%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN343+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN343+1 : TPTP v9.0.0. Released v2.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 12:31:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(big_f_type, type, (
% 0.12/0.36 big_f: ( $i * $i ) > $o)).
% 0.12/0.36 tff(elem_1_type, type, (
% 0.12/0.36 elem_1: $i)).
% 0.12/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.12/0.36 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[X: $i, Y1: $i, Y2: $i] : refl((~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2)))))) <=> (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2)))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2)))))) <=> ![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (^[X: $i, Y1: $i, Y2: $i] : rewrite((~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))) <=> (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2)))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))) <=> ![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 ((~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))) <=> (~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 ((~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : (((big_f(X, Y1) => big_f(Z, X)) => big_f(X, X)) => (big_f(X, X) & big_f(Y1, Y2)))) <=> (~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(7,axiom,(~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : (((big_f(X, Y1) => big_f(Z, X)) => big_f(X, X)) => (big_f(X, X) & big_f(Y1, Y2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_16_2')).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (~?[X: $i, Y1: $i, Y2: $i] : ![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (^[X: $i, Y1: $i, Y2: $i] : sk($oeq((~![Z: $i] : ((~((~((~big_f(X, Y1)) | big_f(Z, X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2)))), (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(13,plain,(
% 0.12/0.36 ![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (big_f(X, X) & big_f(Y1, Y2))))),
% 0.12/0.36 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | (~((~big_f(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, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[18, 16])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | (~((~big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![X: $i, Y1: $i, Y2: $i] : (~((~((~((~big_f(X, Y1)) | big_f(tptp_fun_Z_0(Y2, Y1, X), X))) | big_f(X, X))) | (~((~big_f(X, X)) | (~big_f(Y1, Y2))))))) | (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (~((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 15])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(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, elem!1), elem!1))) | big_f(elem!1, elem!1))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1))) | big_f(elem!1, elem!1))) | big_f(elem!1, elem!1)) | (~big_f(elem!1, elem!1))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (~big_f(elem!1, elem!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1)) | big_f(elem!1, elem!1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, elem!1, elem!1), elem!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((~((~((~big_f(elem!1, elem!1)) | big_f(tptp_fun_Z_0(elem!1, 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, elem!1), elem!1))) | big_f(elem!1, elem!1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[29, 28, 26, 24])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------