%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN110-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:38:16 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.50s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN110-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:28:41 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.50 % SZS status Unsatisfiable
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 tff(k2_type, type, (
% 0.21/0.50 k2: ( $i * $i ) > $o)).
% 0.21/0.50 tff(a_type, type, (
% 0.21/0.50 a: $i)).
% 0.21/0.50 tff(q1_type, type, (
% 0.21/0.50 q1: ( $i * $i * $i ) > $o)).
% 0.21/0.50 tff(m0_type, type, (
% 0.21/0.50 m0: ( $i * $i * $i ) > $o)).
% 0.21/0.50 tff(d_type, type, (
% 0.21/0.50 d: $i)).
% 0.21/0.50 tff(e_type, type, (
% 0.21/0.50 e: $i)).
% 0.21/0.50 tff(k1_type, type, (
% 0.21/0.50 k1: $i > $o)).
% 0.21/0.50 tff(n0_type, type, (
% 0.21/0.50 n0: ( $i * $i ) > $o)).
% 0.21/0.50 tff(b_type, type, (
% 0.21/0.50 b: $i)).
% 0.21/0.50 tff(c_type, type, (
% 0.21/0.50 c: $i)).
% 0.21/0.50 tff(m1_type, type, (
% 0.21/0.50 m1: ( $i * $i * $i ) > $o)).
% 0.21/0.50 tff(q0_type, type, (
% 0.21/0.50 q0: ( $i * $i ) > $o)).
% 0.21/0.50 tff(l0_type, type, (
% 0.21/0.50 l0: $i > $o)).
% 0.21/0.50 tff(1,plain,
% 0.21/0.50 (^[I: $i, A: $i, J: $i] : refl(((~m0(J, A, I)) | q1(I, I, I)) <=> ((~m0(J, A, I)) | q1(I, I, I)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(2,plain,
% 0.21/0.50 (![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I)) <=> ![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.50 tff(3,plain,
% 0.21/0.50 (![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I)) <=> ![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(4,plain,
% 0.21/0.50 (^[I: $i, A: $i, J: $i] : rewrite((q1(I, I, I) | (~m0(J, A, I))) <=> ((~m0(J, A, I)) | q1(I, I, I)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(5,plain,
% 0.21/0.50 (![I: $i, A: $i, J: $i] : (q1(I, I, I) | (~m0(J, A, I))) <=> ![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.50 tff(6,axiom,(![I: $i, A: $i, J: $i] : (q1(I, I, I) | (~m0(J, A, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_121')).
% 0.21/0.50 tff(7,plain,
% 0.21/0.50 (![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.50 tff(8,plain,
% 0.21/0.50 (![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.50 tff(9,plain,(
% 0.21/0.50 ![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))),
% 0.21/0.50 inference(skolemize,[status(sab)],[8])).
% 0.21/0.50 tff(10,plain,
% 0.21/0.50 (![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.50 tff(11,plain,
% 0.21/0.50 (m0(e, d, a) <=> m0(e, d, a)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(12,axiom,(m0(e, d, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_4')).
% 0.21/0.50 tff(13,plain,
% 0.21/0.50 (m0(e, d, a)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.50 tff(14,plain,
% 0.21/0.50 (((~![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))) | ((~m0(e, d, a)) | q1(a, a, a))) <=> ((~![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))) | (~m0(e, d, a)) | q1(a, a, a))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(15,plain,
% 0.21/0.50 ((~![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))) | ((~m0(e, d, a)) | q1(a, a, a))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(16,plain,
% 0.21/0.50 ((~![I: $i, A: $i, J: $i] : ((~m0(J, A, I)) | q1(I, I, I))) | (~m0(e, d, a)) | q1(a, a, a)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.50 tff(17,plain,
% 0.21/0.50 (q1(a, a, a)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.21/0.50 tff(18,plain,
% 0.21/0.50 (^[A: $i, J: $i] : refl(((~q1(A, J, J)) | k2(J, J)) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(19,plain,
% 0.21/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.50 tff(20,plain,
% 0.21/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(21,plain,
% 0.21/0.50 (^[A: $i, J: $i] : rewrite((k2(J, J) | (~q1(A, J, J))) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(22,plain,
% 0.21/0.50 (![A: $i, J: $i] : (k2(J, J) | (~q1(A, J, J))) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.50 tff(23,axiom,(![A: $i, J: $i] : (k2(J, J) | (~q1(A, J, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_129')).
% 0.21/0.50 tff(24,plain,
% 0.21/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.50 tff(25,plain,
% 0.21/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.51 tff(26,plain,(
% 0.21/0.51 ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.21/0.51 inference(skolemize,[status(sab)],[25])).
% 0.21/0.51 tff(27,plain,
% 0.21/0.51 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.51 tff(28,plain,
% 0.21/0.51 (((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | ((~q1(a, a, a)) | k2(a, a))) <=> ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | (~q1(a, a, a)) | k2(a, a))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(29,plain,
% 0.21/0.51 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | ((~q1(a, a, a)) | k2(a, a))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(30,plain,
% 0.21/0.51 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | (~q1(a, a, a)) | k2(a, a)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.51 tff(31,plain,
% 0.21/0.51 (k2(a, a)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.21/0.51 tff(32,plain,
% 0.21/0.51 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(33,plain,
% 0.21/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.51 tff(34,plain,
% 0.21/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(35,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.21/0.51 tff(36,plain,
% 0.21/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.51 tff(37,plain,(
% 0.21/0.51 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[36])).
% 0.21/0.51 tff(38,plain,
% 0.21/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.51 tff(39,plain,
% 0.21/0.51 (n0(b, a) <=> n0(b, a)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(40,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.21/0.51 tff(41,plain,
% 0.21/0.51 (n0(b, a)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.51 tff(42,plain,
% 0.21/0.51 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(43,plain,
% 0.21/0.51 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(44,plain,
% 0.21/0.51 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.51 tff(45,plain,
% 0.21/0.51 (k1(a)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[44, 41, 38])).
% 0.21/0.51 tff(46,plain,
% 0.21/0.51 ((~k2(c, a)) <=> (~k2(c, a))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(47,axiom,(~k2(c, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.51 tff(48,plain,
% 0.21/0.51 (~k2(c, a)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.51 tff(49,assumption,(~m0(a, d, a)), introduced(assumption)).
% 0.21/0.51 tff(50,plain,
% 0.21/0.51 (^[X: $i] : refl(m0(a, X, a) <=> m0(a, X, a))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(51,plain,
% 0.21/0.51 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 0.21/0.51 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.51 tff(52,plain,
% 0.21/0.51 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(53,axiom,(![X: $i] : m0(a, X, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_12')).
% 0.21/0.51 tff(54,plain,
% 0.21/0.51 (![X: $i] : m0(a, X, a)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.51 tff(55,plain,(
% 0.21/0.51 ![X: $i] : m0(a, X, a)),
% 0.21/0.51 inference(skolemize,[status(sab)],[54])).
% 0.21/0.51 tff(56,plain,
% 0.21/0.51 (![X: $i] : m0(a, X, a)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.51 tff(57,plain,
% 0.21/0.51 ((~![X: $i] : m0(a, X, a)) | m0(a, d, a)),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(58,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[57, 56, 49])).
% 0.21/0.51 tff(59,plain,(m0(a, d, a)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(60,plain,
% 0.21/0.51 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)) <=> ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(61,plain,
% 0.21/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.51 tff(62,plain,
% 0.21/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(63,plain,
% 0.21/0.51 (^[H: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1(F, a, G) | (~m0(a, H, a))) <=> ((~m0(a, H, a)) | m1(F, a, G))), (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) <=> (((~m0(a, H, a)) | m1(F, a, G)) | (~q0(F, G))))), rewrite((((~m0(a, H, a)) | m1(F, a, G)) | (~q0(F, G))) <=> ((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G))), (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) <=> ((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G)))), ((((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G))) <=> (((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G)) | (~m1(G, c, G))))), rewrite((((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G)) | (~m1(G, c, G))) <=> ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))), ((((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G))) <=> ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(64,plain,
% 0.21/0.51 (![H: $i, F: $i, G: $i] : (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.51 tff(65,axiom,(![H: $i, F: $i, G: $i] : (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_024')).
% 0.21/0.51 tff(66,plain,
% 0.21/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.51 tff(67,plain,
% 0.21/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.51 tff(68,plain,(
% 0.21/0.51 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.21/0.51 inference(skolemize,[status(sab)],[67])).
% 0.21/0.51 tff(69,plain,
% 0.21/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.51 tff(70,plain,
% 0.21/0.51 (l0(c) <=> l0(c)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(71,axiom,(l0(c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.21/0.51 tff(72,plain,
% 0.21/0.51 (l0(c)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.51 tff(73,plain,
% 0.21/0.51 (((~l0(c)) | m1(c, c, c)) <=> ((~l0(c)) | m1(c, c, c))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(74,plain,
% 0.21/0.51 ((m1(c, c, c) | (~l0(c))) <=> ((~l0(c)) | m1(c, c, c))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(75,axiom,(m1(c, c, c) | (~l0(c))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_020')).
% 0.21/0.51 tff(76,plain,
% 0.21/0.51 ((~l0(c)) | m1(c, c, c)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.51 tff(77,plain,
% 0.21/0.51 ((~l0(c)) | m1(c, c, c)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.21/0.51 tff(78,plain,
% 0.21/0.51 (m1(c, c, c)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[77, 72])).
% 0.21/0.51 tff(79,plain,
% 0.21/0.51 (q0(d, c) <=> q0(d, c)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(80,axiom,(q0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_33')).
% 0.21/0.51 tff(81,plain,
% 0.21/0.51 (q0(d, c)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.51 tff(82,plain,
% 0.21/0.51 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (m1(d, a, c) | (~m0(a, d, a)) | (~m1(c, c, c)) | (~q0(d, c)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | m1(d, a, c) | (~m0(a, d, a)) | (~m1(c, c, c)) | (~q0(d, c)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(83,plain,
% 0.21/0.51 (((~q0(d, c)) | (~m1(c, c, c)) | (~m0(a, d, a)) | m1(d, a, c)) <=> (m1(d, a, c) | (~m0(a, d, a)) | (~m1(c, c, c)) | (~q0(d, c)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(84,plain,
% 0.21/0.51 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(d, c)) | (~m1(c, c, c)) | (~m0(a, d, a)) | m1(d, a, c))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (m1(d, a, c) | (~m0(a, d, a)) | (~m1(c, c, c)) | (~q0(d, c))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.51 tff(85,plain,
% 0.21/0.51 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(d, c)) | (~m1(c, c, c)) | (~m0(a, d, a)) | m1(d, a, c))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | m1(d, a, c) | (~m0(a, d, a)) | (~m1(c, c, c)) | (~q0(d, c)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[84, 82])).
% 0.21/0.51 tff(86,plain,
% 0.21/0.51 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(d, c)) | (~m1(c, c, c)) | (~m0(a, d, a)) | m1(d, a, c))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | m1(d, a, c) | (~m0(a, d, a)) | (~m1(c, c, c)) | (~q0(d, c))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 (m1(d, a, c)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[87, 81, 78, 69, 59])).
% 0.21/0.51 tff(89,plain,
% 0.21/0.51 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k2(C, D) | (~m1(E, D, C))) <=> ((~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> (((~m1(E, D, C)) | k2(C, D)) | (~k1(F))))), rewrite((((~m1(E, D, C)) | k2(C, D)) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D)))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> (((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))))), rewrite((((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.51 tff(94,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_127')).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.21/0.51 tff(97,plain,(
% 0.21/0.51 ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.21/0.51 inference(skolemize,[status(sab)],[96])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.38/0.53 tff(99,plain,
% 0.38/0.53 (((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(a)) | (~k2(a, a)) | (~m1(d, a, c)) | k2(c, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(a)) | (~k2(a, a)) | (~m1(d, a, c)) | k2(c, a))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(100,plain,
% 0.38/0.53 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(a)) | (~k2(a, a)) | (~m1(d, a, c)) | k2(c, a))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(101,plain,
% 0.38/0.53 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(a)) | (~k2(a, a)) | (~m1(d, a, c)) | k2(c, a)),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.38/0.53 tff(102,plain,
% 0.38/0.53 ($false),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[101, 98, 88, 48, 45, 31])).
% 0.38/0.53 % SZS output end Proof
% 0.38/0.53 % E exiting
%------------------------------------------------------------------------------