%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV385+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV385+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:44:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(check_cpq_type, type, (
% 0.13/0.39 check_cpq: $i > $o)).
% 0.13/0.39 tff(triple_type, type, (
% 0.13/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_W_0_type, type, (
% 0.13/0.39 tptp_fun_W_0: $i)).
% 0.13/0.39 tff(tptp_fun_V_1_type, type, (
% 0.13/0.39 tptp_fun_V_1: $i)).
% 0.13/0.39 tff(tptp_fun_U_2_type, type, (
% 0.13/0.39 tptp_fun_U_2: $i)).
% 0.13/0.39 tff(im_succ_cpq_type, type, (
% 0.13/0.39 im_succ_cpq: $i > $i)).
% 0.13/0.39 tff(ok_type, type, (
% 0.13/0.39 ok: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))))) <=> (~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(~![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l21_co')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.39 tff(9,plain,(
% 0.13/0.39 ~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (ok(im_succ_cpq(triple(U!2, V!1, W!0)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[U: $i, V: $i, W: $i] : refl(((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))) <=> ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (^[U: $i, V: $i, W: $i] : rewrite(((~check_cpq(triple(U, V, W))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W)))))) <=> ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.40 tff(18,axiom,(![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l21_li2225')).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.13/0.40 tff(21,plain,(
% 0.13/0.40 ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | ((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0)))) <=> ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | ((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (check_cpq(triple(U!2, V!1, W!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[25, 22, 12, 11])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))) <=> (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (~ok(im_succ_cpq(triple(U, V, W))))) <=> (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(im_succ_cpq(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.40 tff(32,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(im_succ_cpq(triple(U, V, W)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l21_li1316')).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.13/0.40 tff(35,plain,(
% 0.13/0.40 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | (ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | (ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (ok(triple(U!2, V!1, W!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[39, 36, 12])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0)))),
% 0.13/0.40 inference(or_elim,[status(thm)],[10])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[41, 40, 26])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------