%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV386+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : SWV386+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 09:46:16 EDT 2025
% 0.13/0.34 % 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(insert_cpq_type, type, (
% 0.21/0.39 insert_cpq: ( $i * $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(tptp_fun_X_3_type, type, (
% 0.21/0.39 tptp_fun_X_3: $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X))))))),
% 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))) => ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l22_co')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(insert_cpq(triple(U, V, W), X))) | (~ok(insert_cpq(triple(U, V, W), X)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (~check_cpq(triple(U!2, V!1, W!0))),
% 0.21/0.39 inference(and_elim,[status(thm)],[7])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i] : refl((check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i] : rewrite((check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[12, 10])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i] : rewrite(((~check_cpq(triple(U, V, W))) => ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.39 tff(17,axiom,(![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l22_l26')).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.39 tff(20,plain,(
% 0.21/0.39 ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[19])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))) | (check_cpq(triple(U!2, V!1, W!0)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X))))) <=> ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, V!1, W!0)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))) | (check_cpq(triple(U!2, V!1, W!0)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, V!1, W!0)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![X: $i] : (~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[24, 21, 8])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (~((~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(insert_cpq(triple(U!2, V!1, W!0), X!3))))),
% 0.21/0.39 inference(and_elim,[status(thm)],[7])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (check_cpq(insert_cpq(triple(U!2, V!1, W!0), X!3))),
% 0.21/0.39 inference(or_elim,[status(thm)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~![X: $i] : (~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X)))) | (~check_cpq(insert_cpq(triple(U!2, V!1, W!0), X!3)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[28, 27, 25])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------