%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN294-1 : 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 05:38:41 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN294-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:34:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(p0_type, type, (
% 0.20/0.48 p0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(b_type, type, (
% 0.20/0.48 b: $i)).
% 0.20/0.48 tff(k1_type, type, (
% 0.20/0.48 k1: $i > $o)).
% 0.20/0.48 tff(d_type, type, (
% 0.20/0.48 d: $i)).
% 0.20/0.48 tff(n0_type, type, (
% 0.20/0.48 n0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(c_type, type, (
% 0.20/0.48 c: $i)).
% 0.20/0.48 tff(q1_type, type, (
% 0.20/0.48 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(q0_type, type, (
% 0.20/0.48 q0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (![X: $i] : p0(b, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.48 tff(7,plain,(
% 0.20/0.48 ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(skolemize,[status(sab)],[6])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (![X: $i] : p0(b, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.48 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(15,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.48 tff(17,plain,(
% 0.20/0.48 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[16])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (n0(c, d) <=> n0(c, d)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(20,axiom,(n0(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (n0(c, d)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (k1(d)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[24, 21, 18])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 ((~q1(d, d, c)) <=> (~q1(d, d, c))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(27,axiom,(~q1(d, d, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (~q1(d, d, c)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (^[E: $i, F: $i, G: $i] : refl(((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)) <=> ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)) <=> ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F)) <=> ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q1(E, E, F) | (~p0(G, G))) <=> ((~p0(G, G)) | q1(E, E, F))), (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) <=> (((~p0(G, G)) | q1(E, E, F)) | (~q0(F, E))))), rewrite((((~p0(G, G)) | q1(E, E, F)) | (~q0(F, E))) <=> ((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F))), (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) <=> ((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F)))), ((((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E))) <=> (((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F)) | (~k1(E))))), rewrite((((~p0(G, G)) | (~q0(F, E)) | q1(E, E, F)) | (~k1(E))) <=> ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))), ((((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E))) <=> ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![E: $i, F: $i, G: $i] : (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E))) <=> ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.48 tff(34,axiom,(![E: $i, F: $i, G: $i] : (((q1(E, E, F) | (~p0(G, G))) | (~q0(F, E))) | (~k1(E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_109')).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.48 tff(37,plain,(
% 0.20/0.48 ![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.48 inference(skolemize,[status(sab)],[36])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.48 tff(39,assumption,(~q0(c, d)), introduced(assumption)).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (^[X: $i] : refl(q0(X, d) <=> q0(X, d))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,axiom,(![X: $i] : q0(X, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_17')).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (![X: $i] : q0(X, d)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.48 tff(45,plain,(
% 0.20/0.48 ![X: $i] : q0(X, d)),
% 0.20/0.48 inference(skolemize,[status(sab)],[44])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![X: $i] : q0(X, d)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((~![X: $i] : q0(X, d)) | q0(c, d)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[47, 46, 39])).
% 0.20/0.48 tff(49,plain,(q0(c, d)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c)) <=> ((~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c))) <=> ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | ((~p0(b, b)) | (~k1(d)) | (~q0(c, d)) | q1(d, d, c))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 ((~![E: $i, F: $i, G: $i] : ((~p0(G, G)) | (~k1(E)) | (~q0(F, E)) | q1(E, E, F))) | (~q0(c, d)) | q1(d, d, c) | (~k1(d)) | (~p0(b, b))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[55, 49, 38, 28, 25, 11])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------