%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN336+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:48 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN336+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:35:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(big_f_type, type, (
% 0.20/0.37 big_f: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_Z_1_type, type, (
% 0.20/0.37 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 0.20/0.37 tff(elem_2_type, type, (
% 0.20/0.37 elem_2: $i)).
% 0.20/0.37 tff(tptp_fun_X_0_type, type, (
% 0.20/0.37 tptp_fun_X_0: $i)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 ((~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))) <=> (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 ((~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X, Z) => (big_f(Y1, Z) => (big_f(Y2, Z) => (big_f(Y1, X) => big_f(Z, Y2)))))) <=> (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(3,axiom,(~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X, Z) => (big_f(Y1, Z) => (big_f(Y2, Z) => (big_f(Y1, X) => big_f(Z, Y2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_15_1')).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~![X: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X, Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.37 tff(8,plain,(
% 0.20/0.37 $oeq((~?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(Z, Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, Z)) | (~big_f(Y1, Z)) | (~big_f(X!0, Z)))), ![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1))))))),
% 0.20/0.37 inference(transitivity,[status(sab)],[7])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ((~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))) <=> (~((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[11, 9])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (~((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[14, 8])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (((~big_f(tptp_fun_Z_1(elem!2, elem!2), tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0) | (~big_f(tptp_fun_Z_1(elem!2, elem!2), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))) <=> (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))) <=> ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~(big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![Y1: $i, Y2: $i] : (~(big_f(tptp_fun_Z_1(Y2, Y1), Y2) | (~big_f(Y1, X!0)) | (~big_f(Y2, tptp_fun_Z_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z_1(Y2, Y1))) | (~big_f(X!0, tptp_fun_Z_1(Y2, Y1)))))) | (~((~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), X!0)) | (~big_f(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))))) | big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2))), X!0) | (~big_f(tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)), tptp_fun_Z_1(X!0, tptp_fun_Z_1(X!0, tptp_fun_Z_1(elem!2, elem!2)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 8, 19])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------