TSTP Solution File: SWV384+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV384+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Thu Sep 29 15:11:34 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV384+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n008.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 : Sun Sep 4 02:50:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(check_cpq_type, type, (
% 0.21/0.41 check_cpq: $i > $o)).
% 0.21/0.41 tff(triple_type, type, (
% 0.21/0.41 triple: ( $i * $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_W_6_type, type, (
% 0.21/0.41 tptp_fun_W_6: $i)).
% 0.21/0.41 tff(tptp_fun_V_7_type, type, (
% 0.21/0.41 tptp_fun_V_7: $i)).
% 0.21/0.41 tff(tptp_fun_U_8_type, type, (
% 0.21/0.41 tptp_fun_U_8: $i)).
% 0.21/0.41 tff(ok_type, type, (
% 0.21/0.41 ok: $i > $o)).
% 0.21/0.41 tff(succ_cpq_type, type, (
% 0.21/0.41 succ_cpq: ( $i * $i ) > $o)).
% 0.21/0.41 tff(tptp_fun_Z_9_type, type, (
% 0.21/0.41 tptp_fun_Z_9: $i)).
% 0.21/0.41 tff(tptp_fun_Y_10_type, type, (
% 0.21/0.41 tptp_fun_Y_10: $i)).
% 0.21/0.41 tff(tptp_fun_X_11_type, type, (
% 0.21/0.41 tptp_fun_X_11: $i)).
% 0.21/0.41 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.41 tptp_fun_Z_0: $i)).
% 0.21/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.41 tptp_fun_Y_1: $i)).
% 0.21/0.41 tff(tptp_fun_X_2_type, type, (
% 0.21/0.41 tptp_fun_X_2: $i)).
% 0.21/0.41 tff(tptp_fun_W_3_type, type, (
% 0.21/0.41 tptp_fun_W_3: $i)).
% 0.21/0.41 tff(tptp_fun_V_4_type, type, (
% 0.21/0.41 tptp_fun_V_4: $i)).
% 0.21/0.41 tff(tptp_fun_U_5_type, type, (
% 0.21/0.41 tptp_fun_U_5: $i)).
% 0.21/0.41 tff(im_succ_cpq_type, type, (
% 0.21/0.41 im_succ_cpq: $i > $i)).
% 0.21/0.41 tff(1,assumption,(![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X4, X5, X6))))), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (((~(~((~check_cpq(triple(U!8, V!7, W!6))) | (~ok(triple(U!8, V!7, W!6)))))) & (~((~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9)))))) <=> (((~check_cpq(triple(U!8, V!7, W!6))) | (~ok(triple(U!8, V!7, W!6)))) & (~((~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 ((~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))) <=> (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 ((~![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~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))) | (~check_cpq(triple(X, Y, Z))))))) <=> (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(5,axiom,(~![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~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))) | (~check_cpq(triple(X, Y, Z))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l20_co')).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (~![U: $i, V: $i, W: $i] : ((~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))) | ![X: $i, Y: $i, Z: $i] : ((~ok(triple(X, Y, Z))) | (~check_cpq(triple(X, Y, Z))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (((~check_cpq(triple(U!8, V!7, W!6))) | (~ok(triple(U!8, V!7, W!6)))) & (~((~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (~((~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))))),
% 0.21/0.41 inference(and_elim,[status(thm)],[13])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))),
% 0.21/0.41 inference(or_elim,[status(thm)],[14])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (check_cpq(triple(X!11, Y!10, Z!9))),
% 0.21/0.41 inference(or_elim,[status(thm)],[14])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (ok(triple(X!11, Y!10, Z!9))),
% 0.21/0.41 inference(or_elim,[status(thm)],[14])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (((~![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X4, X5, X6))))) | ((~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))))) <=> ((~![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X4, X5, X6))))) | (~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 ((~![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X4, X5, X6))))) | ((~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((~![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X4, X5, X6))))) | (~ok(triple(X!11, Y!10, Z!9))) | (~check_cpq(triple(X!11, Y!10, Z!9))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X!11, Y!10, Z!9)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[20, 17, 16, 15, 1])).
% 0.21/0.41 tff(22,plain,(~![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(U!8, V!7, W!6), triple(X4, X5, X6))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (^[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(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))) | (~ok(triple(U, V, W)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (![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))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i] : rewrite((((~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)))))) <=> ((~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)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (![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))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.42 tff(28,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/sandbox2/benchmark/theBenchmark.p','l12_l13')).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (![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))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![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))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.42 tff(31,plain,(
% 0.21/0.42 ![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))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[30])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![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))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.42 tff(33,assumption,(~((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(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)).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!0))))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0)))) | ((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!0))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 ((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!0)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!0))))) | (~succ_cpq(triple(U!5, V!4, W!3), triple(X!2, Y!1, Z!0)))) | check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (((~![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))))))) | ((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!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(triple(U, V, W))))))) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!0))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 ((~![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))))))) | ((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!0))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))) | (~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(triple(X!2, Y!1, Z!0)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[42, 39, 37, 35, 32])).
% 0.21/0.42 tff(44,plain,((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(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,[]))).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (((~((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(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] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))) <=> ((~((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(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] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (((~((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(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] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))) <=> ((~((~ok(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~check_cpq(im_succ_cpq(triple(X!2, Y!1, Z!0)))) | (~((~check_cpq(triple(X!2, Y!1, Z!0))) | (~ok(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] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(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(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 ((![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))) => ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(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(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (^[X1: $i, X2: $i, X3: $i] : trans(monotonicity(quant_intro(proof_bind(^[X4: $i, X5: $i, X6: $i] : trans(monotonicity(rewrite(((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6)))) <=> ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))))), ((succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))))) <=> (succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))))))), rewrite((succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))))) <=> ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))), ((succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)) => ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))))) <=> ((~ok(triple(X4, X5, X6))) | (~check_cpq(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))) | (~check_cpq(triple(X4, X5, X6))))) <=> ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))), ((((~check_cpq(triple(X1, X2, X3))) | (~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))) | (~check_cpq(triple(X4, X5, X6)))))) <=> (((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3)))) => ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))), rewrite((((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3)))) => ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))) <=> ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))), ((((~check_cpq(triple(X1, X2, X3))) | (~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))) | (~check_cpq(triple(X4, X5, X6)))))) <=> ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![X1: $i, X2: $i, X3: $i] : (((~check_cpq(triple(X1, X2, X3))) | (~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))) | (~check_cpq(triple(X4, X5, X6)))))) <=> ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z)))) => ((~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~ok(im_succ_cpq(triple(X, Y, Z)))))) <=> ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))))), ((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z)))) => ((~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~ok(im_succ_cpq(triple(X, Y, Z))))))) <=> (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))))))), rewrite((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))))) <=> ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))), ((succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z)))) => ((~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~ok(im_succ_cpq(triple(X, Y, Z))))))) <=> ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z)))) => ((~check_cpq(im_succ_cpq(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(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 ((![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z)))) => ((~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~ok(im_succ_cpq(triple(X, Y, Z))))))) => ![X1: $i, X2: $i, X3: $i] : (((~check_cpq(triple(X1, X2, X3))) | (~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))) | (~check_cpq(triple(X4, X5, X6))))))) <=> (![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z)))) => ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[52, 50])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 ((![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z)))) => ((~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~ok(im_succ_cpq(triple(X, Y, Z))))))) => ![X1: $i, X2: $i, X3: $i] : (((~check_cpq(triple(X1, X2, X3))) | (~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))) | (~check_cpq(triple(X4, X5, X6))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[53, 48])).
% 0.21/0.43 tff(55,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : (succ_cpq(triple(U, V, W), triple(X, Y, Z)) => (((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z)))) => ((~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~ok(im_succ_cpq(triple(X, Y, Z))))))) => ![X1: $i, X2: $i, X3: $i] : (((~check_cpq(triple(X1, X2, X3))) | (~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))) | (~check_cpq(triple(X4, X5, X6))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l20_induction')).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[56, 47])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[58, 47])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 47])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[60, 47])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i, Z: $i] : ((~ok(im_succ_cpq(triple(X, Y, Z)))) | (~check_cpq(im_succ_cpq(triple(X, Y, Z)))) | (~((~check_cpq(triple(X, Y, Z))) | (~ok(triple(X, Y, Z))))) | (~succ_cpq(triple(U, V, W), triple(X, Y, Z))))) | ![X1: $i, X2: $i, X3: $i] : ((~((~check_cpq(triple(X1, X2, X3))) | (~ok(triple(X1, X2, X3))))) | ![X4: $i, X5: $i, X6: $i] : ((~ok(triple(X4, X5, X6))) | (~check_cpq(triple(X4, X5, X6))) | (~succ_cpq(triple(X1, X2, X3), triple(X4, X5, X6)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[61, 47])).
% 0.21/0.43 Proof display could not be completed: monotonicity rule is not handled
%------------------------------------------------------------------------------