, a)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(53,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 2.02/1.54 tff(54,plain,
% 2.02/1.54 (n0(b, a)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[53, 52])).
% 2.02/1.54 tff(55,plain,
% 2.02/1.54 (((~![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)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(56,plain,
% 2.02/1.54 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(57,plain,
% 2.02/1.54 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.02/1.54 tff(58,plain,
% 2.02/1.54 (k1(a)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[57, 54, 51])).
% 2.02/1.54 tff(59,plain,
% 2.02/1.54 (^[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)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(60,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[59])).
% 2.02/1.54 tff(61,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(62,plain,
% 2.02/1.54 (^[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))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(63,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[62])).
% 2.02/1.54 tff(64,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 2.02/1.54 tff(65,plain,
% 2.02/1.54 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[64, 63])).
% 2.02/1.54 tff(66,plain,
% 2.02/1.54 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[65, 61])).
% 2.02/1.54 tff(67,plain,(
% 2.02/1.54 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 2.02/1.54 inference(skolemize,[status(sab)],[66])).
% 2.02/1.54 tff(68,plain,
% 2.02/1.54 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[67, 60])).
% 2.02/1.54 tff(69,plain,
% 2.02/1.54 (m0(a, e, e) <=> m0(a, e, e)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(70,axiom,(m0(a, e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 2.02/1.54 tff(71,plain,
% 2.02/1.54 (m0(a, e, e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[70, 69])).
% 2.02/1.54 tff(72,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(73,plain,
% 2.02/1.54 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(74,plain,
% 2.02/1.54 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.02/1.54 tff(75,plain,
% 2.02/1.54 ((~k1(a)) | n1(a, e, e)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[74, 71, 68])).
% 2.02/1.54 tff(76,plain,
% 2.02/1.54 (n1(a, e, e)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[75, 58])).
% 2.02/1.54 tff(77,plain,
% 2.02/1.54 (^[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)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(78,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[77])).
% 2.02/1.54 tff(79,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(80,plain,
% 2.02/1.54 (^[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))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(81,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[80])).
% 2.02/1.54 tff(82,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/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_182')).
% 2.02/1.54 tff(83,plain,
% 2.02/1.54 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[82, 81])).
% 2.02/1.54 tff(84,plain,
% 2.02/1.54 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[83, 79])).
% 2.02/1.54 tff(85,plain,(
% 2.02/1.54 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 2.02/1.54 inference(skolemize,[status(sab)],[84])).
% 2.02/1.54 tff(86,plain,
% 2.02/1.54 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[85, 78])).
% 2.02/1.54 tff(87,plain,
% 2.02/1.54 (p1(e, e, e) <=> p1(e, e, e)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(88,plain,
% 2.02/1.54 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(89,plain,
% 2.02/1.54 (k0(e) <=> $true),
% 2.02/1.54 inference(iff_true,[status(thm)],[38])).
% 2.02/1.54 tff(90,plain,
% 2.02/1.54 ((~k0(e)) <=> (~$true)),
% 2.02/1.54 inference(monotonicity,[status(thm)],[89])).
% 2.02/1.54 tff(91,plain,
% 2.02/1.54 ((~k0(e)) <=> $false),
% 2.02/1.54 inference(transitivity,[status(thm)],[90, 25])).
% 2.02/1.54 tff(92,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 2.02/1.54 tff(93,plain,
% 2.02/1.54 (r0(e) <=> $true),
% 2.02/1.54 inference(iff_true,[status(thm)],[92])).
% 2.02/1.54 tff(94,plain,
% 2.02/1.54 ((~r0(e)) <=> (~$true)),
% 2.02/1.54 inference(monotonicity,[status(thm)],[93])).
% 2.02/1.54 tff(95,plain,
% 2.02/1.54 ((~r0(e)) <=> $false),
% 2.02/1.54 inference(transitivity,[status(thm)],[94, 25])).
% 2.02/1.54 tff(96,plain,
% 2.02/1.54 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[95, 91])).
% 2.02/1.54 tff(97,plain,
% 2.02/1.54 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 2.02/1.54 inference(transitivity,[status(thm)],[96, 88])).
% 2.02/1.54 tff(98,plain,
% 2.02/1.54 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(99,plain,
% 2.02/1.54 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(100,plain,
% 2.02/1.54 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(101,plain,
% 2.02/1.54 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[100])).
% 2.02/1.54 tff(102,plain,
% 2.02/1.54 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 2.02/1.54 inference(transitivity,[status(thm)],[101, 99])).
% 2.02/1.54 tff(103,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 2.02/1.54 tff(104,plain,
% 2.02/1.54 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.02/1.54 tff(105,plain,
% 2.02/1.54 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[104, 98])).
% 2.02/1.54 tff(106,plain,
% 2.02/1.54 (p1(e, e, e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[105, 97])).
% 2.02/1.54 tff(107,plain,
% 2.02/1.54 (p1(e, e, e)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[106, 87])).
% 2.02/1.54 tff(108,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(109,plain,
% 2.02/1.54 (((~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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(110,plain,
% 2.02/1.54 (((~![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)))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[109])).
% 2.02/1.54 tff(111,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(transitivity,[status(thm)],[110, 108])).
% 2.02/1.54 tff(112,plain,
% 2.02/1.54 ((~![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))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(113,plain,
% 2.02/1.54 ((~![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)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.02/1.54 tff(114,plain,
% 2.02/1.54 ((~q2(a, e, e)) | q2(e, a, e)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[113, 107, 86, 76])).
% 2.02/1.54 tff(115,plain,
% 2.02/1.54 (q2(e, a, e)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[114, 44])).
% 2.02/1.54 tff(116,plain,
% 2.02/1.54 (k0(b) <=> k0(b)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(117,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 2.02/1.54 tff(118,plain,
% 2.02/1.54 (k0(b)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[117, 116])).
% 2.02/1.54 tff(119,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(120,plain,
% 2.02/1.54 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(121,plain,
% 2.02/1.54 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[120, 119])).
% 2.02/1.54 tff(122,plain,
% 2.02/1.54 (q2(a, b, b)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[121, 118, 36, 22])).
% 2.02/1.54 tff(123,assumption,(~p0(b, b)), introduced(assumption)).
% 2.02/1.54 tff(124,plain,
% 2.02/1.54 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(125,plain,
% 2.02/1.54 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 2.02/1.54 inference(quant_intro,[status(thm)],[124])).
% 2.02/1.54 tff(126,plain,
% 2.02/1.54 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(127,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 2.02/1.54 tff(128,plain,
% 2.02/1.54 (![X: $i] : p0(b, X)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.02/1.54 tff(129,plain,(
% 2.02/1.54 ![X: $i] : p0(b, X)),
% 2.02/1.54 inference(skolemize,[status(sab)],[128])).
% 2.02/1.54 tff(130,plain,
% 2.02/1.54 (![X: $i] : p0(b, X)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[129, 125])).
% 2.02/1.54 tff(131,plain,
% 2.02/1.54 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(132,plain,
% 2.02/1.54 ($false),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[131, 130, 123])).
% 2.02/1.54 tff(133,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.54 tff(134,plain,
% 2.02/1.54 (^[D: $i, E: $i] : refl(((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(135,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[134])).
% 2.02/1.54 tff(136,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(137,plain,
% 2.02/1.54 (^[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))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(138,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[137])).
% 2.02/1.54 tff(139,plain,
% 2.02/1.54 (^[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))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(140,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[139])).
% 2.02/1.54 tff(141,axiom,(![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_050')).
% 2.02/1.54 tff(142,plain,
% 2.02/1.54 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[141, 140])).
% 2.02/1.54 tff(143,plain,
% 2.02/1.54 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[142, 138])).
% 2.02/1.54 tff(144,plain,
% 2.02/1.54 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[143, 136])).
% 2.02/1.54 tff(145,plain,(
% 2.02/1.54 ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 2.02/1.54 inference(skolemize,[status(sab)],[144])).
% 2.02/1.54 tff(146,plain,
% 2.02/1.54 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[145, 135])).
% 2.02/1.54 tff(147,plain,
% 2.02/1.54 (l0(a) <=> l0(a)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(148,plain,
% 2.02/1.54 (l0(a)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[26, 147])).
% 2.02/1.54 tff(149,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(150,plain,
% 2.02/1.54 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(151,plain,
% 2.02/1.54 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.02/1.54 tff(152,plain,
% 2.02/1.54 (n1(a, b, a)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[151, 148, 146, 133])).
% 2.02/1.54 tff(153,plain,
% 2.02/1.54 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(154,plain,
% 2.02/1.54 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[153])).
% 2.02/1.54 tff(155,plain,
% 2.02/1.54 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(156,plain,
% 2.02/1.54 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(157,plain,
% 2.02/1.54 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[156])).
% 2.02/1.54 tff(158,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 2.02/1.54 tff(159,plain,
% 2.02/1.54 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[158, 157])).
% 2.02/1.54 tff(160,plain,
% 2.02/1.54 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[159, 155])).
% 2.02/1.54 tff(161,plain,(
% 2.02/1.54 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 2.02/1.54 inference(skolemize,[status(sab)],[160])).
% 2.02/1.54 tff(162,plain,
% 2.02/1.54 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[161, 154])).
% 2.02/1.54 tff(163,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(164,plain,
% 2.02/1.54 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(165,plain,
% 2.02/1.54 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[164, 163])).
% 2.02/1.54 tff(166,plain,
% 2.02/1.54 (l1(a, a)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[165, 54, 162])).
% 2.02/1.54 tff(167,plain,
% 2.02/1.54 (^[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)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(168,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[167])).
% 2.02/1.54 tff(169,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(170,plain,
% 2.02/1.54 (^[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))))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(171,plain,
% 2.02/1.54 (![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))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[170])).
% 2.02/1.54 tff(172,axiom,(![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_054')).
% 2.02/1.54 tff(173,plain,
% 2.02/1.54 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[172, 171])).
% 2.02/1.54 tff(174,plain,
% 2.02/1.54 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[173, 169])).
% 2.02/1.54 tff(175,plain,(
% 2.02/1.54 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 2.02/1.54 inference(skolemize,[status(sab)],[174])).
% 2.02/1.54 tff(176,plain,
% 2.02/1.54 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[175, 168])).
% 2.02/1.54 tff(177,plain,
% 2.02/1.54 (((~![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)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(178,plain,
% 2.02/1.54 (((~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)))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(179,plain,
% 2.02/1.54 (((~![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))))),
% 2.02/1.54 inference(monotonicity,[status(thm)],[178])).
% 2.02/1.54 tff(180,plain,
% 2.02/1.54 (((~![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)))),
% 2.02/1.54 inference(transitivity,[status(thm)],[179, 177])).
% 2.02/1.54 tff(181,plain,
% 2.02/1.54 ((~![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))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.54 tff(182,plain,
% 2.02/1.54 ((~![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))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[181, 180])).
% 2.02/1.54 tff(183,plain,
% 2.02/1.54 (n1(a, b, b)),
% 2.02/1.54 inference(unit_resolution,[status(thm)],[182, 148, 176, 166, 152])).
% 2.02/1.54 tff(184,plain,
% 2.02/1.54 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(185,plain,
% 2.02/1.54 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[184])).
% 2.02/1.54 tff(186,plain,
% 2.02/1.54 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(187,plain,
% 2.02/1.54 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 2.02/1.54 inference(bind,[status(th)],[])).
% 2.02/1.54 tff(188,plain,
% 2.02/1.54 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 2.02/1.54 inference(quant_intro,[status(thm)],[187])).
% 2.02/1.54 tff(189,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 2.02/1.54 tff(190,plain,
% 2.02/1.54 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[189, 188])).
% 2.02/1.54 tff(191,plain,
% 2.02/1.54 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[190, 186])).
% 2.02/1.54 tff(192,plain,(
% 2.02/1.54 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 2.02/1.54 inference(skolemize,[status(sab)],[191])).
% 2.02/1.54 tff(193,plain,
% 2.02/1.54 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[192, 185])).
% 2.02/1.54 tff(194,plain,
% 2.02/1.54 (p0(c, b) <=> p0(c, b)),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(195,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 2.02/1.54 tff(196,plain,
% 2.02/1.54 (p0(c, b)),
% 2.02/1.54 inference(modus_ponens,[status(thm)],[195, 194])).
% 2.02/1.54 tff(197,plain,
% 2.02/1.54 (((~![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))),
% 2.02/1.54 inference(rewrite,[status(thm)],[])).
% 2.02/1.54 tff(198,plain,
% 2.02/1.54 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 2.02/1.54 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(199,plain,
% 2.02/1.55 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[198, 197])).
% 2.02/1.55 tff(200,plain,
% 2.02/1.55 (p1(b, b, b)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[199, 196, 193])).
% 2.02/1.55 tff(201,plain,
% 2.02/1.55 (((~![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)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(202,plain,
% 2.02/1.55 (((~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)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(203,plain,
% 2.02/1.55 (((~![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))))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[202])).
% 2.02/1.55 tff(204,plain,
% 2.02/1.55 (((~![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)))),
% 2.02/1.55 inference(transitivity,[status(thm)],[203, 201])).
% 2.02/1.55 tff(205,plain,
% 2.02/1.55 ((~![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))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(206,plain,
% 2.02/1.55 ((~![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))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.02/1.55 tff(207,plain,
% 2.02/1.55 (q2(b, a, b)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[206, 86, 200, 183, 122])).
% 2.02/1.55 tff(208,plain,
% 2.02/1.55 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(209,plain,
% 2.02/1.55 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[208])).
% 2.02/1.55 tff(210,plain,
% 2.02/1.55 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(211,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 2.02/1.55 tff(212,plain,
% 2.02/1.55 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[211, 210])).
% 2.02/1.55 tff(213,plain,(
% 2.02/1.55 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 2.02/1.55 inference(skolemize,[status(sab)],[212])).
% 2.02/1.55 tff(214,plain,
% 2.02/1.55 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[213, 209])).
% 2.02/1.55 tff(215,plain,
% 2.02/1.55 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(216,plain,
% 2.02/1.55 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(217,plain,
% 2.02/1.55 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[216, 215])).
% 2.02/1.55 tff(218,plain,
% 2.02/1.55 (s1(b)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[217, 214, 133])).
% 2.02/1.55 tff(219,plain,
% 2.02/1.55 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(220,plain,
% 2.02/1.55 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[219])).
% 2.02/1.55 tff(221,plain,
% 2.02/1.55 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(222,plain,
% 2.02/1.55 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(223,plain,
% 2.02/1.55 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[222])).
% 2.02/1.55 tff(224,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 2.02/1.55 tff(225,plain,
% 2.02/1.55 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[224, 223])).
% 2.02/1.55 tff(226,plain,
% 2.02/1.55 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[225, 221])).
% 2.02/1.55 tff(227,plain,(
% 2.02/1.55 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 2.02/1.55 inference(skolemize,[status(sab)],[226])).
% 2.02/1.55 tff(228,plain,
% 2.02/1.55 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[227, 220])).
% 2.02/1.55 tff(229,plain,
% 2.02/1.55 (((~![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)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(230,plain,
% 2.02/1.55 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(231,plain,
% 2.02/1.55 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[230, 229])).
% 2.02/1.55 tff(232,plain,
% 2.02/1.55 (s2(a)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[231, 228, 218, 207])).
% 2.02/1.55 tff(233,plain,
% 2.02/1.55 (^[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)))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(234,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[233])).
% 2.02/1.55 tff(235,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(236,plain,
% 2.02/1.55 (^[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))))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(237,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[236])).
% 2.02/1.55 tff(238,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 2.02/1.55 tff(239,plain,
% 2.02/1.55 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[238, 237])).
% 2.02/1.55 tff(240,plain,
% 2.02/1.55 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[239, 235])).
% 2.02/1.55 tff(241,plain,(
% 2.02/1.55 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 2.02/1.55 inference(skolemize,[status(sab)],[240])).
% 2.02/1.55 tff(242,plain,
% 2.02/1.55 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[241, 234])).
% 2.02/1.55 tff(243,plain,
% 2.02/1.55 (((~![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, c)) | (~q2(e, a, e)) | s3(a, c))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, c)) | (~q2(e, a, e)) | s3(a, c))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(244,plain,
% 2.02/1.55 ((~![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, c)) | (~q2(e, a, e)) | s3(a, c))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(245,plain,
% 2.02/1.55 ((~![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, c)) | (~q2(e, a, e)) | s3(a, c)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[244, 243])).
% 2.02/1.55 tff(246,plain,
% 2.02/1.55 (s3(a, c)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[245, 242, 232, 115, 11])).
% 2.02/1.55 tff(247,assumption,(~m0(b, d, d)), introduced(assumption)).
% 2.02/1.55 tff(248,plain,
% 2.02/1.55 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, d)),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(249,plain,
% 2.02/1.55 ($false),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[248, 8, 247])).
% 2.02/1.55 tff(250,plain,(m0(b, d, d)), inference(lemma,lemma(discharge,[]))).
% 2.02/1.55 tff(251,plain,
% 2.02/1.55 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(252,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[251])).
% 2.02/1.55 tff(253,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(254,plain,
% 2.02/1.55 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(255,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[254])).
% 2.02/1.55 tff(256,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 2.02/1.55 tff(257,plain,
% 2.02/1.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[256, 255])).
% 2.02/1.55 tff(258,plain,
% 2.02/1.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[257, 253])).
% 2.02/1.55 tff(259,plain,(
% 2.02/1.55 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 2.02/1.55 inference(skolemize,[status(sab)],[258])).
% 2.02/1.55 tff(260,plain,
% 2.02/1.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[259, 252])).
% 2.02/1.55 tff(261,plain,
% 2.02/1.55 (q0(d, d) <=> q0(d, d)),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(262,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 2.02/1.55 tff(263,plain,
% 2.02/1.55 (q0(d, d)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[262, 261])).
% 2.02/1.55 tff(264,plain,
% 2.02/1.55 (((~![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))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(265,plain,
% 2.02/1.55 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(266,plain,
% 2.02/1.55 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d)),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[265, 264])).
% 2.02/1.55 tff(267,plain,
% 2.02/1.55 (s1(d)),
% 2.02/1.55 inference(unit_resolution,[status(thm)],[266, 263, 260, 218])).
% 2.02/1.55 tff(268,plain,
% 2.02/1.55 (^[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)))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(269,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[268])).
% 2.02/1.55 tff(270,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(271,plain,
% 2.02/1.55 (^[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))))),
% 2.02/1.55 inference(bind,[status(th)],[])).
% 2.02/1.55 tff(272,plain,
% 2.02/1.55 (![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))),
% 2.02/1.55 inference(quant_intro,[status(thm)],[271])).
% 2.02/1.55 tff(273,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 2.02/1.55 tff(274,plain,
% 2.02/1.55 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[273, 272])).
% 2.02/1.55 tff(275,plain,
% 2.02/1.55 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[274, 270])).
% 2.02/1.55 tff(276,plain,(
% 2.02/1.55 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 2.02/1.55 inference(skolemize,[status(sab)],[275])).
% 2.02/1.55 tff(277,plain,
% 2.02/1.55 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 2.02/1.55 inference(modus_ponens,[status(thm)],[276, 269])).
% 2.02/1.55 tff(278,plain,
% 2.02/1.55 (((~![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)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(279,plain,
% 2.02/1.55 (((~p0(b, b)) | (~m0(b, d, d)) | (~s1(d)) | l2(d, d)) <=> ((~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))),
% 2.02/1.55 inference(rewrite,[status(thm)],[])).
% 2.02/1.55 tff(280,plain,
% 2.02/1.55 (((~![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))))),
% 2.02/1.55 inference(monotonicity,[status(thm)],[279])).
% 2.02/1.55 tff(281,plain,
% 2.02/1.55 (((~![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)))),
% 2.02/1.55 inference(transitivity,[status(thm)],[280, 278])).
% 2.02/1.55 tff(282,plain,
% 2.02/1.55 ((~![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))),
% 2.02/1.55 inference(quant_inst,[status(thm)],[])).
% 2.02/1.55 tff(283,plain,
% 2.02/1.55 ((~![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))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[282, 281])).
% 2.02/1.56 tff(284,plain,
% 2.02/1.56 (l2(d, d)),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[283, 277, 267, 133, 250])).
% 2.02/1.56 tff(285,plain,
% 2.02/1.56 (^[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)))),
% 2.02/1.56 inference(bind,[status(th)],[])).
% 2.02/1.56 tff(286,plain,
% 2.02/1.56 (![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))),
% 2.02/1.56 inference(quant_intro,[status(thm)],[285])).
% 2.02/1.56 tff(287,plain,
% 2.02/1.56 (![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))),
% 2.02/1.56 inference(rewrite,[status(thm)],[])).
% 2.02/1.56 tff(288,plain,
% 2.02/1.56 (^[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))))),
% 2.02/1.56 inference(bind,[status(th)],[])).
% 2.02/1.56 tff(289,plain,
% 2.02/1.56 (![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))),
% 2.02/1.56 inference(quant_intro,[status(thm)],[288])).
% 2.02/1.56 tff(290,axiom,(![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_279')).
% 2.02/1.56 tff(291,plain,
% 2.02/1.56 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[290, 289])).
% 2.02/1.56 tff(292,plain,
% 2.02/1.56 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[291, 287])).
% 2.02/1.56 tff(293,plain,(
% 2.02/1.56 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 2.02/1.56 inference(skolemize,[status(sab)],[292])).
% 2.02/1.56 tff(294,plain,
% 2.02/1.56 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[293, 286])).
% 2.02/1.56 tff(295,plain,
% 2.02/1.56 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(d, d)) | (~s3(a, c)) | m4(c, d))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(d, d)) | (~s3(a, c)) | m4(c, d))),
% 2.02/1.56 inference(rewrite,[status(thm)],[])).
% 2.02/1.56 tff(296,plain,
% 2.02/1.56 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(d, d)) | (~s3(a, c)) | m4(c, d))),
% 2.02/1.56 inference(quant_inst,[status(thm)],[])).
% 2.02/1.56 tff(297,plain,
% 2.02/1.56 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(d, d)) | (~s3(a, c)) | m4(c, d)),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[296, 295])).
% 2.02/1.56 tff(298,plain,
% 2.02/1.56 (m4(c, d)),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[297, 294, 284, 246])).
% 2.02/1.56 tff(299,plain,
% 2.02/1.56 (^[X: $i] : refl((~m4(X, d)) <=> (~m4(X, d)))),
% 2.02/1.56 inference(bind,[status(th)],[])).
% 2.02/1.56 tff(300,plain,
% 2.02/1.56 (![X: $i] : (~m4(X, d)) <=> ![X: $i] : (~m4(X, d))),
% 2.02/1.56 inference(quant_intro,[status(thm)],[299])).
% 2.02/1.56 tff(301,plain,
% 2.02/1.56 (![X: $i] : (~m4(X, d)) <=> ![X: $i] : (~m4(X, d))),
% 2.02/1.56 inference(rewrite,[status(thm)],[])).
% 2.02/1.56 tff(302,axiom,(![X: $i] : (~m4(X, d))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 2.02/1.56 tff(303,plain,
% 2.02/1.56 (![X: $i] : (~m4(X, d))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[302, 301])).
% 2.02/1.56 tff(304,plain,(
% 2.02/1.56 ![X: $i] : (~m4(X, d))),
% 2.02/1.56 inference(skolemize,[status(sab)],[303])).
% 2.02/1.56 tff(305,plain,
% 2.02/1.56 (![X: $i] : (~m4(X, d))),
% 2.02/1.56 inference(modus_ponens,[status(thm)],[304, 300])).
% 2.02/1.56 tff(306,plain,
% 2.02/1.56 ((~![X: $i] : (~m4(X, d))) | (~m4(c, d))),
% 2.02/1.56 inference(quant_inst,[status(thm)],[])).
% 2.02/1.56 tff(307,plain,
% 2.02/1.56 ($false),
% 2.02/1.56 inference(unit_resolution,[status(thm)],[306, 305, 298])).
% 2.02/1.56 % SZS output end Proof
%------------------------------------------------------------------------------