%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV401+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:22 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV401+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:49:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(pair_in_list_type, type, (
% 0.21/0.38 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.21/0.38 tff(tptp_fun_X3_1_type, type, (
% 0.21/0.38 tptp_fun_X3_1: $i)).
% 0.21/0.38 tff(tptp_fun_Y_5_type, type, (
% 0.21/0.38 tptp_fun_Y_5: $i)).
% 0.21/0.38 tff(insert_slb_type, type, (
% 0.21/0.38 insert_slb: ( $i * $i ) > $i)).
% 0.21/0.38 tff(pair_type, type, (
% 0.21/0.38 pair: ( $i * $i ) > $i)).
% 0.21/0.38 tff(update_slb_type, type, (
% 0.21/0.38 update_slb: ( $i * $i ) > $i)).
% 0.21/0.38 tff(tptp_fun_X1_3_type, type, (
% 0.21/0.38 tptp_fun_X1_3: $i)).
% 0.21/0.38 tff(tptp_fun_U_0_type, type, (
% 0.21/0.38 tptp_fun_U_0: $i)).
% 0.21/0.38 tff(tptp_fun_Z_4_type, type, (
% 0.21/0.38 tptp_fun_Z_4: $i)).
% 0.21/0.38 tff(tptp_fun_X2_2_type, type, (
% 0.21/0.38 tptp_fun_X2_2: $i)).
% 0.21/0.38 tff(less_than_type, type, (
% 0.21/0.38 less_than: ( $i * $i ) > $o)).
% 0.21/0.38 tff(strictly_less_than_type, type, (
% 0.21/0.38 strictly_less_than: ( $i * $i ) > $o)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (^[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)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (![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))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(6,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.38 tff(8,plain,(
% 0.21/0.38 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.38 inference(skolemize,[status(sab)],[7])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (~(((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.38 tff(13,assumption,(pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)), introduced(assumption)).
% 0.21/0.38 tff(14,assumption,(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))), introduced(assumption)).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)) = update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3)),
% 0.21/0.38 inference(symmetry,[status(thm)],[14])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4) <=> pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)),
% 0.21/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4)),
% 0.21/0.38 inference(symmetry,[status(thm)],[16])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 ((~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)) <=> (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 ((![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & less_than(X, W))) | pair_in_list(update_slb(U!0, X), V, W)) & (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & less_than(X1!3, Z!4))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)))) <=> (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & less_than(X, W))) | pair_in_list(update_slb(U!0, X), V, W)) & (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & less_than(X1!3, Z!4))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 ((~![U: $i] : ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z)))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 ((~![U: $i] : (![V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) => ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z)) => pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z)))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(22,axiom,(~![U: $i] : (![V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) => ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z)) => pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l37_co')).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : ((~(pair_in_list(insert_slb(U, pair(X2, X3)), Y, Z) & less_than(X1, Z))) | pair_in_list(update_slb(insert_slb(U, pair(X2, X3)), X1), Y, Z)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & less_than(X, W))) | pair_in_list(update_slb(U!0, X), V, W)) & (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & less_than(X1!3, Z!4))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.38 tff(28,plain,
% 0.21/0.38 (~((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & less_than(X1!3, Z!4))) | pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4))),
% 0.21/0.38 inference(and_elim,[status(thm)],[27])).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)),
% 0.21/0.38 inference(or_elim,[status(thm)],[28])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[29, 18])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.38 tff(38,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/sandbox/benchmark/Axioms/SWV007+2.ax','ax23')).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.39 tff(41,plain,(
% 0.21/0.39 ![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)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[40])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~![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(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)) | (~pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 ((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[46, 13])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 ((~(pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4) | (~((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 ((~(pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[49, 45])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[50, 30])).
% 0.21/0.39 tff(52,plain,((~(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)))) | (~pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (~(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[52, 13])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((strictly_less_than(X, W) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : (strictly_less_than(X, W) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.39 tff(59,axiom,(![U: $i, V: $i, W: $i, X: $i] : (strictly_less_than(X, W) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax29')).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.39 tff(62,plain,(
% 0.21/0.39 ![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[61])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | ((~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | (~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | ((~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : ((~strictly_less_than(X, W)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, W))))) | (~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 ((~strictly_less_than(X3!1, X1!3)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.21/0.39 tff(68,plain,
% 0.21/0.39 (~strictly_less_than(X3!1, X1!3)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[67, 53])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 ((((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3)) | ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) | strictly_less_than(X3!1, X1!3)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(70,plain,
% 0.21/0.39 ((((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)) <=> strictly_less_than(X3!1, X1!3)) | ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[70, 12])).
% 0.21/0.39 tff(72,assumption,((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)), introduced(assumption)).
% 0.21/0.39 tff(73,assumption,(~less_than(X1!3, X3!1)), introduced(assumption)).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 ((~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))) | (~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 (~less_than(X3!1, X1!3)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[74, 73, 72])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.39 tff(81,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.21/0.39 tff(84,plain,(
% 0.21/0.39 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(skolemize,[status(sab)],[83])).
% 0.21/0.39 tff(85,plain,
% 0.21/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X1!3, X3!1) | less_than(X3!1, X1!3))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X1!3, X3!1) | less_than(X3!1, X1!3))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(87,plain,
% 0.21/0.39 ((less_than(X3!1, X1!3) | less_than(X1!3, X3!1)) <=> (less_than(X1!3, X3!1) | less_than(X3!1, X1!3))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(88,plain,
% 0.21/0.39 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X3!1, X1!3) | less_than(X1!3, X3!1))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X1!3, X3!1) | less_than(X3!1, X1!3)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.39 tff(89,plain,
% 0.21/0.39 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X3!1, X1!3) | less_than(X1!3, X3!1))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X1!3, X3!1) | less_than(X3!1, X1!3))),
% 0.21/0.39 inference(transitivity,[status(thm)],[88, 86])).
% 0.21/0.39 tff(90,plain,
% 0.21/0.39 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X3!1, X1!3) | less_than(X1!3, X3!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(91,plain,
% 0.21/0.39 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X1!3, X3!1) | less_than(X3!1, X1!3)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.39 tff(92,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[91, 85, 73, 75])).
% 0.21/0.40 tff(93,plain,(less_than(X1!3, X3!1) | (~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (less_than(X1!3, X3!1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[93, 71])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((less_than(W, X) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (![U: $i, V: $i, W: $i, X: $i] : (less_than(W, X) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.40 tff(100,axiom,(![U: $i, V: $i, W: $i, X: $i] : (less_than(W, X) => (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax30')).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.21/0.40 tff(103,plain,(
% 0.21/0.40 ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[102])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | ((~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | (~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | ((~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(W, X)) | (update_slb(insert_slb(U, pair(V, X)), W) = insert_slb(update_slb(U, W), pair(V, X))))) | (~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 ((~less_than(X1!3, X3!1)) | (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[108, 94])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 (insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)) = update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3)),
% 0.21/0.40 inference(symmetry,[status(thm)],[109])).
% 0.21/0.40 tff(111,plain,
% 0.21/0.40 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4) <=> pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 (pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.21/0.40 inference(symmetry,[status(thm)],[111])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 ((~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)) <=> (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.40 tff(114,plain,
% 0.21/0.40 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 113])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 ((~![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(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[115, 43])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 (((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)) | (~pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[117, 13])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 ((~(pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4) | (~((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 ((~(pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[120, 116])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[121, 114])).
% 0.21/0.40 tff(123,plain,(~pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(124,assumption,(~pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)), introduced(assumption)).
% 0.21/0.40 tff(125,assumption,(pair_in_list(U!0, Y!5, Z!4)), introduced(assumption)).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & less_than(X1!3, Z!4)),
% 0.21/0.40 inference(or_elim,[status(thm)],[28])).
% 0.21/0.40 tff(127,plain,
% 0.21/0.40 (less_than(X1!3, Z!4)),
% 0.21/0.40 inference(and_elim,[status(thm)],[126])).
% 0.21/0.40 tff(128,plain,
% 0.21/0.40 (^[V: $i, W: $i, X: $i] : refl(((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W))) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(129,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W))) <=> ![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.40 tff(130,plain,
% 0.21/0.40 (^[V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U!0, V, W) & less_than(X, W)) <=> (~((~less_than(X, W)) | (~pair_in_list(U!0, V, W))))), ((~(pair_in_list(U!0, V, W) & less_than(X, W))) <=> (~(~((~less_than(X, W)) | (~pair_in_list(U!0, V, W))))))), rewrite((~(~((~less_than(X, W)) | (~pair_in_list(U!0, V, W))))) <=> ((~less_than(X, W)) | (~pair_in_list(U!0, V, W)))), ((~(pair_in_list(U!0, V, W) & less_than(X, W))) <=> ((~less_than(X, W)) | (~pair_in_list(U!0, V, W))))), (((~(pair_in_list(U!0, V, W) & less_than(X, W))) | pair_in_list(update_slb(U!0, X), V, W)) <=> (((~less_than(X, W)) | (~pair_in_list(U!0, V, W))) | pair_in_list(update_slb(U!0, X), V, W)))), rewrite((((~less_than(X, W)) | (~pair_in_list(U!0, V, W))) | pair_in_list(update_slb(U!0, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))), (((~(pair_in_list(U!0, V, W) & less_than(X, W))) | pair_in_list(update_slb(U!0, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(131,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & less_than(X, W))) | pair_in_list(update_slb(U!0, X), V, W)) <=> ![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.40 tff(132,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~(pair_in_list(U!0, V, W) & less_than(X, W))) | pair_in_list(update_slb(U!0, X), V, W))),
% 0.21/0.40 inference(and_elim,[status(thm)],[27])).
% 0.21/0.40 tff(133,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.40 tff(134,plain,
% 0.21/0.40 (![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.40 tff(135,plain,
% 0.21/0.40 (((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | ((~less_than(X1!3, Z!4)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))) <=> ((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | (~less_than(X1!3, Z!4)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(136,plain,
% 0.21/0.40 (((~less_than(X1!3, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4) | (~pair_in_list(U!0, Y!5, Z!4))) <=> ((~less_than(X1!3, Z!4)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(137,plain,
% 0.21/0.40 (((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | ((~less_than(X1!3, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4) | (~pair_in_list(U!0, Y!5, Z!4)))) <=> ((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | ((~less_than(X1!3, Z!4)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[136])).
% 0.21/0.40 tff(138,plain,
% 0.21/0.40 (((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | ((~less_than(X1!3, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4) | (~pair_in_list(U!0, Y!5, Z!4)))) <=> ((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | (~less_than(X1!3, Z!4)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4))),
% 0.21/0.41 inference(transitivity,[status(thm)],[137, 135])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 ((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | ((~less_than(X1!3, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4) | (~pair_in_list(U!0, Y!5, Z!4)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 ((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | (~less_than(X1!3, Z!4)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[140, 134, 127, 125, 124])).
% 0.21/0.41 tff(142,plain,(pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4) | (~pair_in_list(U!0, Y!5, Z!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 (~pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[142, 123])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 ((~![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(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[144, 43])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.21/0.41 inference(and_elim,[status(thm)],[126])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 ((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)))) | (~pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4)) | ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(148,plain,
% 0.21/0.41 ((~(pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) <=> ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)))) | ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.21/0.41 tff(150,plain,
% 0.21/0.41 ((~((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4))) | (~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(151,plain,
% 0.21/0.41 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.21/0.41 tff(152,plain,
% 0.21/0.41 (~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[151, 143])).
% 0.21/0.41 tff(153,plain,
% 0.21/0.41 (((~(X2!2 = Y!5)) | (~(X3!1 = Z!4))) | (X3!1 = Z!4)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(154,plain,
% 0.21/0.41 (X3!1 = Z!4),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.21/0.41 tff(155,plain,
% 0.21/0.41 (Z!4 = X3!1),
% 0.21/0.41 inference(symmetry,[status(thm)],[154])).
% 0.21/0.41 tff(156,plain,
% 0.21/0.41 (less_than(X1!3, Z!4) <=> less_than(X1!3, X3!1)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.41 tff(157,plain,
% 0.21/0.41 (less_than(X1!3, X3!1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[127, 156])).
% 0.21/0.41 tff(158,plain,
% 0.21/0.41 (update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[108, 157])).
% 0.21/0.41 tff(159,plain,
% 0.21/0.41 (insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)) = update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3)),
% 0.21/0.41 inference(symmetry,[status(thm)],[158])).
% 0.21/0.41 tff(160,plain,
% 0.21/0.41 (((~(X2!2 = Y!5)) | (~(X3!1 = Z!4))) | (X2!2 = Y!5)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(161,plain,
% 0.21/0.41 (X2!2 = Y!5),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[160, 152])).
% 0.21/0.41 tff(162,plain,
% 0.21/0.41 (Y!5 = X2!2),
% 0.21/0.41 inference(symmetry,[status(thm)],[161])).
% 0.21/0.41 tff(163,plain,
% 0.21/0.41 (pair(Y!5, X3!1) = pair(X2!2, X3!1)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.41 tff(164,plain,
% 0.21/0.41 (insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.41 tff(165,plain,
% 0.21/0.41 (insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)) = update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3)),
% 0.21/0.41 inference(transitivity,[status(thm)],[164, 159])).
% 0.21/0.41 tff(166,plain,
% 0.21/0.41 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[165, 154])).
% 0.21/0.41 tff(167,plain,
% 0.21/0.41 (pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.21/0.41 inference(symmetry,[status(thm)],[166])).
% 0.21/0.41 tff(168,plain,
% 0.21/0.41 ((~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)) <=> (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.41 tff(169,plain,
% 0.21/0.41 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 168])).
% 0.21/0.41 tff(170,plain,
% 0.21/0.41 (((~![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(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)) <=> ((~![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(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(171,plain,
% 0.21/0.41 ((pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> $true) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(172,plain,
% 0.21/0.41 (($true | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(173,plain,
% 0.21/0.41 ((~$false) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(174,plain,
% 0.21/0.41 (($false | $false) <=> $false),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(175,plain,
% 0.21/0.41 ((~$true) <=> $false),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(176,plain,
% 0.21/0.41 ((X3!1 = X3!1) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(177,plain,
% 0.21/0.41 ((~(X3!1 = X3!1)) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[176])).
% 0.21/0.41 tff(178,plain,
% 0.21/0.41 ((~(X3!1 = X3!1)) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[177, 175])).
% 0.21/0.41 tff(179,plain,
% 0.21/0.41 ((Y!5 = Y!5) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(180,plain,
% 0.21/0.41 ((~(Y!5 = Y!5)) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[179])).
% 0.21/0.41 tff(181,plain,
% 0.21/0.41 ((~(Y!5 = Y!5)) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[180, 175])).
% 0.21/0.41 tff(182,plain,
% 0.21/0.41 (((~(Y!5 = Y!5)) | (~(X3!1 = X3!1))) <=> ($false | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[181, 178])).
% 0.21/0.41 tff(183,plain,
% 0.21/0.41 (((~(Y!5 = Y!5)) | (~(X3!1 = X3!1))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[182, 174])).
% 0.21/0.41 tff(184,plain,
% 0.21/0.41 ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) <=> (~$false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[183])).
% 0.21/0.41 tff(185,plain,
% 0.21/0.41 ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) <=> $true),
% 0.21/0.41 inference(transitivity,[status(thm)],[184, 173])).
% 0.21/0.41 tff(186,plain,
% 0.21/0.41 (((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)) <=> ($true | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[185])).
% 0.21/0.41 tff(187,plain,
% 0.21/0.41 (((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)) <=> $true),
% 0.21/0.41 inference(transitivity,[status(thm)],[186, 172])).
% 0.21/0.41 tff(188,plain,
% 0.21/0.41 ((pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1))) <=> (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> $true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[187])).
% 0.21/0.41 tff(189,plain,
% 0.21/0.41 ((pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1))) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.21/0.41 inference(transitivity,[status(thm)],[188, 171])).
% 0.21/0.41 tff(190,plain,
% 0.21/0.41 (((~![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(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)))) <=> ((~![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(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[189])).
% 0.21/0.41 tff(191,plain,
% 0.21/0.41 (((~![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(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)))) <=> ((~![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(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1))),
% 0.21/0.41 inference(transitivity,[status(thm)],[190, 170])).
% 0.21/0.41 tff(192,plain,
% 0.21/0.41 ((~![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(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(193,plain,
% 0.21/0.41 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.41 tff(194,plain,
% 0.21/0.41 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[193, 43])).
% 0.21/0.41 tff(195,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[194, 169])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------