%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN327+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:46 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN327+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.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 12:32:27 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(big_f_type, type, (
% 0.19/0.38 big_f: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_Z_1_type, type, (
% 0.19/0.38 tptp_fun_Z_1: $i > $i)).
% 0.19/0.38 tff(tptp_fun_X_0_type, type, (
% 0.19/0.38 tptp_fun_X_0: $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[Y: $i] : refl((~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y)))))))))) <=> (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y)))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![Y: $i] : (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y)))))))))) <=> ![Y: $i] : (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (^[Y: $i] : rewrite((~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & ((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y)))))) <=> (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y)))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![Y: $i] : (~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & ((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y)))))) <=> ![Y: $i] : (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (^[Y: $i] : rewrite((~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & (big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y)) | (~big_f(X!0, Y)))))) <=> (~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & ((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![Y: $i] : (~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & (big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y)) | (~big_f(X!0, Y)))))) <=> ![Y: $i] : (~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & ((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 ((~![X: $i] : ?[Y: $i] : ![Z: $i] : ((~big_f(Y, X)) | (((~big_f(X, Z)) | big_f(X, Y)) & (big_f(X, Z) | (big_f(Y, X) & big_f(Z, Y)) | (~big_f(X, Y)))))) <=> (~![X: $i] : ?[Y: $i] : ![Z: $i] : ((~big_f(Y, X)) | (((~big_f(X, Z)) | big_f(X, Y)) & (big_f(X, Z) | (big_f(Y, X) & big_f(Z, Y)) | (~big_f(X, Y))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![X: $i] : ?[Y: $i] : ![Z: $i] : (big_f(Y, X) => ((big_f(X, Z) => big_f(X, Y)) & (big_f(X, Y) => ((~big_f(X, Z)) => (big_f(Y, X) & big_f(Z, Y))))))) <=> (~![X: $i] : ?[Y: $i] : ![Z: $i] : ((~big_f(Y, X)) | (((~big_f(X, Z)) | big_f(X, Y)) & (big_f(X, Z) | (big_f(Y, X) & big_f(Z, Y)) | (~big_f(X, Y))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(9,axiom,(~![X: $i] : ?[Y: $i] : ![Z: $i] : (big_f(Y, X) => ((big_f(X, Z) => big_f(X, Y)) & (big_f(X, Y) => ((~big_f(X, Z)) => (big_f(Y, X) & big_f(Z, Y))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_12_2')).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~![X: $i] : ?[Y: $i] : ![Z: $i] : ((~big_f(Y, X)) | (((~big_f(X, Z)) | big_f(X, Y)) & (big_f(X, Z) | (big_f(Y, X) & big_f(Z, Y)) | (~big_f(X, Y)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![X: $i] : ?[Y: $i] : ![Z: $i] : ((~big_f(Y, X)) | (((~big_f(X, Z)) | big_f(X, Y)) & (big_f(X, Z) | (big_f(Y, X) & big_f(Z, Y)) | (~big_f(X, Y)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (~![X: $i] : ?[Y: $i] : ![Z: $i] : ((~big_f(Y, X)) | (((~big_f(X, Z)) | big_f(X, Y)) & (big_f(X, Z) | (big_f(Y, X) & big_f(Z, Y)) | (~big_f(X, Y)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~![X: $i] : ?[Y: $i] : ![Z: $i] : ((~big_f(Y, X)) | (((~big_f(X, Z)) | big_f(X, Y)) & (big_f(X, Z) | (big_f(Y, X) & big_f(Z, Y)) | (~big_f(X, Y)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.19/0.39 tff(14,plain,(
% 0.19/0.39 $oeq((~?[Y: $i] : ![Z: $i] : ((~big_f(Y, X!0)) | (((~big_f(X!0, Z)) | big_f(X!0, Y)) & (big_f(X!0, Z) | (big_f(Y, X!0) & big_f(Z, Y)) | (~big_f(X!0, Y)))))), ![Y: $i] : (~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & (big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y)) | (~big_f(X!0, Y)))))))),
% 0.19/0.39 inference(transitivity,[status(sab)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![Y: $i] : (~((~big_f(Y, X!0)) | (((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y)) & ((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (big_f(Y, X!0) & big_f(tptp_fun_Z_1(Y), Y))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![Y: $i] : (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![Y: $i] : (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![Y: $i] : (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y))))))))))) | (~((~big_f(X!0, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~((~big_f(X!0, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (((~big_f(X!0, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))))))))) | big_f(X!0, X!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (big_f(X!0, X!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (((~big_f(X!0, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))))))))) | ((~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0)))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0)) | (~big_f(X!0, X!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~((~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0)))))))) | (~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, X!0))) | (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (~((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[26, 25, 23])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (((~big_f(X!0, X!0)) | big_f(X!0, tptp_fun_Z_1(X!0)) | (~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))))) | ((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~((~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0)))) | (~big_f(X!0, X!0)) | (~big_f(tptp_fun_Z_1(X!0), X!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (~big_f(tptp_fun_Z_1(X!0), X!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[30, 29, 21])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~big_f(tptp_fun_Z_1(X!0), X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(X!0)))) | big_f(X!0, tptp_fun_Z_1(X!0)))) | (~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(X!0))) | (~((~big_f(tptp_fun_Z_1(X!0), X!0)) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(X!0)), tptp_fun_Z_1(X!0)))))))))) | big_f(tptp_fun_Z_1(X!0), X!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~big_f(tptp_fun_Z_1(X!0), X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(X!0)))) | big_f(X!0, tptp_fun_Z_1(X!0)))) | (~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(X!0))) | (~((~big_f(tptp_fun_Z_1(X!0), X!0)) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(X!0)), tptp_fun_Z_1(X!0)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![Y: $i] : (~((~big_f(Y, X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(Y))) | big_f(X!0, Y))) | (~((~big_f(X!0, Y)) | big_f(X!0, tptp_fun_Z_1(Y)) | (~((~big_f(Y, X!0)) | (~big_f(tptp_fun_Z_1(Y), Y))))))))))) | (~((~big_f(tptp_fun_Z_1(X!0), X!0)) | (~((~((~big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(X!0)))) | big_f(X!0, tptp_fun_Z_1(X!0)))) | (~((~big_f(X!0, tptp_fun_Z_1(X!0))) | big_f(X!0, tptp_fun_Z_1(tptp_fun_Z_1(X!0))) | (~((~big_f(tptp_fun_Z_1(X!0), X!0)) | (~big_f(tptp_fun_Z_1(tptp_fun_Z_1(X!0)), tptp_fun_Z_1(X!0)))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 17, 33])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------