TSTP Solution File: SWV394+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV394+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 15:11:36 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV394+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sun Sep 4 03:11:57 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(pair_in_list_type, type, (
% 0.20/0.40 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Y_6_type, type, (
% 0.20/0.40 tptp_fun_Y_6: $i)).
% 0.20/0.40 tff(tptp_fun_X_2_type, type, (
% 0.20/0.40 tptp_fun_X_2: $i)).
% 0.20/0.40 tff(remove_slb_type, type, (
% 0.20/0.40 remove_slb: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_V_4_type, type, (
% 0.20/0.40 tptp_fun_V_4: $i)).
% 0.20/0.40 tff(less_than_type, type, (
% 0.20/0.40 less_than: ( $i * $i ) > $o)).
% 0.20/0.40 tff(check_cpq_type, type, (
% 0.20/0.40 check_cpq: $i > $o)).
% 0.20/0.40 tff(triple_type, type, (
% 0.20/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_W_3_type, type, (
% 0.20/0.40 tptp_fun_W_3: $i)).
% 0.20/0.40 tff(remove_pqp_type, type, (
% 0.20/0.40 remove_pqp: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_U_5_type, type, (
% 0.20/0.40 tptp_fun_U_5: $i)).
% 0.20/0.40 tff(tptp_fun_X_1_type, type, (
% 0.20/0.40 tptp_fun_X_1: $i > $i)).
% 0.20/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.40 tptp_fun_Y_0: $i > $i)).
% 0.20/0.40 tff(remove_cpq_type, type, (
% 0.20/0.40 remove_cpq: ( $i * $i ) > $i)).
% 0.20/0.40 tff(contains_slb_type, type, (
% 0.20/0.40 contains_slb: ( $i * $i ) > $o)).
% 0.20/0.40 tff(bad_type, type, (
% 0.20/0.40 bad: $i)).
% 0.20/0.40 tff(ok_type, type, (
% 0.20/0.40 ok: $i > $o)).
% 0.20/0.40 tff(lookup_slb_type, type, (
% 0.20/0.40 lookup_slb: ( $i * $i ) > $i)).
% 0.20/0.40 tff(strictly_less_than_type, type, (
% 0.20/0.40 strictly_less_than: ( $i * $i ) > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[U: $i, V: $i, W: $i] : refl((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[U: $i, V: $i, W: $i] : rewrite((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[U: $i, V: $i, W: $i] : trans(monotonicity(rewrite(((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))), rewrite((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (^[U: $i, V: $i, W: $i] : rewrite((check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.40 tff(11,axiom,(![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l30_li4142')).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.40 tff(14,plain,(
% 0.20/0.40 ![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~((~pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(remove_slb(V!4, X!2)), tptp_fun_Y_0(remove_slb(V!4, X!2)))) | less_than(tptp_fun_Y_0(remove_slb(V!4, X!2)), tptp_fun_X_1(remove_slb(V!4, X!2)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~((~pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(remove_slb(V!4, X!2)), tptp_fun_Y_0(remove_slb(V!4, X!2)))) | less_than(tptp_fun_Y_0(remove_slb(V!4, X!2)), tptp_fun_X_1(remove_slb(V!4, X!2))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~((~pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(remove_slb(V!4, X!2)), tptp_fun_Y_0(remove_slb(V!4, X!2)))) | less_than(tptp_fun_Y_0(remove_slb(V!4, X!2)), tptp_fun_X_1(remove_slb(V!4, X!2)))))))) | ((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.41 tff(21,assumption,(remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)), introduced(assumption)).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (triple(U!5, V!4, bad) = remove_cpq(triple(U!5, V!4, W!3), X!2)),
% 0.20/0.41 inference(symmetry,[status(thm)],[21])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (ok(triple(U!5, V!4, bad)) <=> ok(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) <=> ok(triple(U!5, V!4, bad))),
% 0.20/0.41 inference(symmetry,[status(thm)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (((check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2))) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2)))) <=> (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~(~(check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) <=> (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (((~(~(check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2)))) <=> ((check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2))) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (((~(~(check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2)))) <=> (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 ((~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) <=> (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~![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))) => ![Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))) <=> (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(31,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))) => ![Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l30_co')).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (~![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)))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 29])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (ok(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.20/0.41 inference(and_elim,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (ok(triple(U!5, V!4, bad))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[40, 24])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.41 tff(47,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.41 tff(50,plain,(
% 0.20/0.41 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(U!5, V!4, bad)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (~ok(triple(U!5, V!4, bad))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 41])).
% 0.20/0.41 tff(55,plain,(~(remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.41 tff(61,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax43')).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.41 tff(64,plain,(
% 0.20/0.41 ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (contains_slb(V!4, X!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 55])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (^[U: $i, V: $i] : refl((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (^[U: $i, V: $i] : rewrite((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(76,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.41 tff(78,plain,(
% 0.20/0.41 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[77])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(X!2, lookup_slb(V!4, X!2)) <=> (~((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (strictly_less_than(X!2, lookup_slb(V!4, X!2)) <=> (~((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.41 tff(83,assumption,(remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)), introduced(assumption)).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad) = remove_cpq(triple(U!5, V!4, W!3), X!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[83])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) <=> ok(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) <=> ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.20/0.42 inference(symmetry,[status(thm)],[85])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 86])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (~ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 51])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 87])).
% 0.20/0.42 tff(91,plain,(~(remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X)))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) <=> (~((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))), ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) <=> (~(~((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))))), rewrite((~(~((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X))))), ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))))), (((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> (((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))))), rewrite((((~contains_slb(V, X)) | (~strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))), (((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.42 tff(99,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X))) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax45')).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.42 tff(102,plain,(
% 0.20/0.42 ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & strictly_less_than(X, lookup_slb(V, X)))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[101])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | ((~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | (~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | ((~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), bad)) | (~strictly_less_than(X, lookup_slb(V, X))))) | (~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((~contains_slb(V!4, X!2)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[108, 91])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (~strictly_less_than(X!2, lookup_slb(V!4, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[109, 70])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~(strictly_less_than(X!2, lookup_slb(V!4, X!2)) <=> (~((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2))))) | strictly_less_than(X!2, lookup_slb(V!4, X!2)) | ((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 ((~(strictly_less_than(X!2, lookup_slb(V!4, X!2)) <=> (~((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2))))) | ((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[112, 82])).
% 0.20/0.42 tff(114,assumption,(~less_than(lookup_slb(V!4, X!2), X!2)), introduced(assumption)).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 ((~((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2))) | (~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (~less_than(X!2, lookup_slb(V!4, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[115, 114, 113])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.42 tff(122,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.20/0.42 tff(125,plain,(
% 0.20/0.42 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.42 inference(skolemize,[status(sab)],[124])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!2, lookup_slb(V!4, X!2)) | less_than(lookup_slb(V!4, X!2), X!2))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, lookup_slb(V!4, X!2)) | less_than(lookup_slb(V!4, X!2), X!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!2, lookup_slb(V!4, X!2)) | less_than(lookup_slb(V!4, X!2), X!2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, lookup_slb(V!4, X!2)) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[129, 126, 114, 116])).
% 0.20/0.42 tff(131,plain,(less_than(lookup_slb(V!4, X!2), X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) <=> (~((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))), ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) <=> (~(~((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))))), rewrite((~(~((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))) <=> ((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X)))), ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) <=> ((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))))), (((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> (((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))))), rewrite((((~contains_slb(V, X)) | (~less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))), (((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.43 tff(139,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & less_than(lookup_slb(V, X), X)) => (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax44')).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.43 tff(142,plain,(
% 0.20/0.43 ![U: $i, V: $i, W: $i, X: $i] : ((~(contains_slb(V, X) & less_than(lookup_slb(V, X), X))) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[141])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | ((~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~less_than(lookup_slb(V!4, X!2), X!2)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | (~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~less_than(lookup_slb(V!4, X!2), X!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | ((~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~less_than(lookup_slb(V!4, X!2), X!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | (remove_cpq(triple(U, V, W), X) = triple(remove_pqp(U, X), remove_slb(V, X), W)) | (~less_than(lookup_slb(V, X), X)))) | (~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~less_than(lookup_slb(V!4, X!2), X!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 ((~contains_slb(V!4, X!2)) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~less_than(lookup_slb(V!4, X!2), X!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[148, 131, 70])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 (triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3) = remove_cpq(triple(U!5, V!4, W!3), X!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[149])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) <=> check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) <=> check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))),
% 0.20/0.43 inference(symmetry,[status(thm)],[151])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.20/0.43 inference(and_elim,[status(thm)],[39])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 (check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 ((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[155, 154, 20])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.20/0.43 inference(and_elim,[status(thm)],[39])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 (~less_than(Y!6, X!2)),
% 0.20/0.43 inference(or_elim,[status(thm)],[157])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | ((~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | (~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | ((~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | (~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[161, 158, 156])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(X!2, Y!6) <=> (~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (strictly_less_than(X!2, Y!6) <=> (~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[163, 80])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!2, Y!6) | less_than(Y!6, X!2))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, Y!6) | less_than(Y!6, X!2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!2, Y!6) | less_than(Y!6, X!2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, Y!6) | less_than(Y!6, X!2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (less_than(X!2, Y!6)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[167, 126, 158])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 ((~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))) | (~less_than(X!2, Y!6)) | less_than(Y!6, X!2)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 ((~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))) | (~less_than(X!2, Y!6))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[169, 158])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[170, 168])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 ((~(strictly_less_than(X!2, Y!6) <=> (~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))))) | strictly_less_than(X!2, Y!6) | ((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (strictly_less_than(X!2, Y!6)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[172, 171, 164])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (pair_in_list(V!4, X!2, Y!6)),
% 0.20/0.43 inference(or_elim,[status(thm)],[157])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[175])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X))) <=> (~((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))), ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) <=> (~(~((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))))), rewrite((~(~((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))) <=> ((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))), ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) <=> ((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))), (((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> (((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)))), rewrite((((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))), (((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : trans(monotonicity(rewrite(((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) <=> (pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))), ((((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ((pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)))), rewrite(((pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))), ((((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.43 tff(182,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l30_li3132')).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.20/0.43 tff(185,plain,(
% 0.20/0.43 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.20/0.43 inference(skolemize,[status(sab)],[184])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | ((~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 ((pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2)))) <=> ((~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(190,plain,
% 0.20/0.44 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | ((~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[189])).
% 0.20/0.44 tff(191,plain,
% 0.20/0.44 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[190, 188])).
% 0.20/0.44 tff(192,plain,
% 0.20/0.44 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(193,plain,
% 0.20/0.44 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.44 tff(194,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[193, 187, 40, 174, 173, 162])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------