%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN319+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 05:38:44 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN319+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.11 % 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 12:32:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(big_g_type, type, (
% 0.11/0.37 big_g: $i > $o)).
% 0.11/0.37 tff(tptp_fun_Z2_0_type, type, (
% 0.11/0.37 tptp_fun_Z2_0: ( $i * $i ) > $i)).
% 0.11/0.37 tff(elem_2_type, type, (
% 0.11/0.37 elem_2: $i)).
% 0.11/0.37 tff(big_f_type, type, (
% 0.11/0.37 big_f: $i > $o)).
% 0.11/0.37 tff(big_h_type, type, (
% 0.11/0.37 big_h: $i > $o)).
% 0.11/0.37 tff(tptp_fun_Z1_1_type, type, (
% 0.11/0.37 tptp_fun_Z1_1: ( $i * $i ) > $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl((~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X)))))))) <=> (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X)))))))) <=> ![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : rewrite((~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))) | (big_h(tptp_fun_Z2_0(Y, X)) & ((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X)))))) <=> (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))) | (big_h(tptp_fun_Z2_0(Y, X)) & ((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X)))))) <=> ![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : rewrite((~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))))) <=> (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))) | (big_h(tptp_fun_Z2_0(Y, X)) & ((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))))) <=> ![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))) | (big_h(tptp_fun_Z2_0(Y, X)) & ((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 ((~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))) <=> (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1)))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : (((big_f(Y) => big_g(Z1)) => (big_g(X) & (~big_f(Z1)))) => (((big_f(X) | big_g(X)) => big_h(X)) => (big_h(Z2) & (big_h(Y) => ((big_f(Z2) | big_g(Z2)) => big_h(Z2))))))) <=> (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1)))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(9,axiom,(~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : (((big_f(Y) => big_g(Z1)) => (big_g(X) & (~big_f(Z1)))) => (((big_f(X) | big_g(X)) => big_h(X)) => (big_h(Z2) & (big_h(Y) => ((big_f(Z2) | big_g(Z2)) => big_h(Z2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_2_5')).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~?[X: $i, Y: $i] : ![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : sk($oeq((~![Z1: $i, Z2: $i] : ((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(Z2) & (big_h(Z2) | (~(big_f(Z2) | big_g(Z2))) | (~big_h(Y)))) | (~((~(big_g(Z1) | (~big_f(Y)))) | (big_g(X) & (~big_f(Z1))))))), (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(15,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (big_h(tptp_fun_Z2_0(Y, X)) & (big_h(tptp_fun_Z2_0(Y, X)) | (~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X))))))))),
% 0.11/0.37 inference(nnf-neg,[status(sab)],[13, 14])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (big_g(X) & (~big_f(tptp_fun_Z1_1(Y, X)))))) | (big_h(tptp_fun_Z2_0(Y, X)) & ((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 2])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))) <=> (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[21, 19])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~((~big_f(elem!2)) | big_g(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2))))) | big_h(tptp_fun_Z2_0(elem!2, tptp_fun_Z2_0(elem!2, elem!2)))))))) | (big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.11/0.38 tff(28,assumption,(big_h(tptp_fun_Z2_0(elem!2, elem!2))), introduced(assumption)).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 ((big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2)))))))) <=> (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))) | (~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~((~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)) | big_h(tptp_fun_Z2_0(elem!2, elem!2))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (~((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[36, 18])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (((~(big_h(elem!2) | (~(big_f(elem!2) | big_g(elem!2))))) | (~((~(big_f(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_g(elem!2)))) | (~(big_g(tptp_fun_Z1_1(elem!2, elem!2)) | (~big_f(elem!2)))))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))))))) | ((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 ((~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2)))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | (~big_h(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[41, 30, 28])).
% 0.19/0.39 tff(43,plain,(~big_h(tptp_fun_Z2_0(elem!2, elem!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[45, 27])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (~big_g(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))) | big_g(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, 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_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (~big_f(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 46])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2)))) | big_f(tptp_fun_Z2_0(elem!2, elem!2))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 54, 50])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))) | ((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))) <=> (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))) <=> ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))))) | (~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~((~(big_h(X) | (~(big_f(X) | big_g(X))))) | (~((~(big_g(tptp_fun_Z1_1(Y, X)) | (~big_f(Y)))) | (~(big_f(tptp_fun_Z1_1(Y, X)) | (~big_g(X)))))) | (~((~big_h(tptp_fun_Z2_0(Y, X))) | (~((~(big_f(tptp_fun_Z2_0(Y, X)) | big_g(tptp_fun_Z2_0(Y, X)))) | (~big_h(Y)) | big_h(tptp_fun_Z2_0(Y, X))))))))) | (~((~(big_h(tptp_fun_Z2_0(elem!2, elem!2)) | (~(big_f(tptp_fun_Z2_0(elem!2, elem!2)) | big_g(tptp_fun_Z2_0(elem!2, elem!2)))))) | (~((~(big_g(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_f(tptp_fun_Z2_0(elem!2, elem!2))))) | (~(big_f(tptp_fun_Z1_1(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~big_g(tptp_fun_Z2_0(elem!2, elem!2))))))) | (~((~big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))) | (~((~big_h(tptp_fun_Z2_0(elem!2, elem!2))) | big_h(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | (~(big_f(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2))) | big_g(tptp_fun_Z2_0(tptp_fun_Z2_0(elem!2, elem!2), tptp_fun_Z2_0(elem!2, elem!2)))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[64, 18, 58])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------