%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV389+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:32:21 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV389+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.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 09:44:35 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(check_cpq_type, type, (
% 0.21/0.39 check_cpq: $i > $o)).
% 0.21/0.39 tff(removemin_cpq_eff_type, type, (
% 0.21/0.39 removemin_cpq_eff: $i > $i)).
% 0.21/0.39 tff(triple_type, type, (
% 0.21/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_W_0_type, type, (
% 0.21/0.39 tptp_fun_W_0: $i)).
% 0.21/0.39 tff(tptp_fun_V_1_type, type, (
% 0.21/0.39 tptp_fun_V_1: $i)).
% 0.21/0.39 tff(tptp_fun_U_2_type, type, (
% 0.21/0.39 tptp_fun_U_2: $i)).
% 0.21/0.39 tff(ok_type, type, (
% 0.21/0.39 ok: $i > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~(check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))))) <=> (~(check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,axiom,(~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l25_co')).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.39 tff(9,plain,(
% 0.21/0.39 ~(check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[8])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (~(check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.21/0.39 inference(or_elim,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.21/0.39 inference(or_elim,[status(thm)],[10])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~check_cpq(triple(U!2, V!1, W!0))),
% 0.21/0.39 inference(or_elim,[status(thm)],[10])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i] : refl((check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W))))) <=> (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))) <=> (~((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W))))))), ((~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))) <=> (~(~((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W))))))))), rewrite((~(~((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W))))))) <=> ((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W)))))), ((~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))) <=> ((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W))))))), ((check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))))) <=> (check_cpq(triple(U, V, W)) | ((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W)))))))), rewrite((check_cpq(triple(U, V, W)) | ((~check_cpq(removemin_cpq_eff(triple(U, V, W)))) | (~ok(removemin_cpq_eff(triple(U, V, W)))))) <=> (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))), ((check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))))) <=> (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i] : rewrite(((check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))) => check_cpq(triple(U, V, W))) <=> (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : ((check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))) => check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.39 tff(21,axiom,(![U: $i, V: $i, W: $i] : ((check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))) => check_cpq(triple(U, V, W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l25_l40')).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.39 tff(24,plain,(
% 0.21/0.39 ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[23])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))) | (check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))))) <=> ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))) | check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))) | (check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))) | (~check_cpq(removemin_cpq_eff(triple(U, V, W)))))) | check_cpq(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))) | (~check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[29, 26, 13, 12, 11])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------