%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN333+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:47 AM UTC 2025
% Result : Theorem 0.11s 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 : SYN333+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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 12:32:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_g_type, type, (
% 0.11/0.36 big_g: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.36 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.11/0.36 tff(elem_1_type, type, (
% 0.11/0.36 elem_1: $i)).
% 0.11/0.36 tff(big_f_type, type, (
% 0.11/0.36 big_f: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,assumption,((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : refl((~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))) <=> (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))) <=> ![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : rewrite((~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))) <=> (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))))))) <=> ![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 ((~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 ((~?[X: $i, Y: $i] : ![Z: $i] : (big_f(X, Y) => ((big_f(Y, Z) & big_f(Z, Z)) & ((big_f(X, Y) & big_g(X, Y)) => (big_g(X, Z) & big_g(Z, Z)))))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(8,axiom,(~?[X: $i, Y: $i] : ![Z: $i] : (big_f(X, Y) => ((big_f(Y, Z) & big_f(Z, Z)) & ((big_f(X, Y) & big_g(X, Y)) => (big_g(X, Z) & big_g(Z, Z)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_14_5')).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (~?[X: $i, Y: $i] : ![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 (^[X: $i, Y: $i] : sk($oeq((~![Z: $i] : ((~big_f(X, Y)) | (big_f(Y, Z) & big_f(Z, Z) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, Z) & big_g(Z, Z)))))), (~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(14,plain,(
% 0.19/0.36 ![X: $i, Y: $i] : (~((~big_f(X, Y)) | (big_f(Y, tptp_fun_Z_0(Y, X)) & big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)) & ((~(big_f(X, Y) & big_g(X, Y))) | (big_g(X, tptp_fun_Z_0(Y, X)) & big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))),
% 0.19/0.36 inference(nnf-neg,[status(sab)],[12, 13])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[15, 3])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[17, 16, 1])).
% 0.19/0.36 tff(19,plain,(~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.37 tff(22,assumption,((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))), introduced(assumption)).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[23, 16, 22])).
% 0.19/0.37 tff(25,plain,(~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))) | big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(elem!1, elem!1)) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (~((~big_f(elem!1, elem!1)) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[28, 16])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (((~big_f(elem!1, elem!1)) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))) | (~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[33, 27])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (~((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[34, 21])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (((~big_f(elem!1, elem!1)) | (~big_g(elem!1, elem!1)) | (~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[38, 19])).
% 0.19/0.37 tff(40,assumption,((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))))))))))), introduced(assumption)).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[41, 16, 40])).
% 0.19/0.38 tff(43,plain,(~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1))))))))))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.38 tff(46,assumption,((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))), introduced(assumption)).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[47, 16, 46])).
% 0.19/0.38 tff(49,plain,(~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))) | big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 51, 45])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))))) | big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.39 tff(57,assumption,((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))), introduced(assumption)).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 16, 57])).
% 0.19/0.39 tff(60,plain,(~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))))) | big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))))) | ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 25])).
% 0.19/0.39 tff(65,assumption,((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))), introduced(assumption)).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~((~big_f(X, Y)) | (~((~big_f(Y, tptp_fun_Z_0(Y, X))) | (~big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X))) | (~((~big_f(X, Y)) | (~big_g(X, Y)) | (~((~big_g(X, tptp_fun_Z_0(Y, X))) | (~big_g(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))))))))))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 16, 65])).
% 0.19/0.40 tff(68,plain,(~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(elem!1, elem!1))))))))))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~((~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 70, 64])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 62])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~((~big_g(elem!1, tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, elem!1), elem!1)))))) | big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~((~big_g(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))))) | (~big_g(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[77, 56, 37])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------