%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV396+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : SWV396+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 09:45:11 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(ok_type, type, (
% 0.23/0.43 ok: $i > $o)).
% 0.23/0.43 tff(triple_type, type, (
% 0.23/0.43 triple: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(bad_type, type, (
% 0.23/0.43 bad: $i)).
% 0.23/0.43 tff(insert_slb_type, type, (
% 0.23/0.43 insert_slb: ( $i * $i ) > $i)).
% 0.23/0.43 tff(pair_type, type, (
% 0.23/0.43 pair: ( $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X5_1_type, type, (
% 0.23/0.43 tptp_fun_X5_1: $i)).
% 0.23/0.43 tff(tptp_fun_X4_2_type, type, (
% 0.23/0.43 tptp_fun_X4_2: $i)).
% 0.23/0.43 tff(remove_slb_type, type, (
% 0.23/0.43 remove_slb: ( $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X2_4_type, type, (
% 0.23/0.43 tptp_fun_X2_4: $i)).
% 0.23/0.43 tff(tptp_fun_U_0_type, type, (
% 0.23/0.43 tptp_fun_U_0: $i)).
% 0.23/0.43 tff(remove_pqp_type, type, (
% 0.23/0.43 remove_pqp: ( $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Z_6_type, type, (
% 0.23/0.43 tptp_fun_Z_6: $i)).
% 0.23/0.43 tff(remove_cpq_type, type, (
% 0.23/0.43 remove_cpq: ( $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X1_5_type, type, (
% 0.23/0.43 tptp_fun_X1_5: $i)).
% 0.23/0.43 tff(strictly_less_than_type, type, (
% 0.23/0.43 strictly_less_than: ( $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_X3_3_type, type, (
% 0.23/0.43 tptp_fun_X3_3: $i)).
% 0.23/0.43 tff(pair_in_list_type, type, (
% 0.23/0.43 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(contains_slb_type, type, (
% 0.23/0.43 contains_slb: ( $i * $i ) > $o)).
% 0.23/0.43 tff(lookup_slb_type, type, (
% 0.23/0.43 lookup_slb: ( $i * $i ) > $i)).
% 0.23/0.43 tff(less_than_type, type, (
% 0.23/0.43 less_than: ( $i * $i ) > $o)).
% 0.23/0.43 tff(1,plain,
% 0.23/0.43 (^[U: $i, V: $i, W: $i] : refl((remove_slb(insert_slb(U, pair(V, W)), V) = U) <=> (remove_slb(insert_slb(U, pair(V, W)), V) = U))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U) <=> ![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U)),
% 0.23/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.43 tff(3,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U) <=> ![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U)),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(4,axiom,(![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax24')).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.43 tff(6,plain,(
% 0.23/0.43 ![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U)),
% 0.23/0.43 inference(skolemize,[status(sab)],[5])).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.43 tff(8,plain,
% 0.23/0.43 ((~![U: $i, V: $i, W: $i] : (remove_slb(insert_slb(U, pair(V, W)), V) = U)) | (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2) = U!0)),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2) = U!0),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.43 tff(10,assumption,(X4!2 = X2!4), introduced(assumption)).
% 0.23/0.43 tff(11,plain,
% 0.23/0.43 (X2!4 = X4!2),
% 0.23/0.43 inference(symmetry,[status(thm)],[10])).
% 0.23/0.43 tff(12,plain,
% 0.23/0.43 (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[11])).
% 0.23/0.43 tff(13,plain,
% 0.23/0.43 (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = U!0),
% 0.23/0.43 inference(transitivity,[status(thm)],[12, 9])).
% 0.23/0.43 tff(14,plain,
% 0.23/0.43 (pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3) <=> pair_in_list(U!0, X2!4, X3!3)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[13])).
% 0.23/0.43 tff(15,plain,
% 0.23/0.43 ((~pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3)) <=> (~pair_in_list(U!0, X2!4, X3!3))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[14])).
% 0.23/0.43 tff(16,plain,
% 0.23/0.43 ((![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)) & (~((~(pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) & strictly_less_than(X2!4, X3!3) & ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)))) | pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3)))) <=> (![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)) & (~((~(pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) & strictly_less_than(X2!4, X3!3) & ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)))) | pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(17,plain,
% 0.23/0.43 ((~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U, W), X)))) | pair_in_list(remove_slb(U, X), X, Y))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : ((~(pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2)))) | pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3)))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U, W), X)))) | pair_in_list(remove_slb(U, X), X, Y))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : ((~(pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2)))) | pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(18,plain,
% 0.23/0.43 ((~![U: $i] : (![V: $i, W: $i, X: $i, Y: $i] : (((pair_in_list(U, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(V, U, W), X))) => pair_in_list(remove_slb(U, X), X, Y)) => ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (((pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3)) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2))) => pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3)))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U, W), X)))) | pair_in_list(remove_slb(U, X), X, Y))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : ((~(pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2)))) | pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(19,axiom,(~![U: $i] : (![V: $i, W: $i, X: $i, Y: $i] : (((pair_in_list(U, X, Y) & strictly_less_than(X, Y)) & ok(remove_cpq(triple(V, U, W), X))) => pair_in_list(remove_slb(U, X), X, Y)) => ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (((pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3)) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2))) => pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l32_co')).
% 0.23/0.43 tff(20,plain,
% 0.23/0.43 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U, W), X)))) | pair_in_list(remove_slb(U, X), X, Y))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : ((~(pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2)))) | pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.23/0.43 tff(21,plain,
% 0.23/0.43 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U, W), X)))) | pair_in_list(remove_slb(U, X), X, Y))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : ((~(pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2)))) | pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.23/0.43 tff(22,plain,
% 0.23/0.43 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U, W), X)))) | pair_in_list(remove_slb(U, X), X, Y))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : ((~(pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2)))) | pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.23/0.44 tff(23,plain,
% 0.23/0.44 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U, W), X)))) | pair_in_list(remove_slb(U, X), X, Y))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : ((~(pair_in_list(insert_slb(U, pair(X4, X5)), X2, X3) & strictly_less_than(X2, X3) & ok(remove_cpq(triple(Z, insert_slb(U, pair(X4, X5)), X1), X2)))) | pair_in_list(remove_slb(insert_slb(U, pair(X4, X5)), X2), X2, X3)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.23/0.44 tff(24,plain,
% 0.23/0.44 (![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)) & (~((~(pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) & strictly_less_than(X2!4, X3!3) & ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)))) | pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.23/0.44 tff(25,plain,
% 0.23/0.44 (~((~(pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) & strictly_less_than(X2!4, X3!3) & ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)))) | pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3))),
% 0.23/0.44 inference(and_elim,[status(thm)],[24])).
% 0.23/0.44 tff(26,plain,
% 0.23/0.44 (~pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3)),
% 0.23/0.44 inference(or_elim,[status(thm)],[25])).
% 0.23/0.44 tff(27,plain,
% 0.23/0.44 (~pair_in_list(U!0, X2!4, X3!3)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[26, 15])).
% 0.23/0.44 tff(28,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(29,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.44 tff(30,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : rewrite((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(31,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[30])).
% 0.23/0.44 tff(32,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(33,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : rewrite((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y)))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(34,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[33])).
% 0.23/0.44 tff(35,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax23')).
% 0.23/0.44 tff(36,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.23/0.44 tff(37,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.23/0.44 tff(38,plain,(
% 0.23/0.44 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[37])).
% 0.23/0.44 tff(39,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.23/0.44 tff(40,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.23/0.44 tff(41,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) <=> ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(42,plain,
% 0.23/0.44 (pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) <=> ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.23/0.44 tff(43,plain,
% 0.23/0.44 (pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) & strictly_less_than(X2!4, X3!3) & ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4))),
% 0.23/0.44 inference(or_elim,[status(thm)],[25])).
% 0.23/0.44 tff(44,plain,
% 0.23/0.44 (pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3)),
% 0.23/0.44 inference(and_elim,[status(thm)],[43])).
% 0.23/0.44 tff(45,plain,
% 0.23/0.44 ((~(pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) <=> ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)))) | (~pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3)) | ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(46,plain,
% 0.23/0.44 ((~(pair_in_list(insert_slb(U!0, pair(X4!2, X5!1)), X2!4, X3!3) <=> ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)))) | ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.23/0.44 tff(47,plain,
% 0.23/0.44 ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[46, 42])).
% 0.23/0.44 tff(48,plain,
% 0.23/0.44 ((~((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3))) | (~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(49,plain,
% 0.23/0.44 ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(U!0, X2!4, X3!3)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.23/0.44 tff(50,plain,
% 0.23/0.44 (~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[49, 27])).
% 0.23/0.44 tff(51,plain,
% 0.23/0.44 (((~(X4!2 = X2!4)) | (~(X5!1 = X3!3))) | (X5!1 = X3!3)),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(52,plain,
% 0.23/0.44 (X5!1 = X3!3),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.23/0.44 tff(53,plain,
% 0.23/0.44 (X3!3 = X5!1),
% 0.23/0.44 inference(symmetry,[status(thm)],[52])).
% 0.23/0.44 tff(54,plain,
% 0.23/0.44 (strictly_less_than(X2!4, X3!3) <=> strictly_less_than(X4!2, X5!1)),
% 0.23/0.44 inference(monotonicity,[status(thm)],[11, 53])).
% 0.23/0.44 tff(55,plain,
% 0.23/0.44 (strictly_less_than(X4!2, X5!1) <=> strictly_less_than(X2!4, X3!3)),
% 0.23/0.44 inference(symmetry,[status(thm)],[54])).
% 0.23/0.44 tff(56,plain,
% 0.23/0.44 ((~strictly_less_than(X4!2, X5!1)) <=> (~strictly_less_than(X2!4, X3!3))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[55])).
% 0.23/0.44 tff(57,assumption,(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad)), introduced(assumption)).
% 0.23/0.44 tff(58,plain,
% 0.23/0.44 (triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad) = remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)),
% 0.23/0.44 inference(symmetry,[status(thm)],[57])).
% 0.23/0.44 tff(59,plain,
% 0.23/0.44 (ok(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad)) <=> ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.23/0.44 tff(60,plain,
% 0.23/0.44 (ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)) <=> ok(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad))),
% 0.23/0.44 inference(symmetry,[status(thm)],[59])).
% 0.23/0.44 tff(61,plain,
% 0.23/0.44 (ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4))),
% 0.23/0.44 inference(and_elim,[status(thm)],[43])).
% 0.23/0.44 tff(62,plain,
% 0.23/0.44 (ok(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.23/0.44 tff(63,plain,
% 0.23/0.44 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(64,plain,
% 0.23/0.44 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[63])).
% 0.23/0.44 tff(65,plain,
% 0.23/0.44 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(66,plain,
% 0.23/0.44 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(67,plain,
% 0.23/0.44 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.23/0.44 tff(68,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.23/0.44 tff(69,plain,
% 0.23/0.44 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.23/0.44 tff(71,plain,(
% 0.23/0.44 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[70])).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 (~ok(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[74, 62])).
% 0.23/0.44 tff(76,plain,(~(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(77,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(78,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)],[77])).
% 0.23/0.44 tff(79,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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(80,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(81,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(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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.23/0.45 tff(82,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/sandbox2/benchmark/Axioms/SWV007+3.ax','ax43')).
% 0.23/0.45 tff(83,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(U, V, bad)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.23/0.45 tff(84,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(U, V, bad)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.23/0.45 tff(85,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(U, V, bad)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[84])).
% 0.23/0.45 tff(86,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(U, V, bad)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.23/0.45 tff(87,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(U, V, bad)))) | (contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), 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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(88,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(U, V, bad)))) | (contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(89,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(U, V, bad)))) | contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.23/0.45 tff(90,plain,
% 0.23/0.45 (contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), bad))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.23/0.45 tff(91,plain,
% 0.23/0.45 (contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[90, 76])).
% 0.23/0.45 tff(92,plain,
% 0.23/0.45 (^[U: $i, V: $i, W: $i] : refl((lookup_slb(insert_slb(U, pair(V, W)), V) = W) <=> (lookup_slb(insert_slb(U, pair(V, W)), V) = W))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(93,plain,
% 0.23/0.45 (![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W) <=> ![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W)),
% 0.23/0.45 inference(quant_intro,[status(thm)],[92])).
% 0.23/0.45 tff(94,plain,
% 0.23/0.45 (![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W) <=> ![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(95,axiom,(![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax26')).
% 0.23/0.45 tff(96,plain,
% 0.23/0.45 (![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.23/0.45 tff(97,plain,(
% 0.23/0.45 ![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W)),
% 0.23/0.45 inference(skolemize,[status(sab)],[96])).
% 0.23/0.45 tff(98,plain,
% 0.23/0.45 (![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.23/0.45 tff(99,plain,
% 0.23/0.45 ((~![U: $i, V: $i, W: $i] : (lookup_slb(insert_slb(U, pair(V, W)), V) = W)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2) = X5!1)),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(100,plain,
% 0.23/0.45 (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2) = X5!1),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.23/0.45 tff(101,plain,
% 0.23/0.45 (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[11])).
% 0.23/0.45 tff(102,plain,
% 0.23/0.45 (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = X5!1),
% 0.23/0.45 inference(transitivity,[status(thm)],[101, 100])).
% 0.23/0.45 tff(103,plain,
% 0.23/0.45 (strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) <=> strictly_less_than(X4!2, X5!1)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[11, 102])).
% 0.23/0.45 tff(104,plain,
% 0.23/0.45 (strictly_less_than(X4!2, X5!1) <=> strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))),
% 0.23/0.45 inference(symmetry,[status(thm)],[103])).
% 0.23/0.45 tff(105,assumption,(strictly_less_than(X4!2, X5!1)), introduced(assumption)).
% 0.23/0.45 tff(106,plain,
% 0.23/0.45 (strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.23/0.45 tff(107,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), 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)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(108,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)))) <=> ![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))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[107])).
% 0.23/0.45 tff(109,plain,
% 0.23/0.45 (^[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))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(110,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[109])).
% 0.23/0.45 tff(111,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(112,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(113,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.23/0.45 tff(114,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/sandbox2/benchmark/Axioms/SWV007+3.ax','ax45')).
% 0.23/0.45 tff(115,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.23/0.45 tff(116,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.23/0.45 tff(117,plain,(
% 0.23/0.45 ![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)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[116])).
% 0.23/0.45 tff(118,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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.23/0.45 tff(119,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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[118, 108])).
% 0.23/0.45 tff(120,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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)) | (~strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))))) <=> ((~![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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)) | (~strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(121,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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)) | (~strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(122,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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)) | (~strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.23/0.45 tff(123,plain,
% 0.23/0.45 ((~contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)) | (~strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.23/0.45 tff(124,plain,
% 0.23/0.45 (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[123, 106, 91])).
% 0.23/0.45 tff(125,plain,
% 0.23/0.45 (triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad) = remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)),
% 0.23/0.45 inference(symmetry,[status(thm)],[124])).
% 0.23/0.45 tff(126,plain,
% 0.23/0.45 (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2) = remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)),
% 0.23/0.45 inference(symmetry,[status(thm)],[12])).
% 0.23/0.45 tff(127,plain,
% 0.23/0.45 (U!0 = remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X4!2)),
% 0.23/0.45 inference(symmetry,[status(thm)],[9])).
% 0.23/0.45 tff(128,plain,
% 0.23/0.45 (U!0 = remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)),
% 0.23/0.45 inference(transitivity,[status(thm)],[127, 126])).
% 0.23/0.45 tff(129,plain,
% 0.23/0.45 (triple(remove_pqp(Z!6, X2!4), U!0, bad) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)),
% 0.23/0.45 inference(monotonicity,[status(thm)],[128])).
% 0.23/0.45 tff(130,plain,
% 0.23/0.45 (triple(remove_pqp(Z!6, X2!4), U!0, bad) = remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)),
% 0.23/0.45 inference(transitivity,[status(thm)],[129, 125])).
% 0.23/0.45 tff(131,plain,
% 0.23/0.45 (ok(triple(remove_pqp(Z!6, X2!4), U!0, bad)) <=> ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[130])).
% 0.23/0.45 tff(132,plain,
% 0.23/0.45 (ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)) <=> ok(triple(remove_pqp(Z!6, X2!4), U!0, bad))),
% 0.23/0.45 inference(symmetry,[status(thm)],[131])).
% 0.23/0.45 tff(133,plain,
% 0.23/0.45 (ok(triple(remove_pqp(Z!6, X2!4), U!0, bad))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[61, 132])).
% 0.23/0.45 tff(134,plain,
% 0.23/0.45 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(remove_pqp(Z!6, X2!4), U!0, bad)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(135,plain,
% 0.23/0.45 (~ok(triple(remove_pqp(Z!6, X2!4), U!0, bad))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[134, 72])).
% 0.23/0.45 tff(136,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[135, 133])).
% 0.23/0.46 tff(137,plain,((~(X4!2 = X2!4)) | (~strictly_less_than(X4!2, X5!1))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(138,plain,
% 0.23/0.46 (~strictly_less_than(X4!2, X5!1)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[137, 10])).
% 0.23/0.46 tff(139,plain,
% 0.23/0.46 (~strictly_less_than(X2!4, X3!3)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[138, 56])).
% 0.23/0.46 tff(140,plain,
% 0.23/0.46 (strictly_less_than(X2!4, X3!3)),
% 0.23/0.46 inference(and_elim,[status(thm)],[43])).
% 0.23/0.46 tff(141,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.23/0.46 tff(142,plain,(~(X4!2 = X2!4)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(143,assumption,(~(X4!2 = X2!4)), introduced(assumption)).
% 0.23/0.46 tff(144,plain,
% 0.23/0.46 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))) <=> (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(145,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[144])).
% 0.23/0.46 tff(146,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(147,plain,
% 0.23/0.46 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((contains_slb(insert_slb(U, pair(V, X)), W) <=> (contains_slb(U, W) | (V = W))) <=> (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(148,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> (contains_slb(U, W) | (V = W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[147])).
% 0.23/0.46 tff(149,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> (contains_slb(U, W) | (V = W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax21')).
% 0.23/0.46 tff(150,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.23/0.46 tff(151,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.23/0.46 tff(152,plain,(
% 0.23/0.46 ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[151])).
% 0.23/0.46 tff(153,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.23/0.46 tff(154,plain,
% 0.23/0.46 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))) | (contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) <=> ((X4!2 = X2!4) | contains_slb(U!0, X2!4)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(155,plain,
% 0.23/0.46 (contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) <=> ((X4!2 = X2!4) | contains_slb(U!0, X2!4))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.23/0.46 tff(156,plain,
% 0.23/0.46 ((~(contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) <=> ((X4!2 = X2!4) | contains_slb(U!0, X2!4)))) | (~contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | ((X4!2 = X2!4) | contains_slb(U!0, X2!4))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(157,plain,
% 0.23/0.46 ((~(contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) <=> ((X4!2 = X2!4) | contains_slb(U!0, X2!4)))) | ((X4!2 = X2!4) | contains_slb(U!0, X2!4))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[156, 91])).
% 0.23/0.46 tff(158,plain,
% 0.23/0.46 ((X4!2 = X2!4) | contains_slb(U!0, X2!4)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[157, 155])).
% 0.23/0.46 tff(159,plain,
% 0.23/0.46 ((~((X4!2 = X2!4) | contains_slb(U!0, X2!4))) | (X4!2 = X2!4) | contains_slb(U!0, X2!4)),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(160,plain,
% 0.23/0.46 ((X4!2 = X2!4) | contains_slb(U!0, X2!4)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.23/0.46 tff(161,plain,
% 0.23/0.46 (contains_slb(U!0, X2!4)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[160, 143])).
% 0.23/0.46 tff(162,plain,
% 0.23/0.46 (^[U: $i, V: $i, W: $i, X: $i] : refl(((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W))) <=> ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(163,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[162])).
% 0.23/0.46 tff(164,plain,
% 0.23/0.46 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = W)) & contains_slb(U, W)) <=> (~((V = W) | (~contains_slb(U, W))))), ((~((~(V = W)) & contains_slb(U, W))) <=> (~(~((V = W) | (~contains_slb(U, W))))))), rewrite((~(~((V = W) | (~contains_slb(U, W))))) <=> ((V = W) | (~contains_slb(U, W)))), ((~((~(V = W)) & contains_slb(U, W))) <=> ((V = W) | (~contains_slb(U, W))))), (((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))) <=> (((V = W) | (~contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))))), rewrite((((V = W) | (~contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))) <=> ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))), (((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))) <=> ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(165,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[164])).
% 0.23/0.46 tff(166,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(167,plain,
% 0.23/0.46 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((((~(V = W)) & contains_slb(U, W)) => (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))) <=> ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(168,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = W)) & contains_slb(U, W)) => (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[167])).
% 0.23/0.46 tff(169,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((~(V = W)) & contains_slb(U, W)) => (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax27')).
% 0.23/0.46 tff(170,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.23/0.46 tff(171,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.23/0.46 tff(172,plain,(
% 0.23/0.46 ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[171])).
% 0.23/0.46 tff(173,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.23/0.46 tff(174,plain,
% 0.23/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[173, 163])).
% 0.23/0.46 tff(175,plain,
% 0.23/0.46 (((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | ((X4!2 = X2!4) | (~contains_slb(U!0, X2!4)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | (X4!2 = X2!4) | (~contains_slb(U!0, X2!4)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(176,plain,
% 0.23/0.46 (((X4!2 = X2!4) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)) | (~contains_slb(U!0, X2!4))) <=> ((X4!2 = X2!4) | (~contains_slb(U!0, X2!4)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(177,plain,
% 0.23/0.46 (((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | ((X4!2 = X2!4) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)) | (~contains_slb(U!0, X2!4)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | ((X4!2 = X2!4) | (~contains_slb(U!0, X2!4)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[176])).
% 0.23/0.46 tff(178,plain,
% 0.23/0.46 (((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | ((X4!2 = X2!4) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)) | (~contains_slb(U!0, X2!4)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | (X4!2 = X2!4) | (~contains_slb(U!0, X2!4)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[177, 175])).
% 0.23/0.46 tff(179,plain,
% 0.23/0.46 ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | ((X4!2 = X2!4) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)) | (~contains_slb(U!0, X2!4)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(180,plain,
% 0.23/0.46 ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (lookup_slb(insert_slb(U, pair(V, X)), W) = lookup_slb(U, W)) | (~contains_slb(U, W)))) | (X4!2 = X2!4) | (~contains_slb(U!0, X2!4)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.23/0.46 tff(181,plain,
% 0.23/0.46 ((X4!2 = X2!4) | (~contains_slb(U!0, X2!4)) | (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[180, 174])).
% 0.23/0.46 tff(182,plain,
% 0.23/0.46 (lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[181, 161, 143])).
% 0.23/0.46 tff(183,plain,
% 0.23/0.46 (lookup_slb(U!0, X2!4) = lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)),
% 0.23/0.46 inference(symmetry,[status(thm)],[182])).
% 0.23/0.46 tff(184,plain,
% 0.23/0.46 (less_than(lookup_slb(U!0, X2!4), X2!4) <=> less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)),
% 0.23/0.46 inference(monotonicity,[status(thm)],[183])).
% 0.23/0.47 tff(185,plain,
% 0.23/0.47 (less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4) <=> less_than(lookup_slb(U!0, X2!4), X2!4)),
% 0.23/0.47 inference(symmetry,[status(thm)],[184])).
% 0.23/0.47 tff(186,plain,
% 0.23/0.47 (^[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))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(187,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[186])).
% 0.23/0.47 tff(188,plain,
% 0.23/0.47 (^[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)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(189,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[188])).
% 0.23/0.47 tff(190,plain,
% 0.23/0.47 (![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))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(191,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.23/0.47 tff(192,plain,
% 0.23/0.47 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.23/0.47 tff(193,plain,(
% 0.23/0.47 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.23/0.47 inference(skolemize,[status(sab)],[192])).
% 0.23/0.47 tff(194,plain,
% 0.23/0.47 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.23/0.47 tff(195,plain,
% 0.23/0.47 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.23/0.47 tff(196,plain,
% 0.23/0.47 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)) <=> strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(197,plain,
% 0.23/0.47 (~(((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)) <=> strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.23/0.47 tff(198,assumption,(~(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad))), introduced(assumption)).
% 0.23/0.47 tff(199,plain,
% 0.23/0.47 ((remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)) | (~strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[123, 91])).
% 0.23/0.47 tff(200,plain,
% 0.23/0.47 (~strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.23/0.47 tff(201,plain,
% 0.23/0.47 ((((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)) <=> strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | ((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)) | strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(202,plain,
% 0.23/0.47 ((((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)) <=> strictly_less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | ((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.23/0.47 tff(203,plain,
% 0.23/0.47 ((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[202, 197])).
% 0.23/0.47 tff(204,assumption,(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4)), introduced(assumption)).
% 0.23/0.47 tff(205,plain,
% 0.23/0.47 (lookup_slb(U!0, X2!4) = lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)),
% 0.23/0.47 inference(symmetry,[status(thm)],[204])).
% 0.23/0.47 tff(206,plain,
% 0.23/0.47 (less_than(lookup_slb(U!0, X2!4), X2!4) <=> less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)),
% 0.23/0.47 inference(monotonicity,[status(thm)],[205])).
% 0.23/0.47 tff(207,plain,
% 0.23/0.47 (less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4) <=> less_than(lookup_slb(U!0, X2!4), X2!4)),
% 0.23/0.47 inference(symmetry,[status(thm)],[206])).
% 0.23/0.47 tff(208,plain,
% 0.23/0.47 ((~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)) <=> (~less_than(lookup_slb(U!0, X2!4), X2!4))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[207])).
% 0.23/0.47 tff(209,assumption,(~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)), introduced(assumption)).
% 0.23/0.47 tff(210,plain,
% 0.23/0.47 (~less_than(lookup_slb(U!0, X2!4), X2!4)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.23/0.47 tff(211,plain,
% 0.23/0.47 (less_than(X2!4, lookup_slb(U!0, X2!4)) <=> less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[205])).
% 0.23/0.47 tff(212,plain,
% 0.23/0.47 (less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) <=> less_than(X2!4, lookup_slb(U!0, X2!4))),
% 0.23/0.47 inference(symmetry,[status(thm)],[211])).
% 0.23/0.47 tff(213,plain,
% 0.23/0.47 ((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) <=> (~less_than(X2!4, lookup_slb(U!0, X2!4)))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[212])).
% 0.23/0.47 tff(214,assumption,((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)), introduced(assumption)).
% 0.23/0.47 tff(215,plain,
% 0.23/0.47 ((~((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4))) | (~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(216,plain,
% 0.23/0.47 (~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[215, 209, 214])).
% 0.23/0.47 tff(217,plain,
% 0.23/0.47 (~less_than(X2!4, lookup_slb(U!0, X2!4))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[216, 213])).
% 0.23/0.47 tff(218,plain,
% 0.23/0.47 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(219,plain,
% 0.23/0.47 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[218])).
% 0.23/0.47 tff(220,plain,
% 0.23/0.47 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(221,plain,
% 0.23/0.47 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(222,plain,
% 0.23/0.47 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[221])).
% 0.23/0.47 tff(223,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.23/0.47 tff(224,plain,
% 0.23/0.47 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.23/0.47 tff(225,plain,
% 0.23/0.47 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.23/0.47 tff(226,plain,(
% 0.23/0.47 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.47 inference(skolemize,[status(sab)],[225])).
% 0.23/0.47 tff(227,plain,
% 0.23/0.47 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.23/0.47 tff(228,plain,
% 0.23/0.47 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X2!4, lookup_slb(U!0, X2!4)) | less_than(lookup_slb(U!0, X2!4), X2!4))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X2!4, lookup_slb(U!0, X2!4)) | less_than(lookup_slb(U!0, X2!4), X2!4))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(229,plain,
% 0.23/0.47 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X2!4, lookup_slb(U!0, X2!4)) | less_than(lookup_slb(U!0, X2!4), X2!4))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(230,plain,
% 0.23/0.47 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X2!4, lookup_slb(U!0, X2!4)) | less_than(lookup_slb(U!0, X2!4), X2!4)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.23/0.47 tff(231,plain,
% 0.23/0.47 (less_than(X2!4, lookup_slb(U!0, X2!4)) | less_than(lookup_slb(U!0, X2!4), X2!4)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.23/0.47 tff(232,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[231, 217, 210])).
% 0.23/0.47 tff(233,plain,(less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4) | (~(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = lookup_slb(U!0, X2!4))) | (~((~less_than(X2!4, lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4))) | less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(234,plain,
% 0.23/0.47 (less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[233, 182, 203])).
% 0.23/0.47 tff(235,plain,
% 0.23/0.47 (less_than(lookup_slb(U!0, X2!4), X2!4)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[234, 185])).
% 0.23/0.47 tff(236,plain,
% 0.23/0.47 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3) <=> ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(237,plain,
% 0.23/0.47 (pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3) <=> ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[236, 40])).
% 0.23/0.47 tff(238,assumption,(~(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)))), introduced(assumption)).
% 0.23/0.47 tff(239,plain,
% 0.23/0.47 (contains_slb(U!0, X2!4)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[159, 143, 158])).
% 0.23/0.47 tff(240,plain,
% 0.23/0.47 (^[U: $i, V: $i, W: $i, X: $i] : refl(((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W))) <=> ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(241,plain,
% 0.23/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[240])).
% 0.23/0.47 tff(242,plain,
% 0.23/0.47 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = W)) & contains_slb(U, W)) <=> (~((V = W) | (~contains_slb(U, W))))), ((~((~(V = W)) & contains_slb(U, W))) <=> (~(~((V = W) | (~contains_slb(U, W))))))), rewrite((~(~((V = W) | (~contains_slb(U, W))))) <=> ((V = W) | (~contains_slb(U, W)))), ((~((~(V = W)) & contains_slb(U, W))) <=> ((V = W) | (~contains_slb(U, W))))), (((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))) <=> (((V = W) | (~contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))))), rewrite((((V = W) | (~contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))) <=> ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))), (((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))) <=> ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(243,plain,
% 0.23/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[242])).
% 0.23/0.47 tff(244,plain,
% 0.23/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(245,plain,
% 0.23/0.47 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((((~(V = W)) & contains_slb(U, W)) => (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))) <=> ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(246,plain,
% 0.23/0.47 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = W)) & contains_slb(U, W)) => (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[245])).
% 0.23/0.47 tff(247,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((~(V = W)) & contains_slb(U, W)) => (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax25')).
% 0.23/0.47 tff(248,plain,
% 0.23/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.23/0.47 tff(249,plain,
% 0.23/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.23/0.47 tff(250,plain,(
% 0.23/0.47 ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = W)) & contains_slb(U, W))) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))))),
% 0.23/0.48 inference(skolemize,[status(sab)],[249])).
% 0.23/0.48 tff(251,plain,
% 0.23/0.48 (![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.23/0.48 tff(252,plain,
% 0.23/0.48 (![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[251, 241])).
% 0.23/0.48 tff(253,plain,
% 0.23/0.48 (((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))) | ((X4!2 = X2!4) | (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1))) | (~contains_slb(U!0, X2!4)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))) | (X4!2 = X2!4) | (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1))) | (~contains_slb(U!0, X2!4)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(254,plain,
% 0.23/0.48 ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))) | ((X4!2 = X2!4) | (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1))) | (~contains_slb(U!0, X2!4)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(255,plain,
% 0.23/0.48 ((~![U: $i, V: $i, W: $i, X: $i] : ((V = W) | (remove_slb(insert_slb(U, pair(V, X)), W) = insert_slb(remove_slb(U, W), pair(V, X))) | (~contains_slb(U, W)))) | (X4!2 = X2!4) | (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1))) | (~contains_slb(U!0, X2!4))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.23/0.48 tff(256,plain,
% 0.23/0.48 ((X4!2 = X2!4) | (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1))) | (~contains_slb(U!0, X2!4))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[255, 252])).
% 0.23/0.48 tff(257,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[256, 239, 143, 238])).
% 0.23/0.48 tff(258,plain,((X4!2 = X2!4) | (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(259,plain,
% 0.23/0.48 (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[258, 143])).
% 0.23/0.48 tff(260,plain,
% 0.23/0.48 (insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)) = remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)),
% 0.23/0.48 inference(symmetry,[status(thm)],[259])).
% 0.23/0.48 tff(261,plain,
% 0.23/0.48 (pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3) <=> pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[260])).
% 0.23/0.48 tff(262,plain,
% 0.23/0.48 (pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3) <=> pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3)),
% 0.23/0.48 inference(symmetry,[status(thm)],[261])).
% 0.23/0.48 tff(263,plain,
% 0.23/0.48 ((~pair_in_list(remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4, X3!3)) <=> (~pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[262])).
% 0.23/0.48 tff(264,plain,
% 0.23/0.48 (~pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[26, 263])).
% 0.23/0.48 tff(265,plain,
% 0.23/0.48 ((~(pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3) <=> ((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3)))) | pair_in_list(insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), X2!4, X3!3) | (~((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3)))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(266,plain,
% 0.23/0.48 (~((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[265, 264, 237])).
% 0.23/0.48 tff(267,plain,
% 0.23/0.48 (((~((~(X4!2 = X2!4)) | (~(X5!1 = X3!3)))) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3)) | (~pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(268,plain,
% 0.23/0.48 (~pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.23/0.48 tff(269,plain,
% 0.23/0.48 (((~(X4!2 = X2!4)) | (~(X5!1 = X3!3))) | (X4!2 = X2!4)),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(270,plain,
% 0.23/0.48 ((~(X4!2 = X2!4)) | (~(X5!1 = X3!3))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[269, 143])).
% 0.23/0.48 tff(271,plain,
% 0.23/0.48 (pair_in_list(U!0, X2!4, X3!3)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[49, 270])).
% 0.23/0.48 tff(272,assumption,(less_than(lookup_slb(U!0, X2!4), X2!4)), introduced(assumption)).
% 0.23/0.48 tff(273,assumption,(contains_slb(U!0, X2!4)), introduced(assumption)).
% 0.23/0.48 tff(274,plain,
% 0.23/0.48 (^[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))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(275,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[274])).
% 0.23/0.48 tff(276,plain,
% 0.23/0.48 (^[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)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(277,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[276])).
% 0.23/0.48 tff(278,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(279,plain,
% 0.23/0.48 (^[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))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(280,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[279])).
% 0.23/0.48 tff(281,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/sandbox2/benchmark/Axioms/SWV007+3.ax','ax44')).
% 0.23/0.48 tff(282,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.23/0.48 tff(283,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.23/0.48 tff(284,plain,(
% 0.23/0.48 ![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)))),
% 0.23/0.48 inference(skolemize,[status(sab)],[283])).
% 0.23/0.48 tff(285,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[284, 277])).
% 0.23/0.48 tff(286,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[285, 275])).
% 0.23/0.48 tff(287,plain,
% 0.23/0.48 (((~![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(U!0, X2!4)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)))) <=> ((~![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(U!0, X2!4)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(288,plain,
% 0.23/0.48 (((~contains_slb(U!0, X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (~less_than(lookup_slb(U!0, X2!4), X2!4))) <=> ((~contains_slb(U!0, X2!4)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(289,plain,
% 0.23/0.48 (((~![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(U!0, X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)))) <=> ((~![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(U!0, X2!4)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[288])).
% 0.23/0.49 tff(290,plain,
% 0.23/0.49 (((~![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(U!0, X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)))) <=> ((~![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(U!0, X2!4)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[289, 287])).
% 0.23/0.49 tff(291,plain,
% 0.23/0.49 ((~![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(U!0, X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(292,plain,
% 0.23/0.49 ((~![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(U!0, X2!4)) | (~less_than(lookup_slb(U!0, X2!4), X2!4)) | (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.23/0.49 tff(293,plain,
% 0.23/0.49 (remove_cpq(triple(Z!6, U!0, X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[292, 286, 273, 272])).
% 0.23/0.49 tff(294,plain,
% 0.23/0.49 (ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4)) <=> ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[293])).
% 0.23/0.49 tff(295,plain,
% 0.23/0.49 (ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) <=> ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))),
% 0.23/0.49 inference(symmetry,[status(thm)],[294])).
% 0.23/0.49 tff(296,assumption,(ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5))), introduced(assumption)).
% 0.23/0.49 tff(297,plain,
% 0.23/0.49 (ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.23/0.49 tff(298,assumption,(~pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3)), introduced(assumption)).
% 0.23/0.49 tff(299,assumption,(pair_in_list(U!0, X2!4, X3!3)), introduced(assumption)).
% 0.23/0.49 tff(300,plain,
% 0.23/0.49 (^[V: $i, W: $i, X: $i, Y: $i] : refl(((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))) <=> ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(301,plain,
% 0.23/0.49 (![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))) <=> ![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[300])).
% 0.23/0.49 tff(302,plain,
% 0.23/0.49 (^[V: $i, W: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X))) <=> (~((~strictly_less_than(X, Y)) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))))), ((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) <=> (~(~((~strictly_less_than(X, Y)) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))))))), rewrite((~(~((~strictly_less_than(X, Y)) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))))) <=> ((~strictly_less_than(X, Y)) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))), ((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) <=> ((~strictly_less_than(X, Y)) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))))), (((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)) <=> (((~strictly_less_than(X, Y)) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)))), rewrite((((~strictly_less_than(X, Y)) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)) <=> ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))), (((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)) <=> ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(303,plain,
% 0.23/0.49 (![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y)) <=> ![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[302])).
% 0.23/0.49 tff(304,plain,
% 0.23/0.49 (![V: $i, W: $i, X: $i, Y: $i] : ((~(pair_in_list(U!0, X, Y) & strictly_less_than(X, Y) & ok(remove_cpq(triple(V, U!0, W), X)))) | pair_in_list(remove_slb(U!0, X), X, Y))),
% 0.23/0.49 inference(and_elim,[status(thm)],[24])).
% 0.23/0.49 tff(305,plain,
% 0.23/0.49 (![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.23/0.49 tff(306,plain,
% 0.23/0.49 (![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.23/0.49 tff(307,plain,
% 0.23/0.49 (((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | ((~strictly_less_than(X2!4, X3!3)) | (~pair_in_list(U!0, X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))))) <=> ((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | (~strictly_less_than(X2!4, X3!3)) | (~pair_in_list(U!0, X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(308,plain,
% 0.23/0.49 (((~strictly_less_than(X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~pair_in_list(U!0, X2!4, X3!3)) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4)))) <=> ((~strictly_less_than(X2!4, X3!3)) | (~pair_in_list(U!0, X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(309,plain,
% 0.23/0.49 (((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | ((~strictly_less_than(X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~pair_in_list(U!0, X2!4, X3!3)) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))))) <=> ((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | ((~strictly_less_than(X2!4, X3!3)) | (~pair_in_list(U!0, X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[308])).
% 0.23/0.49 tff(310,plain,
% 0.23/0.49 (((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | ((~strictly_less_than(X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~pair_in_list(U!0, X2!4, X3!3)) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))))) <=> ((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | (~strictly_less_than(X2!4, X3!3)) | (~pair_in_list(U!0, X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[309, 307])).
% 0.23/0.49 tff(311,plain,
% 0.23/0.49 ((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | ((~strictly_less_than(X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~pair_in_list(U!0, X2!4, X3!3)) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(312,plain,
% 0.23/0.49 ((~![V: $i, W: $i, X: $i, Y: $i] : ((~strictly_less_than(X, Y)) | pair_in_list(remove_slb(U!0, X), X, Y) | (~pair_in_list(U!0, X, Y)) | (~ok(remove_cpq(triple(V, U!0, W), X))))) | (~strictly_less_than(X2!4, X3!3)) | (~pair_in_list(U!0, X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.23/0.49 tff(313,plain,
% 0.23/0.49 (~ok(remove_cpq(triple(Z!6, U!0, X1!5), X2!4))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[312, 306, 140, 299, 298])).
% 0.23/0.49 tff(314,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[313, 297])).
% 0.23/0.49 tff(315,plain,((~ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5))) | (~pair_in_list(U!0, X2!4, X3!3)) | pair_in_list(remove_slb(U!0, X2!4), X2!4, X3!3) | (~contains_slb(U!0, X2!4)) | (~less_than(lookup_slb(U!0, X2!4), X2!4))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.49 tff(316,plain,
% 0.23/0.49 (~ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[315, 271, 268, 161, 235])).
% 0.23/0.49 tff(317,plain,
% 0.23/0.49 (((~![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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)) | (~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)))) <=> ((~![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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)) | (~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(318,plain,
% 0.23/0.49 ((~![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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)) | (~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(319,plain,
% 0.23/0.49 ((~![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(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)) | (~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.23/0.49 tff(320,plain,
% 0.23/0.49 ((~contains_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)) | (~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[319, 286])).
% 0.23/0.49 tff(321,plain,
% 0.23/0.49 ((remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)) | (~less_than(lookup_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X2!4))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[320, 91])).
% 0.23/0.49 tff(322,plain,
% 0.23/0.49 (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[321, 234])).
% 0.23/0.49 tff(323,assumption,(X1!5 = bad), introduced(assumption)).
% 0.23/0.49 tff(324,plain,
% 0.23/0.49 (bad = X1!5),
% 0.23/0.49 inference(symmetry,[status(thm)],[323])).
% 0.23/0.49 tff(325,plain,
% 0.23/0.49 (triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[324])).
% 0.23/0.49 tff(326,plain,
% 0.23/0.49 (triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)),
% 0.23/0.49 inference(symmetry,[status(thm)],[325])).
% 0.23/0.49 tff(327,assumption,(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)), introduced(assumption)).
% 0.23/0.49 tff(328,plain,
% 0.23/0.49 (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)),
% 0.23/0.49 inference(transitivity,[status(thm)],[327, 326])).
% 0.23/0.50 tff(329,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[198, 328])).
% 0.23/0.50 tff(330,plain,((~(X1!5 = bad)) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)) | (~(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), X1!5)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(331,plain,
% 0.23/0.50 (~(X1!5 = bad)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[330, 322, 198])).
% 0.23/0.50 tff(332,plain,
% 0.23/0.50 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(333,plain,
% 0.23/0.50 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[332])).
% 0.23/0.50 tff(334,plain,
% 0.23/0.50 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(335,plain,
% 0.23/0.50 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(336,plain,
% 0.23/0.50 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[335])).
% 0.23/0.50 tff(337,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.23/0.50 tff(338,plain,
% 0.23/0.50 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.23/0.50 tff(339,plain,
% 0.23/0.50 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[338, 334])).
% 0.23/0.50 tff(340,plain,(
% 0.23/0.50 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.50 inference(skolemize,[status(sab)],[339])).
% 0.23/0.50 tff(341,plain,
% 0.23/0.50 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[340, 333])).
% 0.23/0.50 tff(342,plain,
% 0.23/0.50 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (X1!5 = bad))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (X1!5 = bad))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(343,plain,
% 0.23/0.50 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (X1!5 = bad))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(344,plain,
% 0.23/0.50 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(remove_pqp(Z!6, X2!4), remove_slb(U!0, X2!4), X1!5)) | (X1!5 = bad)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.23/0.50 tff(345,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[344, 341, 331, 316])).
% 0.23/0.50 tff(346,plain,((X4!2 = X2!4) | (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(347,plain,
% 0.23/0.50 (remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[346, 142])).
% 0.23/0.50 tff(348,plain,
% 0.23/0.50 (triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad) = remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)),
% 0.23/0.50 inference(symmetry,[status(thm)],[347])).
% 0.23/0.50 tff(349,plain,
% 0.23/0.50 (remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4) = insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[258, 142])).
% 0.23/0.50 tff(350,plain,
% 0.23/0.50 (insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)) = remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4)),
% 0.23/0.50 inference(symmetry,[status(thm)],[349])).
% 0.23/0.50 tff(351,plain,
% 0.23/0.50 (triple(remove_pqp(Z!6, X2!4), insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), bad) = triple(remove_pqp(Z!6, X2!4), remove_slb(insert_slb(U!0, pair(X4!2, X5!1)), X2!4), bad)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[350])).
% 0.23/0.50 tff(352,plain,
% 0.23/0.50 (triple(remove_pqp(Z!6, X2!4), insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), bad) = remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)),
% 0.23/0.50 inference(transitivity,[status(thm)],[351, 348])).
% 0.23/0.50 tff(353,plain,
% 0.23/0.50 (ok(triple(remove_pqp(Z!6, X2!4), insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), bad)) <=> ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[352])).
% 0.23/0.50 tff(354,plain,
% 0.23/0.50 (ok(remove_cpq(triple(Z!6, insert_slb(U!0, pair(X4!2, X5!1)), X1!5), X2!4)) <=> ok(triple(remove_pqp(Z!6, X2!4), insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), bad))),
% 0.23/0.50 inference(symmetry,[status(thm)],[353])).
% 0.23/0.50 tff(355,plain,
% 0.23/0.50 (ok(triple(remove_pqp(Z!6, X2!4), insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), bad))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[61, 354])).
% 0.23/0.50 tff(356,plain,
% 0.23/0.50 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(remove_pqp(Z!6, X2!4), insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), bad)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(357,plain,
% 0.23/0.50 (~ok(triple(remove_pqp(Z!6, X2!4), insert_slb(remove_slb(U!0, X2!4), pair(X4!2, X5!1)), bad))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[356, 72])).
% 0.23/0.50 tff(358,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[357, 355])).
% 0.23/0.50 % SZS output end Proof
% 0.23/0.50 % E exiting
%------------------------------------------------------------------------------