%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN065+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN065+1 : TPTP v9.0.0. Released v2.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n010.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 12:28:57 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(big_h_type, type, (
% 0.21/0.40 big_h: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.40 tptp_fun_Y_0: $i > $i)).
% 0.21/0.40 tff(tptp_fun_X_2_type, type, (
% 0.21/0.40 tptp_fun_X_2: $i)).
% 0.21/0.40 tff(big_g_type, type, (
% 0.21/0.40 big_g: ( $i * $i ) > $o)).
% 0.21/0.40 tff(big_f_type, type, (
% 0.21/0.40 big_f: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (![X: $i] : ?[Y: $i] : big_f(X, Y) <=> ![X: $i] : ?[Y: $i] : big_f(X, Y)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(2,axiom,(![X: $i] : ?[Y: $i] : big_f(X, Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel36_1')).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![X: $i] : ?[Y: $i] : big_f(X, Y)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.40 tff(4,plain,(
% 0.21/0.40 ![X: $i] : big_f(X, tptp_fun_Y_0(X))),
% 0.21/0.40 inference(skolemize,[status(sab)],[3])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 ((~![X: $i] : big_f(X, tptp_fun_Y_0(X))) | big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 ((big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))) | big_g(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2)))) | (~big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))) | big_g(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 ((~![X: $i] : big_f(X, tptp_fun_Y_0(X))) | big_f(X!2, tptp_fun_Y_0(X!2))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (big_f(X!2, tptp_fun_Y_0(X!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[9, 4])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 ((big_f(X!2, tptp_fun_Y_0(X!2)) | big_g(X!2, tptp_fun_Y_0(X!2))) | (~big_f(X!2, tptp_fun_Y_0(X!2)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (big_f(X!2, tptp_fun_Y_0(X!2)) | big_g(X!2, tptp_fun_Y_0(X!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : refl(((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))) <=> ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))) <=> ![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : rewrite(((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))) <=> ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))) <=> ![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))) <=> ![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))) <=> ![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : trans(monotonicity(quant_intro(proof_bind(^[Z: $i] : rewrite(((big_f(Y, Z) | big_g(Y, Z)) => big_h(X, Z)) <=> ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))), (![Z: $i] : ((big_f(Y, Z) | big_g(Y, Z)) => big_h(X, Z)) <=> ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))), (((big_f(X, Y) | big_g(X, Y)) => ![Z: $i] : ((big_f(Y, Z) | big_g(Y, Z)) => big_h(X, Z))) <=> ((big_f(X, Y) | big_g(X, Y)) => ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))))), rewrite(((big_f(X, Y) | big_g(X, Y)) => ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z))) <=> ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))), (((big_f(X, Y) | big_g(X, Y)) => ![Z: $i] : ((big_f(Y, Z) | big_g(Y, Z)) => big_h(X, Z))) <=> ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((big_f(X, Y) | big_g(X, Y)) => ![Z: $i] : ((big_f(Y, Z) | big_g(Y, Z)) => big_h(X, Z))) <=> ![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.40 tff(21,axiom,(![X: $i, Y: $i] : ((big_f(X, Y) | big_g(X, Y)) => ![Z: $i] : ((big_f(Y, Z) | big_g(Y, Z)) => big_h(X, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel36_3')).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.40 tff(24,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[23])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))) | ((~(big_f(X!2, tptp_fun_Y_0(X!2)) | big_g(X!2, tptp_fun_Y_0(X!2)))) | ![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z)))) <=> ((~![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))) | (~(big_f(X!2, tptp_fun_Y_0(X!2)) | big_g(X!2, tptp_fun_Y_0(X!2)))) | ![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))) | ((~(big_f(X!2, tptp_fun_Y_0(X!2)) | big_g(X!2, tptp_fun_Y_0(X!2)))) | ![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~(big_f(X, Y) | big_g(X, Y))) | ![Z: $i] : ((~(big_f(Y, Z) | big_g(Y, Z))) | big_h(X, Z)))) | (~(big_f(X!2, tptp_fun_Y_0(X!2)) | big_g(X!2, tptp_fun_Y_0(X!2)))) | ![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[28, 25, 12])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (((~![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z))) | ((~(big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))) | big_g(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))))) | big_h(X!2, tptp_fun_Y_0(tptp_fun_Y_0(X!2))))) <=> ((~![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z))) | (~(big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))) | big_g(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))))) | big_h(X!2, tptp_fun_Y_0(tptp_fun_Y_0(X!2))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z))) | ((~(big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))) | big_g(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))))) | big_h(X!2, tptp_fun_Y_0(tptp_fun_Y_0(X!2))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 ((~![Z: $i] : ((~(big_f(tptp_fun_Y_0(X!2), Z) | big_g(tptp_fun_Y_0(X!2), Z))) | big_h(X!2, Z))) | (~(big_f(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))) | big_g(tptp_fun_Y_0(X!2), tptp_fun_Y_0(tptp_fun_Y_0(X!2))))) | big_h(X!2, tptp_fun_Y_0(tptp_fun_Y_0(X!2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (big_h(X!2, tptp_fun_Y_0(tptp_fun_Y_0(X!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[32, 29, 8])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (^[Y: $i] : refl((~big_h(X!2, Y)) <=> (~big_h(X!2, Y)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![Y: $i] : (~big_h(X!2, Y)) <=> ![Y: $i] : (~big_h(X!2, Y))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ((~![X: $i] : ?[Y: $i] : big_h(X, Y)) <=> (~![X: $i] : ?[Y: $i] : big_h(X, Y))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(37,axiom,(~![X: $i] : ?[Y: $i] : big_h(X, Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel36')).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (~![X: $i] : ?[Y: $i] : big_h(X, Y)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (~![X: $i] : ?[Y: $i] : big_h(X, Y)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (~![X: $i] : ?[Y: $i] : big_h(X, Y)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (~![X: $i] : ?[Y: $i] : big_h(X, Y)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.41 tff(42,plain,(
% 0.21/0.41 $oeq((~?[Y: $i] : big_h(X!2, Y)), ![Y: $i] : (~big_h(X!2, Y)))),
% 0.21/0.41 inference(transitivity,[status(sab)],[41])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![Y: $i] : (~big_h(X!2, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((~![Y: $i] : (~big_h(X!2, Y))) | (~big_h(X!2, tptp_fun_Y_0(tptp_fun_Y_0(X!2))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[44, 43, 33])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------