%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV376+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:32:19 AM UTC 2025
% Result : Theorem 0.14s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV376+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 09:44:18 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(succ_cpq_type, type, (
% 0.14/0.39 succ_cpq: ( $i * $i ) > $o)).
% 0.14/0.39 tff(triple_type, type, (
% 0.14/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_Z_9_type, type, (
% 0.14/0.39 tptp_fun_Z_9: $i)).
% 0.14/0.39 tff(tptp_fun_Y_10_type, type, (
% 0.14/0.39 tptp_fun_Y_10: $i)).
% 0.14/0.39 tff(tptp_fun_X_11_type, type, (
% 0.14/0.39 tptp_fun_X_11: $i)).
% 0.14/0.39 tff(bad_type, type, (
% 0.14/0.39 bad: $i)).
% 0.14/0.39 tff(tptp_fun_V_7_type, type, (
% 0.14/0.39 tptp_fun_V_7: $i)).
% 0.14/0.39 tff(tptp_fun_U_8_type, type, (
% 0.14/0.39 tptp_fun_U_8: $i)).
% 0.14/0.39 tff(tptp_fun_W_6_type, type, (
% 0.14/0.39 tptp_fun_W_6: $i)).
% 0.14/0.39 tff(ok_type, type, (
% 0.14/0.39 ok: $i > $o)).
% 0.14/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.14/0.39 tptp_fun_Z_0: $i)).
% 0.14/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.39 tptp_fun_Y_1: $i)).
% 0.14/0.39 tff(tptp_fun_X_2_type, type, (
% 0.14/0.39 tptp_fun_X_2: $i)).
% 0.14/0.39 tff(tptp_fun_W_3_type, type, (
% 0.14/0.39 tptp_fun_W_3: $i)).
% 0.14/0.39 tff(tptp_fun_V_4_type, type, (
% 0.14/0.39 tptp_fun_V_4: $i)).
% 0.14/0.39 tff(tptp_fun_U_5_type, type, (
% 0.14/0.39 tptp_fun_U_5: $i)).
% 0.14/0.39 tff(im_succ_cpq_type, type, (
% 0.14/0.39 im_succ_cpq: $i > $i)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))) <=> (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 ((~![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (~ok(triple(X, Y, Z)))))) <=> (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(3,axiom,(~![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => ![X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (~ok(triple(X, Y, Z)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l12_co')).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (~ok(triple(U!8, V!7, W!6))),
% 0.14/0.39 inference(and_elim,[status(thm)],[7])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.39 tff(14,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.40 tff(17,plain,(
% 0.14/0.40 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.14/0.40 inference(skolemize,[status(sab)],[16])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!8, V!7, W!6)) | (W!6 = bad))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!8, V!7, W!6)) | (W!6 = bad))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!8, V!7, W!6)) | (W!6 = bad))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!8, V!7, W!6)) | (W!6 = bad)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (W!6 = bad),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[21, 18, 8])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (bad = W!6),
% 0.14/0.40 inference(symmetry,[status(thm)],[22])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (triple(U!8, V!7, bad) = triple(U!8, V!7, W!6)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (succ_cpq(triple(U!8, V!7, bad), triple(X!11, Y!10, Z!9)) <=> succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9)) <=> succ_cpq(triple(U!8, V!7, bad), triple(X!11, Y!10, Z!9))),
% 0.14/0.40 inference(symmetry,[status(thm)],[25])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (~((~ok(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))))),
% 0.14/0.40 inference(and_elim,[status(thm)],[7])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))),
% 0.14/0.40 inference(or_elim,[status(thm)],[27])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (succ_cpq(triple(U!8, V!7, bad), triple(X!11, Y!10, Z!9))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (ok(triple(U!8, V!7, bad)) <=> ok(triple(U!8, V!7, W!6))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (ok(triple(U!8, V!7, W!6)) <=> ok(triple(U!8, V!7, bad))),
% 0.14/0.40 inference(symmetry,[status(thm)],[30])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 ((~ok(triple(U!8, V!7, W!6))) <=> (~ok(triple(U!8, V!7, bad)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (~ok(triple(U!8, V!7, bad))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 32])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (^[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))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (![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)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![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)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (^[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))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (![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)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.40 tff(39,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','l12_l13')).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.22/0.40 tff(42,plain,(
% 0.22/0.40 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.22/0.40 inference(skolemize,[status(sab)],[41])).
% 0.22/0.40 tff(43,plain,
% 0.22/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.22/0.40 tff(44,assumption,(~(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0))))), introduced(assumption)).
% 0.22/0.40 tff(45,plain,
% 0.22/0.40 ((ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0)))) | ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(46,plain,
% 0.22/0.40 (ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.22/0.40 tff(47,plain,
% 0.22/0.40 ((ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0)))) | (~ok(triple(X!2, Y!1, Z!0)))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(48,plain,
% 0.22/0.40 (~ok(triple(X!2, Y!1, Z!0))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.22/0.40 tff(49,plain,
% 0.22/0.40 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | (ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(50,plain,
% 0.22/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | (ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(51,plain,
% 0.22/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.22/0.40 tff(52,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[51, 48, 46, 43])).
% 0.22/0.40 tff(53,plain,(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.40 tff(54,plain,
% 0.22/0.40 (((~(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))) <=> ((~(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(55,plain,
% 0.22/0.40 ((~(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0))))) <=> (~(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0)))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(56,plain,
% 0.22/0.40 (((~(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))) <=> ((~(ok(triple(X!2, Y!1, Z!0)) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[55])).
% 0.22/0.40 tff(57,plain,
% 0.22/0.40 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(58,plain,
% 0.22/0.40 ((![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))) => ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(59,plain,
% 0.22/0.40 (^[X1: $i, X2: $i, X3: $i] : trans(monotonicity(quant_intro(proof_bind(^[X4: $i, X5: $i, X6: $i] : rewrite((succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6)))) <=> ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))), (![X4: $i, X5: $i, X6: $i] : (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6)))) <=> ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))), (((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6))))) <=> ((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))), rewrite(((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))) <=> (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))), (((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6))))) <=> (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(60,plain,
% 0.22/0.40 (![X1: $i, X2: $i, X3: $i] : ((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6))))) <=> ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.22/0.40 tff(61,plain,
% 0.22/0.40 (^[U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite(((~ok(triple(X, Y, Z))) => (~ok(im_succ_cpq(triple(X, Y, Z))))) <=> (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))))), ((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) => (~ok(im_succ_cpq(triple(X, Y, Z)))))) <=> (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))))))), rewrite((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))))) <=> (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))), ((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) => (~ok(im_succ_cpq(triple(X, Y, Z)))))) <=> (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 (![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) => (~ok(im_succ_cpq(triple(X, Y, Z)))))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 ((![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) => (~ok(im_succ_cpq(triple(X, Y, Z)))))) => ![X1: $i, X2: $i, X3: $i] : ((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6)))))) <=> (![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))) => ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[62, 60])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 ((![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) => (~ok(im_succ_cpq(triple(X, Y, Z)))))) => ![X1: $i, X2: $i, X3: $i] : ((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6)))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[63, 58])).
% 0.22/0.41 tff(65,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(triple(X, Y, Z))) => (~ok(im_succ_cpq(triple(X, Y, Z)))))) => ![X1: $i, X2: $i, X3: $i] : ((~ok(triple(X1, X2, X3))) => ![X4: $i, X5: $i, X6: $i] : (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => (~ok(triple(X4, X5, X6)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l12_induction')).
% 0.22/0.41 tff(66,plain,
% 0.22/0.41 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.22/0.41 tff(67,plain,
% 0.22/0.41 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[66, 57])).
% 0.22/0.41 tff(68,plain,
% 0.22/0.41 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.22/0.41 tff(69,plain,
% 0.22/0.41 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (ok(triple(X, Y, Z)) | (~ok(im_succ_cpq(triple(X, Y, Z)))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : (ok(triple(X1, X2, X3)) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[68, 57])).
% 0.22/0.41 Proof display could not be completed: monotonicity rule is not handled
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------