TSTP Solution File: SYN163-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN163-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 23:54:01 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN163-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n024.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Sep 5 02:03:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(n5_type, type, (
% 0.20/0.49 n5: ( $i * $i ) > $o)).
% 0.20/0.49 tff(a_type, type, (
% 0.20/0.49 a: $i)).
% 0.20/0.49 tff(q4_type, type, (
% 0.20/0.49 q4: ( $i * $i ) > $o)).
% 0.20/0.49 tff(m3_type, type, (
% 0.20/0.49 m3: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(p2_type, type, (
% 0.20/0.49 p2: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(m1_type, type, (
% 0.20/0.49 m1: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(l0_type, type, (
% 0.20/0.49 l0: $i > $o)).
% 0.20/0.49 tff(s0_type, type, (
% 0.20/0.49 s0: $i > $o)).
% 0.20/0.49 tff(d_type, type, (
% 0.20/0.49 d: $i)).
% 0.20/0.49 tff(q2_type, type, (
% 0.20/0.49 q2: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(p1_type, type, (
% 0.20/0.49 p1: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(k3_type, type, (
% 0.20/0.49 k3: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(r2_type, type, (
% 0.20/0.49 r2: $i > $o)).
% 0.20/0.49 tff(r1_type, type, (
% 0.20/0.49 r1: $i > $o)).
% 0.20/0.49 tff(q1_type, type, (
% 0.20/0.49 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(b_type, type, (
% 0.20/0.49 b: $i)).
% 0.20/0.49 tff(n0_type, type, (
% 0.20/0.49 n0: ( $i * $i ) > $o)).
% 0.20/0.49 tff(p0_type, type, (
% 0.20/0.49 p0: ( $i * $i ) > $o)).
% 0.20/0.49 tff(q0_type, type, (
% 0.20/0.49 q0: ( $i * $i ) > $o)).
% 0.20/0.49 tff(e_type, type, (
% 0.20/0.49 e: $i)).
% 0.20/0.49 tff(n2_type, type, (
% 0.20/0.49 n2: $i > $o)).
% 0.20/0.49 tff(k0_type, type, (
% 0.20/0.49 k0: $i > $o)).
% 0.20/0.49 tff(r0_type, type, (
% 0.20/0.49 r0: $i > $o)).
% 0.20/0.49 tff(l1_type, type, (
% 0.20/0.49 l1: ( $i * $i ) > $o)).
% 0.20/0.49 tff(m0_type, type, (
% 0.20/0.49 m0: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(c_type, type, (
% 0.20/0.49 c: $i)).
% 0.20/0.49 tff(m2_type, type, (
% 0.20/0.49 m2: $i > $o)).
% 0.20/0.49 tff(k1_type, type, (
% 0.20/0.49 k1: $i > $o)).
% 0.20/0.49 tff(p4_type, type, (
% 0.20/0.49 p4: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(n4_type, type, (
% 0.20/0.49 n4: ( $i * $i ) > $o)).
% 0.20/0.49 tff(k4_type, type, (
% 0.20/0.49 k4: $i > $o)).
% 0.20/0.49 tff(n3_type, type, (
% 0.20/0.49 n3: $i > $o)).
% 0.20/0.49 tff(q3_type, type, (
% 0.20/0.49 q3: ( $i * $i ) > $o)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(4,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.49 tff(6,plain,(
% 0.20/0.49 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[5])).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(11,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.49 tff(13,plain,(
% 0.20/0.49 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[12])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (m1(a, a, a) <=> m1(a, a, a)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 ((m1(a, a, a) | $false | $false) <=> m1(a, a, a)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 ((~$true) <=> $false),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(18,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (l0(a) <=> $true),
% 0.20/0.49 inference(iff_true,[status(thm)],[18])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 ((~l0(a)) <=> (~$true)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 ((~l0(a)) <=> $false),
% 0.20/0.49 inference(transitivity,[status(thm)],[20, 17])).
% 0.20/0.49 tff(22,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 (s0(d) <=> $true),
% 0.20/0.50 inference(iff_true,[status(thm)],[22])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 ((~s0(d)) <=> (~$true)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 ((~s0(d)) <=> $false),
% 0.20/0.50 inference(transitivity,[status(thm)],[24, 17])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | $false | $false)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[25, 21])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> m1(a, a, a)),
% 0.20/0.50 inference(transitivity,[status(thm)],[26, 16])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[31, 29])).
% 0.20/0.50 tff(33,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (m1(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[35, 27])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (m1(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[36, 15])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (p2(a, a, a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[40, 37, 14])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 ((m3(a, a, a) | (~p2(a, a, a))) <=> ((~p2(a, a, a)) | m3(a, a, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 0.20/0.50 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (m3(a, a, a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[47, 41, 7])).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(52,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.50 tff(54,plain,(
% 0.20/0.50 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[53])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (p1(a, a, a) <=> p1(a, a, a)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 0.20/0.50 inference(transitivity,[status(thm)],[58, 57])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(61,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 ((~l0(a)) | p1(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 (p1(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (p1(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 ((q2(a, a, a) | (~p1(a, a, a))) <=> ((~p1(a, a, a)) | q2(a, a, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.20/0.50 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (q2(a, a, a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[70, 64, 55])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((q4(B, C) | (~k3(D, D, B))) <=> ((~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> (((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))))), rewrite((((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> (((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))))), rewrite((((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 (![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.50 tff(77,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_295')).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.50 tff(80,plain,(
% 0.20/0.50 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.20/0.50 inference(skolemize,[status(sab)],[79])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.50 tff(87,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.50 tff(90,plain,(
% 0.20/0.50 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.50 inference(skolemize,[status(sab)],[89])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (p0(b, d) <=> p0(b, d)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(93,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (p0(b, d)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.50 tff(95,plain,
% 0.20/0.50 (n0(d, b) <=> n0(d, b)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(96,axiom,(n0(d, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 (n0(d, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 (q1(d, b, d)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[100, 97, 94, 91])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(d)), (s0(d) <=> $true)), ((~s0(d)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(d)) <=> $false)), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)))), rewrite(((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.50 tff(109,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.50 tff(111,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.50 tff(113,plain,(
% 0.20/0.50 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(skolemize,[status(sab)],[112])).
% 0.20/0.50 tff(114,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 (q0(a, b) <=> q0(a, b)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(116,axiom,(q0(a, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 (q0(a, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 (((~q0(a, b)) | (~q1(d, b, d)) | r1(a)) <=> (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(120,plain,
% 0.20/0.50 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (r1(a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[123, 117, 114, 101])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.50 tff(130,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.50 tff(133,plain,(
% 0.20/0.50 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.50 inference(skolemize,[status(sab)],[132])).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.50 tff(135,plain,
% 0.20/0.50 (l0(a) <=> l0(a)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(136,plain,
% 0.20/0.50 (l0(a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[18, 135])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(138,plain,
% 0.20/0.50 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 (r2(a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[139, 136, 134, 124])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(143,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 ((~r2(a)) | k3(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 ((~r2(a)) | k3(a, a, a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[144, 141])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 (k3(a, a, a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[145, 140])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(148,plain,
% 0.20/0.51 (((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a)) <=> ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(149,plain,
% 0.20/0.51 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.51 tff(150,plain,
% 0.20/0.51 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(transitivity,[status(thm)],[149, 147])).
% 0.20/0.51 tff(151,plain,
% 0.20/0.51 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(152,plain,
% 0.20/0.51 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 (q4(a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[152, 146, 81, 71, 48])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 (^[D: $i, C: $i] : refl((n5(C, C) | (~q4(D, C))) <=> (n5(C, C) | (~q4(D, C))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(157,axiom,(![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_313')).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.51 tff(159,plain,(
% 0.20/0.51 ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[158])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 (((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | (n5(a, a) | (~q4(a, a)))) <=> ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | n5(a, a) | (~q4(a, a)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | (n5(a, a) | (~q4(a, a)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | n5(a, a) | (~q4(a, a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 (n5(a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[163, 160, 153])).
% 0.20/0.51 tff(165,plain,
% 0.20/0.51 (^[B: $i, A: $i, C: $i] : refl((n2(A) | (~p1(B, C, A))) <=> (n2(A) | (~p1(B, C, A))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(168,axiom,(![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_137')).
% 0.20/0.51 tff(169,plain,
% 0.20/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.51 tff(170,plain,(
% 0.20/0.51 ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[169])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (p1(e, e, e) <=> p1(e, e, e)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(174,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.20/0.51 tff(175,plain,
% 0.20/0.51 (k0(e) <=> $true),
% 0.20/0.51 inference(iff_true,[status(thm)],[174])).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 ((~k0(e)) <=> (~$true)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.51 tff(177,plain,
% 0.20/0.51 ((~k0(e)) <=> $false),
% 0.20/0.51 inference(transitivity,[status(thm)],[176, 17])).
% 0.20/0.51 tff(178,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 (r0(e) <=> $true),
% 0.20/0.51 inference(iff_true,[status(thm)],[178])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 ((~r0(e)) <=> (~$true)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 ((~r0(e)) <=> $false),
% 0.20/0.51 inference(transitivity,[status(thm)],[180, 17])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[181, 177])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 0.20/0.51 inference(transitivity,[status(thm)],[182, 173])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(187,plain,
% 0.20/0.51 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.20/0.51 inference(transitivity,[status(thm)],[187, 185])).
% 0.20/0.51 tff(189,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.20/0.51 tff(190,plain,
% 0.20/0.51 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.51 tff(191,plain,
% 0.20/0.51 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[190, 184])).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 (p1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[191, 183])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 (p1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[192, 172])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 (((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(e) | (~p1(e, e, e)))) <=> ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(e) | (~p1(e, e, e)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(e) | (~p1(e, e, e)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(e) | (~p1(e, e, e))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 (n2(e)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[196, 193, 171])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.51 (m1(e, e, e) <=> m1(e, e, e)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(199,plain,
% 0.20/0.51 (($false | m1(e, e, e)) <=> m1(e, e, e)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 (((~r0(e)) | m1(e, e, e)) <=> ($false | m1(e, e, e))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[181])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 (((~r0(e)) | m1(e, e, e)) <=> m1(e, e, e)),
% 0.20/0.51 inference(transitivity,[status(thm)],[200, 199])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 ((m1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | m1(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(203,axiom,(m1(e, e, e) | (~r0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_012')).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 ((~r0(e)) | m1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 (m1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[204, 201])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 (m1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.20/0.51 tff(207,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(e, e, e)) | p2(e, e, e))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 ((p2(e, e, e) | (~m1(e, e, e))) <=> ((~m1(e, e, e)) | p2(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(e, e, e)) | p2(e, e, e)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[208])).
% 0.20/0.51 tff(210,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e))),
% 0.20/0.51 inference(transitivity,[status(thm)],[209, 207])).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 (p2(e, e, e)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[212, 206, 14])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 (^[D: $i] : refl(((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[214])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (^[D: $i] : trans(monotonicity(rewrite((m3(D, e, e) | (~n2(e))) <=> ((~n2(e)) | m3(D, e, e))), (((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> (((~n2(e)) | m3(D, e, e)) | (~p2(D, e, e))))), rewrite((((~n2(e)) | m3(D, e, e)) | (~p2(D, e, e))) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))), (((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 (![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[217])).
% 0.20/0.51 tff(219,axiom,(![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_234')).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.20/0.51 tff(222,plain,(
% 0.20/0.51 ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.20/0.51 inference(skolemize,[status(sab)],[221])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | ((~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))) <=> ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | (~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | ((~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | (~n2(e)) | (~p2(e, e, e)) | m3(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (m3(e, e, e)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[226, 223, 213, 197])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[228])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1(C, D) | (~p0(E, C))) <=> ((~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> (((~p0(E, C)) | l1(C, D)) | (~r0(F))))), rewrite((((~p0(E, C)) | l1(C, D)) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D)))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> (((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))))), rewrite((((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[231])).
% 0.20/0.51 tff(233,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_003')).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.20/0.51 tff(236,plain,(
% 0.20/0.51 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(skolemize,[status(sab)],[235])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (m0(e, b, c) <=> m0(e, b, c)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(239,axiom,(m0(e, b, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 (m0(e, b, c)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 (p0(c, b) <=> p0(c, b)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(242,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.20/0.51 tff(243,plain,
% 0.20/0.51 (p0(c, b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.51 tff(244,plain,
% 0.20/0.51 (r0(b) <=> r0(b)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(245,axiom,(r0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (r0(b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e)) <=> ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.51 inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (l1(b, e)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[252, 246, 243, 240, 237])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 (^[H: $i, G: $i] : refl(((~l1(H, G)) | q2(G, G, H)) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[254])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 (^[H: $i, G: $i] : rewrite((q2(G, G, H) | (~l1(H, G))) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 (![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G))) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[257])).
% 0.20/0.51 tff(259,axiom,(![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_186')).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.20/0.51 tff(262,plain,(
% 0.20/0.51 ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.51 inference(skolemize,[status(sab)],[261])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.20/0.51 tff(264,plain,
% 0.20/0.51 (((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))) <=> ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(265,plain,
% 0.20/0.51 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(266,plain,
% 0.20/0.51 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.20/0.51 tff(267,plain,
% 0.20/0.51 (q2(e, e, b)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[266, 263, 253])).
% 0.20/0.51 tff(268,plain,
% 0.20/0.52 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[268])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[271])).
% 0.20/0.52 tff(273,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.20/0.52 tff(276,plain,(
% 0.20/0.52 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.20/0.52 inference(skolemize,[status(sab)],[275])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 (((~![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(279,plain,
% 0.20/0.52 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(280,plain,
% 0.20/0.52 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 (p1(b, b, b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[280, 243, 277])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 (^[B: $i, D: $i, E: $i, C: $i] : refl(((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[282])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(285,plain,
% 0.20/0.52 (^[B: $i, D: $i, E: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k3(B, B, C) | (~p1(C, D, B))) <=> ((~p1(C, D, B)) | k3(B, B, C))), (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) <=> (((~p1(C, D, B)) | k3(B, B, C)) | (~m2(E))))), rewrite((((~p1(C, D, B)) | k3(B, B, C)) | (~m2(E))) <=> ((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))), (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) <=> ((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)))), ((((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> (((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) | (~m2(D))))), rewrite((((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) | (~m2(D))) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))), ((((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(286,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, C: $i] : (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[285])).
% 0.20/0.52 tff(287,axiom,(![B: $i, D: $i, E: $i, C: $i] : (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_201')).
% 0.20/0.52 tff(288,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.20/0.52 tff(289,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[288, 284])).
% 0.20/0.52 tff(290,plain,(
% 0.20/0.52 ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.20/0.52 inference(skolemize,[status(sab)],[289])).
% 0.20/0.52 tff(291,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[290, 283])).
% 0.20/0.52 tff(292,plain,
% 0.20/0.52 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(293,plain,
% 0.20/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[292])).
% 0.20/0.52 tff(294,plain,
% 0.20/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(295,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.20/0.52 tff(296,plain,
% 0.20/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.52 tff(297,plain,(
% 0.20/0.52 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[296])).
% 0.20/0.52 tff(298,plain,
% 0.20/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[297, 293])).
% 0.20/0.52 tff(299,plain,
% 0.20/0.52 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(300,plain,
% 0.20/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(301,plain,
% 0.20/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.20/0.52 tff(302,plain,
% 0.20/0.52 (k1(b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[301, 97, 298])).
% 0.20/0.52 tff(303,plain,
% 0.20/0.52 ((m2(b) | (~k1(b))) <=> (m2(b) | (~k1(b)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(304,axiom,(m2(b) | (~k1(b))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_136')).
% 0.20/0.52 tff(305,plain,
% 0.20/0.52 (m2(b) | (~k1(b))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.52 tff(306,plain,
% 0.20/0.52 (m2(b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[305, 302])).
% 0.20/0.52 tff(307,plain,
% 0.20/0.52 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(308,plain,
% 0.20/0.52 (((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b)) <=> ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(309,plain,
% 0.20/0.52 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[308])).
% 0.20/0.52 tff(310,plain,
% 0.20/0.52 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.20/0.52 inference(transitivity,[status(thm)],[309, 307])).
% 0.20/0.52 tff(311,plain,
% 0.20/0.52 ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(312,plain,
% 0.20/0.52 ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.20/0.52 tff(313,plain,
% 0.20/0.52 (k3(b, b, b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[312, 306, 291, 281])).
% 0.20/0.52 tff(314,plain,
% 0.20/0.52 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(315,plain,
% 0.20/0.52 (((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e)) <=> ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(316,plain,
% 0.20/0.52 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[315])).
% 0.20/0.52 tff(317,plain,
% 0.20/0.52 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.20/0.52 inference(transitivity,[status(thm)],[316, 314])).
% 0.20/0.52 tff(318,plain,
% 0.20/0.52 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(319,plain,
% 0.20/0.52 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.20/0.52 tff(320,plain,
% 0.20/0.52 (q4(b, e)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[319, 81, 313, 267, 227])).
% 0.20/0.52 tff(321,plain,
% 0.20/0.52 (^[B: $i, C: $i] : refl((p4(B, C, B) | (~k3(B, B, C))) <=> (p4(B, C, B) | (~k3(B, B, C))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(322,plain,
% 0.20/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[321])).
% 0.20/0.52 tff(323,plain,
% 0.20/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(324,axiom,(![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_287')).
% 0.20/0.52 tff(325,plain,
% 0.20/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.20/0.52 tff(326,plain,(
% 0.20/0.52 ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[325])).
% 0.20/0.52 tff(327,plain,
% 0.20/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.20/0.52 tff(328,plain,
% 0.20/0.52 (((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))) <=> ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(329,plain,
% 0.20/0.52 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(330,plain,
% 0.20/0.52 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.20/0.52 tff(331,plain,
% 0.20/0.52 (p4(a, a, a)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[330, 146, 327])).
% 0.20/0.52 tff(332,plain,
% 0.20/0.52 ((~n5(e, a)) <=> (~n5(e, a))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(333,axiom,(~n5(e, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.52 tff(334,plain,
% 0.20/0.52 (~n5(e, a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.20/0.52 tff(335,plain,
% 0.20/0.52 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(336,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[335])).
% 0.20/0.52 tff(337,plain,
% 0.20/0.52 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(338,plain,
% 0.20/0.52 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((n5(B, C) | (~q4(D, E))) <=> ((~q4(D, E)) | n5(B, C))), (((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) <=> (((~q4(D, E)) | n5(B, C)) | (~n4(B, E))))), rewrite((((~q4(D, E)) | n5(B, C)) | (~n4(B, E))) <=> ((~n4(B, E)) | (~q4(D, E)) | n5(B, C))), (((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) <=> ((~n4(B, E)) | (~q4(D, E)) | n5(B, C)))), ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) <=> (((~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~p4(F, F, C))))), rewrite((((~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~p4(F, F, C))) <=> ((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))), ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) <=> ((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)))), (((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> (((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~n5(F, C))))), rewrite((((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~n5(F, C))) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))), (((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(339,plain,
% 0.20/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[338])).
% 0.20/0.53 tff(340,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_307')).
% 0.20/0.53 tff(341,plain,
% 0.20/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.20/0.53 tff(342,plain,
% 0.20/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[341, 337])).
% 0.20/0.53 tff(343,plain,(
% 0.20/0.53 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.20/0.53 inference(skolemize,[status(sab)],[342])).
% 0.20/0.53 tff(344,plain,
% 0.20/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[343, 336])).
% 0.20/0.53 tff(345,plain,
% 0.20/0.53 (^[I: $i, H: $i] : refl((n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(346,plain,
% 0.20/0.53 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[345])).
% 0.20/0.53 tff(347,plain,
% 0.20/0.53 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(348,plain,
% 0.20/0.53 (^[I: $i, H: $i] : trans(monotonicity(rewrite((n4(H, H) | (~k4(I))) <=> (n4(H, H) | (~k4(I)))), (((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> ((n4(H, H) | (~k4(I))) | (~m3(H, H, H))))), rewrite(((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))), (((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(349,plain,
% 0.20/0.53 (![I: $i, H: $i] : ((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[348])).
% 0.20/0.53 tff(350,axiom,(![I: $i, H: $i] : ((n4(H, H) | (~k4(I))) | (~m3(H, H, H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_284')).
% 0.20/0.53 tff(351,plain,
% 0.20/0.53 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.20/0.53 tff(352,plain,
% 0.20/0.53 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[351, 347])).
% 0.20/0.53 tff(353,plain,(
% 0.20/0.53 ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[352])).
% 0.20/0.53 tff(354,plain,
% 0.20/0.53 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[353, 346])).
% 0.42/0.53 tff(355,assumption,(~n4(e, e)), introduced(assumption)).
% 0.42/0.53 tff(356,plain,
% 0.42/0.53 (^[D: $i, E: $i, F: $i] : refl((n3(D) | (~p2(E, F, D))) <=> (n3(D) | (~p2(E, F, D))))),
% 0.42/0.53 inference(bind,[status(th)],[])).
% 0.42/0.53 tff(357,plain,
% 0.42/0.53 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.42/0.53 inference(quant_intro,[status(thm)],[356])).
% 0.42/0.53 tff(358,plain,
% 0.42/0.53 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(359,axiom,(![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_240')).
% 0.42/0.53 tff(360,plain,
% 0.42/0.53 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.42/0.53 tff(361,plain,(
% 0.42/0.53 ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.42/0.53 inference(skolemize,[status(sab)],[360])).
% 0.42/0.53 tff(362,plain,
% 0.42/0.53 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[361, 357])).
% 0.42/0.53 tff(363,plain,
% 0.42/0.53 (((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(e) | (~p2(e, e, e)))) <=> ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(e) | (~p2(e, e, e)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(364,plain,
% 0.42/0.53 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(e) | (~p2(e, e, e)))),
% 0.42/0.53 inference(quant_inst,[status(thm)],[])).
% 0.42/0.53 tff(365,plain,
% 0.42/0.53 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(e) | (~p2(e, e, e))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.42/0.53 tff(366,plain,
% 0.42/0.53 (n3(e)),
% 0.42/0.53 inference(unit_resolution,[status(thm)],[365, 362, 213])).
% 0.42/0.53 tff(367,plain,
% 0.42/0.53 (^[I: $i, H: $i, G: $i] : refl(((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)))),
% 0.42/0.53 inference(bind,[status(th)],[])).
% 0.42/0.53 tff(368,plain,
% 0.42/0.53 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.42/0.53 inference(quant_intro,[status(thm)],[367])).
% 0.42/0.53 tff(369,plain,
% 0.42/0.53 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(370,plain,
% 0.42/0.53 (^[I: $i, H: $i, G: $i] : trans(monotonicity(rewrite((q3(G, H) | (~q2(I, G, H))) <=> ((~q2(I, G, H)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> (((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))))), rewrite((((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))))),
% 0.42/0.53 inference(bind,[status(th)],[])).
% 0.42/0.53 tff(371,plain,
% 0.42/0.53 (![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.42/0.53 inference(quant_intro,[status(thm)],[370])).
% 0.42/0.53 tff(372,axiom,(![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_255')).
% 0.42/0.53 tff(373,plain,
% 0.42/0.53 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.42/0.53 tff(374,plain,
% 0.42/0.53 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[373, 369])).
% 0.42/0.53 tff(375,plain,(
% 0.42/0.53 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.42/0.53 inference(skolemize,[status(sab)],[374])).
% 0.42/0.53 tff(376,plain,
% 0.42/0.53 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[375, 368])).
% 0.42/0.53 tff(377,plain,
% 0.42/0.53 (n0(e, e) <=> n0(e, e)),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(378,axiom,(n0(e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_30')).
% 0.42/0.53 tff(379,plain,
% 0.42/0.53 (n0(e, e)),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.42/0.53 tff(380,plain,
% 0.42/0.53 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(381,plain,
% 0.42/0.53 (((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b)) <=> (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(382,plain,
% 0.42/0.53 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b))))),
% 0.42/0.53 inference(monotonicity,[status(thm)],[381])).
% 0.42/0.53 tff(383,plain,
% 0.42/0.53 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.42/0.53 inference(transitivity,[status(thm)],[382, 380])).
% 0.42/0.53 tff(384,plain,
% 0.42/0.53 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))),
% 0.42/0.53 inference(quant_inst,[status(thm)],[])).
% 0.42/0.53 tff(385,plain,
% 0.42/0.53 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.42/0.53 tff(386,plain,
% 0.42/0.53 (q3(e, b)),
% 0.42/0.53 inference(unit_resolution,[status(thm)],[385, 379, 376, 267])).
% 0.42/0.53 tff(387,plain,
% 0.42/0.53 (((~q3(e, b)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | k4(c) | (~n3(e)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(388,plain,
% 0.42/0.53 (((~q3(e, b)) | $false | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | k4(c) | (~n3(e)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(389,axiom,(n0(c, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.42/0.53 tff(390,plain,
% 0.42/0.53 (n0(c, d) <=> $true),
% 0.42/0.53 inference(iff_true,[status(thm)],[389])).
% 0.42/0.53 tff(391,plain,
% 0.42/0.53 ((~n0(c, d)) <=> (~$true)),
% 0.42/0.53 inference(monotonicity,[status(thm)],[390])).
% 0.42/0.53 tff(392,plain,
% 0.42/0.53 ((~n0(c, d)) <=> $false),
% 0.42/0.53 inference(transitivity,[status(thm)],[391, 17])).
% 0.42/0.53 tff(393,plain,
% 0.42/0.53 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | $false | k4(c) | (~n3(e)))),
% 0.42/0.53 inference(monotonicity,[status(thm)],[392])).
% 0.42/0.53 tff(394,plain,
% 0.42/0.53 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | k4(c) | (~n3(e)))),
% 0.42/0.53 inference(transitivity,[status(thm)],[393, 388])).
% 0.42/0.53 tff(395,plain,
% 0.42/0.53 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(396,plain,
% 0.42/0.53 ((((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(397,plain,
% 0.42/0.53 (((k4(c) | (~n0(c, d))) | (~q3(e, b))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c))),
% 0.42/0.53 inference(rewrite,[status(thm)],[])).
% 0.42/0.53 tff(398,plain,
% 0.42/0.53 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> (((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e)))),
% 0.42/0.53 inference(monotonicity,[status(thm)],[397])).
% 0.42/0.53 tff(399,plain,
% 0.42/0.53 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.42/0.53 inference(transitivity,[status(thm)],[398, 396])).
% 0.42/0.53 tff(400,axiom,(((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_274')).
% 0.42/0.53 tff(401,plain,
% 0.42/0.53 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.42/0.53 tff(402,plain,
% 0.42/0.53 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[401, 395])).
% 0.42/0.53 tff(403,plain,
% 0.42/0.53 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[402, 394])).
% 0.42/0.53 tff(404,plain,
% 0.42/0.53 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[403, 387])).
% 0.42/0.53 tff(405,plain,
% 0.42/0.53 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[404, 387])).
% 0.42/0.53 tff(406,plain,
% 0.42/0.53 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.42/0.53 inference(modus_ponens,[status(thm)],[405, 387])).
% 0.42/0.53 tff(407,plain,
% 0.42/0.53 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[406, 387])).
% 0.44/0.56 tff(408,plain,
% 0.44/0.56 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[407, 387])).
% 0.44/0.56 tff(409,plain,
% 0.44/0.56 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[408, 387])).
% 0.44/0.56 tff(410,plain,
% 0.44/0.56 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[409, 387])).
% 0.44/0.56 tff(411,plain,
% 0.44/0.56 (k4(c)),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[410, 386, 366])).
% 0.44/0.56 tff(412,plain,
% 0.44/0.56 (((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(e, e) | (~m3(e, e, e)) | (~k4(c)))) <=> ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(e, e) | (~m3(e, e, e)) | (~k4(c)))),
% 0.44/0.56 inference(rewrite,[status(thm)],[])).
% 0.44/0.56 tff(413,plain,
% 0.44/0.56 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(e, e) | (~m3(e, e, e)) | (~k4(c)))),
% 0.44/0.56 inference(quant_inst,[status(thm)],[])).
% 0.44/0.56 tff(414,plain,
% 0.44/0.56 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(e, e) | (~m3(e, e, e)) | (~k4(c))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.44/0.56 tff(415,plain,
% 0.44/0.56 ($false),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[414, 411, 355, 354, 227])).
% 0.44/0.56 tff(416,plain,(n4(e, e)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.56 tff(417,plain,
% 0.44/0.56 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(e, a) | (~n4(e, e)) | (~p4(a, a, a)) | (~q4(b, e)) | (~n5(a, a)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(e, a) | (~n4(e, e)) | (~p4(a, a, a)) | (~q4(b, e)) | (~n5(a, a)))),
% 0.44/0.56 inference(rewrite,[status(thm)],[])).
% 0.44/0.56 tff(418,plain,
% 0.44/0.56 (((~n5(a, a)) | (~p4(a, a, a)) | (~n4(e, e)) | (~q4(b, e)) | n5(e, a)) <=> (n5(e, a) | (~n4(e, e)) | (~p4(a, a, a)) | (~q4(b, e)) | (~n5(a, a)))),
% 0.44/0.56 inference(rewrite,[status(thm)],[])).
% 0.44/0.56 tff(419,plain,
% 0.44/0.56 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(a, a)) | (~p4(a, a, a)) | (~n4(e, e)) | (~q4(b, e)) | n5(e, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(e, a) | (~n4(e, e)) | (~p4(a, a, a)) | (~q4(b, e)) | (~n5(a, a))))),
% 0.44/0.56 inference(monotonicity,[status(thm)],[418])).
% 0.44/0.56 tff(420,plain,
% 0.44/0.56 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(a, a)) | (~p4(a, a, a)) | (~n4(e, e)) | (~q4(b, e)) | n5(e, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(e, a) | (~n4(e, e)) | (~p4(a, a, a)) | (~q4(b, e)) | (~n5(a, a)))),
% 0.44/0.56 inference(transitivity,[status(thm)],[419, 417])).
% 0.44/0.56 tff(421,plain,
% 0.44/0.56 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(a, a)) | (~p4(a, a, a)) | (~n4(e, e)) | (~q4(b, e)) | n5(e, a))),
% 0.44/0.56 inference(quant_inst,[status(thm)],[])).
% 0.44/0.56 tff(422,plain,
% 0.44/0.56 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(e, a) | (~n4(e, e)) | (~p4(a, a, a)) | (~q4(b, e)) | (~n5(a, a))),
% 0.44/0.56 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.44/0.56 tff(423,plain,
% 0.44/0.56 ($false),
% 0.44/0.56 inference(unit_resolution,[status(thm)],[422, 416, 344, 334, 331, 320, 164])).
% 0.44/0.56 % SZS output end Proof
%------------------------------------------------------------------------------