%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV407+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:32:23 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV407+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:45:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(check_cpq_type, type, (
% 0.13/0.40 check_cpq: $i > $o)).
% 0.13/0.40 tff(triple_type, type, (
% 0.13/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_W_3_type, type, (
% 0.13/0.40 tptp_fun_W_3: $i)).
% 0.13/0.40 tff(update_slb_type, type, (
% 0.13/0.40 update_slb: ( $i * $i ) > $i)).
% 0.13/0.40 tff(findmin_pqp_res_type, type, (
% 0.13/0.40 findmin_pqp_res: $i > $i)).
% 0.13/0.40 tff(tptp_fun_U_5_type, type, (
% 0.13/0.40 tptp_fun_U_5: $i)).
% 0.13/0.40 tff(tptp_fun_V_4_type, type, (
% 0.13/0.40 tptp_fun_V_4: $i)).
% 0.13/0.40 tff(findmin_cpq_eff_type, type, (
% 0.13/0.40 findmin_cpq_eff: $i > $i)).
% 0.13/0.40 tff(contains_slb_type, type, (
% 0.13/0.40 contains_slb: ( $i * $i ) > $o)).
% 0.13/0.40 tff(bad_type, type, (
% 0.13/0.40 bad: $i)).
% 0.13/0.40 tff(less_than_type, type, (
% 0.13/0.40 less_than: ( $i * $i ) > $o)).
% 0.13/0.40 tff(pair_in_list_type, type, (
% 0.13/0.40 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_X_6_type, type, (
% 0.13/0.40 tptp_fun_X_6: $i)).
% 0.13/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.13/0.40 tptp_fun_Y_2: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(findmin_cpq_res_type, type, (
% 0.13/0.40 findmin_cpq_res: $i > $i)).
% 0.13/0.40 tff(create_slb_type, type, (
% 0.13/0.40 create_slb: $i)).
% 0.13/0.40 tff(contains_cpq_type, type, (
% 0.13/0.40 contains_cpq: ( $i * $i ) > $o)).
% 0.13/0.40 tff(strictly_less_than_type, type, (
% 0.13/0.40 strictly_less_than: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_X_1_type, type, (
% 0.13/0.40 tptp_fun_X_1: $i > $i)).
% 0.13/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.40 tptp_fun_Y_0: $i > $i)).
% 0.13/0.40 tff(lookup_slb_type, type, (
% 0.13/0.40 lookup_slb: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,assumption,(less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)), introduced(assumption)).
% 0.13/0.40 tff(2,assumption,(V!4 = create_slb), introduced(assumption)).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (create_slb = V!4),
% 0.13/0.40 inference(symmetry,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (contains_slb(create_slb, X!6) <=> contains_slb(V!4, X!6)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (contains_slb(V!4, X!6) <=> contains_slb(create_slb, X!6)),
% 0.13/0.40 inference(symmetry,[status(thm)],[4])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(9,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax39')).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.40 tff(11,plain,(
% 0.13/0.40 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.13/0.40 inference(skolemize,[status(sab)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))) | (contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 ((check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & (contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 ((~![U: $i, V: $i, W: $i] : (?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(18,axiom,(~![U: $i, V: $i, W: $i] : (?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l43_co')).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (contains_cpq(triple(U!5, V!4, W!3), X!6)),
% 0.13/0.41 inference(and_elim,[status(thm)],[23])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 ((~(contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6))) | (~contains_cpq(triple(U!5, V!4, W!3), X!6)) | contains_slb(V!4, X!6)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 ((~(contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6))) | contains_slb(V!4, X!6)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (contains_slb(V!4, X!6)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[26, 14])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (contains_slb(create_slb, X!6)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[27, 5])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (^[U: $i] : refl((~contains_slb(create_slb, U)) <=> (~contains_slb(create_slb, U)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(32,axiom,(![U: $i] : (~contains_slb(create_slb, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax20')).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.41 tff(34,plain,(
% 0.13/0.41 ![U: $i] : (~contains_slb(create_slb, U))),
% 0.13/0.41 inference(skolemize,[status(sab)],[33])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 ((~![U: $i] : (~contains_slb(create_slb, U))) | (~contains_slb(create_slb, X!6))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (~contains_slb(create_slb, X!6)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[37, 28])).
% 0.13/0.41 tff(39,plain,(~(V!4 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[45, 43])).
% 0.13/0.41 tff(47,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.13/0.41 tff(50,plain,(
% 0.13/0.41 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[49])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[50, 41])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[55, 39])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5)) <=> less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)) <=> less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.13/0.41 inference(symmetry,[status(thm)],[57])).
% 0.13/0.41 tff(59,assumption,(~(V!4 = create_slb)), introduced(assumption)).
% 0.13/0.41 tff(60,assumption,(pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))), introduced(assumption)).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[55, 59])).
% 0.13/0.41 tff(62,assumption,(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)), introduced(assumption)).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) <=> pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) <=> pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.13/0.41 inference(symmetry,[status(thm)],[63])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 64])).
% 0.13/0.41 tff(66,assumption,(~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))), introduced(assumption)).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.13/0.41 tff(68,plain,(pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[68, 61, 60])).
% 0.13/0.41 tff(70,assumption,(![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), introduced(assumption)).
% 0.13/0.41 tff(71,assumption,(pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))), introduced(assumption)).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((less_than(U, V) & (~less_than(V, U))) <=> (~((~less_than(U, V)) | less_than(V, U)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))), rewrite((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))), rewrite((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(77,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.41 tff(79,plain,(
% 0.21/0.41 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[78])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)) <=> strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (~(((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)) <=> strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.41 inference(and_elim,[status(thm)],[23])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ((((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)) <=> strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 ((((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)) <=> strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[92, 89, 71, 70])).
% 0.21/0.42 tff(94,plain,((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[94, 69])).
% 0.21/0.42 tff(96,assumption,(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)), introduced(assumption)).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad) = findmin_cpq_eff(triple(U!5, V!4, W!3))),
% 0.21/0.42 inference(symmetry,[status(thm)],[96])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) <=> check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.42 inference(symmetry,[status(thm)],[98])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.42 inference(and_elim,[status(thm)],[23])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i] : refl((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i] : rewrite((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i] : trans(monotonicity(rewrite(((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))), rewrite((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i] : rewrite((check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.42 tff(112,axiom,(![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l43_li4142')).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.42 tff(115,plain,(
% 0.21/0.42 ![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[114])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5)))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))) | ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.42 tff(122,assumption,(~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), introduced(assumption)).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[125, 101])).
% 0.21/0.42 tff(127,plain,((~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[127, 95])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))))), rewrite((~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[136, 134])).
% 0.21/0.43 tff(138,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax47')).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[139, 133])).
% 0.21/0.43 tff(141,plain,(
% 0.21/0.43 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[140])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[141, 132])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[142, 130])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[146, 143])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (contains_slb(V!4, findmin_pqp_res(U!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[147, 128, 59])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.43 tff(150,assumption,(strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))), introduced(assumption)).
% 0.21/0.43 tff(151,assumption,(~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))), introduced(assumption)).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (contains_slb(V!4, findmin_pqp_res(U!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[147, 151, 59])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[153])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[159])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[160, 158])).
% 0.21/0.43 tff(162,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax48')).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[163, 157])).
% 0.21/0.43 tff(165,plain,(
% 0.21/0.43 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[164])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[165, 156])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[166, 154])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[170, 167])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[171, 152, 151, 59, 150])).
% 0.21/0.43 tff(173,plain,((findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (V!4 = create_slb) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(174,plain,
% 0.21/0.44 (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[173, 128, 59])).
% 0.21/0.44 tff(175,plain,
% 0.21/0.44 (strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) <=> strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[62])).
% 0.21/0.44 tff(176,plain,
% 0.21/0.44 (strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))) <=> strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(symmetry,[status(thm)],[175])).
% 0.21/0.44 tff(177,plain,
% 0.21/0.44 ((~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))) <=> (~strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[176])).
% 0.21/0.44 tff(178,assumption,(~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))), introduced(assumption)).
% 0.21/0.44 tff(179,plain,
% 0.21/0.44 (~strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.44 tff(180,plain,
% 0.21/0.44 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))) <=> strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(181,plain,
% 0.21/0.44 (~(((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))) <=> strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[180, 81])).
% 0.21/0.44 tff(182,assumption,(~((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))), introduced(assumption)).
% 0.21/0.44 tff(183,plain,
% 0.21/0.44 ((((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))) <=> strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | ((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(184,plain,
% 0.21/0.44 ((((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))) <=> strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.21/0.44 tff(185,plain,
% 0.21/0.44 (strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[184, 181])).
% 0.21/0.44 tff(186,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[185, 179])).
% 0.21/0.44 tff(187,plain,(strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5))) | ((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(188,plain,
% 0.21/0.44 ((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[187, 174, 61])).
% 0.21/0.44 tff(189,assumption,((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))), introduced(assumption)).
% 0.21/0.44 tff(190,assumption,(~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))), introduced(assumption)).
% 0.21/0.44 tff(191,plain,
% 0.21/0.44 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(192,plain,
% 0.21/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[191])).
% 0.21/0.44 tff(193,plain,
% 0.21/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(194,plain,
% 0.21/0.44 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(195,plain,
% 0.21/0.44 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[194])).
% 0.21/0.44 tff(196,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.21/0.44 tff(197,plain,
% 0.21/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.44 tff(198,plain,
% 0.21/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.21/0.44 tff(199,plain,(
% 0.21/0.44 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.44 inference(skolemize,[status(sab)],[198])).
% 0.21/0.44 tff(200,plain,
% 0.21/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.21/0.44 tff(201,plain,
% 0.21/0.44 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(202,plain,
% 0.21/0.44 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(203,plain,
% 0.21/0.44 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.44 tff(204,plain,
% 0.21/0.44 (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[203, 200, 190])).
% 0.21/0.44 tff(205,plain,
% 0.21/0.44 ((~((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(206,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[205, 204, 190, 189])).
% 0.21/0.44 tff(207,plain,(less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))) | (~((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(208,plain,
% 0.21/0.44 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[207, 188])).
% 0.21/0.44 tff(209,plain,
% 0.21/0.44 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[208, 149])).
% 0.21/0.44 tff(210,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(211,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[210])).
% 0.21/0.44 tff(212,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(213,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[212])).
% 0.21/0.44 tff(214,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(215,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.44 tff(216,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(217,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[216])).
% 0.21/0.45 tff(218,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[217, 215])).
% 0.21/0.45 tff(219,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax49')).
% 0.21/0.45 tff(220,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.45 tff(221,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[220, 214])).
% 0.21/0.45 tff(222,plain,(
% 0.21/0.45 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[221])).
% 0.21/0.45 tff(223,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[222, 213])).
% 0.21/0.45 tff(224,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[223, 211])).
% 0.21/0.45 tff(225,plain,
% 0.21/0.45 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(226,plain,
% 0.21/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(227,plain,
% 0.21/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.21/0.45 tff(228,plain,
% 0.21/0.45 ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[227, 224])).
% 0.21/0.45 tff(229,plain,
% 0.21/0.45 (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[228, 209, 59, 148])).
% 0.21/0.45 tff(230,plain,
% 0.21/0.45 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3) = findmin_cpq_eff(triple(U!5, V!4, W!3))),
% 0.21/0.45 inference(symmetry,[status(thm)],[229])).
% 0.21/0.45 tff(231,plain,
% 0.21/0.45 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) <=> check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[230])).
% 0.21/0.45 tff(232,plain,
% 0.21/0.45 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.45 inference(symmetry,[status(thm)],[231])).
% 0.21/0.45 tff(233,plain,
% 0.21/0.45 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[100, 232])).
% 0.21/0.45 tff(234,plain,
% 0.21/0.45 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(235,plain,
% 0.21/0.45 (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5)))))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[234, 117])).
% 0.21/0.45 tff(236,plain,
% 0.21/0.45 (((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))) | ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(237,plain,
% 0.21/0.45 ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.21/0.45 tff(238,plain,
% 0.21/0.45 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(239,plain,
% 0.21/0.45 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[238, 95])).
% 0.21/0.45 tff(240,plain,
% 0.21/0.45 (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[239, 237])).
% 0.21/0.45 tff(241,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[240, 233])).
% 0.21/0.45 tff(242,plain,((V!4 = create_slb) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(243,plain,
% 0.21/0.45 (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[242, 39])).
% 0.21/0.45 tff(244,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))) <=> ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(245,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[244])).
% 0.21/0.45 tff(246,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) <=> (~((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))), ((~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) <=> (~(~((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))))), rewrite((~(~((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))), ((~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))), rewrite((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) <=> (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))), ((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))) <=> (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))))), rewrite((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))) <=> ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))), ((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))) <=> ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(247,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[246])).
% 0.21/0.45 tff(248,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(249,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[248])).
% 0.21/0.45 tff(250,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(251,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y))) <=> (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)))), (((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)))) <=> ((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)))))), rewrite(((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)))) <=> (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))), (((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)))) <=> (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(252,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[251])).
% 0.21/0.45 tff(253,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l43_l44')).
% 0.21/0.45 tff(254,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.21/0.45 tff(255,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.21/0.46 tff(256,plain,(
% 0.21/0.46 ![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[255])).
% 0.21/0.46 tff(257,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[256, 249])).
% 0.21/0.46 tff(258,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[257, 247])).
% 0.21/0.46 tff(259,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[258, 245])).
% 0.21/0.46 tff(260,plain,
% 0.21/0.46 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | (~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(261,plain,
% 0.21/0.46 (((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))) <=> ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(262,plain,
% 0.21/0.46 ((~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))) <=> (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(263,plain,
% 0.21/0.46 (((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))) <=> ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[262])).
% 0.21/0.46 tff(264,plain,
% 0.21/0.46 (((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))) <=> ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[263, 261])).
% 0.21/0.46 tff(265,plain,
% 0.21/0.46 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[264])).
% 0.21/0.46 tff(266,plain,
% 0.21/0.46 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | (~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[265, 260])).
% 0.21/0.46 tff(267,plain,
% 0.21/0.46 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(268,plain,
% 0.21/0.46 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | (~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.21/0.46 tff(269,plain,
% 0.21/0.46 ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[268, 259, 84])).
% 0.21/0.46 tff(270,plain,
% 0.21/0.46 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[269, 27])).
% 0.21/0.46 tff(271,plain,
% 0.21/0.46 (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[270, 243])).
% 0.21/0.46 tff(272,plain,
% 0.21/0.46 (((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))) | less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(273,plain,
% 0.21/0.46 (less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.21/0.46 tff(274,plain,
% 0.21/0.46 (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[273, 58])).
% 0.21/0.46 tff(275,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V))) <=> ![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(276,plain,
% 0.21/0.46 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than(U, V) & less_than(V, W)) <=> (~((~less_than(V, W)) | (~less_than(U, V))))), ((~(less_than(U, V) & less_than(V, W))) <=> (~(~((~less_than(V, W)) | (~less_than(U, V))))))), rewrite((~(~((~less_than(V, W)) | (~less_than(U, V))))) <=> ((~less_than(V, W)) | (~less_than(U, V)))), ((~(less_than(U, V) & less_than(V, W))) <=> ((~less_than(V, W)) | (~less_than(U, V))))), (((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> (((~less_than(V, W)) | (~less_than(U, V))) | less_than(U, W)))), rewrite((((~less_than(V, W)) | (~less_than(U, V))) | less_than(U, W)) <=> (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))), (((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(277,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[276])).
% 0.21/0.46 tff(278,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(279,plain,
% 0.21/0.46 (^[U: $i, V: $i, W: $i] : rewrite(((less_than(U, V) & less_than(V, W)) => less_than(U, W)) <=> ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(280,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((less_than(U, V) & less_than(V, W)) => less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[279])).
% 0.21/0.46 tff(281,axiom,(![U: $i, V: $i, W: $i] : ((less_than(U, V) & less_than(V, W)) => less_than(U, W))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','transitivity')).
% 0.21/0.46 tff(282,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.21/0.46 tff(283,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.21/0.46 tff(284,plain,(
% 0.21/0.46 ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.46 inference(skolemize,[status(sab)],[283])).
% 0.21/0.46 tff(285,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[284, 277])).
% 0.21/0.46 tff(286,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[285, 275])).
% 0.21/0.46 tff(287,plain,
% 0.21/0.46 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(288,plain,
% 0.21/0.46 ((less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5)))) <=> (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(289,plain,
% 0.21/0.46 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[288])).
% 0.21/0.47 tff(290,plain,
% 0.21/0.47 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[289, 287])).
% 0.21/0.47 tff(291,plain,
% 0.21/0.47 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(292,plain,
% 0.21/0.47 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.21/0.47 tff(293,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[292, 286, 89, 274, 1])).
% 0.21/0.47 tff(294,plain,(~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(295,plain,
% 0.21/0.47 (((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(296,plain,
% 0.21/0.47 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[295, 271])).
% 0.21/0.47 tff(297,plain,
% 0.21/0.47 (((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(298,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(299,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.21/0.47 tff(300,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[299, 296, 70, 294])).
% 0.21/0.47 tff(301,plain,(~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(302,plain,
% 0.21/0.47 (~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[127, 301])).
% 0.21/0.47 tff(303,plain,
% 0.21/0.47 (contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[147, 39])).
% 0.21/0.47 tff(304,plain,
% 0.21/0.47 (contains_slb(V!4, findmin_pqp_res(U!5))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[303, 302])).
% 0.21/0.47 tff(305,plain,
% 0.21/0.47 (findmin_pqp_res(U!5) = findmin_cpq_res(triple(U!5, V!4, W!3))),
% 0.21/0.47 inference(symmetry,[status(thm)],[56])).
% 0.21/0.47 tff(306,plain,
% 0.21/0.47 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5)) <=> less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[305])).
% 0.21/0.47 tff(307,plain,
% 0.21/0.47 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))),
% 0.21/0.47 inference(symmetry,[status(thm)],[306])).
% 0.21/0.47 tff(308,plain,
% 0.21/0.47 ((findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[173, 39])).
% 0.21/0.47 tff(309,plain,
% 0.21/0.47 (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[308, 302])).
% 0.21/0.47 tff(310,plain,
% 0.21/0.47 (strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))) | ((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[187, 56])).
% 0.21/0.47 tff(311,plain,
% 0.21/0.47 ((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.21/0.47 tff(312,plain,
% 0.21/0.47 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[207, 311])).
% 0.21/0.47 tff(313,plain,
% 0.21/0.47 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[312, 307])).
% 0.21/0.47 tff(314,plain,
% 0.21/0.47 ((~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[228, 39])).
% 0.21/0.47 tff(315,plain,
% 0.21/0.47 (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[314, 313, 304])).
% 0.21/0.47 tff(316,plain,
% 0.21/0.47 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3) = findmin_cpq_eff(triple(U!5, V!4, W!3))),
% 0.21/0.47 inference(symmetry,[status(thm)],[315])).
% 0.21/0.47 tff(317,plain,
% 0.21/0.47 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) <=> check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[316])).
% 0.21/0.47 tff(318,plain,
% 0.21/0.47 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.47 inference(symmetry,[status(thm)],[317])).
% 0.21/0.47 tff(319,plain,
% 0.21/0.47 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[100, 318])).
% 0.21/0.47 tff(320,plain,
% 0.21/0.47 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[238, 301])).
% 0.21/0.47 tff(321,plain,
% 0.21/0.47 (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[320, 237])).
% 0.21/0.47 tff(322,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[321, 319])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------