TSTP Solution File: SWV391+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV391+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV391+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n017.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Sep 4 02:13:54 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.17/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.17/0.33 Usage: tptp [options] [-file:]file
% 0.17/0.33 -h, -? prints this message.
% 0.17/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.17/0.33 -m, -model generate model.
% 0.17/0.33 -p, -proof generate proof.
% 0.17/0.33 -c, -core generate unsat core of named formulas.
% 0.17/0.33 -st, -statistics display statistics.
% 0.17/0.33 -t:timeout set timeout (in second).
% 0.17/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.17/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.17/0.33 -<param>:<value> configuration parameter and value.
% 0.17/0.33 -o:<output-file> file to place output in.
% 0.17/0.39 % SZS status Theorem
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 tff(less_than_type, type, (
% 0.17/0.39 less_than: ( $i * $i ) > $o)).
% 0.17/0.39 tff(pair_in_list_type, type, (
% 0.17/0.39 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.17/0.39 tff(remove_slb_type, type, (
% 0.17/0.39 remove_slb: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_X_2_type, type, (
% 0.17/0.39 tptp_fun_X_2: $i)).
% 0.17/0.39 tff(tptp_fun_V_4_type, type, (
% 0.17/0.39 tptp_fun_V_4: $i)).
% 0.17/0.39 tff(check_cpq_type, type, (
% 0.17/0.39 check_cpq: $i > $o)).
% 0.17/0.39 tff(triple_type, type, (
% 0.17/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_W_3_type, type, (
% 0.17/0.39 tptp_fun_W_3: $i)).
% 0.17/0.39 tff(remove_pqp_type, type, (
% 0.17/0.39 remove_pqp: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_U_5_type, type, (
% 0.17/0.39 tptp_fun_U_5: $i)).
% 0.17/0.39 tff(tptp_fun_X_1_type, type, (
% 0.17/0.39 tptp_fun_X_1: $i > $i)).
% 0.17/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.17/0.39 tptp_fun_Y_0: $i > $i)).
% 0.17/0.39 tff(remove_cpq_type, type, (
% 0.17/0.39 remove_cpq: ( $i * $i ) > $i)).
% 0.17/0.39 tff(lookup_slb_type, type, (
% 0.17/0.39 lookup_slb: ( $i * $i ) > $i)).
% 0.17/0.39 tff(strictly_less_than_type, type, (
% 0.17/0.39 strictly_less_than: ( $i * $i ) > $o)).
% 0.17/0.39 tff(bad_type, type, (
% 0.17/0.39 bad: $i)).
% 0.17/0.39 tff(ok_type, type, (
% 0.17/0.39 ok: $i > $o)).
% 0.17/0.39 tff(contains_slb_type, type, (
% 0.17/0.39 contains_slb: ( $i * $i ) > $o)).
% 0.17/0.39 tff(1,plain,
% 0.17/0.39 (^[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)))))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(2,plain,
% 0.17/0.39 (![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))))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.39 tff(3,plain,
% 0.17/0.39 (^[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)))))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(4,plain,
% 0.17/0.39 (![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))))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.39 tff(5,plain,
% 0.17/0.39 (![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))))))))),
% 0.17/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.17/0.39 tff(6,plain,
% 0.17/0.39 (^[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))))))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(7,plain,
% 0.17/0.39 (![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))))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.39 tff(8,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(9,plain,
% 0.17/0.39 (^[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))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(10,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.17/0.39 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','l27_li4142')).
% 0.17/0.39 tff(12,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.17/0.39 tff(13,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.17/0.39 tff(14,plain,(
% 0.17/0.39 ![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))))))),
% 0.17/0.40 inference(skolemize,[status(sab)],[13])).
% 0.17/0.40 tff(15,plain,
% 0.17/0.40 (![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))))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.17/0.40 tff(16,plain,
% 0.17/0.40 (![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))))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.17/0.40 tff(17,plain,
% 0.17/0.40 ((~![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))))))))) | (~((~((~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)))))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(18,plain,
% 0.17/0.40 (~((~((~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))))))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.17/0.40 tff(19,plain,
% 0.17/0.40 (((~((~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)))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(20,plain,
% 0.17/0.40 ((~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))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.17/0.40 tff(21,plain,
% 0.17/0.40 (^[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)))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(22,plain,
% 0.17/0.40 (![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))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.17/0.40 tff(23,plain,
% 0.17/0.40 (^[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)))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(24,plain,
% 0.17/0.40 (![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))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.17/0.40 tff(25,plain,
% 0.17/0.40 (![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))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(26,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')).
% 0.17/0.40 tff(27,plain,
% 0.17/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.17/0.40 tff(28,plain,(
% 0.17/0.40 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.17/0.40 inference(skolemize,[status(sab)],[27])).
% 0.17/0.40 tff(29,plain,
% 0.17/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.17/0.40 tff(30,plain,
% 0.17/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.17/0.40 tff(31,plain,
% 0.17/0.40 ((~![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))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(32,plain,
% 0.17/0.40 (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)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.17/0.40 tff(33,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)).
% 0.17/0.40 tff(34,plain,
% 0.17/0.40 (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)),
% 0.17/0.40 inference(symmetry,[status(thm)],[33])).
% 0.17/0.40 tff(35,plain,
% 0.17/0.40 (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))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.17/0.40 tff(36,plain,
% 0.17/0.40 (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))),
% 0.17/0.40 inference(symmetry,[status(thm)],[35])).
% 0.17/0.40 tff(37,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(38,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W)))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(39,axiom,(~![U: $i, V: $i, W: $i, X: $i] : ((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l27_co')).
% 0.17/0.40 tff(40,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.17/0.40 tff(41,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.17/0.40 tff(42,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.17/0.40 tff(43,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.17/0.40 tff(44,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[43, 37])).
% 0.17/0.40 tff(45,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.17/0.40 tff(46,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[45, 37])).
% 0.17/0.40 tff(47,plain,(
% 0.17/0.40 ~(check_cpq(triple(U!5, V!4, W!3)) | (~(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)))))),
% 0.17/0.40 inference(skolemize,[status(sab)],[46])).
% 0.17/0.40 tff(48,plain,
% 0.17/0.40 (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))),
% 0.17/0.40 inference(or_elim,[status(thm)],[47])).
% 0.17/0.40 tff(49,plain,
% 0.17/0.40 (ok(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.17/0.40 inference(and_elim,[status(thm)],[48])).
% 0.17/0.40 tff(50,plain,
% 0.17/0.40 (ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[49, 36])).
% 0.17/0.40 tff(51,plain,
% 0.17/0.40 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(52,plain,
% 0.17/0.40 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.17/0.40 tff(53,plain,
% 0.17/0.40 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(54,plain,
% 0.17/0.40 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(55,plain,
% 0.17/0.40 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.17/0.40 tff(56,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.17/0.40 tff(57,plain,
% 0.17/0.40 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.17/0.40 tff(58,plain,
% 0.17/0.40 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.17/0.40 tff(59,plain,(
% 0.17/0.40 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.17/0.40 inference(skolemize,[status(sab)],[58])).
% 0.17/0.40 tff(60,plain,
% 0.17/0.40 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.17/0.40 tff(61,plain,
% 0.17/0.40 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(62,plain,
% 0.17/0.40 (~ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.17/0.40 tff(63,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[62, 50])).
% 0.17/0.40 tff(64,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,[]))).
% 0.17/0.40 tff(65,plain,
% 0.17/0.40 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X)) <=> ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X)))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(66,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.17/0.40 tff(67,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(68,plain,
% 0.17/0.40 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((ok(remove_cpq(triple(U, V, W), X)) => contains_slb(V, X)) <=> ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X)))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(69,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : (ok(remove_cpq(triple(U, V, W), X)) => contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.17/0.40 tff(70,axiom,(![U: $i, V: $i, W: $i, X: $i] : (ok(remove_cpq(triple(U, V, W), X)) => contains_slb(V, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l27_l33')).
% 0.17/0.40 tff(71,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.17/0.40 tff(72,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.17/0.40 tff(73,plain,(
% 0.17/0.40 ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.17/0.40 inference(skolemize,[status(sab)],[72])).
% 0.17/0.40 tff(74,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.17/0.40 tff(75,plain,
% 0.17/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))) | ((~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))) | contains_slb(V!4, X!2))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))) | contains_slb(V!4, X!2))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(76,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))) | ((~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))) | contains_slb(V!4, X!2))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(77,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))) | contains_slb(V!4, X!2)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.17/0.40 tff(78,plain,
% 0.17/0.40 (contains_slb(V!4, X!2)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[77, 74, 49])).
% 0.17/0.40 tff(79,plain,
% 0.17/0.40 (^[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)))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(80,plain,
% 0.17/0.40 (![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))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.17/0.40 tff(81,plain,
% 0.17/0.40 (^[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))))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(82,plain,
% 0.17/0.41 (![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))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.17/0.41 tff(83,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(84,plain,
% 0.17/0.41 (^[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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(85,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.17/0.41 tff(86,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')).
% 0.17/0.41 tff(87,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.17/0.41 tff(88,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.17/0.41 tff(89,plain,(
% 0.17/0.41 ![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)))),
% 0.17/0.41 inference(skolemize,[status(sab)],[88])).
% 0.17/0.41 tff(90,plain,
% 0.17/0.41 (![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))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.17/0.41 tff(91,plain,
% 0.17/0.41 (![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))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.17/0.41 tff(92,plain,
% 0.17/0.41 (((~![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))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(93,plain,
% 0.17/0.41 ((~![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))))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(94,plain,
% 0.17/0.41 ((~![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.17/0.41 tff(95,plain,
% 0.17/0.41 ((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)))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[94, 91, 78])).
% 0.17/0.41 tff(96,plain,
% 0.17/0.41 (~strictly_less_than(X!2, lookup_slb(V!4, X!2))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[95, 64])).
% 0.17/0.41 tff(97,plain,
% 0.17/0.41 ((~(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))))) | 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))),
% 0.17/0.41 inference(tautology,[status(thm)],[])).
% 0.17/0.41 tff(98,plain,
% 0.17/0.41 ((~(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))))) | ((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.17/0.41 tff(99,plain,
% 0.17/0.41 ((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[98, 32])).
% 0.17/0.41 tff(100,assumption,((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)), introduced(assumption)).
% 0.17/0.41 tff(101,assumption,(~less_than(lookup_slb(V!4, X!2), X!2)), introduced(assumption)).
% 0.17/0.41 tff(102,plain,
% 0.17/0.41 ((~((~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)),
% 0.17/0.41 inference(tautology,[status(thm)],[])).
% 0.17/0.41 tff(103,plain,
% 0.17/0.41 (~less_than(X!2, lookup_slb(V!4, X!2))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[102, 101, 100])).
% 0.17/0.41 tff(104,plain,
% 0.17/0.41 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(105,plain,
% 0.17/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[104])).
% 0.17/0.41 tff(106,plain,
% 0.17/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(107,plain,
% 0.17/0.41 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(108,plain,
% 0.17/0.41 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.17/0.41 tff(109,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.17/0.41 tff(110,plain,
% 0.17/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.17/0.41 tff(111,plain,
% 0.17/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.17/0.41 tff(112,plain,(
% 0.17/0.41 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.17/0.41 inference(skolemize,[status(sab)],[111])).
% 0.17/0.41 tff(113,plain,
% 0.17/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.17/0.41 tff(114,plain,
% 0.17/0.41 (((~![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))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(115,plain,
% 0.17/0.41 ((~![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))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(116,plain,
% 0.17/0.41 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, lookup_slb(V!4, X!2)) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.17/0.41 tff(117,plain,
% 0.17/0.41 ($false),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[116, 113, 101, 103])).
% 0.17/0.41 tff(118,plain,(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)))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.41 tff(119,plain,
% 0.17/0.41 (less_than(lookup_slb(V!4, X!2), X!2)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[118, 99])).
% 0.17/0.41 tff(120,plain,
% 0.17/0.41 (^[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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(121,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[120])).
% 0.17/0.41 tff(122,plain,
% 0.17/0.41 (^[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)))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(123,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[122])).
% 0.17/0.41 tff(124,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(125,plain,
% 0.17/0.41 (^[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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(126,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[125])).
% 0.17/0.41 tff(127,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')).
% 0.17/0.41 tff(128,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.17/0.41 tff(129,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.17/0.41 tff(130,plain,(
% 0.17/0.41 ![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)))),
% 0.17/0.41 inference(skolemize,[status(sab)],[129])).
% 0.17/0.41 tff(131,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.17/0.41 tff(132,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.17/0.41 tff(133,plain,
% 0.17/0.41 (((~![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(134,plain,
% 0.17/0.41 ((~![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)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(135,plain,
% 0.17/0.42 ((~![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)))) | (~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))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.17/0.42 tff(136,plain,
% 0.17/0.42 ((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))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[135, 132, 78])).
% 0.17/0.42 tff(137,plain,
% 0.17/0.42 (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)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[136, 119])).
% 0.17/0.42 tff(138,plain,
% 0.17/0.42 (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)),
% 0.17/0.42 inference(symmetry,[status(thm)],[137])).
% 0.17/0.42 tff(139,plain,
% 0.17/0.42 (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))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[138])).
% 0.17/0.42 tff(140,plain,
% 0.17/0.42 (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))),
% 0.17/0.42 inference(symmetry,[status(thm)],[139])).
% 0.17/0.42 tff(141,plain,
% 0.17/0.42 (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.17/0.42 inference(and_elim,[status(thm)],[48])).
% 0.17/0.42 tff(142,plain,
% 0.17/0.42 (check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.17/0.42 tff(143,plain,
% 0.17/0.42 ((~((~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))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(144,plain,
% 0.17/0.42 (![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[143, 142, 20])).
% 0.17/0.42 tff(145,assumption,(tptp_fun_X_1(V!4) = X!2), introduced(assumption)).
% 0.17/0.42 tff(146,plain,
% 0.17/0.42 (X!2 = tptp_fun_X_1(V!4)),
% 0.17/0.42 inference(symmetry,[status(thm)],[145])).
% 0.17/0.42 tff(147,plain,
% 0.17/0.42 (pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4)) <=> pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[146])).
% 0.17/0.42 tff(148,plain,
% 0.17/0.42 (pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) <=> pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))),
% 0.17/0.42 inference(symmetry,[status(thm)],[147])).
% 0.17/0.42 tff(149,plain,
% 0.17/0.42 ((~![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(U!5, V!4, W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(V!4, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))))))))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(150,plain,
% 0.17/0.42 (~((~((~check_cpq(triple(U!5, V!4, W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(V!4, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[149, 16])).
% 0.17/0.42 tff(151,plain,
% 0.17/0.42 (((~((~check_cpq(triple(U!5, V!4, W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(V!4, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))))))) | (check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(152,plain,
% 0.17/0.42 (check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.17/0.42 tff(153,plain,
% 0.17/0.42 (~check_cpq(triple(U!5, V!4, W!3))),
% 0.17/0.42 inference(or_elim,[status(thm)],[47])).
% 0.17/0.42 tff(154,plain,
% 0.17/0.42 ((~(check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))))) | check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(155,plain,
% 0.17/0.42 ((~(check_cpq(triple(U!5, V!4, W!3)) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))))) | (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.17/0.42 tff(156,plain,
% 0.17/0.42 (~((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.17/0.42 tff(157,plain,
% 0.17/0.42 (((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))) | pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(158,plain,
% 0.17/0.42 (pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.17/0.42 tff(159,plain,
% 0.17/0.42 (pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.17/0.42 tff(160,plain,
% 0.17/0.42 (less_than(tptp_fun_Y_0(V!4), X!2) <=> less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[146])).
% 0.17/0.42 tff(161,plain,
% 0.17/0.42 (less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)) <=> less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.17/0.42 inference(symmetry,[status(thm)],[160])).
% 0.17/0.42 tff(162,plain,
% 0.17/0.42 ((~less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))) <=> (~less_than(tptp_fun_Y_0(V!4), X!2))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.17/0.42 tff(163,plain,
% 0.17/0.42 (((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))) | (~less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(164,plain,
% 0.17/0.42 (~less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[163, 156])).
% 0.17/0.42 tff(165,plain,
% 0.17/0.42 (~less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[164, 162])).
% 0.17/0.42 tff(166,plain,
% 0.17/0.42 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))) <=> ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(167,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[166])).
% 0.17/0.42 tff(168,plain,
% 0.17/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl((![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))) <=> (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(169,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[168])).
% 0.17/0.42 tff(170,plain,
% 0.17/0.42 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))) <=> (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(171,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[170])).
% 0.17/0.42 tff(172,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))),
% 0.17/0.42 inference(transitivity,[status(thm)],[171, 169])).
% 0.17/0.42 tff(173,plain,
% 0.17/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) <=> (~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))), ((~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))) <=> (~(~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))))), rewrite((~(~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))) <=> ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))), ((~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))) <=> ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))), (((~(check_cpq(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))) <=> (((~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))))), rewrite((((~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))) <=> (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))), (((~(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))) <=> (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(174,plain,
% 0.17/0.42 (![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] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[173])).
% 0.17/0.42 tff(175,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(176,plain,
% 0.17/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite((pair_in_list(V, X, Y) => less_than(Y, X)) <=> ((~pair_in_list(V, X, Y)) | less_than(Y, X)))), (![Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)) <=> ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))), (((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))) <=> ((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))))), rewrite(((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))) <=> ((~(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)))), (((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))) <=> ((~(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)))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(177,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[176])).
% 0.17/0.42 tff(178,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','l27_l30')).
% 0.17/0.42 tff(179,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.17/0.42 tff(180,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.17/0.42 tff(181,plain,(
% 0.17/0.42 ![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)))),
% 0.17/0.42 inference(skolemize,[status(sab)],[180])).
% 0.17/0.42 tff(182,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.17/0.42 tff(183,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i, X: $i] : (![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)) | (~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.17/0.42 tff(184,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[183, 167])).
% 0.17/0.42 tff(185,plain,
% 0.17/0.42 (((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | ((~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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(186,plain,
% 0.17/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | ((~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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(187,plain,
% 0.17/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | ![Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.17/0.43 tff(188,plain,
% 0.17/0.43 (![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[187, 184, 141, 49])).
% 0.17/0.43 tff(189,plain,
% 0.17/0.43 (((~![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))) | ((~pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), X!2))) <=> ((~![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))) | (~pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), X!2))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(190,plain,
% 0.17/0.43 ((~![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))) | ((~pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), X!2))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(191,plain,
% 0.17/0.43 ((~![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))) | (~pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.17/0.43 tff(192,plain,
% 0.17/0.43 ((~pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[191, 188])).
% 0.17/0.43 tff(193,plain,
% 0.17/0.43 ($false),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[192, 165, 159])).
% 0.17/0.43 tff(194,plain,(~(tptp_fun_X_1(V!4) = X!2)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.43 tff(195,plain,
% 0.17/0.43 (^[U: $i, V: $i, W: $i] : refl(((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))) <=> ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))))),
% 0.17/0.43 inference(bind,[status(th)],[])).
% 0.17/0.43 tff(196,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))) <=> ![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(quant_intro,[status(thm)],[195])).
% 0.17/0.43 tff(197,plain,
% 0.17/0.43 (^[U: $i, V: $i, W: $i] : rewrite(((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))) <=> ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))))),
% 0.17/0.43 inference(bind,[status(th)],[])).
% 0.17/0.43 tff(198,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))) <=> ![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(quant_intro,[status(thm)],[197])).
% 0.17/0.43 tff(199,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))) <=> ![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(transitivity,[status(thm)],[198, 196])).
% 0.17/0.43 tff(200,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))) <=> ![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(201,plain,
% 0.17/0.43 (^[U: $i, V: $i, W: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((pair_in_list(remove_slb(U, X), V, W) | (V = X)) <=> ((V = X) | pair_in_list(remove_slb(U, X), V, W))), ((contains_slb(U, X) => (pair_in_list(remove_slb(U, X), V, W) | (V = X))) <=> (contains_slb(U, X) => ((V = X) | pair_in_list(remove_slb(U, X), V, W))))), rewrite((contains_slb(U, X) => ((V = X) | pair_in_list(remove_slb(U, X), V, W))) <=> ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))), ((contains_slb(U, X) => (pair_in_list(remove_slb(U, X), V, W) | (V = X))) <=> ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))))), (![X: $i] : (contains_slb(U, X) => (pair_in_list(remove_slb(U, X), V, W) | (V = X))) <=> ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))), ((pair_in_list(U, V, W) => ![X: $i] : (contains_slb(U, X) => (pair_in_list(remove_slb(U, X), V, W) | (V = X)))) <=> (pair_in_list(U, V, W) => ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))))), rewrite((pair_in_list(U, V, W) => ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X)))) <=> ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))), ((pair_in_list(U, V, W) => ![X: $i] : (contains_slb(U, X) => (pair_in_list(remove_slb(U, X), V, W) | (V = X)))) <=> ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))))),
% 0.17/0.43 inference(bind,[status(th)],[])).
% 0.17/0.43 tff(202,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : (pair_in_list(U, V, W) => ![X: $i] : (contains_slb(U, X) => (pair_in_list(remove_slb(U, X), V, W) | (V = X)))) <=> ![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(quant_intro,[status(thm)],[201])).
% 0.17/0.43 tff(203,axiom,(![U: $i, V: $i, W: $i] : (pair_in_list(U, V, W) => ![X: $i] : (contains_slb(U, X) => (pair_in_list(remove_slb(U, X), V, W) | (V = X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l27_li2829')).
% 0.17/0.43 tff(204,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.17/0.43 tff(205,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.17/0.43 tff(206,plain,(
% 0.17/0.43 ![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(skolemize,[status(sab)],[205])).
% 0.17/0.43 tff(207,plain,
% 0.17/0.43 (![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.17/0.43 tff(208,plain,
% 0.17/0.43 (((~![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))) | ((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | ![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X))))) <=> ((~![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))) | (~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | ![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X))))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(209,plain,
% 0.17/0.43 ((~![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))) | ((~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | ![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X))))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(210,plain,
% 0.17/0.43 ((~![U: $i, V: $i, W: $i] : ((~pair_in_list(U, V, W)) | ![X: $i] : ((V = X) | pair_in_list(remove_slb(U, X), V, W) | (~contains_slb(U, X))))) | (~pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | ![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.17/0.43 tff(211,plain,
% 0.17/0.43 (![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[210, 207, 158])).
% 0.17/0.43 tff(212,plain,
% 0.17/0.43 (((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | ((~contains_slb(V!4, X!2)) | (tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)))) <=> ((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | (~contains_slb(V!4, X!2)) | (tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(213,plain,
% 0.17/0.43 (((tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X!2))) <=> ((~contains_slb(V!4, X!2)) | (tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(214,plain,
% 0.17/0.43 (((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | ((tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X!2)))) <=> ((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | ((~contains_slb(V!4, X!2)) | (tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))))),
% 0.17/0.43 inference(monotonicity,[status(thm)],[213])).
% 0.17/0.43 tff(215,plain,
% 0.17/0.43 (((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | ((tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X!2)))) <=> ((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | (~contains_slb(V!4, X!2)) | (tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)))),
% 0.17/0.43 inference(transitivity,[status(thm)],[214, 212])).
% 0.17/0.43 tff(216,plain,
% 0.17/0.43 ((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | ((tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X!2)))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(217,plain,
% 0.17/0.43 ((~![X: $i] : ((tptp_fun_X_1(V!4) = X) | pair_in_list(remove_slb(V!4, X), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4)) | (~contains_slb(V!4, X)))) | (~contains_slb(V!4, X!2)) | (tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.17/0.43 tff(218,plain,
% 0.17/0.43 ((tptp_fun_X_1(V!4) = X!2) | pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[217, 78, 211])).
% 0.17/0.44 tff(219,plain,
% 0.17/0.44 (pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[218, 194])).
% 0.17/0.44 tff(220,plain,
% 0.17/0.44 (((~![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), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))) <=> ((~![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), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(221,plain,
% 0.17/0.44 ((~![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), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(222,plain,
% 0.17/0.44 ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | (~pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.17/0.44 tff(223,plain,
% 0.17/0.44 ($false),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[222, 164, 219, 144])).
% 0.17/0.44 % SZS output end Proof
%------------------------------------------------------------------------------