%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN341+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:38:49 AM UTC 2025
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN341+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 12:31:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 tff(big_f_type, type, (
% 0.21/0.53 big_f: ( $i * $i * $i ) > $o)).
% 0.21/0.53 tff(tptp_fun_X4_1_type, type, (
% 0.21/0.53 tptp_fun_X4_1: ( $i * $i ) > $i)).
% 0.21/0.53 tff(tptp_fun_X2_0_type, type, (
% 0.21/0.53 tptp_fun_X2_0: $i > $i)).
% 0.21/0.53 tff(elem_2_type, type, (
% 0.21/0.53 elem_2: $i)).
% 0.21/0.53 tff(1,plain,
% 0.21/0.53 (![X1: $i] : ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1)))) <=> ![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))),
% 0.21/0.53 inference(pull_quant,[status(thm)],[])).
% 0.21/0.53 tff(2,plain,
% 0.21/0.53 ((~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))) <=> (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(3,plain,
% 0.21/0.53 ((~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : (big_f(X1, X2, X3) => big_f(X2, X3, X4))) <=> (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(4,axiom,(~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : (big_f(X1, X2, X3) => big_f(X2, X3, X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_15_6')).
% 0.21/0.53 tff(5,plain,
% 0.21/0.53 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.53 tff(6,plain,
% 0.21/0.53 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.53 tff(7,plain,
% 0.21/0.53 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.53 tff(8,plain,
% 0.21/0.53 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.53 tff(9,plain,
% 0.21/0.53 (^[X1: $i] : trans(sk($oeq((~![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))), (~?[X3: $i] : ![X4: $i] : ((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, X4))))), nnf_neg(proof_bind(^[X3: $i] : sk($oeq((~![X4: $i] : ((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, X4))), (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))))), $oeq((~?[X3: $i] : ![X4: $i] : ((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, X4))), ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1)))))), $oeq((~![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))), ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(10,plain,(
% 0.21/0.53 ![X1: $i] : ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))),
% 0.21/0.53 inference(nnf-neg,[status(sab)],[8, 9])).
% 0.21/0.53 tff(11,plain,
% 0.21/0.53 (![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.21/0.53 tff(12,plain,
% 0.21/0.53 ((~![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))) | (~((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(13,plain,
% 0.21/0.53 (~((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.53 tff(14,plain,
% 0.21/0.53 (((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | (~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(15,plain,
% 0.21/0.53 (~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.53 tff(16,plain,
% 0.21/0.53 (((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(17,plain,
% 0.21/0.53 ((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.53 tff(18,plain,
% 0.21/0.53 ((~![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))) | (~((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(19,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[18, 11, 17])).
% 0.21/0.53 % SZS output end Proof
% 0.21/0.53 % E exiting
%------------------------------------------------------------------------------