TSTP Solution File: SYN253-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN253-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 0.86s 0.84s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN253-1 : 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 : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:18:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.86/0.84 % SZS status Unsatisfiable
% 0.86/0.84 % SZS output start Proof
% 0.86/0.84 tff(m4_type, type, (
% 0.86/0.84 m4: ( $i * $i ) > $o)).
% 0.86/0.84 tff(e_type, type, (
% 0.86/0.84 e: $i)).
% 0.86/0.84 tff(s3_type, type, (
% 0.86/0.84 s3: ( $i * $i ) > $o)).
% 0.86/0.84 tff(a_type, type, (
% 0.86/0.84 a: $i)).
% 0.86/0.84 tff(q2_type, type, (
% 0.86/0.84 q2: ( $i * $i * $i ) > $o)).
% 0.86/0.84 tff(p1_type, type, (
% 0.86/0.84 p1: ( $i * $i * $i ) > $o)).
% 0.86/0.84 tff(k0_type, type, (
% 0.86/0.84 k0: $i > $o)).
% 0.86/0.84 tff(l0_type, type, (
% 0.86/0.84 l0: $i > $o)).
% 0.86/0.84 tff(n1_type, type, (
% 0.86/0.84 n1: ( $i * $i * $i ) > $o)).
% 0.86/0.84 tff(k1_type, type, (
% 0.86/0.84 k1: $i > $o)).
% 0.86/0.84 tff(n0_type, type, (
% 0.86/0.84 n0: ( $i * $i ) > $o)).
% 0.86/0.84 tff(b_type, type, (
% 0.86/0.84 b: $i)).
% 0.86/0.84 tff(m0_type, type, (
% 0.86/0.84 m0: ( $i * $i * $i ) > $o)).
% 0.86/0.84 tff(r0_type, type, (
% 0.86/0.84 r0: $i > $o)).
% 0.86/0.84 tff(s2_type, type, (
% 0.86/0.84 s2: $i > $o)).
% 0.86/0.84 tff(p0_type, type, (
% 0.86/0.84 p0: ( $i * $i ) > $o)).
% 0.86/0.84 tff(s0_type, type, (
% 0.86/0.84 s0: $i > $o)).
% 0.86/0.84 tff(l1_type, type, (
% 0.86/0.84 l1: ( $i * $i ) > $o)).
% 0.86/0.84 tff(c_type, type, (
% 0.86/0.84 c: $i)).
% 0.86/0.84 tff(s1_type, type, (
% 0.86/0.84 s1: $i > $o)).
% 0.86/0.84 tff(d_type, type, (
% 0.86/0.84 d: $i)).
% 0.86/0.84 tff(l2_type, type, (
% 0.86/0.84 l2: ( $i * $i ) > $o)).
% 0.86/0.84 tff(1,assumption,(~s3(a, e)), introduced(assumption)).
% 0.86/0.84 tff(2,assumption,(~q2(a, e, e)), introduced(assumption)).
% 0.86/0.84 tff(3,plain,
% 0.86/0.84 (^[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)))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(4,plain,
% 0.86/0.84 (![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))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[3])).
% 0.86/0.84 tff(5,plain,
% 0.86/0.84 (![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))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(6,plain,
% 0.86/0.84 (^[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))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(7,plain,
% 0.86/0.84 (![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))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[6])).
% 0.86/0.84 tff(8,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')).
% 0.86/0.84 tff(9,plain,
% 0.86/0.84 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.86/0.84 tff(10,plain,
% 0.86/0.84 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.86/0.84 tff(11,plain,(
% 0.86/0.84 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.86/0.84 inference(skolemize,[status(sab)],[10])).
% 0.86/0.84 tff(12,plain,
% 0.86/0.84 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.86/0.84 tff(13,plain,
% 0.86/0.84 (p1(a, a, a) <=> p1(a, a, a)),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(14,plain,
% 0.86/0.84 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(15,plain,
% 0.86/0.84 ((~$true) <=> $false),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(16,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.86/0.84 tff(17,plain,
% 0.86/0.84 (l0(a) <=> $true),
% 0.86/0.84 inference(iff_true,[status(thm)],[16])).
% 0.86/0.84 tff(18,plain,
% 0.86/0.84 ((~l0(a)) <=> (~$true)),
% 0.86/0.84 inference(monotonicity,[status(thm)],[17])).
% 0.86/0.84 tff(19,plain,
% 0.86/0.84 ((~l0(a)) <=> $false),
% 0.86/0.84 inference(transitivity,[status(thm)],[18, 15])).
% 0.86/0.84 tff(20,plain,
% 0.86/0.84 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[19])).
% 0.86/0.84 tff(21,plain,
% 0.86/0.84 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 0.86/0.84 inference(transitivity,[status(thm)],[20, 14])).
% 0.86/0.84 tff(22,plain,
% 0.86/0.84 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(23,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.86/0.84 tff(24,plain,
% 0.86/0.84 ((~l0(a)) | p1(a, a, a)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.86/0.84 tff(25,plain,
% 0.86/0.84 (p1(a, a, a)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.86/0.84 tff(26,plain,
% 0.86/0.84 (p1(a, a, a)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.86/0.84 tff(27,plain,
% 0.86/0.84 (k0(e) <=> k0(e)),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(28,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.86/0.84 tff(29,plain,
% 0.86/0.84 (k0(e)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.86/0.84 tff(30,plain,
% 0.86/0.84 (((~![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))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(31,plain,
% 0.86/0.84 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(32,plain,
% 0.86/0.84 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.86/0.84 tff(33,plain,
% 0.86/0.84 ($false),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[32, 29, 26, 12, 2])).
% 0.86/0.84 tff(34,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.84 tff(35,plain,
% 0.86/0.84 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(36,plain,
% 0.86/0.84 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[35])).
% 0.86/0.84 tff(37,plain,
% 0.86/0.84 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(38,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.86/0.84 tff(39,plain,
% 0.86/0.84 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.86/0.84 tff(40,plain,(
% 0.86/0.84 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.86/0.84 inference(skolemize,[status(sab)],[39])).
% 0.86/0.84 tff(41,plain,
% 0.86/0.84 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.86/0.84 tff(42,plain,
% 0.86/0.84 (n0(b, a) <=> n0(b, a)),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(43,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.86/0.84 tff(44,plain,
% 0.86/0.84 (n0(b, a)),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.86/0.84 tff(45,plain,
% 0.86/0.84 (((~![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)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(46,plain,
% 0.86/0.84 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(47,plain,
% 0.86/0.84 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.86/0.84 tff(48,plain,
% 0.86/0.84 (k1(a)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 0.86/0.84 tff(49,plain,
% 0.86/0.84 (^[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)))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(50,plain,
% 0.86/0.84 (![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))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[49])).
% 0.86/0.84 tff(51,plain,
% 0.86/0.84 (![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))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(52,plain,
% 0.86/0.84 (^[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))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(53,plain,
% 0.86/0.84 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[52])).
% 0.86/0.85 tff(54,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 0.86/0.85 tff(55,plain,
% 0.86/0.85 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.86/0.85 tff(56,plain,
% 0.86/0.85 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.86/0.85 tff(57,plain,(
% 0.86/0.85 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.86/0.85 inference(skolemize,[status(sab)],[56])).
% 0.86/0.85 tff(58,plain,
% 0.86/0.85 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.86/0.85 tff(59,plain,
% 0.86/0.85 (m0(a, e, e) <=> m0(a, e, e)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(60,axiom,(m0(a, e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 0.86/0.85 tff(61,plain,
% 0.86/0.85 (m0(a, e, e)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.86/0.85 tff(62,plain,
% 0.86/0.85 (((~![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(63,plain,
% 0.86/0.85 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(64,plain,
% 0.86/0.85 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.86/0.85 tff(65,plain,
% 0.86/0.85 ((~k1(a)) | n1(a, e, e)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[64, 61, 58])).
% 0.86/0.85 tff(66,plain,
% 0.86/0.85 (n1(a, e, e)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[65, 48])).
% 0.86/0.85 tff(67,plain,
% 0.86/0.85 (^[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)))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(68,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[67])).
% 0.86/0.85 tff(69,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(70,plain,
% 0.86/0.85 (^[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))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(71,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[70])).
% 0.86/0.85 tff(72,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')).
% 0.86/0.85 tff(73,plain,
% 0.86/0.85 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.86/0.85 tff(74,plain,
% 0.86/0.85 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.86/0.85 tff(75,plain,(
% 0.86/0.85 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.86/0.85 inference(skolemize,[status(sab)],[74])).
% 0.86/0.85 tff(76,plain,
% 0.86/0.85 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.86/0.85 tff(77,plain,
% 0.86/0.85 (p1(e, e, e) <=> p1(e, e, e)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(78,plain,
% 0.86/0.85 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(79,plain,
% 0.86/0.85 (k0(e) <=> $true),
% 0.86/0.85 inference(iff_true,[status(thm)],[28])).
% 0.86/0.85 tff(80,plain,
% 0.86/0.85 ((~k0(e)) <=> (~$true)),
% 0.86/0.85 inference(monotonicity,[status(thm)],[79])).
% 0.86/0.85 tff(81,plain,
% 0.86/0.85 ((~k0(e)) <=> $false),
% 0.86/0.85 inference(transitivity,[status(thm)],[80, 15])).
% 0.86/0.85 tff(82,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.86/0.85 tff(83,plain,
% 0.86/0.85 (r0(e) <=> $true),
% 0.86/0.85 inference(iff_true,[status(thm)],[82])).
% 0.86/0.85 tff(84,plain,
% 0.86/0.85 ((~r0(e)) <=> (~$true)),
% 0.86/0.85 inference(monotonicity,[status(thm)],[83])).
% 0.86/0.85 tff(85,plain,
% 0.86/0.85 ((~r0(e)) <=> $false),
% 0.86/0.85 inference(transitivity,[status(thm)],[84, 15])).
% 0.86/0.85 tff(86,plain,
% 0.86/0.85 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[85, 81])).
% 0.86/0.85 tff(87,plain,
% 0.86/0.85 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 0.86/0.85 inference(transitivity,[status(thm)],[86, 78])).
% 0.86/0.85 tff(88,plain,
% 0.86/0.85 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(89,plain,
% 0.86/0.85 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(90,plain,
% 0.86/0.85 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(91,plain,
% 0.86/0.85 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[90])).
% 0.86/0.85 tff(92,plain,
% 0.86/0.85 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.86/0.85 inference(transitivity,[status(thm)],[91, 89])).
% 0.86/0.85 tff(93,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.86/0.85 tff(94,plain,
% 0.86/0.85 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.86/0.85 tff(95,plain,
% 0.86/0.85 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[94, 88])).
% 0.86/0.85 tff(96,plain,
% 0.86/0.85 (p1(e, e, e)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[95, 87])).
% 0.86/0.85 tff(97,plain,
% 0.86/0.85 (p1(e, e, e)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[96, 77])).
% 0.86/0.85 tff(98,plain,
% 0.86/0.85 (((~![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(99,plain,
% 0.86/0.85 (((~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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(100,plain,
% 0.86/0.85 (((~![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)))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[99])).
% 0.86/0.85 tff(101,plain,
% 0.86/0.85 (((~![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))),
% 0.86/0.85 inference(transitivity,[status(thm)],[100, 98])).
% 0.86/0.85 tff(102,plain,
% 0.86/0.85 ((~![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))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(103,plain,
% 0.86/0.85 ((~![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)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.86/0.85 tff(104,plain,
% 0.86/0.85 ((~q2(a, e, e)) | q2(e, a, e)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[103, 97, 76, 66])).
% 0.86/0.85 tff(105,plain,
% 0.86/0.85 (q2(e, a, e)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[104, 34])).
% 0.86/0.85 tff(106,plain,
% 0.86/0.85 (k0(b) <=> k0(b)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(107,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.86/0.85 tff(108,plain,
% 0.86/0.85 (k0(b)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.86/0.85 tff(109,plain,
% 0.86/0.85 (((~![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(110,plain,
% 0.86/0.85 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(111,plain,
% 0.86/0.85 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.86/0.85 tff(112,plain,
% 0.86/0.85 (q2(a, b, b)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[111, 108, 26, 12])).
% 0.86/0.85 tff(113,assumption,(~p0(b, b)), introduced(assumption)).
% 0.86/0.85 tff(114,plain,
% 0.86/0.85 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(115,plain,
% 0.86/0.85 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.86/0.85 inference(quant_intro,[status(thm)],[114])).
% 0.86/0.85 tff(116,plain,
% 0.86/0.85 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(117,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.86/0.85 tff(118,plain,
% 0.86/0.85 (![X: $i] : p0(b, X)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.86/0.85 tff(119,plain,(
% 0.86/0.85 ![X: $i] : p0(b, X)),
% 0.86/0.85 inference(skolemize,[status(sab)],[118])).
% 0.86/0.85 tff(120,plain,
% 0.86/0.85 (![X: $i] : p0(b, X)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.86/0.85 tff(121,plain,
% 0.86/0.85 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(122,plain,
% 0.86/0.85 ($false),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[121, 120, 113])).
% 0.86/0.85 tff(123,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.85 tff(124,plain,
% 0.86/0.85 (^[D: $i, E: $i] : refl(((~l0(D)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~p0(b, E)) | n1(D, E, D)))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(125,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[124])).
% 0.86/0.85 tff(126,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(127,plain,
% 0.86/0.85 (^[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))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(128,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[127])).
% 0.86/0.85 tff(129,plain,
% 0.86/0.85 (^[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))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(130,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[129])).
% 0.86/0.85 tff(131,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')).
% 0.86/0.85 tff(132,plain,
% 0.86/0.85 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.86/0.85 tff(133,plain,
% 0.86/0.85 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.86/0.85 tff(134,plain,
% 0.86/0.85 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.86/0.85 tff(135,plain,(
% 0.86/0.85 ![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 0.86/0.85 inference(skolemize,[status(sab)],[134])).
% 0.86/0.85 tff(136,plain,
% 0.86/0.85 (![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.86/0.85 tff(137,plain,
% 0.86/0.85 (l0(a) <=> l0(a)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(138,plain,
% 0.86/0.85 (l0(a)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[16, 137])).
% 0.86/0.85 tff(139,plain,
% 0.86/0.85 (((~![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(140,plain,
% 0.86/0.85 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~p0(b, b)) | n1(a, b, a))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(141,plain,
% 0.86/0.85 ((~![D: $i, E: $i] : ((~l0(D)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~p0(b, b)) | n1(a, b, a)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.86/0.85 tff(142,plain,
% 0.86/0.85 (n1(a, b, a)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[141, 138, 136, 123])).
% 0.86/0.85 tff(143,plain,
% 0.86/0.85 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(144,plain,
% 0.86/0.85 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[143])).
% 0.86/0.85 tff(145,plain,
% 0.86/0.85 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(146,plain,
% 0.86/0.85 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(147,plain,
% 0.86/0.85 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[146])).
% 0.86/0.85 tff(148,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.86/0.85 tff(149,plain,
% 0.86/0.85 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.86/0.85 tff(150,plain,
% 0.86/0.85 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.86/0.85 tff(151,plain,(
% 0.86/0.85 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.86/0.85 inference(skolemize,[status(sab)],[150])).
% 0.86/0.85 tff(152,plain,
% 0.86/0.85 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.86/0.85 tff(153,plain,
% 0.86/0.85 (((~![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(154,plain,
% 0.86/0.85 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(155,plain,
% 0.86/0.85 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.86/0.85 tff(156,plain,
% 0.86/0.85 (l1(a, a)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[155, 44, 152])).
% 0.86/0.85 tff(157,plain,
% 0.86/0.85 (^[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)))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(158,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[157])).
% 0.86/0.85 tff(159,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(160,plain,
% 0.86/0.85 (^[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))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(161,plain,
% 0.86/0.85 (![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))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[160])).
% 0.86/0.85 tff(162,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')).
% 0.86/0.85 tff(163,plain,
% 0.86/0.85 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.86/0.85 tff(164,plain,
% 0.86/0.85 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.86/0.85 tff(165,plain,(
% 0.86/0.85 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.86/0.85 inference(skolemize,[status(sab)],[164])).
% 0.86/0.85 tff(166,plain,
% 0.86/0.85 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.86/0.85 tff(167,plain,
% 0.86/0.85 (((~![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)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(168,plain,
% 0.86/0.85 (((~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)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(169,plain,
% 0.86/0.85 (((~![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))))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[168])).
% 0.86/0.85 tff(170,plain,
% 0.86/0.85 (((~![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)))),
% 0.86/0.85 inference(transitivity,[status(thm)],[169, 167])).
% 0.86/0.85 tff(171,plain,
% 0.86/0.85 ((~![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))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(172,plain,
% 0.86/0.85 ((~![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))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.86/0.85 tff(173,plain,
% 0.86/0.85 (n1(a, b, b)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[172, 138, 166, 156, 142])).
% 0.86/0.85 tff(174,plain,
% 0.86/0.85 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(175,plain,
% 0.86/0.85 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[174])).
% 0.86/0.85 tff(176,plain,
% 0.86/0.85 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(177,plain,
% 0.86/0.85 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(178,plain,
% 0.86/0.85 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[177])).
% 0.86/0.85 tff(179,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.86/0.85 tff(180,plain,
% 0.86/0.85 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.86/0.85 tff(181,plain,
% 0.86/0.85 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.86/0.85 tff(182,plain,(
% 0.86/0.85 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.86/0.85 inference(skolemize,[status(sab)],[181])).
% 0.86/0.85 tff(183,plain,
% 0.86/0.85 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.86/0.85 tff(184,plain,
% 0.86/0.85 (p0(c, b) <=> p0(c, b)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(185,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.86/0.85 tff(186,plain,
% 0.86/0.85 (p0(c, b)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.86/0.85 tff(187,plain,
% 0.86/0.85 (((~![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))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(188,plain,
% 0.86/0.85 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(189,plain,
% 0.86/0.85 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.86/0.85 tff(190,plain,
% 0.86/0.85 (p1(b, b, b)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[189, 186, 183])).
% 0.86/0.85 tff(191,plain,
% 0.86/0.85 (((~![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)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(192,plain,
% 0.86/0.85 (((~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)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(193,plain,
% 0.86/0.85 (((~![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))))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[192])).
% 0.86/0.85 tff(194,plain,
% 0.86/0.85 (((~![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)))),
% 0.86/0.85 inference(transitivity,[status(thm)],[193, 191])).
% 0.86/0.85 tff(195,plain,
% 0.86/0.85 ((~![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))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(196,plain,
% 0.86/0.85 ((~![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))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.86/0.85 tff(197,plain,
% 0.86/0.85 (q2(b, a, b)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[196, 76, 190, 173, 112])).
% 0.86/0.85 tff(198,plain,
% 0.86/0.85 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(199,plain,
% 0.86/0.85 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[198])).
% 0.86/0.85 tff(200,plain,
% 0.86/0.85 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(201,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.86/0.85 tff(202,plain,
% 0.86/0.85 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.86/0.85 tff(203,plain,(
% 0.86/0.85 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.86/0.85 inference(skolemize,[status(sab)],[202])).
% 0.86/0.85 tff(204,plain,
% 0.86/0.85 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.86/0.85 tff(205,plain,
% 0.86/0.85 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(206,plain,
% 0.86/0.85 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.86/0.85 inference(quant_inst,[status(thm)],[])).
% 0.86/0.85 tff(207,plain,
% 0.86/0.85 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.86/0.85 tff(208,plain,
% 0.86/0.85 (s1(b)),
% 0.86/0.85 inference(unit_resolution,[status(thm)],[207, 204, 123])).
% 0.86/0.85 tff(209,plain,
% 0.86/0.85 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(210,plain,
% 0.86/0.85 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[209])).
% 0.86/0.85 tff(211,plain,
% 0.86/0.85 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(212,plain,
% 0.86/0.85 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(213,plain,
% 0.86/0.85 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[212])).
% 0.86/0.85 tff(214,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.86/0.85 tff(215,plain,
% 0.86/0.85 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.86/0.85 tff(216,plain,
% 0.86/0.85 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.86/0.85 tff(217,plain,(
% 0.86/0.85 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.86/0.85 inference(skolemize,[status(sab)],[216])).
% 0.86/0.85 tff(218,plain,
% 0.86/0.85 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.86/0.85 inference(modus_ponens,[status(thm)],[217, 210])).
% 0.86/0.85 tff(219,plain,
% 0.86/0.85 (((~![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)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(220,plain,
% 0.86/0.86 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(221,plain,
% 0.86/0.86 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.86/0.86 tff(222,plain,
% 0.86/0.86 (s2(a)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[221, 218, 208, 197])).
% 0.86/0.86 tff(223,plain,
% 0.86/0.86 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 0.86/0.86 inference(bind,[status(th)],[])).
% 0.86/0.86 tff(224,plain,
% 0.86/0.86 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.86/0.86 inference(quant_intro,[status(thm)],[223])).
% 0.86/0.86 tff(225,plain,
% 0.86/0.86 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(226,plain,
% 0.86/0.86 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 0.86/0.86 inference(bind,[status(th)],[])).
% 0.86/0.86 tff(227,plain,
% 0.86/0.86 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.86/0.86 inference(quant_intro,[status(thm)],[226])).
% 0.86/0.86 tff(228,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')).
% 0.86/0.86 tff(229,plain,
% 0.86/0.86 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.86/0.86 tff(230,plain,
% 0.86/0.86 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.86/0.86 tff(231,plain,(
% 0.86/0.86 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.86/0.86 inference(skolemize,[status(sab)],[230])).
% 0.86/0.86 tff(232,plain,
% 0.86/0.86 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.86/0.86 tff(233,plain,
% 0.86/0.86 (m0(e, d, e) <=> m0(e, d, e)),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(234,axiom,(m0(e, d, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_8')).
% 0.86/0.86 tff(235,plain,
% 0.86/0.86 (m0(e, d, e)),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.86/0.86 tff(236,plain,
% 0.86/0.86 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(237,plain,
% 0.86/0.86 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(238,plain,
% 0.86/0.86 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e)),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.86/0.86 tff(239,plain,
% 0.86/0.86 ($false),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[238, 235, 232, 222, 105, 1])).
% 0.86/0.86 tff(240,plain,(s3(a, e)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.86 tff(241,assumption,(~m4(e, e)), introduced(assumption)).
% 0.86/0.86 tff(242,plain,
% 0.86/0.86 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 0.86/0.86 inference(bind,[status(th)],[])).
% 0.86/0.86 tff(243,plain,
% 0.86/0.86 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.86/0.86 inference(quant_intro,[status(thm)],[242])).
% 0.86/0.86 tff(244,plain,
% 0.86/0.86 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(245,plain,
% 0.86/0.86 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 0.86/0.86 inference(bind,[status(th)],[])).
% 0.86/0.86 tff(246,plain,
% 0.86/0.86 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.86/0.86 inference(quant_intro,[status(thm)],[245])).
% 0.86/0.86 tff(247,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')).
% 0.86/0.86 tff(248,plain,
% 0.86/0.86 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.86/0.86 tff(249,plain,
% 0.86/0.86 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.86/0.86 tff(250,plain,(
% 0.86/0.86 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.86/0.86 inference(skolemize,[status(sab)],[249])).
% 0.86/0.86 tff(251,plain,
% 0.86/0.86 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.86/0.86 tff(252,plain,
% 0.86/0.86 (m0(b, b, e) <=> m0(b, b, e)),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(253,axiom,(m0(b, b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.86/0.86 tff(254,plain,
% 0.86/0.86 (m0(b, b, e)),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.86/0.86 tff(255,plain,
% 0.86/0.86 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(256,plain,
% 0.86/0.86 (((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e)) <=> ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(257,plain,
% 0.86/0.86 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))))),
% 0.86/0.86 inference(monotonicity,[status(thm)],[256])).
% 0.86/0.86 tff(258,plain,
% 0.86/0.86 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.86/0.86 inference(transitivity,[status(thm)],[257, 255])).
% 0.86/0.86 tff(259,plain,
% 0.86/0.86 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(260,plain,
% 0.86/0.86 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.86/0.86 tff(261,plain,
% 0.86/0.86 ((~s1(b)) | l2(e, e)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[260, 254, 251, 123])).
% 0.86/0.86 tff(262,plain,
% 0.86/0.86 (l2(e, e)),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[261, 208])).
% 0.86/0.86 tff(263,plain,
% 0.86/0.86 (^[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)))),
% 0.86/0.86 inference(bind,[status(th)],[])).
% 0.86/0.86 tff(264,plain,
% 0.86/0.86 (![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))),
% 0.86/0.86 inference(quant_intro,[status(thm)],[263])).
% 0.86/0.86 tff(265,plain,
% 0.86/0.86 (![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))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(266,plain,
% 0.86/0.86 (^[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))))),
% 0.86/0.86 inference(bind,[status(th)],[])).
% 0.86/0.86 tff(267,plain,
% 0.86/0.86 (![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))),
% 0.86/0.86 inference(quant_intro,[status(thm)],[266])).
% 0.86/0.86 tff(268,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')).
% 0.86/0.86 tff(269,plain,
% 0.86/0.86 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.86/0.86 tff(270,plain,
% 0.86/0.86 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.86/0.86 tff(271,plain,(
% 0.86/0.86 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.86/0.86 inference(skolemize,[status(sab)],[270])).
% 0.86/0.86 tff(272,plain,
% 0.86/0.86 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.86/0.86 tff(273,plain,
% 0.86/0.86 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(274,plain,
% 0.86/0.86 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 0.86/0.86 inference(quant_inst,[status(thm)],[])).
% 0.86/0.86 tff(275,plain,
% 0.86/0.86 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e)),
% 0.86/0.86 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.86/0.86 tff(276,plain,
% 0.86/0.86 ($false),
% 0.86/0.86 inference(unit_resolution,[status(thm)],[275, 272, 262, 241, 240])).
% 0.86/0.86 tff(277,plain,(m4(e, e)), inference(lemma,lemma(discharge,[]))).
% 0.86/0.86 tff(278,plain,
% 0.86/0.86 (^[X: $i] : refl((~m4(e, X)) <=> (~m4(e, X)))),
% 0.86/0.86 inference(bind,[status(th)],[])).
% 0.86/0.86 tff(279,plain,
% 0.86/0.86 (![X: $i] : (~m4(e, X)) <=> ![X: $i] : (~m4(e, X))),
% 0.86/0.86 inference(quant_intro,[status(thm)],[278])).
% 0.86/0.86 tff(280,plain,
% 0.86/0.86 (![X: $i] : (~m4(e, X)) <=> ![X: $i] : (~m4(e, X))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(281,axiom,(![X: $i] : (~m4(e, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.96/0.87 tff(282,plain,
% 0.96/0.87 (![X: $i] : (~m4(e, X))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.96/0.87 tff(283,plain,(
% 0.96/0.87 ![X: $i] : (~m4(e, X))),
% 0.96/0.87 inference(skolemize,[status(sab)],[282])).
% 0.96/0.87 tff(284,plain,
% 0.96/0.87 (![X: $i] : (~m4(e, X))),
% 0.96/0.87 inference(modus_ponens,[status(thm)],[283, 279])).
% 0.96/0.87 tff(285,plain,
% 0.96/0.87 ((~![X: $i] : (~m4(e, X))) | (~m4(e, e))),
% 0.96/0.87 inference(quant_inst,[status(thm)],[])).
% 0.96/0.87 tff(286,plain,
% 0.96/0.87 ($false),
% 0.96/0.87 inference(unit_resolution,[status(thm)],[285, 284, 277])).
% 0.96/0.87 % SZS output end Proof
%------------------------------------------------------------------------------