%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV391+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:21 AM UTC 2025
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV391+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:46:31 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(pair_in_list_type, type, (
% 0.12/0.40 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.40 tptp_fun_Y_0: $i > $i)).
% 0.12/0.40 tff(tptp_fun_V_4_type, type, (
% 0.12/0.40 tptp_fun_V_4: $i)).
% 0.12/0.40 tff(tptp_fun_X_2_type, type, (
% 0.12/0.40 tptp_fun_X_2: $i)).
% 0.12/0.40 tff(tptp_fun_X_1_type, type, (
% 0.12/0.40 tptp_fun_X_1: $i > $i)).
% 0.12/0.40 tff(remove_slb_type, type, (
% 0.12/0.40 remove_slb: ( $i * $i ) > $i)).
% 0.12/0.40 tff(less_than_type, type, (
% 0.12/0.40 less_than: ( $i * $i ) > $o)).
% 0.12/0.40 tff(check_cpq_type, type, (
% 0.12/0.40 check_cpq: $i > $o)).
% 0.12/0.40 tff(triple_type, type, (
% 0.12/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_W_3_type, type, (
% 0.12/0.40 tptp_fun_W_3: $i)).
% 0.12/0.40 tff(remove_pqp_type, type, (
% 0.12/0.40 remove_pqp: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_U_5_type, type, (
% 0.12/0.40 tptp_fun_U_5: $i)).
% 0.12/0.40 tff(remove_cpq_type, type, (
% 0.12/0.40 remove_cpq: ( $i * $i ) > $i)).
% 0.12/0.40 tff(lookup_slb_type, type, (
% 0.12/0.40 lookup_slb: ( $i * $i ) > $i)).
% 0.12/0.40 tff(strictly_less_than_type, type, (
% 0.12/0.40 strictly_less_than: ( $i * $i ) > $o)).
% 0.12/0.40 tff(bad_type, type, (
% 0.12/0.40 bad: $i)).
% 0.12/0.40 tff(ok_type, type, (
% 0.12/0.40 ok: $i > $o)).
% 0.12/0.40 tff(contains_slb_type, type, (
% 0.12/0.40 contains_slb: ( $i * $i ) > $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[U: $i, V: $i] : refl((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((less_than(U, V) & (~less_than(V, U))) <=> (~((~less_than(U, V)) | less_than(V, U)))), ((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)))))), rewrite((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))), rewrite((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,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')).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.40 tff(8,plain,(
% 0.12/0.40 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[7])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~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))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (~(((~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)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.40 tff(13,assumption,(~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))), introduced(assumption)).
% 0.12/0.40 tff(14,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)).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (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)),
% 0.12/0.40 inference(symmetry,[status(thm)],[14])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) <=> check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (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), bad))),
% 0.12/0.40 inference(symmetry,[status(thm)],[16])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 ((~![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))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 ((~![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))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(20,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')).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (~![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)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (~![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)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (~![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)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (~![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)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.12/0.40 tff(25,plain,(
% 0.12/0.40 ~(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)))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[24])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (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))),
% 0.12/0.40 inference(or_elim,[status(thm)],[25])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.12/0.40 inference(and_elim,[status(thm)],[26])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (^[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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (![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))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (^[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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (![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))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![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))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (^[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))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![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)))))) <=> ![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))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![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))) <=> ![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![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))) <=> ![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.41 tff(39,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')).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.41 tff(42,plain,(
% 0.21/0.41 ![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))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[41])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![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))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![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))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 ((~![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), bad))) | ![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), bad)) | (~((~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)))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (~((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))) | ![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), bad)) | (~((~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))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))) | ![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), bad)) | (~((~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), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))) | ![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), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[49, 13])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[50, 48])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[51, 28])).
% 0.21/0.41 tff(53,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))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (~(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))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 13])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (ok(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.21/0.41 inference(and_elim,[status(thm)],[26])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (^[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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (^[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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.41 tff(61,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')).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.21/0.41 tff(64,plain,(
% 0.21/0.41 ![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.21/0.41 inference(skolemize,[status(sab)],[63])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~![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)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (contains_slb(V!4, X!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 65, 55])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (^[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), 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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (![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)))) <=> ![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.41 tff(77,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')).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.21/0.41 tff(80,plain,(
% 0.21/0.41 ![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)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[79])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (((~![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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((~![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))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((~![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[85, 82, 69])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (~strictly_less_than(X!2, lookup_slb(V!4, X!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[86, 54])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((((~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)) | strictly_less_than(X!2, lookup_slb(V!4, X!2))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((((~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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 ((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 12])).
% 0.21/0.42 tff(91,assumption,((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)), introduced(assumption)).
% 0.21/0.42 tff(92,assumption,(~less_than(lookup_slb(V!4, X!2), X!2)), introduced(assumption)).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~((~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)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (~less_than(X!2, lookup_slb(V!4, X!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 92, 91])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.42 tff(100,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.21/0.42 tff(103,plain,(
% 0.21/0.42 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(skolemize,[status(sab)],[102])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (((~![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 ((~![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))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, lookup_slb(V!4, X!2)) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[107, 104, 92, 94])).
% 0.21/0.42 tff(109,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,[]))).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (less_than(lookup_slb(V!4, X!2), X!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[109, 90])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.42 tff(118,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')).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.42 tff(121,plain,(
% 0.21/0.42 ![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)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[120])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[122, 112])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (((~![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)))) <=> ((~![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 ((~![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)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ((~![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))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 ((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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[126, 123, 69])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (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)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[127, 110])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (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)),
% 0.21/0.42 inference(symmetry,[status(thm)],[128])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (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))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (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))),
% 0.21/0.42 inference(symmetry,[status(thm)],[130])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[27, 131])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 ((~![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(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)))))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 (~((~((~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)) | (~((~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))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[133, 44])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 (((~((~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)) | (~((~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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 ((~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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 ((~((~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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 ((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[137, 13])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[138, 136])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[139, 132])).
% 0.21/0.43 tff(141,plain,(![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(142,assumption,(![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))), introduced(assumption)).
% 0.21/0.43 tff(143,assumption,(pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))), introduced(assumption)).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 ((~![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))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (~((~((~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)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[144, 44])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (((~((~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)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (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))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (~check_cpq(triple(U!5, V!4, W!3))),
% 0.21/0.43 inference(or_elim,[status(thm)],[25])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 ((~(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))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 ((~(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))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 (~((~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)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (((~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)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (~less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (((~![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), 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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 ((~![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), 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)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | (~pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[156, 153, 143, 142])).
% 0.21/0.43 tff(158,plain,((~![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)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (~pair_in_list(remove_slb(V!4, X!2), tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[158, 141])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (((~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))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (pair_in_list(V!4, tptp_fun_X_1(V!4), tptp_fun_Y_0(V!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[160, 151])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[164])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[165, 163])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (^[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))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[168])).
% 0.21/0.43 tff(170,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')).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.21/0.43 tff(173,plain,(
% 0.21/0.43 ![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))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[172])).
% 0.21/0.43 tff(174,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.21/0.43 tff(175,plain,
% 0.21/0.43 (((~![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(176,plain,
% 0.21/0.43 ((~![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))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 ((~![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.44 tff(178,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[177, 174, 161])).
% 0.21/0.44 tff(179,plain,
% 0.21/0.44 (((~![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(180,plain,
% 0.21/0.44 (((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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(181,plain,
% 0.21/0.44 (((~![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))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.44 tff(182,plain,
% 0.21/0.44 (((~![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)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[181, 179])).
% 0.21/0.44 tff(183,plain,
% 0.21/0.44 ((~![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)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(184,plain,
% 0.21/0.44 ((~![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))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.44 tff(185,plain,
% 0.21/0.44 ((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))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[184, 69, 178])).
% 0.21/0.44 tff(186,plain,
% 0.21/0.44 (tptp_fun_X_1(V!4) = X!2),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[185, 159])).
% 0.21/0.44 tff(187,plain,
% 0.21/0.44 (X!2 = tptp_fun_X_1(V!4)),
% 0.21/0.44 inference(symmetry,[status(thm)],[186])).
% 0.21/0.44 tff(188,plain,
% 0.21/0.44 (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))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[187])).
% 0.21/0.44 tff(189,plain,
% 0.21/0.44 (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))),
% 0.21/0.44 inference(symmetry,[status(thm)],[188])).
% 0.21/0.44 tff(190,plain,
% 0.21/0.44 (pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[161, 189])).
% 0.21/0.44 tff(191,plain,
% 0.21/0.44 (less_than(tptp_fun_Y_0(V!4), X!2) <=> less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[187])).
% 0.21/0.44 tff(192,plain,
% 0.21/0.44 (less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4)) <=> less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.21/0.44 inference(symmetry,[status(thm)],[191])).
% 0.21/0.44 tff(193,plain,
% 0.21/0.44 ((~less_than(tptp_fun_Y_0(V!4), tptp_fun_X_1(V!4))) <=> (~less_than(tptp_fun_Y_0(V!4), X!2))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[192])).
% 0.21/0.44 tff(194,plain,
% 0.21/0.44 (~less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[153, 193])).
% 0.21/0.44 tff(195,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(196,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[195])).
% 0.21/0.44 tff(197,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(198,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[197])).
% 0.21/0.44 tff(199,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(200,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[199])).
% 0.21/0.44 tff(201,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[200, 198])).
% 0.21/0.44 tff(202,plain,
% 0.21/0.44 (^[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))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(203,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[202])).
% 0.21/0.44 tff(204,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(205,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(206,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[205])).
% 0.21/0.44 tff(207,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')).
% 0.21/0.44 tff(208,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.21/0.44 tff(209,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.21/0.44 tff(210,plain,(
% 0.21/0.44 ![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)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[209])).
% 0.21/0.44 tff(211,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.21/0.44 tff(212,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[211, 201])).
% 0.21/0.44 tff(213,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[212, 196])).
% 0.21/0.44 tff(214,plain,
% 0.21/0.44 (((~![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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)) | (~check_cpq(remove_cpq(triple(U!5, V!4, W!3), 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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)) | (~check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(215,plain,
% 0.21/0.44 (((~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))) <=> ((~ok(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)) | (~check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(216,plain,
% 0.21/0.44 (((~![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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)) | (~check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[215])).
% 0.21/0.44 tff(217,plain,
% 0.21/0.44 (((~![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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)) | (~check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[216, 214])).
% 0.21/0.45 tff(218,plain,
% 0.21/0.45 ((~![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)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(219,plain,
% 0.21/0.45 ((~![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))) | ![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2)) | (~check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.21/0.45 tff(220,plain,
% 0.21/0.45 (![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[219, 213, 27, 55])).
% 0.21/0.45 tff(221,plain,
% 0.21/0.45 (((~![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))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(222,plain,
% 0.21/0.45 ((~![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))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(223,plain,
% 0.21/0.45 ((~![Y: $i] : ((~pair_in_list(V!4, X!2, Y)) | less_than(Y, X!2))) | (~pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.21/0.45 tff(224,plain,
% 0.21/0.45 ((~pair_in_list(V!4, X!2, tptp_fun_Y_0(V!4))) | less_than(tptp_fun_Y_0(V!4), X!2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[223, 220])).
% 0.21/0.45 tff(225,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[224, 194, 190])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------