%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN338+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:38:48 AM UTC 2025
% Result : Theorem 0.21s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN338+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 12:31:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start Proof
% 0.21/0.37 tff(big_f_type, type, (
% 0.21/0.37 big_f: ( $i * $i ) > $o)).
% 0.21/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.37 tptp_fun_Y_0: $i > $i)).
% 0.21/0.37 tff(elem_1_type, type, (
% 0.21/0.37 elem_1: $i)).
% 0.21/0.37 tff(1,plain,
% 0.21/0.37 (^[X: $i, Z: $i] : refl((~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))) <=> (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(2,plain,
% 0.21/0.37 (![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))) <=> ![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.37 tff(3,plain,
% 0.21/0.37 (![X: $i] : ![Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))) <=> ![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))),
% 0.21/0.37 inference(pull_quant,[status(thm)],[])).
% 0.21/0.37 tff(4,plain,
% 0.21/0.37 ((~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y)))) <=> (~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y))))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(5,plain,
% 0.21/0.37 ((~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(X, Y) => (big_f(Z, X) => big_f(Y, Y)))) <=> (~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y))))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(6,axiom,(~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(X, Y) => (big_f(Z, X) => big_f(Y, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_15_3')).
% 0.21/0.37 tff(7,plain,
% 0.21/0.37 (~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.37 tff(8,plain,
% 0.21/0.37 (~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.21/0.37 tff(9,plain,
% 0.21/0.37 (~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.37 tff(10,plain,
% 0.21/0.37 (~?[X: $i] : ![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.21/0.37 tff(11,plain,
% 0.21/0.37 (^[X: $i] : trans(sk($oeq((~![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y)))), (~?[Z: $i] : (big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))))), nnf_neg(proof_bind(^[Z: $i] : refl($oeq((~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))), (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))))), $oeq((~?[Z: $i] : (big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))), ![Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X))))))), $oeq((~![Y: $i] : ?[Z: $i] : (big_f(Y, Y) | (~big_f(Z, X)) | (~big_f(X, Y)))), ![Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(12,plain,(
% 0.21/0.37 ![X: $i] : ![Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))),
% 0.21/0.37 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.21/0.37 tff(13,plain,
% 0.21/0.37 (![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.21/0.37 tff(14,plain,
% 0.21/0.37 (![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.21/0.37 tff(15,plain,
% 0.21/0.37 ((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~(big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)) | (~big_f(elem!1, elem!1)) | (~big_f(elem!1, tptp_fun_Y_0(elem!1)))))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(16,plain,
% 0.21/0.37 (~(big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)) | (~big_f(elem!1, elem!1)) | (~big_f(elem!1, tptp_fun_Y_0(elem!1))))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.37 tff(17,plain,
% 0.21/0.37 ((big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)) | (~big_f(elem!1, elem!1)) | (~big_f(elem!1, tptp_fun_Y_0(elem!1)))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)))),
% 0.21/0.37 inference(tautology,[status(thm)],[])).
% 0.21/0.37 tff(18,plain,
% 0.21/0.37 (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.37 tff(19,plain,
% 0.21/0.37 (((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))),
% 0.21/0.37 inference(tautology,[status(thm)],[])).
% 0.21/0.37 tff(20,plain,
% 0.21/0.37 ((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.37 tff(21,plain,
% 0.21/0.37 (((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))) <=> ((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(22,plain,
% 0.21/0.37 ((~(big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))) <=> (~((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(23,plain,
% 0.21/0.37 (((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~(big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))) <=> ((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.21/0.37 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.37 tff(24,plain,
% 0.21/0.37 (((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~(big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))) <=> ((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.21/0.37 inference(transitivity,[status(thm)],[23, 21])).
% 0.21/0.37 tff(25,plain,
% 0.21/0.37 ((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~(big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(26,plain,
% 0.21/0.37 ((~![X: $i, Z: $i] : (~(big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)) | (~big_f(Z, X)) | (~big_f(X, tptp_fun_Y_0(X)))))) | (~((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.37 tff(27,plain,
% 0.21/0.37 ($false),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[26, 14, 20])).
% 0.21/0.37 % SZS output end Proof
% 0.21/0.37 % E exiting
%------------------------------------------------------------------------------