TSTP Solution File: SWV409+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 15:11:40 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n026.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 : Sun Sep 4 03:07:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(less_than_type, type, (
% 0.12/0.40 less_than: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_W_0_type, type, (
% 0.12/0.40 tptp_fun_W_0: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_U_4_type, type, (
% 0.12/0.40 tptp_fun_U_4: $i)).
% 0.12/0.40 tff(tptp_fun_V_3_type, type, (
% 0.12/0.40 tptp_fun_V_3: $i)).
% 0.12/0.40 tff(tptp_fun_W_2_type, type, (
% 0.12/0.40 tptp_fun_W_2: $i)).
% 0.12/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.40 tptp_fun_Y_1: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(pair_in_list_type, type, (
% 0.12/0.40 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(update_slb_type, type, (
% 0.12/0.40 update_slb: ( $i * $i ) > $i)).
% 0.12/0.40 tff(strictly_less_than_type, type, (
% 0.12/0.40 strictly_less_than: ( $i * $i ) > $o)).
% 0.12/0.40 tff(contains_slb_type, type, (
% 0.12/0.40 contains_slb: ( $i * $i ) > $o)).
% 0.12/0.40 tff(1,assumption,(~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))) | less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))) | pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[X: $i] : refl(((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X))) <=> ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X))) <=> ![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (^[X: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X)) <=> (~((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X))))), ((~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) <=> (~(~((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X))))))), rewrite((~(~((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X))))) <=> ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))), ((~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) <=> ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) <=> ![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 ((![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) & (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)) & (contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2))) <=> (![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) & (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)) & contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 ((~(~(contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2)))) <=> (contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 ((![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) & (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)) & (~(~(contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2))))) <=> (![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) & (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)) & (contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[11])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 ((![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) & (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)) & (~(~(contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2))))) <=> (![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) & (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)) & contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2))),
% 0.12/0.40 inference(transitivity,[status(thm)],[12, 10])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 ((~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))) <=> (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 ((~![U: $i, V: $i, W: $i] : ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X))))) <=> (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(16,axiom,(~![U: $i, V: $i, W: $i] : ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l45_co')).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X))) & (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)) & contains_slb(U!4, V!3) & strictly_less_than(V!3, W!2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X)))),
% 0.12/0.40 inference(and_elim,[status(thm)],[24])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[25, 9])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[26, 7])).
% 0.12/0.41 tff(28,plain,
% 0.12/0.41 (((~![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))) | ((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))) <=> ((~![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))) | (~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 ((~![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))) | ((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 ((~![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))) | (~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[30, 27, 5, 3])).
% 0.12/0.41 tff(32,plain,((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.41 tff(33,assumption,(less_than(W!2, tptp_fun_W_0(V!3, U!4))), introduced(assumption)).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 (contains_slb(U!4, V!3)),
% 0.12/0.41 inference(and_elim,[status(thm)],[24])).
% 0.12/0.41 tff(35,plain,
% 0.12/0.41 (^[U: $i, V: $i] : refl(((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))) <=> ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 (![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W)) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 (^[U: $i, V: $i] : rewrite((contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W)) <=> ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 (![U: $i, V: $i] : (contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W)) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.41 tff(40,axiom,(![U: $i, V: $i] : (contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l45_li4647')).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.41 tff(43,plain,(
% 0.12/0.41 ![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[42])).
% 0.12/0.41 tff(44,plain,
% 0.12/0.41 (![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | ((~contains_slb(U!4, V!3)) | pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4)))) <=> ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | (~contains_slb(U!4, V!3)) | pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | ((~contains_slb(U!4, V!3)) | pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | (~contains_slb(U!4, V!3)) | pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 (strictly_less_than(V!3, W!2)),
% 0.12/0.41 inference(and_elim,[status(thm)],[24])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U)))))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U)))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U)))))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W)) <=> (~((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X))))), ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) <=> (~(~((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X))))))), rewrite((~(~((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X))))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)))), ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X))))), rewrite((pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U)) & less_than(X, tptp_fun_Y_1(X, V, U))) <=> (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U)))))), (((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | (pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U)) & less_than(X, tptp_fun_Y_1(X, V, U)))) <=> (((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X))) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U)))))))), rewrite((((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X))) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U)))))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))), (((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | (pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U)) & less_than(X, tptp_fun_Y_1(X, V, U)))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | (pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U)) & less_than(X, tptp_fun_Y_1(X, V, U)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite(((pair_in_list(U, V, W) & strictly_less_than(V, X)) & less_than(X, W)) <=> (pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))), ((((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))) <=> ((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))))), rewrite(((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))) <=> ((~(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)))), ((((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))) <=> ((~(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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.41 tff(57,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','l45_l49')).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.41 tff(60,plain,(
% 0.19/0.41 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & less_than(X, W))) | (pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U)) & less_than(X, tptp_fun_Y_1(X, V, U))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[59])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | ((~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (((~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))))) <=> ((~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))) <=> (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))))) <=> ((~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))))) <=> ((~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | ((~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | ((~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | ((~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[68, 63])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | ((~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[71, 62, 49, 48, 33, 32])).
% 0.19/0.42 tff(73,plain,(~less_than(W!2, tptp_fun_W_0(V!3, U!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(79,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')).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.42 tff(81,plain,(
% 0.19/0.42 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2) <=> (~((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2) <=> (~((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)),
% 0.19/0.42 inference(and_elim,[status(thm)],[24])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl((pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X)) <=> (~((~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))))), ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) <=> (~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))))))), rewrite((~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))), ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))))), (((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (((~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))), rewrite((((~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))), (((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite(((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) <=> (pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))), ((((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)))), rewrite(((pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))), ((((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.42 tff(94,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l45_l48')).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.42 tff(97,plain,(
% 0.19/0.42 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[96])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2))) <=> (pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(V!3, W!2)) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~strictly_less_than(W, X)))) | pair_in_list(update_slb(U!4, W!2), V!3, W!2) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 99, 86, 49, 48])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((~(strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2) <=> (~((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))))) | strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2) | ((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ((~(strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2) <=> (~((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))))) | ((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[108, 85])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))) | (~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (~less_than(tptp_fun_W_0(V!3, U!4), W!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 73])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.43 tff(118,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.19/0.43 tff(121,plain,(
% 0.19/0.43 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(skolemize,[status(sab)],[120])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(V!3, U!4), W!2) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(tptp_fun_W_0(V!3, U!4), W!2) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(V!3, U!4), W!2) | less_than(W!2, tptp_fun_W_0(V!3, U!4)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(tptp_fun_W_0(V!3, U!4), W!2) | less_than(W!2, tptp_fun_W_0(V!3, U!4))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[125, 122, 112, 73])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------