%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN123-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:38:18 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.55s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SYN123-1 : TPTP v9.0.0. Released v1.1.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 12:28:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.55 % SZS status Unsatisfiable
% 0.23/0.55 % SZS output start Proof
% 0.23/0.55 tff(m0_type, type, (
% 0.23/0.55 m0: ( $i * $i * $i ) > $o)).
% 0.23/0.55 tff(d_type, type, (
% 0.23/0.55 d: $i)).
% 0.23/0.55 tff(b_type, type, (
% 0.23/0.55 b: $i)).
% 0.23/0.55 tff(p0_type, type, (
% 0.23/0.55 p0: ( $i * $i ) > $o)).
% 0.23/0.55 tff(l2_type, type, (
% 0.23/0.55 l2: ( $i * $i ) > $o)).
% 0.23/0.55 tff(s1_type, type, (
% 0.23/0.55 s1: $i > $o)).
% 0.23/0.55 tff(q0_type, type, (
% 0.23/0.55 q0: ( $i * $i ) > $o)).
% 0.23/0.55 tff(1,assumption,(~m0(b, d, d)), introduced(assumption)).
% 0.23/0.55 tff(2,plain,
% 0.23/0.55 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(3,plain,
% 0.23/0.55 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.23/0.55 inference(quant_intro,[status(thm)],[2])).
% 0.23/0.55 tff(4,plain,
% 0.23/0.55 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.23/0.55 tff(6,plain,
% 0.23/0.55 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.23/0.55 tff(7,plain,(
% 0.23/0.55 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.23/0.55 inference(skolemize,[status(sab)],[6])).
% 0.23/0.55 tff(8,plain,
% 0.23/0.55 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.23/0.55 tff(9,plain,
% 0.23/0.55 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, d)),
% 0.23/0.55 inference(quant_inst,[status(thm)],[])).
% 0.23/0.55 tff(10,plain,
% 0.23/0.55 ($false),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.23/0.55 tff(11,plain,(m0(b, d, d)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.55 tff(12,assumption,(~p0(b, b)), introduced(assumption)).
% 0.23/0.55 tff(13,plain,
% 0.23/0.55 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(14,plain,
% 0.23/0.55 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.23/0.55 inference(quant_intro,[status(thm)],[13])).
% 0.23/0.55 tff(15,plain,
% 0.23/0.55 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(16,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.23/0.55 tff(17,plain,
% 0.23/0.55 (![X: $i] : p0(b, X)),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.23/0.55 tff(18,plain,(
% 0.23/0.55 ![X: $i] : p0(b, X)),
% 0.23/0.55 inference(skolemize,[status(sab)],[17])).
% 0.23/0.55 tff(19,plain,
% 0.23/0.55 (![X: $i] : p0(b, X)),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.23/0.55 tff(20,plain,
% 0.23/0.55 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.23/0.55 inference(quant_inst,[status(thm)],[])).
% 0.23/0.55 tff(21,plain,
% 0.23/0.55 ($false),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.23/0.55 tff(22,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.55 tff(23,plain,
% 0.23/0.55 ((~l2(d, d)) <=> (~l2(d, d))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(24,axiom,(~l2(d, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.23/0.55 tff(25,plain,
% 0.23/0.55 (~l2(d, d)),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.23/0.55 tff(26,plain,
% 0.23/0.55 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(27,plain,
% 0.23/0.55 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.55 tff(28,plain,
% 0.23/0.55 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(29,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.23/0.55 tff(30,plain,
% 0.23/0.55 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.23/0.55 tff(31,plain,(
% 0.23/0.55 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.23/0.55 inference(skolemize,[status(sab)],[30])).
% 0.23/0.55 tff(32,plain,
% 0.23/0.55 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.23/0.55 tff(33,plain,
% 0.23/0.55 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(34,plain,
% 0.23/0.55 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.23/0.55 inference(quant_inst,[status(thm)],[])).
% 0.23/0.55 tff(35,plain,
% 0.23/0.55 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.55 tff(36,plain,
% 0.23/0.55 (s1(b)),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.23/0.55 tff(37,plain,
% 0.23/0.55 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(38,plain,
% 0.23/0.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[37])).
% 0.23/0.55 tff(39,plain,
% 0.23/0.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(40,plain,
% 0.23/0.55 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(41,plain,
% 0.23/0.55 (![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[40])).
% 0.23/0.55 tff(42,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.23/0.55 tff(43,plain,
% 0.23/0.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.23/0.55 tff(44,plain,
% 0.23/0.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.23/0.55 tff(45,plain,(
% 0.23/0.55 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.23/0.55 inference(skolemize,[status(sab)],[44])).
% 0.23/0.55 tff(46,plain,
% 0.23/0.55 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.23/0.55 tff(47,plain,
% 0.23/0.55 (q0(d, d) <=> q0(d, d)),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(48,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.23/0.55 tff(49,plain,
% 0.23/0.55 (q0(d, d)),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.23/0.55 tff(50,plain,
% 0.23/0.55 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(51,plain,
% 0.23/0.55 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))),
% 0.23/0.55 inference(quant_inst,[status(thm)],[])).
% 0.23/0.55 tff(52,plain,
% 0.23/0.55 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d)),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.23/0.55 tff(53,plain,
% 0.23/0.55 (s1(d)),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[52, 49, 46, 36])).
% 0.23/0.55 tff(54,plain,
% 0.23/0.55 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(55,plain,
% 0.23/0.55 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[54])).
% 0.23/0.55 tff(56,plain,
% 0.23/0.55 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(57,plain,
% 0.23/0.55 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(58,plain,
% 0.23/0.55 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[57])).
% 0.40/0.57 tff(59,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 0.40/0.57 tff(60,plain,
% 0.40/0.57 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.40/0.57 tff(61,plain,
% 0.40/0.57 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.40/0.57 tff(62,plain,(
% 0.40/0.57 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.40/0.57 inference(skolemize,[status(sab)],[61])).
% 0.40/0.57 tff(63,plain,
% 0.40/0.57 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.40/0.57 tff(64,plain,
% 0.40/0.57 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(65,plain,
% 0.40/0.57 (((~p0(b, b)) | (~m0(b, d, d)) | (~s1(d)) | l2(d, d)) <=> ((~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(66,plain,
% 0.40/0.57 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, d, d)) | (~s1(d)) | l2(d, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[65])).
% 0.40/0.57 tff(67,plain,
% 0.40/0.57 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, d, d)) | (~s1(d)) | l2(d, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[66, 64])).
% 0.40/0.57 tff(68,plain,
% 0.40/0.57 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, d, d)) | (~s1(d)) | l2(d, d))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(69,plain,
% 0.40/0.57 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(d)) | l2(d, d) | (~p0(b, b)) | (~m0(b, d, d))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.40/0.57 tff(70,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[69, 63, 53, 25, 22, 11])).
% 0.40/0.57 % SZS output end Proof
% 0.40/0.57 % E exiting
%------------------------------------------------------------------------------