%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV409+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:24 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV409+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:45:47 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(less_than_type, type, (
% 0.11/0.37 less_than: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_W_0_type, type, (
% 0.11/0.37 tptp_fun_W_0: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_U_4_type, type, (
% 0.11/0.37 tptp_fun_U_4: $i)).
% 0.11/0.37 tff(tptp_fun_V_3_type, type, (
% 0.11/0.37 tptp_fun_V_3: $i)).
% 0.11/0.37 tff(tptp_fun_W_2_type, type, (
% 0.11/0.37 tptp_fun_W_2: $i)).
% 0.11/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.37 tptp_fun_Y_1: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(pair_in_list_type, type, (
% 0.11/0.37 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(update_slb_type, type, (
% 0.11/0.37 update_slb: ( $i * $i ) > $i)).
% 0.11/0.37 tff(strictly_less_than_type, type, (
% 0.11/0.37 strictly_less_than: ( $i * $i ) > $o)).
% 0.11/0.37 tff(contains_slb_type, type, (
% 0.11/0.37 contains_slb: ( $i * $i ) > $o)).
% 0.11/0.37 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)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (((~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))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (((~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))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (^[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))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (^[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)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((![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))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~![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)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 ((~![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)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(13,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')).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (~![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))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (~![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))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~![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))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (~![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))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![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)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![X: $i] : (~(pair_in_list(update_slb(U!4, W!2), V!3, X) & less_than(W!2, X)))),
% 0.11/0.37 inference(and_elim,[status(thm)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (((~![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))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((~![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))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~![X: $i] : ((~pair_in_list(update_slb(U!4, W!2), V!3, X)) | (~less_than(W!2, X)))) | (~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[24, 21, 5, 3])).
% 0.11/0.37 tff(26,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,[]))).
% 0.11/0.37 tff(27,assumption,(less_than(W!2, tptp_fun_W_0(V!3, U!4))), introduced(assumption)).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (contains_slb(U!4, V!3)),
% 0.11/0.37 inference(and_elim,[status(thm)],[18])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (^[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))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (^[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)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.11/0.38 tff(34,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')).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.11/0.38 tff(37,plain,(
% 0.11/0.38 ![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[36])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (((~![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 ((~![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)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 ((~![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))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (strictly_less_than(V!3, W!2)),
% 0.11/0.38 inference(and_elim,[status(thm)],[18])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (^[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)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (^[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))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.38 tff(51,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')).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.38 tff(54,plain,(
% 0.19/0.38 ![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))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[53])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![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))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![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))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (((~![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))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (((~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))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 ((~((~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)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (((~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))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (((~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))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (((~![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)))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (((~![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))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[62, 57])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ((~![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))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | (~pair_in_list(U, V, W)) | (~strictly_less_than(V, X)) | (~((~pair_in_list(update_slb(U, X), V, tptp_fun_Y_1(X, V, U))) | (~less_than(X, tptp_fun_Y_1(X, V, U))))))) | (~strictly_less_than(V!3, W!2)) | (~pair_in_list(U!4, V!3, tptp_fun_W_0(V!3, U!4))) | (~less_than(W!2, tptp_fun_W_0(V!3, U!4))) | (~((~pair_in_list(update_slb(U!4, W!2), V!3, tptp_fun_Y_1(W!2, V!3, U!4))) | (~less_than(W!2, tptp_fun_Y_1(W!2, V!3, U!4)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[65, 56, 43, 42, 27, 26])).
% 0.19/0.38 tff(67,plain,(~less_than(W!2, tptp_fun_W_0(V!3, U!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (^[U: $i, V: $i] : refl((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((less_than(U, V) & (~less_than(V, U))) <=> (~((~less_than(U, V)) | less_than(V, U)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))), rewrite((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))), rewrite((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(73,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')).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.39 tff(75,plain,(
% 0.19/0.39 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[74])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_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))) <=> strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (~(((~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))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (~pair_in_list(update_slb(U!4, W!2), V!3, W!2)),
% 0.19/0.39 inference(and_elim,[status(thm)],[18])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.39 tff(88,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')).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.39 tff(91,plain,(
% 0.19/0.39 ![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))),
% 0.19/0.39 inference(skolemize,[status(sab)],[90])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 ((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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (((~![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))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 ((~![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)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~![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))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (~strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 93, 80, 43, 42])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 ((((~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))) | strictly_less_than(tptp_fun_W_0(V!3, U!4), W!2)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 ((((~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)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 ((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[102, 79])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 ((~((~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))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 ((~less_than(tptp_fun_W_0(V!3, U!4), W!2)) | less_than(W!2, tptp_fun_W_0(V!3, U!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (~less_than(tptp_fun_W_0(V!3, U!4), W!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[105, 67])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.39 tff(112,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.19/0.39 tff(115,plain,(
% 0.19/0.39 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.39 inference(skolemize,[status(sab)],[114])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.19/0.39 tff(117,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(118,plain,
% 0.19/0.39 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(tptp_fun_W_0(V!3, U!4), W!2) | less_than(W!2, tptp_fun_W_0(V!3, U!4))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[119, 116, 106, 67])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------