%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN325+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:38:46 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN325+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:30:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(big_g_type, type, (
% 0.18/0.37 big_g: $i > $o)).
% 0.18/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.18/0.37 tptp_fun_Y_0: $i > $i)).
% 0.18/0.37 tff(elem_1_type, type, (
% 0.18/0.37 elem_1: $i)).
% 0.18/0.37 tff(big_f_type, type, (
% 0.18/0.37 big_f: ( $i * $i ) > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[X: $i] : refl((~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X)))))))) <=> (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X)))))))) <=> ![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X))))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (^[X: $i] : rewrite((~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (big_f(X, tptp_fun_Y_0(X)) & big_g(X)))))) <=> (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (big_f(X, tptp_fun_Y_0(X)) & big_g(X)))))) <=> ![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X))))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 ((~?[X: $i] : ![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X)))))) <=> (~?[X: $i] : ![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 ((~?[X: $i] : ![Y: $i] : (((big_f(X, X) => big_f(Y, Y)) => (big_f(X, Y) & big_g(X))) => big_g(Y))) <=> (~?[X: $i] : ![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(7,axiom,(~?[X: $i] : ![Y: $i] : (((big_f(X, X) => big_f(Y, Y)) => (big_f(X, Y) & big_g(X))) => big_g(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_9_2')).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (~?[X: $i] : ![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (~?[X: $i] : ![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (~?[X: $i] : ![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (~?[X: $i] : ![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (^[X: $i] : sk($oeq((~![Y: $i] : (big_g(Y) | (~((~((~big_f(X, X)) | big_f(Y, Y))) | (big_f(X, Y) & big_g(X)))))), (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (big_f(X, tptp_fun_Y_0(X)) & big_g(X))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(13,plain,(
% 0.18/0.37 ![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (big_f(X, tptp_fun_Y_0(X)) & big_g(X))))))),
% 0.18/0.37 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X))))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X))))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 ((~![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X))))))))) | (~(big_g(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)))) | (~big_g(tptp_fun_Y_0(elem!1)))))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (~(big_g(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)))) | (~big_g(tptp_fun_Y_0(elem!1))))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 ((big_g(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)))) | (~big_g(tptp_fun_Y_0(elem!1)))))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 ((big_g(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)))) | (~big_g(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)))) | (~big_g(tptp_fun_Y_0(elem!1))))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 ((~((~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_g(tptp_fun_Y_0(elem!1)))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[22, 17])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 ((~![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X))))))))) | (~(big_g(tptp_fun_Y_0(elem!1)) | (~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)))) | (~((~big_f(elem!1, tptp_fun_Y_0(elem!1))) | (~big_g(elem!1))))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (~(big_g(tptp_fun_Y_0(elem!1)) | (~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)))) | (~((~big_f(elem!1, tptp_fun_Y_0(elem!1))) | (~big_g(elem!1)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[24, 15])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 ((big_g(tptp_fun_Y_0(elem!1)) | (~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(elem!1)))) | (~((~big_f(elem!1, tptp_fun_Y_0(elem!1))) | (~big_g(elem!1))))))) | (~big_g(tptp_fun_Y_0(elem!1)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (~big_g(tptp_fun_Y_0(elem!1))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))) | (~big_g(tptp_fun_Y_0(elem!1)))) | big_g(tptp_fun_Y_0(elem!1))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 ((~big_f(tptp_fun_Y_0(elem!1), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))) | (~big_g(tptp_fun_Y_0(elem!1)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 ((~((~((~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_g(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)))) | (~big_g(tptp_fun_Y_0(elem!1)))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 ((~((~((~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_g(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)))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (~((~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))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[31, 23])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (((~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(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (~big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (((~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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(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)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 ((~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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 ((~((~((~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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 (~((~((~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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[37, 36, 21])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 ((big_g(tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (big_g(tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(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(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 ((~![X: $i] : (~(big_g(tptp_fun_Y_0(X)) | (~((~((~big_f(X, X)) | big_f(tptp_fun_Y_0(X), tptp_fun_Y_0(X)))) | (~((~big_f(X, tptp_fun_Y_0(X))) | (~big_g(X))))))))) | (~(big_g(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))) | (~((~((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))) | (~((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | (~big_g(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[41, 15, 40])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------