TSTP Solution File: SWV401+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV401+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:11:38 EDT 2022
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV401+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Sep 4 03:13:03 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% 0.11/0.39 tff(pair_in_list_type, type, (
% 0.11/0.39 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.11/0.39 tff(tptp_fun_X3_1_type, type, (
% 0.11/0.39 tptp_fun_X3_1: $i)).
% 0.11/0.39 tff(tptp_fun_Y_5_type, type, (
% 0.11/0.39 tptp_fun_Y_5: $i)).
% 0.11/0.39 tff(insert_slb_type, type, (
% 0.11/0.39 insert_slb: ( $i * $i ) > $i)).
% 0.11/0.39 tff(pair_type, type, (
% 0.11/0.39 pair: ( $i * $i ) > $i)).
% 0.11/0.39 tff(update_slb_type, type, (
% 0.11/0.39 update_slb: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_X1_3_type, type, (
% 0.11/0.39 tptp_fun_X1_3: $i)).
% 0.11/0.39 tff(tptp_fun_U_0_type, type, (
% 0.11/0.39 tptp_fun_U_0: $i)).
% 0.11/0.39 tff(tptp_fun_Z_4_type, type, (
% 0.11/0.39 tptp_fun_Z_4: $i)).
% 0.11/0.39 tff(tptp_fun_X2_2_type, type, (
% 0.11/0.39 tptp_fun_X2_2: $i)).
% 0.11/0.39 tff(less_than_type, type, (
% 0.11/0.39 less_than: ( $i * $i ) > $o)).
% 0.11/0.39 tff(strictly_less_than_type, type, (
% 0.11/0.39 strictly_less_than: ( $i * $i ) > $o)).
% 0.11/0.39 tff(1,plain,
% 0.11/0.39 (^[U: $i, V: $i] : refl((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(2,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.39 tff(3,plain,
% 0.11/0.39 (^[U: $i, V: $i] : rewrite((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(4,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.39 tff(5,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(6,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')).
% 0.11/0.39 tff(7,plain,
% 0.11/0.39 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.39 tff(8,plain,(
% 0.11/0.39 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[7])).
% 0.11/0.39 tff(9,plain,
% 0.11/0.39 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.39 tff(10,plain,
% 0.11/0.39 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.39 tff(11,plain,
% 0.11/0.39 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(X3!1, X1!3) <=> (~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(12,plain,
% 0.11/0.39 (strictly_less_than(X3!1, X1!3) <=> (~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.39 tff(13,assumption,(pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)), introduced(assumption)).
% 0.11/0.39 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)).
% 0.11/0.39 tff(15,plain,
% 0.11/0.39 (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)),
% 0.11/0.39 inference(symmetry,[status(thm)],[14])).
% 0.11/0.39 tff(16,plain,
% 0.11/0.39 (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)),
% 0.11/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.11/0.39 tff(17,plain,
% 0.11/0.39 (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)),
% 0.11/0.39 inference(symmetry,[status(thm)],[16])).
% 0.11/0.39 tff(18,plain,
% 0.11/0.39 ((~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))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[17])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 ((![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(20,plain,
% 0.11/0.39 ((~![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 ((~![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 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/sandbox2/benchmark/theBenchmark.p','l37_co')).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 (~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 (~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 (~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.11/0.39 tff(30,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.11/0.39 tff(31,plain,
% 0.11/0.39 (~((~(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))),
% 0.11/0.39 inference(and_elim,[status(thm)],[30])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 (~pair_in_list(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3), Y!5, Z!4)),
% 0.11/0.39 inference(or_elim,[status(thm)],[31])).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[32, 18])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (![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))) <=> ![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (![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))) <=> ![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 (![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))) <=> ![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(40,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.11/0.40 tff(41,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')).
% 0.11/0.40 tff(42,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.40 tff(43,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.11/0.40 tff(44,plain,(
% 0.11/0.40 ![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)))),
% 0.11/0.40 inference(skolemize,[status(sab)],[43])).
% 0.11/0.40 tff(45,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.11/0.40 tff(46,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.11/0.40 tff(47,plain,
% 0.11/0.40 ((~![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, 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)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(48,plain,
% 0.11/0.40 (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))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.11/0.40 tff(49,plain,
% 0.11/0.40 (((~((~(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))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(50,plain,
% 0.11/0.40 ((~((~(X2!2 = Y!5)) | (~(X1!3 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[49, 13])).
% 0.11/0.40 tff(51,plain,
% 0.11/0.40 ((~(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)))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(52,plain,
% 0.11/0.40 ((~(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)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.11/0.40 tff(53,plain,
% 0.11/0.40 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)), Y!5, Z!4)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[52, 48])).
% 0.11/0.40 tff(54,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[53, 33])).
% 0.11/0.40 tff(55,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,[]))).
% 0.11/0.40 tff(56,plain,
% 0.11/0.40 (~(update_slb(insert_slb(U!0, pair(X2!2, X3!1)), X1!3) = insert_slb(update_slb(U!0, X1!3), pair(X2!2, X1!3)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[55, 13])).
% 0.11/0.40 tff(57,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(58,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.11/0.40 tff(59,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(60,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(61,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.11/0.40 tff(62,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/sandbox2/benchmark/Axioms/SWV007+2.ax','ax29')).
% 0.11/0.40 tff(63,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.11/0.40 tff(64,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.11/0.40 tff(65,plain,(
% 0.11/0.40 ![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))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[64])).
% 0.11/0.40 tff(66,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.11/0.40 tff(67,plain,
% 0.11/0.40 (((~![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))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(68,plain,
% 0.11/0.40 ((~![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))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(69,plain,
% 0.11/0.40 ((~![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.11/0.40 tff(70,plain,
% 0.11/0.40 ((~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)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.11/0.40 tff(71,plain,
% 0.11/0.40 (~strictly_less_than(X3!1, X1!3)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[70, 56])).
% 0.11/0.40 tff(72,plain,
% 0.11/0.40 ((~(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) | ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(73,plain,
% 0.11/0.40 ((~(strictly_less_than(X3!1, X1!3) <=> (~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))))) | ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.11/0.40 tff(74,plain,
% 0.11/0.40 ((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[73, 12])).
% 0.11/0.40 tff(75,assumption,((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)), introduced(assumption)).
% 0.11/0.40 tff(76,assumption,(~less_than(X1!3, X3!1)), introduced(assumption)).
% 0.11/0.40 tff(77,plain,
% 0.11/0.40 ((~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1))) | (~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(78,plain,
% 0.11/0.40 (~less_than(X3!1, X1!3)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[77, 76, 75])).
% 0.11/0.40 tff(79,plain,
% 0.11/0.40 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(80,plain,
% 0.11/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.11/0.40 tff(81,plain,
% 0.11/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(82,plain,
% 0.11/0.40 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(83,plain,
% 0.11/0.40 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[82])).
% 0.11/0.40 tff(84,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.11/0.40 tff(85,plain,
% 0.11/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.11/0.40 tff(86,plain,
% 0.11/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.11/0.40 tff(87,plain,(
% 0.11/0.40 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.40 inference(skolemize,[status(sab)],[86])).
% 0.11/0.40 tff(88,plain,
% 0.11/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.11/0.40 tff(89,plain,
% 0.11/0.40 (((~![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))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(90,plain,
% 0.11/0.40 ((less_than(X3!1, X1!3) | less_than(X1!3, X3!1)) <=> (less_than(X1!3, X3!1) | less_than(X3!1, X1!3))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(91,plain,
% 0.11/0.40 (((~![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)))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[90])).
% 0.11/0.40 tff(92,plain,
% 0.11/0.40 (((~![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))),
% 0.11/0.40 inference(transitivity,[status(thm)],[91, 89])).
% 0.11/0.40 tff(93,plain,
% 0.11/0.40 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(X3!1, X1!3) | less_than(X1!3, X3!1))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(94,plain,
% 0.11/0.40 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(X1!3, X3!1) | less_than(X3!1, X1!3)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.11/0.40 tff(95,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[94, 88, 76, 78])).
% 0.11/0.40 tff(96,plain,(less_than(X1!3, X3!1) | (~((~less_than(X3!1, X1!3)) | less_than(X1!3, X3!1)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.40 tff(97,plain,
% 0.11/0.40 (less_than(X1!3, X3!1)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[96, 74])).
% 0.11/0.40 tff(98,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(99,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.11/0.40 tff(100,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(101,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(102,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.11/0.40 tff(103,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/sandbox2/benchmark/Axioms/SWV007+2.ax','ax30')).
% 0.11/0.40 tff(104,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.11/0.40 tff(105,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.11/0.40 tff(106,plain,(
% 0.11/0.40 ![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))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[105])).
% 0.11/0.40 tff(107,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.11/0.40 tff(108,plain,
% 0.11/0.40 (((~![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))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(109,plain,
% 0.11/0.41 ((~![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))))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(110,plain,
% 0.11/0.41 ((~![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)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.11/0.41 tff(111,plain,
% 0.11/0.41 ((~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)))),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.11/0.41 tff(112,plain,
% 0.11/0.41 (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))),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.11/0.41 tff(113,plain,
% 0.11/0.41 (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)),
% 0.11/0.41 inference(symmetry,[status(thm)],[112])).
% 0.11/0.41 tff(114,plain,
% 0.11/0.41 (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)),
% 0.11/0.41 inference(monotonicity,[status(thm)],[113])).
% 0.11/0.41 tff(115,plain,
% 0.11/0.41 (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(X2!2, X3!1)), Y!5, Z!4)),
% 0.11/0.41 inference(symmetry,[status(thm)],[114])).
% 0.11/0.41 tff(116,plain,
% 0.11/0.41 ((~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(X2!2, X3!1)), Y!5, Z!4))),
% 0.11/0.41 inference(monotonicity,[status(thm)],[115])).
% 0.11/0.41 tff(117,plain,
% 0.11/0.41 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[32, 116])).
% 0.11/0.41 tff(118,plain,
% 0.11/0.41 ((~![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(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)))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(119,plain,
% 0.11/0.41 (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))),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[118, 46])).
% 0.11/0.41 tff(120,plain,
% 0.11/0.41 (((~((~(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))),
% 0.11/0.41 inference(tautology,[status(thm)],[])).
% 0.11/0.41 tff(121,plain,
% 0.11/0.41 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[120, 13])).
% 0.11/0.41 tff(122,plain,
% 0.11/0.41 ((~(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)))),
% 0.11/0.41 inference(tautology,[status(thm)],[])).
% 0.11/0.41 tff(123,plain,
% 0.11/0.41 ((~(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)),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.11/0.41 tff(124,plain,
% 0.11/0.41 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[123, 119])).
% 0.11/0.41 tff(125,plain,
% 0.11/0.41 ($false),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[124, 117])).
% 0.11/0.41 tff(126,plain,(~pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.41 tff(127,assumption,(~pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)), introduced(assumption)).
% 0.11/0.41 tff(128,assumption,(pair_in_list(U!0, Y!5, Z!4)), introduced(assumption)).
% 0.11/0.41 tff(129,plain,
% 0.11/0.41 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4) & less_than(X1!3, Z!4)),
% 0.11/0.41 inference(or_elim,[status(thm)],[31])).
% 0.11/0.41 tff(130,plain,
% 0.11/0.41 (less_than(X1!3, Z!4)),
% 0.11/0.41 inference(and_elim,[status(thm)],[129])).
% 0.11/0.41 tff(131,plain,
% 0.11/0.41 (^[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))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(132,plain,
% 0.11/0.41 (![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))) <=> ![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)))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[131])).
% 0.11/0.41 tff(133,plain,
% 0.11/0.41 (^[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)))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(134,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[133])).
% 0.11/0.41 tff(135,plain,
% 0.11/0.41 (![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))),
% 0.11/0.41 inference(and_elim,[status(thm)],[30])).
% 0.11/0.41 tff(136,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.11/0.41 tff(137,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.11/0.41 tff(138,plain,
% 0.11/0.41 (((~![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))) <=> ((~![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))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(139,plain,
% 0.11/0.41 (((~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))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(140,plain,
% 0.11/0.41 (((~![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)))) <=> ((~![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)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[139])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 (((~![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)))) <=> ((~![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))),
% 0.18/0.41 inference(transitivity,[status(thm)],[140, 138])).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(143,plain,
% 0.18/0.41 ((~![V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U!0, X), V, W) | (~pair_in_list(U!0, V, W)))) | (~less_than(X1!3, Z!4)) | (~pair_in_list(U!0, Y!5, Z!4)) | pair_in_list(update_slb(U!0, X1!3), Y!5, Z!4)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[143, 137, 130, 128, 127])).
% 0.18/0.41 tff(145,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,[]))).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 (~pair_in_list(U!0, Y!5, Z!4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[145, 126])).
% 0.18/0.41 tff(147,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(148,plain,
% 0.18/0.41 (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))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[147, 46])).
% 0.18/0.41 tff(149,plain,
% 0.18/0.41 (pair_in_list(insert_slb(U!0, pair(X2!2, X3!1)), Y!5, Z!4)),
% 0.18/0.41 inference(and_elim,[status(thm)],[129])).
% 0.18/0.41 tff(150,plain,
% 0.18/0.41 ((~(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))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(151,plain,
% 0.18/0.41 ((~(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))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.18/0.41 tff(152,plain,
% 0.18/0.41 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[151, 148])).
% 0.18/0.41 tff(153,plain,
% 0.18/0.41 ((~((~((~(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)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(154,plain,
% 0.18/0.41 ((~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))) | pair_in_list(U!0, Y!5, Z!4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.18/0.41 tff(155,plain,
% 0.18/0.41 (~((~(X2!2 = Y!5)) | (~(X3!1 = Z!4)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[154, 146])).
% 0.18/0.41 tff(156,plain,
% 0.18/0.41 (((~(X2!2 = Y!5)) | (~(X3!1 = Z!4))) | (X3!1 = Z!4)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(157,plain,
% 0.18/0.41 (X3!1 = Z!4),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.18/0.41 tff(158,plain,
% 0.18/0.41 (Z!4 = X3!1),
% 0.18/0.41 inference(symmetry,[status(thm)],[157])).
% 0.18/0.42 tff(159,plain,
% 0.18/0.42 (less_than(X1!3, Z!4) <=> less_than(X1!3, X3!1)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[158])).
% 0.18/0.42 tff(160,plain,
% 0.18/0.42 (less_than(X1!3, X3!1)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[130, 159])).
% 0.18/0.42 tff(161,plain,
% 0.18/0.42 (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))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[111, 160])).
% 0.18/0.42 tff(162,plain,
% 0.18/0.42 (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)),
% 0.18/0.42 inference(symmetry,[status(thm)],[161])).
% 0.18/0.42 tff(163,plain,
% 0.18/0.42 (((~(X2!2 = Y!5)) | (~(X3!1 = Z!4))) | (X2!2 = Y!5)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(164,plain,
% 0.18/0.42 (X2!2 = Y!5),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[163, 155])).
% 0.18/0.42 tff(165,plain,
% 0.18/0.42 (Y!5 = X2!2),
% 0.18/0.42 inference(symmetry,[status(thm)],[164])).
% 0.18/0.42 tff(166,plain,
% 0.18/0.42 (pair(Y!5, X3!1) = pair(X2!2, X3!1)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[165])).
% 0.18/0.42 tff(167,plain,
% 0.18/0.42 (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))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[166])).
% 0.18/0.42 tff(168,plain,
% 0.18/0.42 (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)),
% 0.18/0.42 inference(transitivity,[status(thm)],[167, 162])).
% 0.18/0.42 tff(169,plain,
% 0.18/0.42 (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)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[168, 157])).
% 0.18/0.42 tff(170,plain,
% 0.18/0.42 (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)),
% 0.18/0.42 inference(symmetry,[status(thm)],[169])).
% 0.18/0.42 tff(171,plain,
% 0.18/0.42 ((~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))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[170])).
% 0.18/0.42 tff(172,plain,
% 0.18/0.42 (~pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[32, 171])).
% 0.18/0.42 tff(173,plain,
% 0.18/0.42 (((~![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))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(174,plain,
% 0.18/0.42 ((pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1) <=> $true) <=> pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(175,plain,
% 0.18/0.42 (($true | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)) <=> $true),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(176,plain,
% 0.18/0.42 ((~$false) <=> $true),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(177,plain,
% 0.18/0.42 (($false | $false) <=> $false),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(178,plain,
% 0.18/0.42 ((~$true) <=> $false),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(179,plain,
% 0.18/0.42 ((X3!1 = X3!1) <=> $true),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(180,plain,
% 0.18/0.42 ((~(X3!1 = X3!1)) <=> (~$true)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[179])).
% 0.18/0.42 tff(181,plain,
% 0.18/0.42 ((~(X3!1 = X3!1)) <=> $false),
% 0.18/0.42 inference(transitivity,[status(thm)],[180, 178])).
% 0.18/0.42 tff(182,plain,
% 0.18/0.42 ((Y!5 = Y!5) <=> $true),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(183,plain,
% 0.18/0.42 ((~(Y!5 = Y!5)) <=> (~$true)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.42 tff(184,plain,
% 0.18/0.42 ((~(Y!5 = Y!5)) <=> $false),
% 0.18/0.42 inference(transitivity,[status(thm)],[183, 178])).
% 0.18/0.42 tff(185,plain,
% 0.18/0.42 (((~(Y!5 = Y!5)) | (~(X3!1 = X3!1))) <=> ($false | $false)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[184, 181])).
% 0.18/0.42 tff(186,plain,
% 0.18/0.42 (((~(Y!5 = Y!5)) | (~(X3!1 = X3!1))) <=> $false),
% 0.18/0.42 inference(transitivity,[status(thm)],[185, 177])).
% 0.18/0.42 tff(187,plain,
% 0.18/0.42 ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) <=> (~$false)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[186])).
% 0.18/0.42 tff(188,plain,
% 0.18/0.42 ((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) <=> $true),
% 0.18/0.42 inference(transitivity,[status(thm)],[187, 176])).
% 0.18/0.42 tff(189,plain,
% 0.18/0.42 (((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)) <=> ($true | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[188])).
% 0.18/0.42 tff(190,plain,
% 0.18/0.42 (((~((~(Y!5 = Y!5)) | (~(X3!1 = X3!1)))) | pair_in_list(update_slb(U!0, X1!3), Y!5, X3!1)) <=> $true),
% 0.18/0.42 inference(transitivity,[status(thm)],[189, 175])).
% 0.18/0.42 tff(191,plain,
% 0.18/0.42 ((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)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[190])).
% 0.18/0.42 tff(192,plain,
% 0.18/0.42 ((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)),
% 0.18/0.42 inference(transitivity,[status(thm)],[191, 174])).
% 0.18/0.42 tff(193,plain,
% 0.18/0.42 (((~![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))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[192])).
% 0.18/0.42 tff(194,plain,
% 0.18/0.42 (((~![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))),
% 0.18/0.42 inference(transitivity,[status(thm)],[193, 173])).
% 0.18/0.42 tff(195,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(196,plain,
% 0.18/0.42 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.18/0.42 tff(197,plain,
% 0.18/0.42 (pair_in_list(insert_slb(update_slb(U!0, X1!3), pair(Y!5, X3!1)), Y!5, X3!1)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[196, 46])).
% 0.18/0.42 tff(198,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[197, 172])).
% 0.18/0.42 % SZS output end Proof
%------------------------------------------------------------------------------