%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN192-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:27 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN192-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:33:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(n3_type, type, (
% 0.19/0.46 n3: $i > $o)).
% 0.19/0.46 tff(a_type, type, (
% 0.19/0.46 a: $i)).
% 0.19/0.46 tff(p2_type, type, (
% 0.19/0.46 p2: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(m1_type, type, (
% 0.19/0.46 m1: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(l0_type, type, (
% 0.19/0.46 l0: $i > $o)).
% 0.19/0.46 tff(s0_type, type, (
% 0.19/0.46 s0: $i > $o)).
% 0.19/0.46 tff(d_type, type, (
% 0.19/0.46 d: $i)).
% 0.19/0.46 tff(r4_type, type, (
% 0.19/0.46 r4: $i > $o)).
% 0.19/0.46 tff(q3_type, type, (
% 0.19/0.46 q3: ( $i * $i ) > $o)).
% 0.19/0.46 tff(p0_type, type, (
% 0.19/0.46 p0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(b_type, type, (
% 0.19/0.46 b: $i)).
% 0.19/0.46 tff(e_type, type, (
% 0.19/0.46 e: $i)).
% 0.19/0.46 tff(q2_type, type, (
% 0.19/0.46 q2: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(l1_type, type, (
% 0.19/0.46 l1: ( $i * $i ) > $o)).
% 0.19/0.46 tff(r0_type, type, (
% 0.19/0.46 r0: $i > $o)).
% 0.19/0.46 tff(m0_type, type, (
% 0.19/0.46 m0: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(c_type, type, (
% 0.19/0.46 c: $i)).
% 0.19/0.46 tff(n0_type, type, (
% 0.19/0.46 n0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 (^[D: $i, E: $i, F: $i] : refl((n3(D) | (~p2(E, F, D))) <=> (n3(D) | (~p2(E, F, D))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(4,axiom,(![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_240')).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.46 tff(6,plain,(
% 0.19/0.46 ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[5])).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.46 tff(8,plain,
% 0.19/0.46 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 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')).
% 0.19/0.46 tff(12,plain,
% 0.19/0.46 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.46 tff(13,plain,(
% 0.19/0.46 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[12])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (l0(a) <=> l0(a)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(16,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (l0(a)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 (s0(d) <=> s0(d)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(19,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (s0(d)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[24, 22])).
% 0.19/0.46 tff(26,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (m1(a, a, a)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[31, 20, 17])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (((~![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (p2(a, a, a)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[35, 32, 14])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(a) | (~p2(a, a, a)))) <=> ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(a) | (~p2(a, a, a)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(a) | (~p2(a, a, a)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(a) | (~p2(a, a, a))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (n3(a)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[39, 36, 7])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 ((~r4(a)) <=> (~r4(a))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(42,axiom,(~r4(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (~r4(a)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (^[I: $i, J: $i, H: $i, G: $i] : refl(((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G)) <=> ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G)) <=> ![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 (![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G)) <=> ![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (^[I: $i, J: $i, H: $i, G: $i] : trans(monotonicity(rewrite(((r4(G) | (~n3(G))) | (~q3(H, I))) <=> ((~n3(G)) | (~q3(H, I)) | r4(G))), ((((r4(G) | (~n3(G))) | (~q3(H, I))) | (~p0(J, G))) <=> (((~n3(G)) | (~q3(H, I)) | r4(G)) | (~p0(J, G))))), rewrite((((~n3(G)) | (~q3(H, I)) | r4(G)) | (~p0(J, G))) <=> ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))), ((((r4(G) | (~n3(G))) | (~q3(H, I))) | (~p0(J, G))) <=> ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 (![I: $i, J: $i, H: $i, G: $i] : (((r4(G) | (~n3(G))) | (~q3(H, I))) | (~p0(J, G))) <=> ![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.46 tff(49,axiom,(![I: $i, J: $i, H: $i, G: $i] : (((r4(G) | (~n3(G))) | (~q3(H, I))) | (~p0(J, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_298')).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 (![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.46 tff(52,plain,(
% 0.19/0.46 ![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))),
% 0.19/0.46 inference(skolemize,[status(sab)],[51])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (^[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)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.46 tff(59,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')).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.46 tff(62,plain,(
% 0.19/0.46 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.19/0.46 inference(skolemize,[status(sab)],[61])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (m0(e, b, c) <=> m0(e, b, c)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(65,axiom,(m0(e, b, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (m0(e, b, c)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (p0(c, b) <=> p0(c, b)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(68,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (p0(c, b)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (r0(b) <=> r0(b)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(71,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (r0(b)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 (((~![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e)) <=> ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (((~![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)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (((~![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))),
% 0.19/0.46 inference(transitivity,[status(thm)],[75, 73])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 ((~![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))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 ((~![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)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (l1(b, e)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[78, 72, 69, 66, 63])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (^[H: $i, G: $i] : refl(((~l1(H, G)) | q2(G, G, H)) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (^[H: $i, G: $i] : rewrite((q2(G, G, H) | (~l1(H, G))) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G))) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.46 tff(85,axiom,(![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_186')).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.46 tff(88,plain,(
% 0.19/0.46 ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.19/0.46 inference(skolemize,[status(sab)],[87])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (((~![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (q2(e, e, b)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (^[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)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.47 tff(99,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')).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.47 tff(102,plain,(
% 0.19/0.47 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.19/0.47 inference(skolemize,[status(sab)],[101])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (n0(e, e) <=> n0(e, e)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(105,axiom,(n0(e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_30')).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (n0(e, e)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b)) <=> (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (q3(e, b)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[112, 106, 103, 93])).
% 0.19/0.47 tff(114,assumption,(~p0(b, a)), introduced(assumption)).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.19/0.47 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(118,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (![X: $i] : p0(b, X)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.47 tff(120,plain,(
% 0.19/0.47 ![X: $i] : p0(b, X)),
% 0.19/0.47 inference(skolemize,[status(sab)],[119])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (![X: $i] : p0(b, X)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 ((~![X: $i] : p0(b, X)) | p0(b, a)),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[122, 121, 114])).
% 0.19/0.47 tff(124,plain,(p0(b, a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | ((~p0(b, a)) | (~q3(e, b)) | (~n3(a)) | r4(a))) <=> ((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | (~p0(b, a)) | (~q3(e, b)) | (~n3(a)) | r4(a))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (((~p0(b, a)) | (~n3(a)) | (~q3(e, b)) | r4(a)) <=> ((~p0(b, a)) | (~q3(e, b)) | (~n3(a)) | r4(a))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | ((~p0(b, a)) | (~n3(a)) | (~q3(e, b)) | r4(a))) <=> ((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | ((~p0(b, a)) | (~q3(e, b)) | (~n3(a)) | r4(a)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[126])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | ((~p0(b, a)) | (~n3(a)) | (~q3(e, b)) | r4(a))) <=> ((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | (~p0(b, a)) | (~q3(e, b)) | (~n3(a)) | r4(a))),
% 0.19/0.48 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 ((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | ((~p0(b, a)) | (~n3(a)) | (~q3(e, b)) | r4(a))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 ((~![I: $i, J: $i, H: $i, G: $i] : ((~p0(J, G)) | (~n3(G)) | (~q3(H, I)) | r4(G))) | (~p0(b, a)) | (~q3(e, b)) | (~n3(a)) | r4(a)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[130, 124, 113, 53, 43, 40])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------