%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV408+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV408+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:45:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(less_than_type, type, (
% 0.11/0.38 less_than: ( $i * $i ) > $o)).
% 0.11/0.38 tff(findmin_cpq_res_type, type, (
% 0.11/0.38 findmin_cpq_res: $i > $i)).
% 0.11/0.38 tff(triple_type, type, (
% 0.11/0.38 triple: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_W_2_type, type, (
% 0.11/0.38 tptp_fun_W_2: $i)).
% 0.11/0.38 tff(tptp_fun_V_3_type, type, (
% 0.11/0.38 tptp_fun_V_3: $i)).
% 0.11/0.38 tff(tptp_fun_U_4_type, type, (
% 0.11/0.38 tptp_fun_U_4: $i)).
% 0.11/0.38 tff(tptp_fun_W_0_type, type, (
% 0.11/0.38 tptp_fun_W_0: ( $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_X_1_type, type, (
% 0.11/0.38 tptp_fun_X_1: $i)).
% 0.11/0.38 tff(findmin_pqp_res_type, type, (
% 0.11/0.38 findmin_pqp_res: $i > $i)).
% 0.11/0.38 tff(create_slb_type, type, (
% 0.11/0.38 create_slb: $i)).
% 0.11/0.38 tff(contains_slb_type, type, (
% 0.11/0.38 contains_slb: ( $i * $i ) > $o)).
% 0.11/0.38 tff(strictly_less_than_type, type, (
% 0.11/0.38 strictly_less_than: ( $i * $i ) > $o)).
% 0.11/0.38 tff(pair_in_list_type, type, (
% 0.11/0.38 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(update_slb_type, type, (
% 0.11/0.38 update_slb: ( $i * $i ) > $i)).
% 0.11/0.38 tff(1,assumption,(V!3 = create_slb), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (create_slb = V!3),
% 0.11/0.38 inference(symmetry,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (contains_slb(create_slb, X!1) <=> contains_slb(V!3, X!1)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (contains_slb(V!3, X!1) <=> contains_slb(create_slb, X!1)),
% 0.11/0.38 inference(symmetry,[status(thm)],[3])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 ((![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & (contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))) <=> (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 ((~![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)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 ((~![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)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(8,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','l44_co')).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (~![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))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (~![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))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (~![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))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (~![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))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (contains_slb(V!3, X!1)),
% 0.11/0.38 inference(and_elim,[status(thm)],[13])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (contains_slb(create_slb, X!1)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (^[U: $i] : refl((~contains_slb(create_slb, U)) <=> (~contains_slb(create_slb, U)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(19,axiom,(![U: $i] : (~contains_slb(create_slb, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax20')).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.38 tff(21,plain,(
% 0.11/0.38 ![U: $i] : (~contains_slb(create_slb, U))),
% 0.11/0.38 inference(skolemize,[status(sab)],[20])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 ((~![U: $i] : (~contains_slb(create_slb, U))) | (~contains_slb(create_slb, X!1))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (~contains_slb(create_slb, X!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[24, 15])).
% 0.11/0.38 tff(26,plain,(~(V!3 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[32, 30])).
% 0.11/0.38 tff(34,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')).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.11/0.38 tff(37,plain,(
% 0.11/0.38 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[36])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 28])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[42, 26])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) <=> less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)) <=> less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.11/0.38 inference(symmetry,[status(thm)],[44])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) <=> (~less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) <=> less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) <=> (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))) = update_slb(V!3, findmin_pqp_res(U!4))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) <=> pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3)) <=> pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.39 inference(symmetry,[status(thm)],[50])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))) <=> (~pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.11/0.39 tff(53,assumption,(less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))), introduced(assumption)).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 (less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[53, 47])).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 (^[Y: $i] : refl(((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))) <=> ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))) <=> ![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (^[Y: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y)) <=> (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))), ((~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) <=> (~(~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))))), rewrite((~(~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))) <=> ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))), ((~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) <=> ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(58,plain,
% 0.11/0.39 (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) <=> ![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y)))),
% 0.11/0.39 inference(and_elim,[status(thm)],[13])).
% 0.11/0.39 tff(60,plain,
% 0.11/0.39 (![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | ((~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))))) <=> ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))) <=> ((~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))))) <=> ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | ((~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3)))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[63])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 (((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))))) <=> ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[64, 62])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[67, 61, 54])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 (~pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[68, 52])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (^[U: $i, V: $i] : refl(((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))) <=> ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W)) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (^[U: $i, V: $i] : rewrite((contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W)) <=> ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 (![U: $i, V: $i] : (contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W)) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.11/0.39 tff(75,axiom,(![U: $i, V: $i] : (contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l45_li4647')).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.11/0.39 tff(77,plain,
% 0.11/0.39 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.11/0.39 tff(78,plain,(
% 0.11/0.39 ![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[77])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 (![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 (((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | ((~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | (~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | ((~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | (~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[82, 79, 14])).
% 0.11/0.39 tff(84,plain,
% 0.11/0.39 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[84])).
% 0.11/0.39 tff(86,plain,
% 0.11/0.39 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & less_than(X, W)) <=> (~((~less_than(X, W)) | (~pair_in_list(U, V, W))))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> (~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))))), rewrite((~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W))))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> (((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)))), rewrite((((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(89,plain,
% 0.11/0.39 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) <=> ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(90,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.11/0.40 tff(91,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l49_li3637')).
% 0.11/0.40 tff(92,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.11/0.40 tff(93,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.11/0.40 tff(94,plain,(
% 0.11/0.40 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.11/0.40 inference(skolemize,[status(sab)],[93])).
% 0.11/0.40 tff(95,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.11/0.40 tff(96,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.11/0.40 tff(97,plain,
% 0.11/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(98,plain,
% 0.11/0.40 (((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))) <=> ((~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(99,plain,
% 0.11/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.11/0.40 tff(100,plain,
% 0.11/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.40 inference(transitivity,[status(thm)],[99, 97])).
% 0.11/0.40 tff(101,plain,
% 0.11/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(102,plain,
% 0.11/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.11/0.40 tff(103,plain,
% 0.11/0.40 (pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[102, 96, 83, 53])).
% 0.11/0.40 tff(104,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[103, 69])).
% 0.11/0.40 tff(105,plain,(~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.40 tff(106,plain,
% 0.11/0.40 (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[105, 48])).
% 0.11/0.40 tff(107,plain,
% 0.11/0.40 (^[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))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(108,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[107])).
% 0.11/0.40 tff(109,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(110,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[109])).
% 0.11/0.40 tff(111,plain,
% 0.11/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(112,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')).
% 0.11/0.40 tff(113,plain,
% 0.11/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.11/0.40 tff(114,plain,(
% 0.11/0.40 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[113])).
% 0.11/0.40 tff(115,plain,
% 0.11/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.11/0.40 tff(116,plain,
% 0.11/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.11/0.40 tff(117,plain,
% 0.11/0.40 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) <=> strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(118,plain,
% 0.11/0.40 (~(((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) <=> strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.11/0.40 tff(119,plain,
% 0.11/0.40 (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))),
% 0.11/0.40 inference(and_elim,[status(thm)],[13])).
% 0.11/0.40 tff(120,plain,
% 0.11/0.40 (^[U: $i, V: $i, W: $i, X: $i] : refl((pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) <=> (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(121,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[120])).
% 0.11/0.40 tff(122,plain,
% 0.11/0.40 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(W, X)) <=> (~((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> (~(~((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))))), rewrite((~(~((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))) <=> ((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> ((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, X)))), rewrite((((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(123,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[122])).
% 0.11/0.40 tff(124,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(125,plain,
% 0.11/0.40 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(126,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[125])).
% 0.11/0.40 tff(127,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l48_li3839')).
% 0.11/0.40 tff(128,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.11/0.40 tff(129,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.11/0.40 tff(130,plain,(
% 0.11/0.40 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.11/0.40 inference(skolemize,[status(sab)],[129])).
% 0.11/0.40 tff(131,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.11/0.40 tff(132,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.11/0.40 tff(133,plain,
% 0.11/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(134,plain,
% 0.11/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(135,plain,
% 0.11/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.11/0.40 tff(136,plain,
% 0.11/0.40 (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[135, 132, 119, 83])).
% 0.11/0.40 tff(137,plain,
% 0.11/0.40 ((((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) <=> strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(138,plain,
% 0.11/0.40 ((((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) <=> strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.11/0.40 tff(139,plain,
% 0.11/0.40 ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[138, 118])).
% 0.11/0.40 tff(140,plain,
% 0.11/0.40 ((~((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))) | (~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 (~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[141, 106])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (~less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[142, 46])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[147])).
% 0.19/0.41 tff(149,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.19/0.41 tff(152,plain,(
% 0.19/0.41 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.41 inference(skolemize,[status(sab)],[151])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 ((less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) <=> (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 153, 105])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[160, 143])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------