%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN346+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 05:38:50 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN346+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % 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 12:35:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(big_f_type, type, (
% 0.12/0.37 big_f: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_Z2_1_type, type, (
% 0.12/0.37 tptp_fun_Z2_1: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_X2_0_type, type, (
% 0.12/0.37 tptp_fun_X2_0: $i)).
% 0.12/0.37 tff(tptp_fun_Z1_2_type, type, (
% 0.12/0.37 tptp_fun_Z1_2: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))) | $false) <=> (~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~$true) <=> $false),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) <=> $true),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~(~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))) <=> big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))) <=> (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 ((~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))))) <=> (~(~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 ((~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))))) <=> big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))),
% 0.12/0.37 inference(transitivity,[status(thm)],[6, 4])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~(~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0)))) <=> big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0)))) <=> (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ((~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) <=> (~(~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) <=> big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))),
% 0.12/0.37 inference(transitivity,[status(thm)],[10, 8])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))))) <=> ((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[11, 7])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))))) <=> $true),
% 0.12/0.37 inference(transitivity,[status(thm)],[12, 3])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 ((~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))))))) <=> (~$true)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))))))) <=> $false),
% 0.12/0.38 inference(transitivity,[status(thm)],[14, 2])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))) | $false)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))))))) <=> (~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[16, 1])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~((~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z1_2(X2!0, X2!0))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0))) | (~big_f(X2!0, tptp_fun_Z2_1(X2!0, X2!0)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[Y1: $i, Y2: $i] : rewrite((~((big_f(Y1, tptp_fun_Z1_2(Y2, Y1)) & big_f(Y2, tptp_fun_Z1_2(Y2, Y1))) | (big_f(X2!0, tptp_fun_Z2_1(Y2, Y1)) & big_f(Y2, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))))) <=> (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![Y1: $i, Y2: $i] : (~((big_f(Y1, tptp_fun_Z1_2(Y2, Y1)) & big_f(Y2, tptp_fun_Z1_2(Y2, Y1))) | (big_f(X2!0, tptp_fun_Z2_1(Y2, Y1)) & big_f(Y2, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2, Z1)))) <=> (~![X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2, Z1))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : (big_f(X2, Z1) => (big_f(Y1, Z2) => ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)))))) <=> (~![X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2, Z1))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,axiom,(~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : (big_f(X2, Z1) => (big_f(Y1, Z2) => ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_17_2')).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (~![X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2, Z1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (~![X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2, Z1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2, Z1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (~![X2: $i] : ?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2, Z1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.12/0.38 tff(29,plain,(
% 0.12/0.38 $oeq((~?[Y1: $i, Y2: $i] : ![Z1: $i, Z2: $i] : ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2!0, Z2) & big_f(Y2, Z2)) | (~big_f(Y1, Z2)) | (~big_f(X2!0, Z1)))), ![Y1: $i, Y2: $i] : (~((big_f(Y1, tptp_fun_Z1_2(Y2, Y1)) & big_f(Y2, tptp_fun_Z1_2(Y2, Y1))) | (big_f(X2!0, tptp_fun_Z2_1(Y2, Y1)) & big_f(Y2, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))))))),
% 0.12/0.38 inference(transitivity,[status(sab)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![Y1: $i, Y2: $i] : (~((~big_f(Y1, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(X2!0, tptp_fun_Z1_2(Y2, Y1))) | (~((~big_f(Y1, tptp_fun_Z1_2(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z1_2(Y2, Y1))))) | (~((~big_f(X2!0, tptp_fun_Z2_1(Y2, Y1))) | (~big_f(Y2, tptp_fun_Z2_1(Y2, Y1)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 19])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------