%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN066-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:07 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN066-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:27:07 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(big_r_type, type, (
% 0.11/0.38 big_r: ( $i * $i ) > $o)).
% 0.11/0.38 tff(a_type, type, (
% 0.11/0.38 a: $i)).
% 0.11/0.38 tff(big_q_type, type, (
% 0.11/0.38 big_q: ( $i * $i ) > $o)).
% 0.11/0.38 tff(g_type, type, (
% 0.11/0.38 g: $i > $i)).
% 0.11/0.38 tff(elem_0_type, type, (
% 0.11/0.38 elem_0: $i)).
% 0.11/0.38 tff(h_type, type, (
% 0.11/0.38 h: ( $i * $i ) > $i)).
% 0.11/0.38 tff(f_type, type, (
% 0.11/0.38 f: ( $i * $i ) > $i)).
% 0.11/0.38 tff(big_p_type, type, (
% 0.11/0.38 big_p: ( $i * $i ) > $o)).
% 0.11/0.38 tff(1,assumption,(big_r(a, a)), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (^[Z: $i] : refl((~big_r(a, Z)) <=> (~big_r(a, Z)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![Z: $i] : (~big_r(a, Z)) <=> ![Z: $i] : (~big_r(a, Z))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![Z: $i] : (~big_r(a, Z)) <=> ![Z: $i] : (~big_r(a, Z))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(5,axiom,(![Z: $i] : (~big_r(a, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (![Z: $i] : (~big_r(a, Z))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.38 tff(7,plain,(
% 0.11/0.38 ![Z: $i] : (~big_r(a, Z))),
% 0.11/0.38 inference(skolemize,[status(sab)],[6])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![Z: $i] : (~big_r(a, Z))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 ((~![Z: $i] : (~big_r(a, Z))) | (~big_r(a, a))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.38 tff(11,plain,(~big_r(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : refl(big_p(f(X, Y), X) <=> big_p(f(X, Y), X))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![Y: $i, X: $i] : big_p(f(X, Y), X) <=> ![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![Y: $i, X: $i] : big_p(f(X, Y), X) <=> ![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,axiom,(![Y: $i, X: $i] : big_p(f(X, Y), X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.11/0.38 inference(skolemize,[status(sab)],[16])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : big_p(f(X, Y), X)) | big_p(f(elem!0, elem!0), elem!0)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (big_p(f(elem!0, elem!0), elem!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : refl(((~big_p(Y, X)) | big_p(f(X, Y), g(X))) <=> ((~big_p(Y, X)) | big_p(f(X, Y), g(X))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(24,axiom,(![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.38 tff(26,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[25])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | ((~big_p(f(elem!0, elem!0), elem!0)) | big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0)))) <=> ((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | (~big_p(f(elem!0, elem!0), elem!0)) | big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | ((~big_p(f(elem!0, elem!0), elem!0)) | big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | (~big_p(f(elem!0, elem!0), elem!0)) | big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (^[Y: $i, X: $i] : refl(((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))) <=> ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(35,axiom,(![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.38 tff(37,plain,(
% 0.11/0.38 ![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[36])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | ((~big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0)))) <=> ((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | (~big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | ((~big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 ((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | (~big_p(f(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (^[Z: $i, Y: $i, X: $i] : refl(((~big_q(X, Y)) | big_r(Z, Z)) <=> ((~big_q(X, Y)) | big_r(Z, Z)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(46,axiom,(![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.38 tff(48,plain,(
% 0.18/0.38 ![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.18/0.38 inference(skolemize,[status(sab)],[47])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | ((~big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_r(a, a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | (~big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_r(a, a))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 ((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | ((~big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_r(a, a))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 ((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | (~big_q(h(elem!0, f(elem!0, elem!0)), g(elem!0))) | big_r(a, a)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[52, 49, 42, 11])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------