%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN328+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN328+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 12:30:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(big_f_type, type, (
% 0.19/0.37 big_f: $i > $o)).
% 0.19/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.37 tptp_fun_Y_1: $i > $i)).
% 0.19/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.37 tptp_fun_Z_0: $i > $i)).
% 0.19/0.37 tff(elem_2_type, type, (
% 0.19/0.37 elem_2: $i)).
% 0.19/0.37 tff(big_g_type, type, (
% 0.19/0.37 big_g: $i > $o)).
% 0.19/0.37 tff(big_h_type, type, (
% 0.19/0.37 big_h: $i > $o)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[X: $i] : refl((~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))) <=> (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))) <=> ![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (^[X: $i] : rewrite((~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))))) <=> (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![X: $i] : (~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))))) <=> ![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 ((~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 ((~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y) => big_g(Y)) <=> big_f(X)) => (((big_f(Y) => big_h(Y)) <=> big_g(X)) => ((((big_f(Y) => big_g(Y)) => big_h(Y)) <=> big_h(X)) => ((big_f(Z) & big_g(Z)) & big_h(Z)))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(7,axiom,(~?[X: $i] : ![Y: $i, Z: $i] : (((big_f(Y) => big_g(Y)) <=> big_f(X)) => (((big_f(Y) => big_h(Y)) <=> big_g(X)) => ((((big_f(Y) => big_g(Y)) => big_h(Y)) <=> big_h(X)) => ((big_f(Z) & big_g(Z)) & big_h(Z)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_12_3')).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (^[X: $i] : sk($oeq((~![Y: $i, Z: $i] : ((big_f(Z) & big_g(Z) & big_h(Z)) | (~((big_h(Y) | (~(big_g(Y) | (~big_f(Y))))) <=> big_h(X))) | (~((big_h(Y) | (~big_f(Y))) <=> big_g(X))) | (~((big_g(Y) | (~big_f(Y))) <=> big_f(X))))), (~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(13,plain,(
% 0.19/0.38 ![X: $i] : (~((big_f(tptp_fun_Z_0(X)) & big_g(tptp_fun_Z_0(X)) & big_h(tptp_fun_Z_0(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X)))))),
% 0.19/0.38 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ((~![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((big_h(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)))))) <=> big_g(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)))))) <=> big_f(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))))) | (~big_g(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)))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (~((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((big_h(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)))))) <=> big_g(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)))))) <=> big_f(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))))) | (~big_g(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))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((big_h(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)))))) <=> big_g(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)))))) <=> big_f(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))))) | (~big_g(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_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.38 tff(20,assumption,((~((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2)))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(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))))) <=> big_f(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))), introduced(assumption)).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ((~![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~((~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2)))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(tptp_fun_Z_0(elem!2)))) | (~((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_f(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[21, 15, 20])).
% 0.19/0.38 tff(23,plain,(~((~((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2)))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(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))))) <=> big_f(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (((~((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2)))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(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))))) <=> big_f(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(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_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (((~((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2)))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(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))))) <=> big_f(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(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))))) <=> big_f(tptp_fun_Z_0(elem!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 ((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_f(tptp_fun_Z_0(elem!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[26, 23])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 ((~![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (~((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[28, 15])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) | ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((big_h(tptp_fun_Y_1(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_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_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(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_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (~((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((big_h(tptp_fun_Y_1(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_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_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(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_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[32, 15])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((big_h(tptp_fun_Y_1(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_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_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(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_Y_1(tptp_fun_Z_0(elem!2))))))))) | ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((big_h(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)))))) <=> big_g(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)))))) <=> big_f(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))))) | (~big_g(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_h(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)))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 ((big_h(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)))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[36, 17])).
% 0.19/0.38 tff(38,assumption,(~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))), introduced(assumption)).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 ((~((big_h(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)))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(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))))))) | big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~((big_h(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)))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(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)))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (~(big_h(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))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[42, 37])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 ((big_h(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)))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))))) | big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 35])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))) | big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 31])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Z_0(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) | ((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 29])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((big_h(tptp_fun_Y_1(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_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_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(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_Y_1(tptp_fun_Z_0(elem!2))))))))) | ((big_h(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 33])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~((big_h(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)))))) <=> big_g(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)))))) <=> big_f(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))))) | (~big_g(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_Y_1(tptp_fun_Z_0(elem!2)))) | (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((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)))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 17])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[60, 38])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((~((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)))))) <=> big_f(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)))))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~((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)))))) <=> big_f(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))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (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)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 59])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ((big_h(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)))))) | big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[65, 43])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~(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))))))) | 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)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[67, 66, 64])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(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_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_h(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(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_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_h(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (big_h(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[70, 57])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((~(big_h(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[72, 50, 71])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ((~((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))) | big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 ((~((big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[75, 55])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))))) | (big_g(tptp_fun_Y_1(tptp_fun_Y_1(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_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[77, 76, 53])).
% 0.19/0.39 tff(79,plain,(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 ((~((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_f(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)))))) | big_f(tptp_fun_Z_0(elem!2))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((~((big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_f(tptp_fun_Z_0(elem!2)))) | big_f(tptp_fun_Z_0(elem!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (big_f(tptp_fun_Z_0(elem!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[81, 27])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (((~((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(tptp_fun_Z_0(elem!2)))) | (~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(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))))) <=> big_f(tptp_fun_Z_0(elem!2)))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_g(tptp_fun_Z_0(tptp_fun_Z_0(elem!2)))) | (~big_h(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))))))) | ((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(tptp_fun_Z_0(elem!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[83, 23])).
% 0.19/0.39 tff(85,assumption,(~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))), introduced(assumption)).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (~big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Y_1(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))))))))) | big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Y_1(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)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (~(big_h(tptp_fun_Y_1(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))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[89, 19])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(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)))))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (~big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 92])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (~(big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[93, 35])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (((~((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((big_h(tptp_fun_Y_1(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_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_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~((~big_f(tptp_fun_Z_0(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~big_g(tptp_fun_Z_0(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_Y_1(tptp_fun_Z_0(elem!2))))))))) | ((big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 ((big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[95, 33])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[97, 85])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~(big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(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_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 79])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[100, 98])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 ((~((big_h(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)))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (big_h(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)))))) | (~big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 ((~((big_h(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)))))) <=> big_g(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (big_h(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))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (big_h(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)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[103, 37])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 ((~(big_h(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))))))) | big_h(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)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (~big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[105, 92, 104])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 ((~((big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 ((~((big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[108, 96])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 ((big_h(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2))))))))) | (big_g(tptp_fun_Y_1(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_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[110, 109, 94])).
% 0.19/0.39 tff(112,plain,(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 ((~((big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) <=> big_g(tptp_fun_Z_0(elem!2)))) | (~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | big_g(tptp_fun_Z_0(elem!2))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 (big_g(tptp_fun_Z_0(elem!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[113, 112, 84])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 ((~![X: $i] : (~((~((big_h(tptp_fun_Y_1(X)) | (~(big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))))) <=> big_h(X))) | (~((big_h(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_g(X))) | (~((big_g(tptp_fun_Y_1(X)) | (~big_f(tptp_fun_Y_1(X)))) <=> big_f(X))) | (~((~big_f(tptp_fun_Z_0(X))) | (~big_g(tptp_fun_Z_0(X))) | (~big_h(tptp_fun_Z_0(X)))))))) | (~((~((big_h(tptp_fun_Y_1(elem!2)) | (~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))))) <=> big_h(elem!2))) | (~((big_h(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))) <=> big_g(elem!2))) | (~((big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))) <=> big_f(elem!2))) | (~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 (~((~((big_h(tptp_fun_Y_1(elem!2)) | (~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))))) <=> big_h(elem!2))) | (~((big_h(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))) <=> big_g(elem!2))) | (~((big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))) <=> big_f(elem!2))) | (~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[115, 15])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (((~((big_h(tptp_fun_Y_1(elem!2)) | (~(big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))))) <=> big_h(elem!2))) | (~((big_h(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))) <=> big_g(elem!2))) | (~((big_g(tptp_fun_Y_1(elem!2)) | (~big_f(tptp_fun_Y_1(elem!2)))) <=> big_f(elem!2))) | (~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))))) | ((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 ((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 ((~((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2))))) | (~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 ((~big_f(tptp_fun_Z_0(elem!2))) | (~big_g(tptp_fun_Z_0(elem!2))) | (~big_h(tptp_fun_Z_0(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (~big_h(tptp_fun_Z_0(elem!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[120, 114, 82])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) <=> big_h(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_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))))) | big_h(tptp_fun_Z_0(elem!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (~(big_h(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_Y_1(tptp_fun_Z_0(elem!2)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[122, 121, 25])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 ((big_h(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_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (~big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 ((~((big_h(tptp_fun_Y_1(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)))))))) <=> big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))) | (~(big_h(tptp_fun_Y_1(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)))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 125])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 (~(big_h(tptp_fun_Y_1(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))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[126, 19])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 ((~(big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))))) | big_h(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))) | (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (~big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[128, 125, 112])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 ((~((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)))))) <=> big_f(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))))))) | big_f(tptp_fun_Y_1(tptp_fun_Z_0(elem!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 ((~((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)))))) <=> big_f(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)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 (~(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))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[131, 59])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 ((big_h(tptp_fun_Y_1(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)))))))) | (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))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[133, 132, 127])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------