%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN326+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN326+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:30:22 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(big_f_type, type, (
% 0.12/0.36 big_f: ( $i * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.12/0.36 tptp_fun_Z_0: $i > $i)).
% 0.12/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.36 tptp_fun_Y_1: $i > $i)).
% 0.12/0.36 tff(elem_2_type, type, (
% 0.12/0.36 elem_2: $i)).
% 0.12/0.36 tff(big_g_type, type, (
% 0.12/0.36 big_g: $i > $o)).
% 0.12/0.36 tff(big_h_type, type, (
% 0.12/0.36 big_h: $i > $o)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[X: $i] : refl((~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X))))) <=> (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X))))) <=> ![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 ((~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 ((~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y, Z) => (big_g(Y) => big_h(X))) => big_f(X, X)) => (((big_f(Z, X) => big_g(X)) => big_h(Z)) => (big_f(X, Y) => big_f(Z, Z))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y, Z) => (big_g(Y) => big_h(X))) => big_f(X, X)) => (((big_f(Z, X) => big_g(X)) => big_h(Z)) => (big_f(X, Y) => big_f(Z, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_12_1')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~?[X: $i] : ![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[X: $i] : sk($oeq((~![Y: $i, Z: $i] : (big_f(Z, Z) | (~big_f(X, Y)) | (~(big_h(Z) | (~(big_g(X) | (~big_f(Z, X)))))) | (~((~(big_h(X) | (~big_g(Y)) | (~big_f(Y, Z)))) | big_f(X, X))))), (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,(
% 0.12/0.37 ![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[9, 10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (~(big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Z_0(elem!2)) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Z_0(elem!2)) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 12])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Z_0(elem!2)) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(elem!2))))))) | (~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))))) | ((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)) | (~big_f(elem!2, tptp_fun_Y_1(elem!2))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~(big_g(elem!2) | (~big_f(tptp_fun_Z_0(elem!2), elem!2)))))) | (~((~(big_h(elem!2) | (~big_g(tptp_fun_Y_1(elem!2))) | (~big_f(tptp_fun_Y_1(elem!2), tptp_fun_Z_0(elem!2))))) | big_f(elem!2, elem!2)))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (~(big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)) | (~big_f(elem!2, tptp_fun_Y_1(elem!2))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~(big_g(elem!2) | (~big_f(tptp_fun_Z_0(elem!2), elem!2)))))) | (~((~(big_h(elem!2) | (~big_g(tptp_fun_Y_1(elem!2))) | (~big_f(tptp_fun_Y_1(elem!2), tptp_fun_Z_0(elem!2))))) | big_f(elem!2, elem!2))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 12])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)) | (~big_f(elem!2, tptp_fun_Y_1(elem!2))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~(big_g(elem!2) | (~big_f(tptp_fun_Z_0(elem!2), elem!2)))))) | (~((~(big_h(elem!2) | (~big_g(tptp_fun_Y_1(elem!2))) | (~big_f(tptp_fun_Y_1(elem!2), tptp_fun_Z_0(elem!2))))) | big_f(elem!2, elem!2)))) | (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (~big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ((~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ((~((~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))) | big_f(tptp_fun_Z_0(elem!2), tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~(big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[26, 20])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ((big_h(tptp_fun_Z_0(elem!2)) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))) | big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 16])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 ((big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | (~((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)), tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 14])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[39, 38, 36])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | ((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 ((~![X: $i] : (~(big_f(tptp_fun_Z_0(X), tptp_fun_Z_0(X)) | (~big_f(X, tptp_fun_Y_1(X))) | (~(big_h(tptp_fun_Z_0(X)) | (~(big_g(X) | (~big_f(tptp_fun_Z_0(X), X)))))) | (~((~(big_h(X) | (~big_g(tptp_fun_Y_1(X))) | (~big_f(tptp_fun_Y_1(X), tptp_fun_Z_0(X))))) | big_f(X, X)))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~((~(big_h(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))), tptp_fun_Z_0(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))), tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[43, 12, 42])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------