%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN332+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:47 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN332+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:30:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(big_f_type, type, (
% 0.20/0.38 big_f: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.38 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.20/0.38 tff(elem_1_type, type, (
% 0.20/0.38 elem_1: $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : refl((~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) <=> (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))) <=> ![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : rewrite((~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))))) <=> (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))))) <=> ![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X))))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~?[X: $i, Y: $i] : ![Z: $i] : ((~((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z))) => ((big_f(X, Z) <=> big_f(Z, X)) => ((big_f(X, Z) <=> big_f(Y, Z)) => (((big_f(Y, X) => big_f(X, Y)) <=> big_f(Z, Z)) => ((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y))))))) <=> (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,axiom,(~?[X: $i, Y: $i] : ![Z: $i] : ((~((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z))) => ((big_f(X, Z) <=> big_f(Z, X)) => ((big_f(X, Z) <=> big_f(Y, Z)) => (((big_f(Y, X) => big_f(X, Y)) <=> big_f(Z, Z)) => ((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_14_4')).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (~?[X: $i, Y: $i] : ![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : sk($oeq((~![Z: $i] : (((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(Z, Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, Z)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(Z, Z))) | (~(big_f(X, Z) <=> big_f(Y, Z))) | (~(big_f(X, Z) <=> big_f(Z, X))))), (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(13,plain,(
% 0.20/0.39 ![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | ((big_f(X, Y) & big_f(Y, X)) <=> big_f(X, tptp_fun_Z_0(Y, X))) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X)))))),
% 0.20/0.39 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))) <=> (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(((~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (~(big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[21, 15])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (~big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 22])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 ((~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) <=> big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | big_f(tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[29, 28, 26])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~(((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 15])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~(big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) | (((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (~(((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[35, 15])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 ((((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~(((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~(((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) <=> (~((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~(((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~(((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~(((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~(((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))) <=> ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~(((big_f(elem!1, elem!1) <=> big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) | (~(((~big_f(elem!1, elem!1)) | big_f(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~(((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (~(((big_f(X, Y) <=> big_f(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), Y)) | (~(((~big_f(Y, X)) | big_f(X, Y)) <=> big_f(tptp_fun_Z_0(Y, X), tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(Y, tptp_fun_Z_0(Y, X)))) | (~(big_f(X, tptp_fun_Z_0(Y, X)) <=> big_f(tptp_fun_Z_0(Y, X), X))) | (~(((~big_f(Y, X)) | (~big_f(X, Y))) <=> big_f(X, tptp_fun_Z_0(Y, X))))))) | (~((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (~((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[46, 15])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, elem!1))) | (big_f(elem!1, elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((~(big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | (~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[52, 51, 49])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) | big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ((~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 ((~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[57, 40])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 ((~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[59, 58, 38])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), tptp_fun_Z_0(elem!1, elem!1)))) | (~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | (~big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, elem!1), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (~((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[61, 36])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) | big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) | big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[63, 53, 51])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~(big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (((big_f(tptp_fun_Z_0(elem!1, elem!1), elem!1) <=> big_f(elem!1, tptp_fun_Z_0(elem!1, elem!1))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[66, 62])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 ((~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))) | (~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (~((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[68, 67, 60])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | ((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((~(((~big_f(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)), elem!1)) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (~big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[71, 34])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 ((big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))) <=> big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))) | big_f(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1))), tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, tptp_fun_Z_0(elem!1, elem!1)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 30, 24])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------