%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN371+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:38:55 AM UTC 2025
% Result : Theorem 0.21s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN371+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:31:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start Proof
% 0.21/0.37 tff(big_r_type, type, (
% 0.21/0.37 big_r: ( $i * $i ) > $o)).
% 0.21/0.37 tff(tptp_fun_V_0_type, type, (
% 0.21/0.37 tptp_fun_V_0: $i > $i)).
% 0.21/0.37 tff(elem_1_type, type, (
% 0.21/0.37 elem_1: $i)).
% 0.21/0.37 tff(1,plain,
% 0.21/0.37 (^[U: $i] : refl((~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U)))) <=> (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U)))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(2,plain,
% 0.21/0.37 (![U: $i] : (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U)))) <=> ![U: $i] : (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U))))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.37 tff(3,plain,
% 0.21/0.37 ((~?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V))) <=> (~?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V)))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(4,plain,
% 0.21/0.37 ((~((?[X: $i] : big_r(X, X) => ![Y: $i] : big_r(Y, Y)) => ?[U: $i] : ![V: $i] : (big_r(U, U) => big_r(V, V)))) <=> (~((~((~?[X: $i] : big_r(X, X)) | ![Y: $i] : big_r(Y, Y))) | ?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V))))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(5,axiom,(~((?[X: $i] : big_r(X, X) => ![Y: $i] : big_r(Y, Y)) => ?[U: $i] : ![V: $i] : (big_r(U, U) => big_r(V, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2122')).
% 0.21/0.37 tff(6,plain,
% 0.21/0.37 (~((~((~?[X: $i] : big_r(X, X)) | ![Y: $i] : big_r(Y, Y))) | ?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V)))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.37 tff(7,plain,
% 0.21/0.37 (~?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V))),
% 0.21/0.37 inference(or_elim,[status(thm)],[6])).
% 0.21/0.37 tff(8,plain,
% 0.21/0.37 (~?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.37 tff(9,plain,
% 0.21/0.37 (~?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.21/0.37 tff(10,plain,
% 0.21/0.37 (~?[U: $i] : ![V: $i] : ((~big_r(U, U)) | big_r(V, V))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.21/0.37 tff(11,plain,
% 0.21/0.37 (^[U: $i] : sk($oeq((~![V: $i] : ((~big_r(U, U)) | big_r(V, V))), (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U))))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(12,plain,(
% 0.21/0.37 ![U: $i] : (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U))))),
% 0.21/0.37 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.21/0.37 tff(13,plain,
% 0.21/0.37 (![U: $i] : (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U))))),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.37 tff(14,plain,
% 0.21/0.37 ((~![U: $i] : (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U))))) | (~((~big_r(elem!1, elem!1)) | big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1))))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(15,plain,
% 0.21/0.37 (~((~big_r(elem!1, elem!1)) | big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1)))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.37 tff(16,plain,
% 0.21/0.37 (((~big_r(elem!1, elem!1)) | big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1))) | (~big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1)))),
% 0.21/0.37 inference(tautology,[status(thm)],[])).
% 0.21/0.37 tff(17,plain,
% 0.21/0.37 (~big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.37 tff(18,plain,
% 0.21/0.37 (((~big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1))) | big_r(tptp_fun_V_0(tptp_fun_V_0(elem!1)), tptp_fun_V_0(tptp_fun_V_0(elem!1)))) | big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1))),
% 0.21/0.37 inference(tautology,[status(thm)],[])).
% 0.21/0.37 tff(19,plain,
% 0.21/0.37 ((~big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1))) | big_r(tptp_fun_V_0(tptp_fun_V_0(elem!1)), tptp_fun_V_0(tptp_fun_V_0(elem!1)))),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.37 tff(20,plain,
% 0.21/0.37 ((~![U: $i] : (~((~big_r(U, U)) | big_r(tptp_fun_V_0(U), tptp_fun_V_0(U))))) | (~((~big_r(tptp_fun_V_0(elem!1), tptp_fun_V_0(elem!1))) | big_r(tptp_fun_V_0(tptp_fun_V_0(elem!1)), tptp_fun_V_0(tptp_fun_V_0(elem!1)))))),
% 0.21/0.37 inference(quant_inst,[status(thm)],[])).
% 0.21/0.37 tff(21,plain,
% 0.21/0.37 ($false),
% 0.21/0.37 inference(unit_resolution,[status(thm)],[20, 13, 19])).
% 0.21/0.37 % SZS output end Proof
% 0.21/0.37 % E exiting
%------------------------------------------------------------------------------