TSTP Solution File: SWV413+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV413+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 15:11:41 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV413+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 02:56:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(pair_in_list_type, type, (
% 0.12/0.39 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_W_1_type, type, (
% 0.12/0.39 tptp_fun_W_1: $i)).
% 0.12/0.39 tff(tptp_fun_V_2_type, type, (
% 0.12/0.39 tptp_fun_V_2: $i)).
% 0.12/0.39 tff(update_slb_type, type, (
% 0.12/0.39 update_slb: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_X_0_type, type, (
% 0.12/0.39 tptp_fun_X_0: $i)).
% 0.12/0.39 tff(tptp_fun_U_3_type, type, (
% 0.12/0.39 tptp_fun_U_3: $i)).
% 0.12/0.39 tff(less_than_type, type, (
% 0.12/0.39 less_than: ( $i * $i ) > $o)).
% 0.12/0.39 tff(strictly_less_than_type, type, (
% 0.12/0.39 strictly_less_than: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[Y: $i] : refl(((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y))) <=> ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y))) <=> ![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[Y: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y)) <=> (~((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y))))), ((~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y))) <=> (~(~((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y))))))), rewrite((~(~((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y))))) <=> ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))), ((~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y))) <=> ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y))) <=> ![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (((pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1)) & ![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y)))) <=> (pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1) & ![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((~(~(pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1)))) <=> (pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (((~(~(pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1)))) & ![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y)))) <=> ((pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1)) & ![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (((~(~(pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1)))) & ![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y)))) <=> (pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1) & ![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[7, 5])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & less_than(X, W)) => ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(11,axiom,(~![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & less_than(X, W)) => ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l49_co')).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | ?[Y: $i] : (pair_in_list(update_slb(U, X), V, Y) & less_than(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & less_than(X!0, W!1) & ![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![Y: $i] : (~(pair_in_list(update_slb(U!3, X!0), V!2, Y) & less_than(X!0, Y)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 4])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (less_than(X!0, W!1)),
% 0.12/0.39 inference(and_elim,[status(thm)],[19])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (((~![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))) | ((~pair_in_list(update_slb(U!3, X!0), V!2, W!1)) | (~less_than(X!0, W!1)))) <=> ((~![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))) | (~pair_in_list(update_slb(U!3, X!0), V!2, W!1)) | (~less_than(X!0, W!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 ((~![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))) | ((~pair_in_list(update_slb(U!3, X!0), V!2, W!1)) | (~less_than(X!0, W!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((~![Y: $i] : ((~pair_in_list(update_slb(U!3, X!0), V!2, Y)) | (~less_than(X!0, Y)))) | (~pair_in_list(update_slb(U!3, X!0), V!2, W!1)) | (~less_than(X!0, W!1))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (~pair_in_list(update_slb(U!3, X!0), V!2, W!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[26, 23, 22])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (pair_in_list(U!3, V!2, W!1)),
% 0.12/0.39 inference(and_elim,[status(thm)],[19])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & less_than(X, W)) <=> (~((~less_than(X, W)) | (~pair_in_list(U, V, W))))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> (~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))))), rewrite((~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W))))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> (((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)))), rewrite((((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![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)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![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)) <=> ![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) <=> ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![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)) <=> ![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.39 tff(36,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))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l49_li3637')).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.39 tff(39,plain,(
% 0.12/0.39 ![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))),
% 0.12/0.39 inference(skolemize,[status(sab)],[38])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~less_than(X!0, W!1)) | (~pair_in_list(U!3, V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~less_than(X!0, W!1)) | (~pair_in_list(U!3, V!2, W!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (((~less_than(X!0, W!1)) | pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~pair_in_list(U!3, V!2, W!1))) <=> (pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~less_than(X!0, W!1)) | (~pair_in_list(U!3, V!2, W!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(X!0, W!1)) | pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~pair_in_list(U!3, V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~less_than(X!0, W!1)) | (~pair_in_list(U!3, V!2, W!1))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(X!0, W!1)) | pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~pair_in_list(U!3, V!2, W!1)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~less_than(X!0, W!1)) | (~pair_in_list(U!3, V!2, W!1)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(X!0, W!1)) | pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~pair_in_list(U!3, V!2, W!1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(U!3, X!0), V!2, W!1) | (~less_than(X!0, W!1)) | (~pair_in_list(U!3, V!2, W!1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 41, 28, 23, 27])).
% 0.12/0.40 % SZS output end Proof
%------------------------------------------------------------------------------