%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV408+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SWV408+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 09:45:41 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(strictly_less_than_type, type, (
% 0.23/0.42 strictly_less_than: ( $i * $i ) > $o)).
% 0.23/0.42 tff(findmin_pqp_res_type, type, (
% 0.23/0.42 findmin_pqp_res: $i > $i)).
% 0.23/0.42 tff(tptp_fun_U_4_type, type, (
% 0.23/0.42 tptp_fun_U_4: $i)).
% 0.23/0.42 tff(tptp_fun_X_1_type, type, (
% 0.23/0.42 tptp_fun_X_1: $i)).
% 0.23/0.42 tff(findmin_cpq_res_type, type, (
% 0.23/0.42 findmin_cpq_res: $i > $i)).
% 0.23/0.42 tff(triple_type, type, (
% 0.23/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_W_2_type, type, (
% 0.23/0.42 tptp_fun_W_2: $i)).
% 0.23/0.42 tff(tptp_fun_V_3_type, type, (
% 0.23/0.42 tptp_fun_V_3: $i)).
% 0.23/0.42 tff(create_slb_type, type, (
% 0.23/0.42 create_slb: $i)).
% 0.23/0.42 tff(contains_slb_type, type, (
% 0.23/0.42 contains_slb: ( $i * $i ) > $o)).
% 0.23/0.42 tff(pair_in_list_type, type, (
% 0.23/0.42 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(update_slb_type, type, (
% 0.23/0.42 update_slb: ( $i * $i ) > $i)).
% 0.23/0.42 tff(less_than_type, type, (
% 0.23/0.42 less_than: ( $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_X_0_type, type, (
% 0.23/0.42 tptp_fun_X_0: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(1,assumption,(V!3 = create_slb), introduced(assumption)).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 (create_slb = V!3),
% 0.23/0.42 inference(symmetry,[status(thm)],[1])).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (contains_slb(create_slb, X!1) <=> contains_slb(V!3, X!1)),
% 0.23/0.42 inference(monotonicity,[status(thm)],[2])).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (contains_slb(V!3, X!1) <=> contains_slb(create_slb, X!1)),
% 0.23/0.42 inference(symmetry,[status(thm)],[3])).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 ((![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))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 ((~![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)))))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 ((~![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)))))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 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/sandbox2/benchmark/theBenchmark.p','l44_co')).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (~![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))))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 (~![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))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.23/0.43 tff(11,plain,
% 0.23/0.43 (~![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))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.23/0.43 tff(12,plain,
% 0.23/0.43 (~![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))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.23/0.43 tff(13,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.23/0.43 tff(14,plain,
% 0.23/0.43 (contains_slb(V!3, X!1)),
% 0.23/0.43 inference(and_elim,[status(thm)],[13])).
% 0.23/0.43 tff(15,plain,
% 0.23/0.43 (contains_slb(create_slb, X!1)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.23/0.43 tff(16,plain,
% 0.23/0.43 (^[U: $i] : refl((~contains_slb(create_slb, U)) <=> (~contains_slb(create_slb, U)))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(17,plain,
% 0.23/0.43 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.23/0.43 tff(18,plain,
% 0.23/0.43 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(19,axiom,(![U: $i] : (~contains_slb(create_slb, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax20')).
% 0.23/0.43 tff(20,plain,
% 0.23/0.43 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.23/0.43 tff(21,plain,(
% 0.23/0.43 ![U: $i] : (~contains_slb(create_slb, U))),
% 0.23/0.43 inference(skolemize,[status(sab)],[20])).
% 0.23/0.43 tff(22,plain,
% 0.23/0.43 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.23/0.43 tff(23,plain,
% 0.23/0.43 ((~![U: $i] : (~contains_slb(create_slb, U))) | (~contains_slb(create_slb, X!1))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(24,plain,
% 0.23/0.43 (~contains_slb(create_slb, X!1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.23/0.43 tff(25,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[24, 15])).
% 0.23/0.43 tff(26,plain,(~(V!3 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(27,plain,
% 0.23/0.43 (^[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))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(28,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.23/0.43 tff(29,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(30,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.43 tff(31,plain,
% 0.23/0.43 (^[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))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(32,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[31])).
% 0.23/0.43 tff(33,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[32, 30])).
% 0.23/0.43 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/sandbox2/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.23/0.43 tff(35,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.43 tff(36,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.23/0.43 tff(37,plain,(
% 0.23/0.43 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[36])).
% 0.23/0.43 tff(38,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[37, 28])).
% 0.23/0.43 tff(39,plain,
% 0.23/0.43 (((~![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)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(40,plain,
% 0.23/0.43 ((~![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)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(41,plain,
% 0.23/0.43 ((~![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))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.23/0.43 tff(42,plain,
% 0.23/0.43 ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.23/0.43 tff(43,plain,
% 0.23/0.43 (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[42, 26])).
% 0.23/0.43 tff(44,plain,
% 0.23/0.43 (findmin_pqp_res(U!4) = findmin_cpq_res(triple(U!4, V!3, W!2))),
% 0.23/0.43 inference(symmetry,[status(thm)],[43])).
% 0.23/0.43 tff(45,plain,
% 0.23/0.43 (strictly_less_than(X!1, findmin_pqp_res(U!4)) <=> strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[44])).
% 0.23/0.43 tff(46,plain,
% 0.23/0.43 (strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))) <=> strictly_less_than(X!1, findmin_pqp_res(U!4))),
% 0.23/0.43 inference(symmetry,[status(thm)],[45])).
% 0.23/0.43 tff(47,plain,
% 0.23/0.43 (strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.23/0.43 inference(and_elim,[status(thm)],[13])).
% 0.23/0.43 tff(48,plain,
% 0.23/0.43 (strictly_less_than(X!1, findmin_pqp_res(U!4))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.23/0.43 tff(49,assumption,(~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))), introduced(assumption)).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 (((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))) | less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(51,plain,
% 0.23/0.43 (less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.23/0.43 tff(52,plain,
% 0.23/0.43 (((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(53,plain,
% 0.23/0.43 (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.23/0.43 tff(54,plain,
% 0.23/0.43 (^[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))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(55,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[54])).
% 0.23/0.43 tff(56,plain,
% 0.23/0.43 (^[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)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(57,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.23/0.43 tff(58,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(and_elim,[status(thm)],[13])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.23/0.43 tff(60,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (((~![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_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), 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)))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(62,plain,
% 0.23/0.43 ((~![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_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(63,plain,
% 0.23/0.43 ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.23/0.43 tff(64,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[63, 60, 53, 51])).
% 0.23/0.43 tff(65,plain,((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(66,plain,
% 0.23/0.43 (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))),
% 0.23/0.43 inference(and_elim,[status(thm)],[13])).
% 0.23/0.43 tff(67,plain,
% 0.23/0.43 (^[U: $i, V: $i, W: $i] : refl((pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))) <=> (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(68,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))) <=> ![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.23/0.43 tff(69,plain,
% 0.23/0.43 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(U, V) & strictly_less_than(V, W)) <=> (~((~contains_slb(U, V)) | (~strictly_less_than(V, W))))), ((~(contains_slb(U, V) & strictly_less_than(V, W))) <=> (~(~((~contains_slb(U, V)) | (~strictly_less_than(V, W))))))), rewrite((~(~((~contains_slb(U, V)) | (~strictly_less_than(V, W))))) <=> ((~contains_slb(U, V)) | (~strictly_less_than(V, W)))), ((~(contains_slb(U, V) & strictly_less_than(V, W))) <=> ((~contains_slb(U, V)) | (~strictly_less_than(V, W))))), rewrite((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) <=> (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))), ((pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))) <=> (pair_in_list(update_slb(U, W), V, W) | ((~contains_slb(U, V)) | (~strictly_less_than(V, W))) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))))), rewrite((pair_in_list(update_slb(U, W), V, W) | ((~contains_slb(U, V)) | (~strictly_less_than(V, W))) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))) <=> (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))), ((pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))) <=> (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))) <=> ![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.23/0.44 tff(71,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i] : rewrite(((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))) <=> (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))) <=> ![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))) <=> ![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X))) <=> (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))), (((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))))), rewrite(((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))), (((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> ![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[74])).
% 0.23/0.44 tff(76,axiom,(![U: $i, V: $i, W: $i] : ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l44_l45')).
% 0.23/0.44 tff(77,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.23/0.44 tff(78,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.23/0.44 tff(79,plain,(
% 0.23/0.44 ![U: $i, V: $i, W: $i] : ((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.23/0.44 inference(skolemize,[status(sab)],[78])).
% 0.23/0.44 tff(80,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.23/0.44 tff(81,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.23/0.44 tff(82,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[81, 68])).
% 0.23/0.44 tff(83,plain,
% 0.23/0.44 (((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))))) <=> ((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(84,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(85,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.23/0.44 tff(86,plain,
% 0.23/0.44 ((~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[85, 82, 66, 14])).
% 0.23/0.44 tff(87,plain,
% 0.23/0.44 (~strictly_less_than(X!1, findmin_pqp_res(U!4))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[86, 65])).
% 0.23/0.44 tff(88,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[87, 48])).
% 0.23/0.44 % SZS output end Proof
% 0.23/0.44 % E exiting
%------------------------------------------------------------------------------