%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN163-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 : Sat Jun 21 05:38:23 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN163-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:30:27 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 tff(n5_type, type, (
% 0.21/0.48 n5: ( $i * $i ) > $o)).
% 0.21/0.48 tff(a_type, type, (
% 0.21/0.48 a: $i)).
% 0.21/0.48 tff(q4_type, type, (
% 0.21/0.48 q4: ( $i * $i ) > $o)).
% 0.21/0.48 tff(m3_type, type, (
% 0.21/0.48 m3: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(p2_type, type, (
% 0.21/0.48 p2: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(m1_type, type, (
% 0.21/0.48 m1: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(l0_type, type, (
% 0.21/0.48 l0: $i > $o)).
% 0.21/0.48 tff(s0_type, type, (
% 0.21/0.48 s0: $i > $o)).
% 0.21/0.48 tff(d_type, type, (
% 0.21/0.48 d: $i)).
% 0.21/0.48 tff(q2_type, type, (
% 0.21/0.48 q2: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(p1_type, type, (
% 0.21/0.48 p1: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(k3_type, type, (
% 0.21/0.48 k3: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(r2_type, type, (
% 0.21/0.48 r2: $i > $o)).
% 0.21/0.48 tff(r1_type, type, (
% 0.21/0.48 r1: $i > $o)).
% 0.21/0.48 tff(q1_type, type, (
% 0.21/0.48 q1: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(b_type, type, (
% 0.21/0.48 b: $i)).
% 0.21/0.48 tff(n0_type, type, (
% 0.21/0.48 n0: ( $i * $i ) > $o)).
% 0.21/0.48 tff(p0_type, type, (
% 0.21/0.48 p0: ( $i * $i ) > $o)).
% 0.21/0.48 tff(q0_type, type, (
% 0.21/0.48 q0: ( $i * $i ) > $o)).
% 0.21/0.48 tff(e_type, type, (
% 0.21/0.48 e: $i)).
% 0.21/0.48 tff(n2_type, type, (
% 0.21/0.48 n2: $i > $o)).
% 0.21/0.48 tff(k0_type, type, (
% 0.21/0.48 k0: $i > $o)).
% 0.21/0.48 tff(r0_type, type, (
% 0.21/0.48 r0: $i > $o)).
% 0.21/0.48 tff(l1_type, type, (
% 0.21/0.48 l1: ( $i * $i ) > $o)).
% 0.21/0.48 tff(m0_type, type, (
% 0.21/0.48 m0: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(c_type, type, (
% 0.21/0.48 c: $i)).
% 0.21/0.48 tff(m2_type, type, (
% 0.21/0.48 m2: $i > $o)).
% 0.21/0.48 tff(k1_type, type, (
% 0.21/0.48 k1: $i > $o)).
% 0.21/0.48 tff(p4_type, type, (
% 0.21/0.48 p4: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(n4_type, type, (
% 0.21/0.48 n4: ( $i * $i ) > $o)).
% 0.21/0.48 tff(k4_type, type, (
% 0.21/0.48 k4: $i > $o)).
% 0.21/0.48 tff(n3_type, type, (
% 0.21/0.48 n3: $i > $o)).
% 0.21/0.48 tff(q3_type, type, (
% 0.21/0.48 q3: ( $i * $i ) > $o)).
% 0.21/0.48 tff(1,plain,
% 0.21/0.48 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(2,plain,
% 0.21/0.48 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.48 tff(3,plain,
% 0.21/0.48 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(4,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 0.21/0.48 tff(5,plain,
% 0.21/0.48 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.48 tff(6,plain,(
% 0.21/0.48 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[5])).
% 0.21/0.48 tff(7,plain,
% 0.21/0.48 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.48 tff(8,plain,
% 0.21/0.48 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(9,plain,
% 0.21/0.48 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.48 tff(10,plain,
% 0.21/0.48 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(11,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.21/0.48 tff(12,plain,
% 0.21/0.48 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.48 tff(13,plain,(
% 0.21/0.48 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[12])).
% 0.21/0.48 tff(14,plain,
% 0.21/0.48 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.48 tff(15,plain,
% 0.21/0.48 (l0(a) <=> l0(a)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(16,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.21/0.48 tff(17,plain,
% 0.21/0.48 (l0(a)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.48 tff(18,plain,
% 0.21/0.48 (s0(d) <=> s0(d)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(19,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.21/0.48 tff(20,plain,
% 0.21/0.48 (s0(d)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.48 tff(21,plain,
% 0.21/0.48 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(22,plain,
% 0.21/0.48 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(24,plain,
% 0.21/0.48 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[24, 22])).
% 0.21/0.48 tff(26,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.48 tff(30,plain,
% 0.21/0.48 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.21/0.48 tff(31,plain,
% 0.21/0.48 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.21/0.48 tff(32,plain,
% 0.21/0.48 (m1(a, a, a)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[31, 20, 17])).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(34,plain,
% 0.21/0.48 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(35,plain,
% 0.21/0.48 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 (p2(a, a, a)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[35, 32, 14])).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 ((m3(a, a, a) | (~p2(a, a, a))) <=> ((~p2(a, a, a)) | m3(a, a, a))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(transitivity,[status(thm)],[39, 37])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 (m3(a, a, a)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[42, 36, 7])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(45,plain,
% 0.21/0.48 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.48 tff(46,plain,
% 0.21/0.48 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(47,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.21/0.48 tff(48,plain,
% 0.21/0.48 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.48 tff(49,plain,(
% 0.21/0.48 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[48])).
% 0.21/0.48 tff(50,plain,
% 0.21/0.48 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.48 tff(51,plain,
% 0.21/0.48 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(53,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 ((~l0(a)) | p1(a, a, a)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 ((~l0(a)) | p1(a, a, a)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (p1(a, a, a)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[55, 17])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 ((q2(a, a, a) | (~p1(a, a, a))) <=> ((~p1(a, a, a)) | q2(a, a, a))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (((~![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)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (q2(a, a, a)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[62, 56, 50])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (^[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)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.49 tff(69,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/sandbox/benchmark/Axioms/SYN001-0.ax','rule_295')).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.21/0.49 tff(72,plain,(
% 0.21/0.49 ![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))),
% 0.21/0.49 inference(skolemize,[status(sab)],[71])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.49 tff(74,plain,
% 0.21/0.49 (^[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)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(75,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.49 tff(76,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(77,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.49 tff(79,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.49 tff(81,plain,
% 0.21/0.49 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.49 tff(82,plain,(
% 0.21/0.49 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.49 inference(skolemize,[status(sab)],[81])).
% 0.21/0.49 tff(83,plain,
% 0.21/0.49 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.21/0.49 tff(84,plain,
% 0.21/0.49 (p0(b, d) <=> p0(b, d)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(85,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.21/0.49 tff(86,plain,
% 0.21/0.49 (p0(b, d)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.49 tff(87,plain,
% 0.21/0.49 (n0(d, b) <=> n0(d, b)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(88,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.21/0.49 tff(89,plain,
% 0.21/0.49 (n0(d, b)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.49 tff(90,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(91,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(92,plain,
% 0.21/0.49 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.49 tff(93,plain,
% 0.21/0.49 (q1(d, b, d)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[92, 89, 86, 83])).
% 0.21/0.49 tff(94,plain,
% 0.21/0.49 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(95,plain,
% 0.21/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.49 tff(96,plain,
% 0.21/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(97,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(98,plain,
% 0.21/0.49 (![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))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.49 tff(99,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.21/0.49 tff(100,plain,
% 0.21/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.49 tff(101,plain,
% 0.21/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.21/0.49 tff(102,plain,(
% 0.21/0.49 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.49 inference(skolemize,[status(sab)],[101])).
% 0.21/0.49 tff(103,plain,
% 0.21/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.21/0.49 tff(104,plain,
% 0.21/0.49 (q0(a, b) <=> q0(a, b)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(105,axiom,(q0(a, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.21/0.49 tff(106,plain,
% 0.21/0.49 (q0(a, b)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.49 tff(107,plain,
% 0.21/0.49 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(108,plain,
% 0.21/0.49 (((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a)) <=> ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(109,plain,
% 0.21/0.49 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.49 tff(110,plain,
% 0.21/0.49 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.49 tff(111,plain,
% 0.21/0.49 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(112,plain,
% 0.21/0.49 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.49 tff(113,plain,
% 0.21/0.49 (r1(a)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[112, 20, 106, 103, 93])).
% 0.21/0.49 tff(114,plain,
% 0.21/0.49 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(115,plain,
% 0.21/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.49 tff(116,plain,
% 0.21/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(117,plain,
% 0.21/0.49 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(118,plain,
% 0.21/0.49 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.49 tff(119,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.21/0.49 tff(120,plain,
% 0.21/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.49 tff(121,plain,
% 0.21/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.21/0.49 tff(122,plain,(
% 0.21/0.49 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.49 inference(skolemize,[status(sab)],[121])).
% 0.21/0.49 tff(123,plain,
% 0.21/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(125,plain,
% 0.21/0.49 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.49 tff(127,plain,
% 0.21/0.49 (r2(a)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[126, 17, 123, 113])).
% 0.21/0.49 tff(128,plain,
% 0.21/0.49 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(130,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 0.21/0.49 tff(131,plain,
% 0.21/0.49 ((~r2(a)) | k3(a, a, a)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.49 tff(132,plain,
% 0.21/0.49 ((~r2(a)) | k3(a, a, a)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[131, 128])).
% 0.21/0.49 tff(133,plain,
% 0.21/0.49 (k3(a, a, a)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[132, 127])).
% 0.21/0.49 tff(134,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(135,plain,
% 0.21/0.49 (((~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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(136,plain,
% 0.21/0.49 (((~![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)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[135])).
% 0.21/0.49 tff(137,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(transitivity,[status(thm)],[136, 134])).
% 0.21/0.49 tff(138,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(139,plain,
% 0.21/0.49 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.49 tff(140,plain,
% 0.21/0.49 (q4(a, a)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[139, 133, 73, 63, 43])).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 (^[D: $i, C: $i] : refl((n5(C, C) | (~q4(D, C))) <=> (n5(C, C) | (~q4(D, C))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(142,plain,
% 0.21/0.49 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[141])).
% 0.21/0.49 tff(143,plain,
% 0.21/0.49 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(144,axiom,(![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_313')).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.49 tff(146,plain,(
% 0.21/0.49 ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[145])).
% 0.21/0.49 tff(147,plain,
% 0.21/0.49 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.21/0.49 tff(148,plain,
% 0.21/0.49 (((~![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(149,plain,
% 0.21/0.49 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | (n5(a, a) | (~q4(a, a)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | n5(a, a) | (~q4(a, a))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 (n5(a, a)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[150, 147, 140])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 (^[B: $i, A: $i, C: $i] : refl((n2(A) | (~p1(B, C, A))) <=> (n2(A) | (~p1(B, C, A))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(155,axiom,(![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_137')).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.49 tff(157,plain,(
% 0.21/0.49 ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[156])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.21/0.49 tff(159,plain,
% 0.21/0.49 (k0(e) <=> k0(e)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(160,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 (k0(e)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.49 tff(162,plain,
% 0.21/0.49 (r0(e) <=> r0(e)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(163,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.21/0.49 tff(164,plain,
% 0.21/0.49 (r0(e)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.21/0.49 inference(transitivity,[status(thm)],[168, 166])).
% 0.21/0.49 tff(170,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.21/0.50 tff(171,plain,
% 0.21/0.50 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.50 tff(172,plain,
% 0.21/0.50 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[171, 165])).
% 0.21/0.50 tff(173,plain,
% 0.21/0.50 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.21/0.50 tff(174,plain,
% 0.21/0.50 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[173, 165])).
% 0.21/0.50 tff(175,plain,
% 0.21/0.50 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[174, 165])).
% 0.21/0.50 tff(176,plain,
% 0.21/0.50 (p1(e, e, e)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[175, 164, 161])).
% 0.21/0.50 tff(177,plain,
% 0.21/0.50 (((~![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(178,plain,
% 0.21/0.50 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(e) | (~p1(e, e, e)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(179,plain,
% 0.21/0.50 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(e) | (~p1(e, e, e))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.50 tff(180,plain,
% 0.21/0.50 (n2(e)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[179, 176, 158])).
% 0.21/0.50 tff(181,plain,
% 0.21/0.50 (((~r0(e)) | m1(e, e, e)) <=> ((~r0(e)) | m1(e, e, e))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(182,plain,
% 0.21/0.50 ((m1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | m1(e, e, e))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(183,axiom,(m1(e, e, e) | (~r0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_012')).
% 0.21/0.50 tff(184,plain,
% 0.21/0.50 ((~r0(e)) | m1(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.50 tff(185,plain,
% 0.21/0.50 ((~r0(e)) | m1(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[184, 181])).
% 0.21/0.50 tff(186,plain,
% 0.21/0.50 (m1(e, e, e)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[185, 164])).
% 0.21/0.50 tff(187,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(188,plain,
% 0.21/0.50 ((p2(e, e, e) | (~m1(e, e, e))) <=> ((~m1(e, e, e)) | p2(e, e, e))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(189,plain,
% 0.21/0.50 (((~![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)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.50 tff(190,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(transitivity,[status(thm)],[189, 187])).
% 0.21/0.50 tff(191,plain,
% 0.21/0.50 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(192,plain,
% 0.21/0.50 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.50 tff(193,plain,
% 0.21/0.50 (p2(e, e, e)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[192, 186, 14])).
% 0.21/0.50 tff(194,plain,
% 0.21/0.50 (^[D: $i] : refl(((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(195,plain,
% 0.21/0.50 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[194])).
% 0.21/0.50 tff(196,plain,
% 0.21/0.50 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(197,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(198,plain,
% 0.21/0.50 (![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[197])).
% 0.21/0.50 tff(199,axiom,(![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_234')).
% 0.21/0.50 tff(200,plain,
% 0.21/0.50 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.21/0.50 tff(201,plain,
% 0.21/0.50 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.21/0.50 tff(202,plain,(
% 0.21/0.50 ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.50 inference(skolemize,[status(sab)],[201])).
% 0.21/0.50 tff(203,plain,
% 0.21/0.50 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.21/0.50 tff(204,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(205,plain,
% 0.21/0.50 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | ((~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(206,plain,
% 0.21/0.50 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | (~n2(e)) | (~p2(e, e, e)) | m3(e, e, e)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.21/0.50 tff(207,plain,
% 0.21/0.50 (m3(e, e, e)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[206, 203, 193, 180])).
% 0.21/0.50 tff(208,plain,
% 0.21/0.50 (^[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)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(209,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[208])).
% 0.21/0.50 tff(210,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(211,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(212,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[211])).
% 0.21/0.50 tff(213,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_003')).
% 0.21/0.50 tff(214,plain,
% 0.21/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.21/0.50 tff(215,plain,
% 0.21/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.21/0.50 tff(216,plain,(
% 0.21/0.50 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.50 inference(skolemize,[status(sab)],[215])).
% 0.21/0.50 tff(217,plain,
% 0.21/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.21/0.50 tff(218,plain,
% 0.21/0.50 (m0(e, b, c) <=> m0(e, b, c)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(219,axiom,(m0(e, b, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 (m0(e, b, c)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.50 tff(221,plain,
% 0.21/0.50 (p0(c, b) <=> p0(c, b)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(222,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.21/0.50 tff(223,plain,
% 0.21/0.50 (p0(c, b)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.21/0.50 tff(224,plain,
% 0.21/0.50 (r0(b) <=> r0(b)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(225,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.21/0.50 tff(226,plain,
% 0.21/0.50 (r0(b)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.50 tff(227,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(228,plain,
% 0.21/0.50 (((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e)) <=> ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(229,plain,
% 0.21/0.50 (((~![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)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[228])).
% 0.21/0.50 tff(230,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(transitivity,[status(thm)],[229, 227])).
% 0.21/0.50 tff(231,plain,
% 0.21/0.50 ((~![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))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(232,plain,
% 0.21/0.50 ((~![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)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.50 tff(233,plain,
% 0.21/0.50 (l1(b, e)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[232, 226, 223, 220, 217])).
% 0.21/0.50 tff(234,plain,
% 0.21/0.50 (^[H: $i, G: $i] : refl(((~l1(H, G)) | q2(G, G, H)) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(235,plain,
% 0.21/0.50 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[234])).
% 0.21/0.50 tff(236,plain,
% 0.21/0.50 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(237,plain,
% 0.21/0.50 (^[H: $i, G: $i] : rewrite((q2(G, G, H) | (~l1(H, G))) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(238,plain,
% 0.21/0.50 (![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G))) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[237])).
% 0.21/0.50 tff(239,axiom,(![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_186')).
% 0.21/0.50 tff(240,plain,
% 0.21/0.50 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.21/0.50 tff(241,plain,
% 0.21/0.50 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.21/0.50 tff(242,plain,(
% 0.21/0.50 ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.50 inference(skolemize,[status(sab)],[241])).
% 0.21/0.50 tff(243,plain,
% 0.21/0.50 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[242, 235])).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(245,plain,
% 0.21/0.50 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(246,plain,
% 0.21/0.50 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (q2(e, e, b)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[246, 243, 233])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[248])).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(251,plain,
% 0.21/0.50 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[251])).
% 0.21/0.50 tff(253,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.21/0.50 tff(255,plain,
% 0.21/0.50 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.21/0.50 tff(256,plain,(
% 0.21/0.50 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.50 inference(skolemize,[status(sab)],[255])).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[256, 249])).
% 0.21/0.50 tff(258,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.50 tff(261,plain,
% 0.21/0.50 (p1(b, b, b)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[260, 223, 257])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 (^[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)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(263,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[262])).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(266,plain,
% 0.21/0.50 (![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))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[265])).
% 0.21/0.50 tff(267,axiom,(![B: $i, D: $i, E: $i, C: $i] : (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_201')).
% 0.21/0.50 tff(268,plain,
% 0.21/0.50 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.21/0.50 tff(269,plain,
% 0.21/0.50 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.21/0.50 tff(270,plain,(
% 0.21/0.50 ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.50 inference(skolemize,[status(sab)],[269])).
% 0.21/0.50 tff(271,plain,
% 0.21/0.50 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[270, 263])).
% 0.21/0.50 tff(272,plain,
% 0.21/0.50 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(273,plain,
% 0.21/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[272])).
% 0.21/0.50 tff(274,plain,
% 0.21/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(275,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.21/0.50 tff(276,plain,
% 0.21/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.21/0.50 tff(277,plain,(
% 0.21/0.50 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[276])).
% 0.21/0.50 tff(278,plain,
% 0.21/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.21/0.50 tff(279,plain,
% 0.21/0.50 (((~![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(280,plain,
% 0.21/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(281,plain,
% 0.21/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.21/0.50 tff(282,plain,
% 0.21/0.50 (k1(b)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[281, 89, 278])).
% 0.21/0.50 tff(283,plain,
% 0.21/0.50 ((m2(b) | (~k1(b))) <=> (m2(b) | (~k1(b)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(284,axiom,(m2(b) | (~k1(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_136')).
% 0.21/0.50 tff(285,plain,
% 0.21/0.50 (m2(b) | (~k1(b))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.21/0.50 tff(286,plain,
% 0.21/0.50 (m2(b)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[285, 282])).
% 0.21/0.50 tff(287,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(288,plain,
% 0.21/0.50 (((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b)) <=> ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(289,plain,
% 0.21/0.50 (((~![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)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[288])).
% 0.21/0.50 tff(290,plain,
% 0.21/0.50 (((~![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))),
% 0.21/0.51 inference(transitivity,[status(thm)],[289, 287])).
% 0.21/0.51 tff(291,plain,
% 0.21/0.51 ((~![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))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(292,plain,
% 0.21/0.51 ((~![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)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.21/0.51 tff(293,plain,
% 0.21/0.51 (k3(b, b, b)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[292, 286, 271, 261])).
% 0.21/0.51 tff(294,plain,
% 0.21/0.51 (((~![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(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))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(295,plain,
% 0.21/0.51 (((~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))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(296,plain,
% 0.21/0.51 (((~![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(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)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[295])).
% 0.21/0.51 tff(297,plain,
% 0.21/0.51 (((~![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(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))),
% 0.21/0.51 inference(transitivity,[status(thm)],[296, 294])).
% 0.21/0.51 tff(298,plain,
% 0.21/0.51 ((~![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(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(299,plain,
% 0.21/0.51 ((~![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(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.21/0.51 tff(300,plain,
% 0.21/0.51 (q4(b, e)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[299, 73, 293, 247, 207])).
% 0.21/0.51 tff(301,plain,
% 0.21/0.51 (^[B: $i, C: $i] : refl((p4(B, C, B) | (~k3(B, B, C))) <=> (p4(B, C, B) | (~k3(B, B, C))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(302,plain,
% 0.21/0.51 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[301])).
% 0.21/0.51 tff(303,plain,
% 0.21/0.51 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(304,axiom,(![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_287')).
% 0.21/0.51 tff(305,plain,
% 0.21/0.51 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.21/0.51 tff(306,plain,(
% 0.21/0.51 ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[305])).
% 0.21/0.51 tff(307,plain,
% 0.21/0.51 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[306, 302])).
% 0.21/0.51 tff(308,plain,
% 0.21/0.51 (((~![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(309,plain,
% 0.21/0.51 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(310,plain,
% 0.21/0.51 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.21/0.51 tff(311,plain,
% 0.21/0.51 (p4(a, a, a)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[310, 133, 307])).
% 0.21/0.51 tff(312,plain,
% 0.21/0.51 ((~n5(e, a)) <=> (~n5(e, a))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(313,axiom,(~n5(e, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.51 tff(314,plain,
% 0.21/0.51 (~n5(e, a)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.21/0.51 tff(315,plain,
% 0.21/0.51 (^[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)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(316,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[315])).
% 0.21/0.51 tff(317,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(318,plain,
% 0.21/0.51 (^[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))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(319,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[318])).
% 0.21/0.51 tff(320,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/sandbox/benchmark/Axioms/SYN001-0.ax','rule_307')).
% 0.21/0.51 tff(321,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.21/0.51 tff(322,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[321, 317])).
% 0.21/0.51 tff(323,plain,(
% 0.21/0.51 ![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))),
% 0.21/0.51 inference(skolemize,[status(sab)],[322])).
% 0.21/0.51 tff(324,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[323, 316])).
% 0.21/0.51 tff(325,plain,
% 0.21/0.51 (^[I: $i, H: $i] : refl((n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(326,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[325])).
% 0.21/0.51 tff(327,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(328,plain,
% 0.21/0.51 (^[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)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(329,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[328])).
% 0.21/0.51 tff(330,axiom,(![I: $i, H: $i] : ((n4(H, H) | (~k4(I))) | (~m3(H, H, H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_284')).
% 0.21/0.51 tff(331,plain,
% 0.21/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.21/0.51 tff(332,plain,
% 0.21/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.21/0.51 tff(333,plain,(
% 0.21/0.51 ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[332])).
% 0.21/0.51 tff(334,plain,
% 0.21/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.21/0.51 tff(335,assumption,(~n4(e, e)), introduced(assumption)).
% 0.21/0.51 tff(336,plain,
% 0.21/0.51 (^[D: $i, E: $i, F: $i] : refl((n3(D) | (~p2(E, F, D))) <=> (n3(D) | (~p2(E, F, D))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(337,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[336])).
% 0.21/0.51 tff(338,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(339,axiom,(![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_240')).
% 0.21/0.51 tff(340,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.21/0.51 tff(341,plain,(
% 0.21/0.51 ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[340])).
% 0.21/0.51 tff(342,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[341, 337])).
% 0.21/0.51 tff(343,plain,
% 0.21/0.51 (((~![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(344,plain,
% 0.21/0.51 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(e) | (~p2(e, e, e)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(345,plain,
% 0.21/0.51 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(e) | (~p2(e, e, e))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.21/0.51 tff(346,plain,
% 0.21/0.51 (n3(e)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[345, 342, 193])).
% 0.21/0.51 tff(347,plain,
% 0.21/0.51 (^[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)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(348,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[347])).
% 0.21/0.51 tff(349,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(350,plain,
% 0.21/0.51 (^[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))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(351,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[350])).
% 0.21/0.51 tff(352,axiom,(![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_255')).
% 0.21/0.51 tff(353,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.21/0.51 tff(354,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.21/0.51 tff(355,plain,(
% 0.21/0.51 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.51 inference(skolemize,[status(sab)],[354])).
% 0.21/0.51 tff(356,plain,
% 0.21/0.51 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[355, 348])).
% 0.21/0.51 tff(357,plain,
% 0.21/0.51 (n0(e, e) <=> n0(e, e)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(358,axiom,(n0(e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_30')).
% 0.21/0.51 tff(359,plain,
% 0.21/0.51 (n0(e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.21/0.51 tff(360,plain,
% 0.21/0.51 (((~![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(361,plain,
% 0.21/0.51 (((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b)) <=> (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(362,plain,
% 0.21/0.51 (((~![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))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[361])).
% 0.21/0.51 tff(363,plain,
% 0.21/0.51 (((~![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)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[362, 360])).
% 0.21/0.51 tff(364,plain,
% 0.21/0.51 ((~![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))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(365,plain,
% 0.21/0.51 ((~![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.21/0.51 tff(366,plain,
% 0.21/0.51 (q3(e, b)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[365, 359, 356, 247])).
% 0.21/0.51 tff(367,plain,
% 0.21/0.51 (n0(c, d) <=> n0(c, d)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(368,axiom,(n0(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.21/0.51 tff(369,plain,
% 0.21/0.51 (n0(c, d)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.21/0.51 tff(370,plain,
% 0.21/0.51 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(371,plain,
% 0.21/0.51 ((((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(372,plain,
% 0.21/0.51 (((k4(c) | (~n0(c, d))) | (~q3(e, b))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(373,plain,
% 0.21/0.51 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> (((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[372])).
% 0.21/0.51 tff(374,plain,
% 0.21/0.51 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[373, 371])).
% 0.21/0.52 tff(375,axiom,(((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_274')).
% 0.21/0.52 tff(376,plain,
% 0.21/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.21/0.52 tff(377,plain,
% 0.21/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[376, 370])).
% 0.21/0.52 tff(378,plain,
% 0.21/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[377, 370])).
% 0.21/0.52 tff(379,plain,
% 0.21/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[378, 370])).
% 0.21/0.52 tff(380,plain,
% 0.21/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[379, 370])).
% 0.21/0.52 tff(381,plain,
% 0.21/0.52 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[380, 369])).
% 0.21/0.52 tff(382,plain,
% 0.21/0.52 (k4(c)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[381, 366, 346])).
% 0.21/0.53 tff(383,plain,
% 0.21/0.53 (((~![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)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(384,plain,
% 0.21/0.53 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(e, e) | (~m3(e, e, e)) | (~k4(c)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(385,plain,
% 0.21/0.53 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(e, e) | (~m3(e, e, e)) | (~k4(c))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.21/0.53 tff(386,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[385, 382, 335, 334, 207])).
% 0.21/0.53 tff(387,plain,(n4(e, e)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(388,plain,
% 0.21/0.53 (((~![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))) | (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)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(389,plain,
% 0.21/0.53 (((~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)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(390,plain,
% 0.21/0.53 (((~![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))) | ((~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))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[389])).
% 0.21/0.53 tff(391,plain,
% 0.21/0.53 (((~![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))) | ((~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)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[390, 388])).
% 0.21/0.53 tff(392,plain,
% 0.21/0.53 ((~![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))) | ((~n5(a, a)) | (~p4(a, a, a)) | (~n4(e, e)) | (~q4(b, e)) | n5(e, a))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(393,plain,
% 0.21/0.53 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(e, a) | (~n4(e, e)) | (~p4(a, a, a)) | (~q4(b, e)) | (~n5(a, a))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.21/0.53 tff(394,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[393, 387, 324, 314, 311, 300, 151])).
% 0.21/0.53 % SZS output end Proof
% 0.21/0.53 % E exiting
%------------------------------------------------------------------------------