%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN318+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:38:44 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN318+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:30:33 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(big_f_type, type, (
% 0.19/0.36 big_f: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_1_type, type, (
% 0.19/0.36 tptp_fun_X_1: $i > $i)).
% 0.19/0.36 tff(elem_2_type, type, (
% 0.19/0.36 elem_2: $i)).
% 0.19/0.36 tff(big_g_type, type, (
% 0.19/0.36 big_g: $i > $o)).
% 0.19/0.36 tff(k!0_type, type, (
% 0.19/0.36 k!0: $o)).
% 0.19/0.36 tff(p_type, type, (
% 0.19/0.36 p: $o)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 (^[Y: $i] : refl((~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (^[Y: $i] : rewrite((~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (^[Y: $i] : rewrite(((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))) <=> (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (![Y: $i] : ((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))) <=> ![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 ((~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | k!0 | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 ((~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | k!0 | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 ((~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))) <=> (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 ((~?[Y: $i] : (![X: $i] : (big_f(X) => (big_f(Y) => big_g(X))) => (p => ![X: $i] : (big_f(X) => big_g(Y))))) <=> (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(12,axiom,(~?[Y: $i] : (![X: $i] : (big_f(X) => (big_f(Y) => big_g(X))) => (p => ![X: $i] : (big_f(X) => big_g(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_2_4')).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | (~p) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (~?[Y: $i] : (![X: $i] : (big_g(Y) | (~big_f(X))) | k!0 | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 (~?[Y: $i] : (k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[17, 8])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (^[Y: $i] : nnf_neg(refl($oeq((~k!0), (~k!0))), sk($oeq((~![X: $i] : (big_g(Y) | (~big_f(X)))), (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))))), nnf_neg(nnf_pos(proof_bind(^[X: $i] : refl($oeq((big_g(X) | (~big_f(Y)) | (~big_f(X))), (big_g(X) | (~big_f(Y)) | (~big_f(X)))))), $oeq(![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))), ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))), $oeq((~(~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))), ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))), $oeq((~(k!0 | ![X: $i] : (big_g(Y) | (~big_f(X))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X)))))), ((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(20,plain,(
% 0.19/0.36 ![Y: $i] : ((~k!0) & (~(big_g(Y) | (~big_f(tptp_fun_X_1(Y))))) & ![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))),
% 0.19/0.36 inference(nnf-neg,[status(sab)],[18, 19])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[21, 5])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 ((~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X)))))) <=> (~(k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))))),
% 0.19/0.36 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[25, 23])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(elem!2)) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(X))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (~(k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 ((k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))) | ![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 ((k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(elem!2)) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2)))))) | big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[32, 29])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2)))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 ((~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))))) <=> (~(k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(elem!2) | k!0 | (~big_f(tptp_fun_X_1(elem!2))) | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (~(k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[39, 22])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 ((k!0 | (~![X: $i] : (big_g(X) | (~big_f(elem!2)) | (~big_f(X)))) | (~big_f(tptp_fun_X_1(elem!2))) | big_g(elem!2)) | big_f(tptp_fun_X_1(elem!2))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (big_f(tptp_fun_X_1(elem!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | ((~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) <=> ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 ((big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2)))) <=> ((~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2))))) <=> ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | ((~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2))))) <=> ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[45, 43])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(tptp_fun_X_1(elem!2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 ((~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(elem!2))))) | (~big_f(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[48, 42, 33, 31])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 ((k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))) | (~big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 ((~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X)))))) <=> (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X))))))) <=> ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | k!0 | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2)))) | (~big_f(X))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ((~![Y: $i] : (~(big_g(Y) | k!0 | (~big_f(tptp_fun_X_1(Y))) | (~![X: $i] : (big_g(X) | (~big_f(Y)) | (~big_f(X))))))) | (~(k!0 | big_g(tptp_fun_X_1(tptp_fun_X_1(elem!2))) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(tptp_fun_X_1(elem!2))))) | (~![X: $i] : (big_g(X) | (~big_f(X)) | (~big_f(tptp_fun_X_1(tptp_fun_X_1(elem!2))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[57, 22, 51])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------