%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV387+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV387+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 09:45:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(ok_type, type, (
% 0.18/0.37 ok: $i > $o)).
% 0.18/0.37 tff(remove_cpq_type, type, (
% 0.18/0.37 remove_cpq: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_X_3_type, type, (
% 0.18/0.37 tptp_fun_X_3: $i)).
% 0.18/0.37 tff(triple_type, type, (
% 0.18/0.37 triple: ( $i * $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_W_0_type, type, (
% 0.18/0.37 tptp_fun_W_0: $i)).
% 0.18/0.37 tff(tptp_fun_V_1_type, type, (
% 0.18/0.37 tptp_fun_V_1: $i)).
% 0.18/0.37 tff(tptp_fun_U_2_type, type, (
% 0.18/0.37 tptp_fun_U_2: $i)).
% 0.18/0.37 tff(check_cpq_type, type, (
% 0.18/0.37 check_cpq: $i > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 ((~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(3,axiom,(~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l23_co')).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (~((~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))))),
% 0.18/0.37 inference(and_elim,[status(thm)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (ok(remove_cpq(triple(U!2, V!1, W!0), X!3))),
% 0.18/0.37 inference(or_elim,[status(thm)],[8])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))),
% 0.18/0.37 inference(or_elim,[status(thm)],[8])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (~check_cpq(triple(U!2, V!1, W!0))),
% 0.18/0.37 inference(and_elim,[status(thm)],[7])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W))) <=> ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) <=> (~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))), ((~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))) <=> (~(~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))))), rewrite((~(~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))) <=> ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))), ((~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))) <=> ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))), ((check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> (check_cpq(triple(U, V, W)) | ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))))), rewrite((check_cpq(triple(U, V, W)) | ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) <=> ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))), ((check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W))) <=> (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.38 tff(19,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l23_l027')).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.18/0.38 tff(22,plain,(
% 0.18/0.38 ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[21])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | (check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (((~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | check_cpq(triple(U!2, V!1, W!0))) <=> (check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | ((~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | check_cpq(triple(U!2, V!1, W!0)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | (check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(remove_cpq(triple(U!2, V!1, W!0), X!3)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[26])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | ((~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | check_cpq(triple(U!2, V!1, W!0)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[27, 25])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | ((~ok(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | check_cpq(triple(U!2, V!1, W!0)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | check_cpq(triple(U, V, W)))) | check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(remove_cpq(triple(U!2, V!1, W!0), X!3))) | (~ok(remove_cpq(triple(U!2, V!1, W!0), X!3)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[30, 24, 11, 10, 9])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------