%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV394+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:32:22 AM UTC 2025
% Result : Theorem 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SWV394+1 : TPTP v9.0.0. Released v3.3.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 09:45:17 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(pair_in_list_type, type, (
% 0.23/0.42 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_Y_6_type, type, (
% 0.23/0.42 tptp_fun_Y_6: $i)).
% 0.23/0.42 tff(tptp_fun_X_2_type, type, (
% 0.23/0.42 tptp_fun_X_2: $i)).
% 0.23/0.42 tff(remove_slb_type, type, (
% 0.23/0.42 remove_slb: ( $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_V_4_type, type, (
% 0.23/0.42 tptp_fun_V_4: $i)).
% 0.23/0.42 tff(strictly_less_than_type, type, (
% 0.23/0.42 strictly_less_than: ( $i * $i ) > $o)).
% 0.23/0.42 tff(less_than_type, type, (
% 0.23/0.42 less_than: ( $i * $i ) > $o)).
% 0.23/0.42 tff(ok_type, type, (
% 0.23/0.42 ok: $i > $o)).
% 0.23/0.42 tff(remove_cpq_type, type, (
% 0.23/0.42 remove_cpq: ( $i * $i ) > $i)).
% 0.23/0.42 tff(triple_type, type, (
% 0.23/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_W_3_type, type, (
% 0.23/0.42 tptp_fun_W_3: $i)).
% 0.23/0.42 tff(tptp_fun_U_5_type, type, (
% 0.23/0.42 tptp_fun_U_5: $i)).
% 0.23/0.42 tff(check_cpq_type, type, (
% 0.23/0.42 check_cpq: $i > $o)).
% 0.23/0.42 tff(remove_pqp_type, type, (
% 0.23/0.42 remove_pqp: ( $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_X_1_type, type, (
% 0.23/0.42 tptp_fun_X_1: $i > $i)).
% 0.23/0.42 tff(tptp_fun_Y_0_type, type, (
% 0.23/0.42 tptp_fun_Y_0: $i > $i)).
% 0.23/0.42 tff(contains_slb_type, type, (
% 0.23/0.42 contains_slb: ( $i * $i ) > $o)).
% 0.23/0.42 tff(bad_type, type, (
% 0.23/0.42 bad: $i)).
% 0.23/0.42 tff(lookup_slb_type, type, (
% 0.23/0.42 lookup_slb: ( $i * $i ) > $i)).
% 0.23/0.42 tff(1,assumption,(~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)), introduced(assumption)).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 (^[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))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (^[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)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 (![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))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(7,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')).
% 0.23/0.42 tff(8,plain,
% 0.23/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.23/0.42 tff(9,plain,(
% 0.23/0.42 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[8])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X!2, Y!6)) | less_than(Y!6, X!2)) <=> strictly_less_than(X!2, Y!6)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (~(((~less_than(X!2, Y!6)) | less_than(Y!6, X!2)) <=> strictly_less_than(X!2, Y!6))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.23/0.42 tff(14,plain,
% 0.23/0.42 (((check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2))) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2)))) <=> (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 ((~![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))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(16,plain,
% 0.23/0.42 ((~![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))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(17,axiom,(~![U: $i, V: $i, W: $i, X: $i] : ((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => ![Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l30_co')).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 (~![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 (~![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 (~![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 (~![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.23/0.42 tff(22,plain,
% 0.23/0.42 (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2)) & ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) & (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (~((~pair_in_list(V!4, X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.23/0.42 inference(and_elim,[status(thm)],[22])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 (~less_than(Y!6, X!2)),
% 0.23/0.42 inference(or_elim,[status(thm)],[23])).
% 0.23/0.42 tff(25,plain,
% 0.23/0.42 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.42 tff(30,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.23/0.42 tff(33,plain,(
% 0.23/0.42 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.42 inference(skolemize,[status(sab)],[32])).
% 0.23/0.42 tff(34,plain,
% 0.23/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!2, Y!6) | less_than(Y!6, X!2))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, Y!6) | less_than(Y!6, X!2))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X!2, Y!6) | less_than(Y!6, X!2))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(37,plain,
% 0.23/0.42 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, Y!6) | less_than(Y!6, X!2)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.23/0.42 tff(38,plain,
% 0.23/0.42 (less_than(X!2, Y!6)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[37, 34, 24])).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 ((~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))) | (~less_than(X!2, Y!6)) | less_than(Y!6, X!2)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(40,plain,
% 0.23/0.42 ((~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))) | (~less_than(X!2, Y!6))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[39, 24])).
% 0.23/0.42 tff(41,plain,
% 0.23/0.42 (~((~less_than(X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[40, 38])).
% 0.23/0.42 tff(42,plain,
% 0.23/0.42 ((((~less_than(X!2, Y!6)) | less_than(Y!6, X!2)) <=> strictly_less_than(X!2, Y!6)) | ((~less_than(X!2, Y!6)) | less_than(Y!6, X!2)) | strictly_less_than(X!2, Y!6)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(43,plain,
% 0.23/0.42 (strictly_less_than(X!2, Y!6)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[42, 41, 13])).
% 0.23/0.42 tff(44,plain,
% 0.23/0.42 (pair_in_list(V!4, X!2, Y!6)),
% 0.23/0.42 inference(or_elim,[status(thm)],[23])).
% 0.23/0.42 tff(45,plain,
% 0.23/0.42 (ok(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.23/0.42 inference(and_elim,[status(thm)],[22])).
% 0.23/0.42 tff(46,plain,
% 0.23/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(47,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.23/0.42 tff(48,plain,
% 0.23/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X))) <=> (~((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))), ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) <=> (~(~((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))))), rewrite((~(~((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))) <=> ((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))), ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) <=> ((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))))), (((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> (((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)))), rewrite((((~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))), (((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(49,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.23/0.42 tff(50,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(51,plain,
% 0.23/0.42 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : trans(monotonicity(rewrite(((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) <=> (pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))), ((((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ((pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)))), rewrite(((pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))), ((((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(52,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.23/0.42 tff(53,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (((pair_in_list(V, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(U, V, W), X))) => pair_in_list(remove_slb(V, X), X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l30_li3132')).
% 0.23/0.42 tff(54,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.23/0.42 tff(55,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.23/0.42 tff(56,plain,(
% 0.23/0.42 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(V, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(U, V, W), X)))) | pair_in_list(remove_slb(V, X), X, Y))),
% 0.23/0.43 inference(skolemize,[status(sab)],[55])).
% 0.23/0.43 tff(57,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.23/0.43 tff(58,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | ((~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(60,plain,
% 0.23/0.43 ((pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2)))) <=> ((~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | ((~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2)))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[60])).
% 0.23/0.43 tff(62,plain,
% 0.23/0.43 (((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))) <=> ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[61, 59])).
% 0.23/0.43 tff(63,plain,
% 0.23/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~strictly_less_than(X!2, Y!6)) | (~pair_in_list(V!4, X!2, Y!6)) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(64,plain,
% 0.23/0.43 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(remove_slb(V, X), X, Y) | (~strictly_less_than(X, Y)) | (~pair_in_list(V, X, Y)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (~pair_in_list(V!4, X!2, Y!6)) | (~strictly_less_than(X!2, Y!6)) | pair_in_list(remove_slb(V!4, X!2), X!2, Y!6) | (~ok(remove_cpq(triple(U!5, V!4, W!3), X!2)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.23/0.43 tff(65,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[64, 58, 45, 44, 43, 1])).
% 0.23/0.43 tff(66,plain,(pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(67,plain,
% 0.23/0.43 (^[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)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(68,plain,
% 0.23/0.43 (![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)))))))) <=> ![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))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.23/0.43 tff(69,plain,
% 0.23/0.43 (^[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)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(70,plain,
% 0.23/0.43 (![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)))))))) <=> ![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))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[69])).
% 0.23/0.43 tff(71,plain,
% 0.23/0.43 (![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)))))))) <=> ![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))))))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[70, 68])).
% 0.23/0.43 tff(72,plain,
% 0.23/0.43 (^[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))))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(73,plain,
% 0.23/0.43 (![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)))))) <=> ![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))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.23/0.43 tff(74,plain,
% 0.23/0.43 (![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))) <=> ![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)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(75,plain,
% 0.23/0.43 (^[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))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(76,plain,
% 0.23/0.43 (![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))) <=> ![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.23/0.43 tff(77,axiom,(![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l30_li4142')).
% 0.23/0.43 tff(78,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.43 tff(79,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.23/0.43 tff(80,plain,(
% 0.23/0.43 ![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))))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[79])).
% 0.23/0.43 tff(81,plain,
% 0.23/0.43 (![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))))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.23/0.43 tff(82,plain,
% 0.23/0.43 (![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))))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.23/0.43 tff(83,plain,
% 0.23/0.43 ((~![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(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)))))))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(84,plain,
% 0.23/0.43 (~((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~((~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))))))))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.23/0.43 tff(85,plain,
% 0.23/0.43 (((~((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3)) | (~((~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)))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(86,plain,
% 0.23/0.43 ((~check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.23/0.43 tff(87,assumption,(remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)), introduced(assumption)).
% 0.23/0.43 tff(88,plain,
% 0.23/0.43 (triple(U!5, V!4, bad) = remove_cpq(triple(U!5, V!4, W!3), X!2)),
% 0.23/0.43 inference(symmetry,[status(thm)],[87])).
% 0.23/0.43 tff(89,plain,
% 0.23/0.43 (ok(triple(U!5, V!4, bad)) <=> ok(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.23/0.43 tff(90,plain,
% 0.23/0.43 (ok(remove_cpq(triple(U!5, V!4, W!3), X!2)) <=> ok(triple(U!5, V!4, bad))),
% 0.23/0.43 inference(symmetry,[status(thm)],[89])).
% 0.23/0.43 tff(91,plain,
% 0.23/0.43 (ok(triple(U!5, V!4, bad))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[45, 90])).
% 0.23/0.43 tff(92,plain,
% 0.23/0.43 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(93,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.23/0.43 tff(94,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(95,plain,
% 0.23/0.43 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(96,plain,
% 0.23/0.43 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.23/0.43 tff(97,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.23/0.43 tff(98,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.23/0.43 tff(99,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.23/0.43 tff(100,plain,(
% 0.23/0.43 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[99])).
% 0.23/0.43 tff(101,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.23/0.44 tff(102,plain,
% 0.23/0.44 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(U!5, V!4, bad)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(103,plain,
% 0.23/0.44 (~ok(triple(U!5, V!4, bad))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.23/0.44 tff(104,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[103, 91])).
% 0.23/0.44 tff(105,plain,(~(remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(106,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(107,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[106])).
% 0.23/0.44 tff(108,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(109,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(110,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.23/0.44 tff(111,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax43')).
% 0.23/0.44 tff(112,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.23/0.44 tff(113,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.23/0.44 tff(114,plain,(
% 0.23/0.44 ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[113])).
% 0.23/0.44 tff(115,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.23/0.44 tff(116,plain,
% 0.23/0.44 (((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(117,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(118,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.23/0.44 tff(119,plain,
% 0.23/0.44 (contains_slb(V!4, X!2) | (remove_cpq(triple(U!5, V!4, W!3), X!2) = triple(U!5, V!4, bad))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.23/0.44 tff(120,plain,
% 0.23/0.44 (contains_slb(V!4, X!2)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[119, 105])).
% 0.23/0.44 tff(121,plain,
% 0.23/0.44 ((~![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))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(122,plain,
% 0.23/0.44 (~(((~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)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[121, 11])).
% 0.23/0.44 tff(123,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)).
% 0.23/0.44 tff(124,plain,
% 0.23/0.44 (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)),
% 0.23/0.44 inference(symmetry,[status(thm)],[123])).
% 0.23/0.44 tff(125,plain,
% 0.23/0.44 (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))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[124])).
% 0.23/0.44 tff(126,plain,
% 0.23/0.44 (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))),
% 0.23/0.44 inference(symmetry,[status(thm)],[125])).
% 0.23/0.44 tff(127,plain,
% 0.23/0.44 (ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[45, 126])).
% 0.23/0.44 tff(128,plain,
% 0.23/0.44 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(129,plain,
% 0.23/0.44 (~ok(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), bad))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[128, 101])).
% 0.23/0.44 tff(130,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[129, 127])).
% 0.23/0.44 tff(131,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,[]))).
% 0.23/0.44 tff(132,plain,
% 0.23/0.44 (^[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)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(133,plain,
% 0.23/0.44 (![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))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[132])).
% 0.23/0.44 tff(134,plain,
% 0.23/0.44 (^[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))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(135,plain,
% 0.23/0.44 (![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))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[134])).
% 0.23/0.44 tff(136,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(137,plain,
% 0.23/0.44 (^[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))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(138,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[137])).
% 0.23/0.44 tff(139,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')).
% 0.23/0.44 tff(140,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.23/0.44 tff(141,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.23/0.44 tff(142,plain,(
% 0.23/0.44 ![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)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[141])).
% 0.23/0.44 tff(143,plain,
% 0.23/0.44 (![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))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.23/0.44 tff(144,plain,
% 0.23/0.44 (![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))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.23/0.44 tff(145,plain,
% 0.23/0.44 (((~![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))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(146,plain,
% 0.23/0.45 ((~![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))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(147,plain,
% 0.23/0.45 ((~![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.23/0.45 tff(148,plain,
% 0.23/0.45 ((~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)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.23/0.45 tff(149,plain,
% 0.23/0.45 ((~contains_slb(V!4, X!2)) | (~strictly_less_than(X!2, lookup_slb(V!4, X!2)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[148, 131])).
% 0.23/0.45 tff(150,plain,
% 0.23/0.45 (~strictly_less_than(X!2, lookup_slb(V!4, X!2))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[149, 120])).
% 0.23/0.45 tff(151,plain,
% 0.23/0.45 ((((~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))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(152,plain,
% 0.23/0.45 ((((~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))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.23/0.45 tff(153,plain,
% 0.23/0.45 ((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[152, 122])).
% 0.23/0.45 tff(154,assumption,((~less_than(X!2, lookup_slb(V!4, X!2))) | less_than(lookup_slb(V!4, X!2), X!2)), introduced(assumption)).
% 0.23/0.45 tff(155,assumption,(~less_than(lookup_slb(V!4, X!2), X!2)), introduced(assumption)).
% 0.23/0.45 tff(156,plain,
% 0.23/0.45 ((~((~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)),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(157,plain,
% 0.23/0.45 (~less_than(X!2, lookup_slb(V!4, X!2))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[156, 155, 154])).
% 0.23/0.45 tff(158,plain,
% 0.23/0.45 (((~![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))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(159,plain,
% 0.23/0.45 ((~![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))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(160,plain,
% 0.23/0.45 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X!2, lookup_slb(V!4, X!2)) | less_than(lookup_slb(V!4, X!2), X!2)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.23/0.45 tff(161,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[160, 34, 155, 157])).
% 0.23/0.45 tff(162,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,[]))).
% 0.23/0.45 tff(163,plain,
% 0.23/0.45 (less_than(lookup_slb(V!4, X!2), X!2)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[162, 153])).
% 0.23/0.45 tff(164,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(165,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[164])).
% 0.23/0.45 tff(166,plain,
% 0.23/0.45 (^[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)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(167,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[166])).
% 0.23/0.45 tff(168,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(169,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(170,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[169])).
% 0.23/0.45 tff(171,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')).
% 0.23/0.45 tff(172,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.23/0.45 tff(173,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.23/0.45 tff(174,plain,(
% 0.23/0.45 ![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)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[173])).
% 0.23/0.45 tff(175,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.23/0.45 tff(176,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[175, 165])).
% 0.23/0.45 tff(177,plain,
% 0.23/0.45 (((~![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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(178,plain,
% 0.23/0.45 ((~![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)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(179,plain,
% 0.23/0.45 ((~![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))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.23/0.45 tff(180,plain,
% 0.23/0.45 ((~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))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.23/0.45 tff(181,plain,
% 0.23/0.45 (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)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[180, 163, 120])).
% 0.23/0.45 tff(182,plain,
% 0.23/0.45 (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)),
% 0.23/0.45 inference(symmetry,[status(thm)],[181])).
% 0.23/0.45 tff(183,plain,
% 0.23/0.45 (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))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[182])).
% 0.23/0.45 tff(184,plain,
% 0.23/0.45 (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))),
% 0.23/0.46 inference(symmetry,[status(thm)],[183])).
% 0.23/0.46 tff(185,plain,
% 0.23/0.46 (check_cpq(remove_cpq(triple(U!5, V!4, W!3), X!2))),
% 0.23/0.46 inference(and_elim,[status(thm)],[22])).
% 0.23/0.46 tff(186,plain,
% 0.23/0.46 (check_cpq(triple(remove_pqp(U!5, X!2), remove_slb(V!4, X!2), W!3))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.23/0.46 tff(187,plain,
% 0.23/0.46 ((~((~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))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(188,plain,
% 0.23/0.46 (![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[187, 186, 86])).
% 0.23/0.46 tff(189,plain,
% 0.23/0.46 (((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | ((~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | (~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(190,plain,
% 0.23/0.46 ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | ((~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(191,plain,
% 0.23/0.46 ((~![X: $i, Y: $i] : ((~pair_in_list(remove_slb(V!4, X!2), X, Y)) | less_than(Y, X))) | (~pair_in_list(remove_slb(V!4, X!2), X!2, Y!6)) | less_than(Y!6, X!2)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.23/0.46 tff(192,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[191, 24, 188, 66])).
% 0.23/0.46 % SZS output end Proof
% 0.23/0.46 % E exiting
%------------------------------------------------------------------------------