%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN340+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN340+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 12:31:24 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(big_f_type, type, (
% 0.21/0.47 big_f: ( $i * $i * $i * $i * $i ) > $o)).
% 0.21/0.47 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.47 tptp_fun_Y_0: $i > $i)).
% 0.21/0.47 tff(elem_1_type, type, (
% 0.21/0.47 elem_1: $i)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 (![X: $i] : ![Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2))) <=> ![X: $i, Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2)))),
% 0.21/0.47 inference(pull_quant,[status(thm)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 ((~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2))) <=> (~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 ((~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : (big_f(X, Y, Z1, Z2, Z1) => big_f(Z1, X, Y, Z1, Z2))) <=> (~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(4,axiom,(~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : (big_f(X, Y, Z1, Z2, Z1) => big_f(Z1, X, Y, Z1, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_15_5')).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (~?[X: $i] : ![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (^[X: $i] : trans(sk($oeq((~![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2))), (~?[Z1: $i, Z2: $i] : ((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2))))), nnf_neg(proof_bind(^[Z1: $i, Z2: $i] : refl($oeq((~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2))), (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2)))))), $oeq((~?[Z1: $i, Z2: $i] : ((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2))), ![Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2))))), $oeq((~![Y: $i] : ?[Z1: $i, Z2: $i] : ((~big_f(X, Y, Z1, Z2, Z1)) | big_f(Z1, X, Y, Z1, Z2))), ![Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(10,plain,(
% 0.21/0.47 ![X: $i] : ![Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2)))),
% 0.21/0.47 inference(nnf-neg,[status(sab)],[8, 9])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (![X: $i, Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 ((~![X: $i, Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2)))) | (~((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (~((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))) | (~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 ((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 ((~![X: $i, Z1: $i, Z2: $i] : (~((~big_f(X, tptp_fun_Y_0(X), Z1, Z2, Z1)) | big_f(Z1, X, tptp_fun_Y_0(X), Z1, Z2)))) | (~((~big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | big_f(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))), tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[18, 11, 17])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------