%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM860+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:22:15 AM UTC 2025
% Result : Theorem 0.18s 0.44s
% Output : Proof 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM860+1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:06:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 % SZS output start Proof
% 0.18/0.44 tff(tptp_fun_Z_3_type, type, (
% 0.18/0.44 tptp_fun_Z_3: $i)).
% 0.18/0.44 tff(max_type, type, (
% 0.18/0.44 max: ( $i * $i ) > $i)).
% 0.18/0.44 tff(summation_type, type, (
% 0.18/0.44 summation: $i > $i)).
% 0.18/0.44 tff(tptp_fun_Y_4_type, type, (
% 0.18/0.44 tptp_fun_Y_4: $i)).
% 0.18/0.44 tff(tptp_fun_X_5_type, type, (
% 0.18/0.44 tptp_fun_X_5: $i)).
% 0.18/0.44 tff(lesseq_type, type, (
% 0.18/0.44 lesseq: ( $i * $i ) > $o)).
% 0.18/0.44 tff(model_max_type, type, (
% 0.18/0.44 model_max: ( $i * $i * $i ) > $o)).
% 0.18/0.44 tff(minsol_model_max_type, type, (
% 0.18/0.44 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.18/0.44 tff(tptp_fun_Z_1_type, type, (
% 0.18/0.44 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.18/0.44 tff(tptp_fun_Z_0_type, type, (
% 0.18/0.44 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.18/0.44 tff(ub_type, type, (
% 0.18/0.44 ub: ( $i * $i * $i ) > $o)).
% 0.18/0.44 tff(model_ub_type, type, (
% 0.18/0.44 model_ub: ( $i * $i * $i ) > $o)).
% 0.18/0.44 tff(minsol_model_ub_type, type, (
% 0.18/0.44 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.18/0.44 tff(tptp_fun_Z_2_type, type, (
% 0.18/0.44 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 0.18/0.44 tff(1,plain,
% 0.18/0.44 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N)) <=> (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(2,plain,
% 0.18/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.44 tff(3,plain,
% 0.18/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(4,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_max_3')).
% 0.18/0.44 tff(5,plain,
% 0.18/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.44 tff(6,plain,(
% 0.18/0.44 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))),
% 0.18/0.44 inference(skolemize,[status(sab)],[5])).
% 0.18/0.44 tff(7,plain,
% 0.18/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.44 tff(8,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))) | (model_max(X!5, Y!4, Z!3) <=> lesseq(summation(max(X!5, Y!4)), Z!3))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(9,plain,
% 0.18/0.44 (model_max(X!5, Y!4, Z!3) <=> lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.44 tff(10,assumption,(lesseq(Y!4, X!5)), introduced(assumption)).
% 0.18/0.44 tff(11,assumption,(~(max(X!5, Y!4) = X!5)), introduced(assumption)).
% 0.18/0.44 tff(12,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(13,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.44 tff(14,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(15,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = X) | (~lesseq(Y, X))) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(16,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.44 tff(17,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_1')).
% 0.18/0.44 tff(18,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.44 tff(19,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.44 tff(20,plain,(
% 0.18/0.44 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.18/0.44 inference(skolemize,[status(sab)],[19])).
% 0.18/0.44 tff(21,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.18/0.44 tff(22,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(23,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(24,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.44 tff(25,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[24, 21, 11, 10])).
% 0.18/0.44 tff(26,plain,((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(27,plain,
% 0.18/0.44 (max(X!5, Y!4) = X!5),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[26, 10])).
% 0.18/0.44 tff(28,plain,
% 0.18/0.44 (X!5 = max(X!5, Y!4)),
% 0.18/0.44 inference(symmetry,[status(thm)],[27])).
% 0.18/0.44 tff(29,plain,
% 0.18/0.44 (summation(X!5) = summation(max(X!5, Y!4))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[28])).
% 0.18/0.44 tff(30,plain,
% 0.18/0.44 (lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[29])).
% 0.18/0.44 tff(31,plain,
% 0.18/0.44 (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.44 inference(symmetry,[status(thm)],[30])).
% 0.18/0.44 tff(32,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))) | (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(33,plain,
% 0.18/0.44 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[32, 7])).
% 0.18/0.44 tff(34,assumption,(~minsol_model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))) | (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(36,plain,
% 0.18/0.44 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[35, 7])).
% 0.18/0.44 tff(37,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(38,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.44 tff(39,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(40,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lesseq_total')).
% 0.18/0.44 tff(41,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.44 tff(42,plain,(
% 0.18/0.44 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.18/0.44 inference(skolemize,[status(sab)],[41])).
% 0.18/0.44 tff(43,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.18/0.44 tff(44,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(45,plain,
% 0.18/0.44 ((lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(46,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[45])).
% 0.18/0.44 tff(47,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[46, 44])).
% 0.18/0.44 tff(48,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(49,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.44 tff(50,plain,
% 0.18/0.44 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.18/0.44 tff(51,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(52,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.44 tff(53,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(54,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(55,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.44 tff(56,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_2')).
% 0.18/0.44 tff(57,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.44 tff(58,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.18/0.44 tff(59,plain,(
% 0.18/0.44 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.18/0.44 inference(skolemize,[status(sab)],[58])).
% 0.18/0.44 tff(60,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.18/0.44 tff(61,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(62,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 (max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[64, 50])).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 (summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[65])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 (lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.45 tff(68,plain,
% 0.18/0.45 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.45 inference(symmetry,[status(thm)],[67])).
% 0.18/0.45 tff(69,plain,
% 0.18/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(70,plain,
% 0.18/0.45 ((lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(71,plain,
% 0.18/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.45 tff(72,plain,
% 0.18/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[71, 69])).
% 0.18/0.45 tff(73,plain,
% 0.18/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(74,plain,
% 0.18/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.45 tff(75,plain,
% 0.18/0.45 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[74, 43])).
% 0.18/0.45 tff(76,plain,
% 0.18/0.45 (lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.18/0.45 tff(77,plain,
% 0.18/0.45 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) | model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(78,plain,
% 0.18/0.45 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[77, 76, 36])).
% 0.18/0.45 tff(79,plain,
% 0.18/0.45 (^[X: $i, Y: $i, N: $i] : refl((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(80,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.45 tff(81,plain,
% 0.18/0.45 (^[X: $i, Y: $i, N: $i] : rewrite((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(82,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.45 tff(83,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[82, 80])).
% 0.18/0.45 tff(84,plain,
% 0.18/0.45 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) <=> ((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))), rewrite((minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))) <=> (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))), rewrite((((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(85,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.45 tff(86,plain,
% 0.18/0.45 (^[X: $i, Y: $i, N: $i] : rewrite((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))) <=> (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(87,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))) <=> ![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.45 tff(88,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(89,plain,
% 0.18/0.45 (^[X: $i, Y: $i, N: $i] : rewrite((minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z)))) <=> (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(90,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[89])).
% 0.18/0.45 tff(91,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','minsol_model_max')).
% 0.18/0.45 tff(92,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.45 tff(93,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.18/0.45 tff(94,plain,(
% 0.18/0.45 ![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[93])).
% 0.18/0.45 tff(95,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.18/0.45 tff(96,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.18/0.45 tff(97,plain,
% 0.18/0.45 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[96, 83])).
% 0.18/0.45 tff(98,plain,
% 0.18/0.45 (((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(99,plain,
% 0.18/0.45 ((~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))))))) <=> (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(100,plain,
% 0.18/0.45 (((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))))))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[99])).
% 0.18/0.45 tff(101,plain,
% 0.18/0.45 (((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[100, 98])).
% 0.18/0.45 tff(102,plain,
% 0.18/0.45 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(103,plain,
% 0.18/0.45 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.45 tff(104,plain,
% 0.18/0.45 (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.18/0.46 tff(105,plain,
% 0.18/0.46 (((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))) | ((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(106,plain,
% 0.18/0.46 ((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.18/0.46 tff(107,plain,
% 0.18/0.46 (((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))))) | ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(108,plain,
% 0.18/0.46 ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.18/0.46 tff(109,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))) | (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(110,plain,
% 0.18/0.46 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[109, 7])).
% 0.18/0.46 tff(111,plain,
% 0.18/0.46 (lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.46 tff(112,plain,
% 0.18/0.46 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.18/0.46 inference(symmetry,[status(thm)],[111])).
% 0.18/0.46 tff(113,plain,
% 0.18/0.46 ((~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))) <=> (~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(114,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))) <=> (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(115,axiom,(~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.18/0.46 tff(116,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.46 tff(117,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[116, 114])).
% 0.18/0.46 tff(118,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.18/0.46 tff(119,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.18/0.46 tff(120,plain,(
% 0.18/0.46 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.18/0.46 inference(skolemize,[status(sab)],[119])).
% 0.18/0.46 tff(121,plain,
% 0.18/0.46 (~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.18/0.46 tff(122,plain,
% 0.18/0.46 ((minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3)) | minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(123,plain,
% 0.18/0.46 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.18/0.46 tff(124,plain,
% 0.18/0.46 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[123, 34])).
% 0.18/0.46 tff(125,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(126,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[125])).
% 0.18/0.46 tff(127,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : refl((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(128,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[127])).
% 0.18/0.46 tff(129,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(130,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[129])).
% 0.18/0.46 tff(131,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[130, 128])).
% 0.18/0.46 tff(132,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) <=> ((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))), rewrite((minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))) <=> (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))), rewrite((((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(133,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[132])).
% 0.18/0.46 tff(134,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : rewrite((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))) <=> (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(135,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))) <=> ![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[134])).
% 0.18/0.46 tff(136,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(137,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : rewrite((minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z)))) <=> (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(138,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[137])).
% 0.18/0.46 tff(139,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.18/0.46 tff(140,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.18/0.46 tff(141,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.18/0.46 tff(142,plain,(
% 0.18/0.46 ![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[141])).
% 0.18/0.46 tff(143,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.18/0.46 tff(144,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.18/0.46 tff(145,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[144, 131])).
% 0.18/0.46 tff(146,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[145, 126])).
% 0.18/0.46 tff(147,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(148,plain,
% 0.18/0.46 (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.18/0.46 tff(149,plain,
% 0.18/0.46 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(150,plain,
% 0.18/0.46 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.18/0.46 tff(151,plain,
% 0.18/0.46 ((~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))) | (~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(152,plain,
% 0.18/0.46 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.18/0.46 tff(153,plain,
% 0.18/0.46 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[152, 124])).
% 0.18/0.46 tff(154,plain,
% 0.18/0.46 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | model_ub(X!5, Y!4, Z!3)),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(155,plain,
% 0.18/0.46 (model_ub(X!5, Y!4, Z!3)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.18/0.46 tff(156,assumption,((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))), introduced(assumption)).
% 0.18/0.46 tff(157,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(158,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[157])).
% 0.18/0.46 tff(159,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(160,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[159])).
% 0.18/0.46 tff(161,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[160, 158])).
% 0.18/0.46 tff(162,plain,
% 0.18/0.46 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(summation(tptp_fun_Z_0(N, Y, X)), N))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))), rewrite((model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(summation(Z), N)))) <=> (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(summation(tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(summation(Z), N))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(summation(tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(summation(Z), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(163,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(summation(tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(summation(Z), N))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[162])).
% 0.18/0.46 tff(164,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(summation(Z), N))) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(summation(Z), N)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(165,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(summation(Z), N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_ub_3')).
% 0.18/0.46 tff(166,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(summation(Z), N)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.46 tff(167,plain,(
% 0.18/0.46 ![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(summation(tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(summation(Z), N)))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[166])).
% 0.18/0.46 tff(168,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.18/0.46 tff(169,plain,
% 0.18/0.46 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.18/0.46 tff(170,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(171,plain,
% 0.18/0.46 ((~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))))) <=> (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(172,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[171])).
% 0.18/0.46 tff(173,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[172, 170])).
% 0.18/0.46 tff(174,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(175,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.46 tff(176,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[175, 169, 156])).
% 0.18/0.46 tff(177,plain,(~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(178,plain,
% 0.18/0.47 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))) | ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(179,plain,
% 0.18/0.47 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.18/0.47 tff(180,plain,
% 0.18/0.47 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))) | (~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(181,plain,
% 0.18/0.47 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.18/0.47 tff(182,plain,
% 0.18/0.47 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[181, 155])).
% 0.18/0.47 tff(183,plain,
% 0.18/0.47 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(184,plain,
% 0.18/0.47 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.18/0.47 tff(185,plain,
% 0.18/0.47 (lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[184, 112])).
% 0.18/0.47 tff(186,plain,
% 0.18/0.47 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))) | model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(187,plain,
% 0.18/0.47 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[186, 185, 110])).
% 0.18/0.47 tff(188,plain,
% 0.18/0.47 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | ![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(189,plain,
% 0.18/0.47 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[188, 153])).
% 0.18/0.47 tff(190,plain,
% 0.18/0.47 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))) | ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(191,plain,
% 0.18/0.47 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[190, 182])).
% 0.18/0.47 tff(192,plain,
% 0.18/0.47 (summation(tptp_fun_Z_0(Z!3, Y!4, X!5)) = summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[66])).
% 0.18/0.47 tff(193,plain,
% 0.18/0.47 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[192])).
% 0.18/0.47 tff(194,plain,
% 0.18/0.47 (lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[193])).
% 0.18/0.47 tff(195,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))) | (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(196,plain,
% 0.18/0.47 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[195, 7])).
% 0.18/0.47 tff(197,assumption,(~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))), introduced(assumption)).
% 0.18/0.47 tff(198,plain,
% 0.18/0.47 (((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(199,plain,
% 0.18/0.47 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.18/0.47 tff(200,plain,
% 0.18/0.47 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(201,plain,
% 0.18/0.47 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))) | lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.18/0.47 tff(202,plain,
% 0.18/0.47 (lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[201, 196])).
% 0.18/0.47 tff(203,plain,
% 0.18/0.47 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[202, 194])).
% 0.18/0.47 tff(204,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(205,plain,
% 0.18/0.47 ((~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))))) <=> (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(206,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[205])).
% 0.18/0.47 tff(207,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[206, 204])).
% 0.18/0.47 tff(208,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(209,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.18/0.47 tff(210,plain,
% 0.18/0.47 (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[209, 169])).
% 0.18/0.47 tff(211,plain,
% 0.18/0.47 (((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))))) | (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(212,plain,
% 0.18/0.47 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.18/0.47 tff(213,plain,
% 0.18/0.47 (((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(214,plain,
% 0.18/0.47 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[213, 197])).
% 0.18/0.47 tff(215,assumption,(![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.18/0.47 tff(216,plain,
% 0.18/0.47 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(217,plain,
% 0.18/0.47 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(218,plain,
% 0.18/0.47 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.18/0.48 tff(219,plain,
% 0.18/0.48 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[218, 215, 214])).
% 0.18/0.48 tff(220,plain,
% 0.18/0.48 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(221,plain,
% 0.18/0.48 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.18/0.48 tff(222,plain,
% 0.18/0.48 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[221, 212])).
% 0.18/0.48 tff(223,assumption,(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.18/0.48 tff(224,plain,
% 0.18/0.48 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | ((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(225,plain,
% 0.18/0.48 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | ((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(226,plain,
% 0.18/0.48 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.18/0.48 tff(227,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[226, 223, 222, 203])).
% 0.18/0.48 tff(228,plain,(((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(229,plain,
% 0.18/0.48 ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[228, 191, 189])).
% 0.18/0.48 tff(230,plain,
% 0.18/0.48 ((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(231,plain,
% 0.18/0.48 ((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.18/0.48 tff(232,plain,
% 0.18/0.48 (minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[231, 187, 108])).
% 0.18/0.48 tff(233,plain,
% 0.18/0.48 ((~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))))) | (~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(234,plain,
% 0.18/0.48 (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[233, 232, 106])).
% 0.18/0.48 tff(235,plain,
% 0.18/0.48 (((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z)))) | ![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(236,plain,
% 0.18/0.48 (![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.18/0.48 tff(237,plain,
% 0.18/0.48 (((~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))) | ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(238,plain,
% 0.18/0.48 ((~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))) | ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(239,plain,
% 0.18/0.48 ((~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.18/0.48 tff(240,plain,
% 0.18/0.48 (lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[239, 236, 78])).
% 0.18/0.48 tff(241,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(242,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(243,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.18/0.48 tff(244,plain,
% 0.18/0.48 ((~lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[243, 21])).
% 0.18/0.48 tff(245,plain,
% 0.18/0.48 (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[244, 240])).
% 0.18/0.48 tff(246,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(247,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(248,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.18/0.48 tff(249,plain,
% 0.18/0.48 (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[248, 60, 184])).
% 0.18/0.48 tff(250,plain,
% 0.18/0.48 (Z!3 = max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.18/0.48 inference(symmetry,[status(thm)],[249])).
% 0.18/0.48 tff(251,plain,
% 0.18/0.48 (Z!3 = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(transitivity,[status(thm)],[250, 245])).
% 0.18/0.48 tff(252,plain,
% 0.18/0.48 (lesseq(summation(max(X!5, Y!4)), Z!3) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[251])).
% 0.18/0.48 tff(253,plain,
% 0.18/0.48 (^[X: $i, Y: $i, Z: $i] : refl((~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(254,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[253])).
% 0.18/0.48 tff(255,plain,
% 0.18/0.48 (^[X: $i, Y: $i, Z: $i] : trans(trans(monotonicity(rewrite((lesseq(X, Z) & lesseq(Y, Z)) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))), ((ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))))), rewrite((ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))), ((ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))))), rewrite((~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))), ((ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(256,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[255])).
% 0.18/0.48 tff(257,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(258,axiom,(![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ub')).
% 0.18/0.48 tff(259,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.18/0.48 tff(260,plain,(
% 0.18/0.48 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[259])).
% 0.18/0.48 tff(261,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.18/0.48 tff(262,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[261, 254])).
% 0.18/0.48 tff(263,plain,
% 0.18/0.48 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(264,plain,
% 0.18/0.48 (~(((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.18/0.48 tff(265,plain,
% 0.18/0.48 ((((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(266,plain,
% 0.18/0.48 ((((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[265, 191])).
% 0.18/0.48 tff(267,plain,
% 0.18/0.48 (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[266, 264])).
% 0.18/0.48 tff(268,plain,
% 0.18/0.48 (((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(269,plain,
% 0.18/0.48 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.18/0.48 tff(270,plain,
% 0.18/0.48 (((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(271,plain,
% 0.18/0.48 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[270, 267])).
% 0.18/0.48 tff(272,assumption,(lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.18/0.48 tff(273,assumption,(~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.18/0.48 tff(274,assumption,(max(X!5, Y!4) = X!5), introduced(assumption)).
% 0.18/0.48 tff(275,plain,
% 0.18/0.48 (X!5 = max(X!5, Y!4)),
% 0.18/0.48 inference(symmetry,[status(thm)],[274])).
% 0.18/0.48 tff(276,plain,
% 0.18/0.48 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[275])).
% 0.18/0.48 tff(277,plain,
% 0.18/0.48 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(symmetry,[status(thm)],[276])).
% 0.18/0.48 tff(278,plain,
% 0.18/0.48 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[277])).
% 0.18/0.48 tff(279,plain,
% 0.18/0.48 (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[273, 278])).
% 0.18/0.48 tff(280,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[272, 279])).
% 0.18/0.48 tff(281,plain,((~(max(X!5, Y!4) = X!5)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(282,plain,
% 0.18/0.48 (~(max(X!5, Y!4) = X!5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[281, 273, 272])).
% 0.18/0.48 tff(283,plain,
% 0.18/0.48 ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.18/0.48 tff(284,plain,
% 0.18/0.48 (~lesseq(Y!4, X!5)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.18/0.48 tff(285,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(286,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(287,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.18/0.48 tff(288,plain,
% 0.18/0.48 (lesseq(X!5, Y!4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[287, 43, 284])).
% 0.18/0.48 tff(289,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(290,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(291,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.18/0.48 tff(292,plain,
% 0.18/0.48 ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[291, 60])).
% 0.18/0.48 tff(293,plain,
% 0.18/0.48 (max(X!5, Y!4) = Y!4),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[292, 288])).
% 0.18/0.48 tff(294,plain,
% 0.18/0.48 (Y!4 = max(X!5, Y!4)),
% 0.18/0.48 inference(symmetry,[status(thm)],[293])).
% 0.18/0.48 tff(295,plain,
% 0.18/0.48 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[294])).
% 0.18/0.48 tff(296,plain,
% 0.18/0.48 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(symmetry,[status(thm)],[295])).
% 0.18/0.48 tff(297,plain,
% 0.18/0.48 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[296])).
% 0.18/0.48 tff(298,plain,
% 0.18/0.48 (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[273, 297])).
% 0.18/0.48 tff(299,assumption,(lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.18/0.48 tff(300,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.18/0.48 tff(301,plain,(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(302,plain,
% 0.18/0.48 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[301, 271, 269])).
% 0.18/0.48 tff(303,assumption,(~lesseq(summation(max(X!5, Y!4)), Z!3)), introduced(assumption)).
% 0.18/0.48 tff(304,assumption,(lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)), introduced(assumption)).
% 0.18/0.48 tff(305,plain,
% 0.18/0.48 (^[X: $i, Y: $i] : refl((lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(306,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[305])).
% 0.18/0.48 tff(307,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(308,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','summation_monotone')).
% 0.18/0.48 tff(309,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.18/0.48 tff(310,plain,(
% 0.18/0.48 ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[309])).
% 0.18/0.48 tff(311,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.18/0.48 tff(312,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(313,plain,
% 0.18/0.48 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[312, 311])).
% 0.18/0.48 tff(314,assumption,(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.18/0.48 tff(315,plain,
% 0.18/0.48 ((~(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(316,plain,
% 0.18/0.48 ((~(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) | lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.18/0.48 tff(317,plain,
% 0.18/0.48 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[316, 313])).
% 0.18/0.48 tff(318,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(319,plain,
% 0.18/0.48 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((lesseq(X, Y) & lesseq(Y, Z)) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Y))))), ((~(lesseq(X, Y) & lesseq(Y, Z))) <=> (~(~((~lesseq(Y, Z)) | (~lesseq(X, Y))))))), rewrite((~(~((~lesseq(Y, Z)) | (~lesseq(X, Y))))) <=> ((~lesseq(Y, Z)) | (~lesseq(X, Y)))), ((~(lesseq(X, Y) & lesseq(Y, Z))) <=> ((~lesseq(Y, Z)) | (~lesseq(X, Y))))), (((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> (((~lesseq(Y, Z)) | (~lesseq(X, Y))) | lesseq(X, Z)))), rewrite((((~lesseq(Y, Z)) | (~lesseq(X, Y))) | lesseq(X, Z)) <=> (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))), (((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(320,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[319])).
% 0.18/0.48 tff(321,plain,
% 0.18/0.48 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(322,plain,
% 0.18/0.49 (^[X: $i, Y: $i, Z: $i] : rewrite(((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z)) <=> ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(323,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[322])).
% 0.18/0.49 tff(324,axiom,(![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lesseq_trans')).
% 0.18/0.49 tff(325,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.18/0.49 tff(326,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.18/0.49 tff(327,plain,(
% 0.18/0.49 ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.18/0.49 inference(skolemize,[status(sab)],[326])).
% 0.18/0.49 tff(328,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[327, 320])).
% 0.18/0.49 tff(329,plain,
% 0.18/0.49 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[328, 318])).
% 0.18/0.49 tff(330,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(331,plain,
% 0.18/0.49 ((lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(332,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[331])).
% 0.18/0.49 tff(333,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[332, 330])).
% 0.18/0.49 tff(334,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(335,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.18/0.49 tff(336,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[335, 329, 317, 304, 303])).
% 0.18/0.49 tff(337,plain,(lesseq(summation(max(X!5, Y!4)), Z!3) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(338,plain,
% 0.18/0.49 (lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[337, 302, 184])).
% 0.18/0.49 tff(339,plain,
% 0.18/0.49 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[338, 252])).
% 0.18/0.49 tff(340,assumption,(max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3), introduced(assumption)).
% 0.18/0.49 tff(341,assumption,(max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.18/0.49 tff(342,plain,
% 0.18/0.49 (summation(tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.18/0.49 inference(symmetry,[status(thm)],[341])).
% 0.18/0.49 tff(343,plain,
% 0.18/0.49 (summation(tptp_fun_Z_0(Z!3, Y!4, X!5)) = Z!3),
% 0.18/0.49 inference(transitivity,[status(thm)],[342, 340])).
% 0.18/0.49 tff(344,plain,
% 0.18/0.49 (model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> model_max(X!5, Y!4, Z!3)),
% 0.18/0.49 inference(monotonicity,[status(thm)],[343])).
% 0.18/0.49 tff(345,plain,
% 0.18/0.49 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(symmetry,[status(thm)],[344])).
% 0.18/0.49 tff(346,plain,
% 0.18/0.49 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[345])).
% 0.18/0.49 tff(347,assumption,(~model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.18/0.49 tff(348,plain,
% 0.18/0.49 (~model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.18/0.49 tff(349,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))) | (model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(350,plain,
% 0.18/0.49 (model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[349, 7])).
% 0.18/0.49 tff(351,assumption,(lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), introduced(assumption)).
% 0.18/0.49 tff(352,plain,
% 0.18/0.49 ((~(model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) | model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(353,plain,
% 0.18/0.49 ((~(model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) | model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[352, 351])).
% 0.18/0.49 tff(354,plain,
% 0.18/0.49 (model_max(X!5, Y!4, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[353, 350])).
% 0.18/0.49 tff(355,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[354, 348])).
% 0.18/0.49 tff(356,plain,(model_max(X!5, Y!4, Z!3) | (~(max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3)) | (~(max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(357,plain,
% 0.18/0.49 (model_max(X!5, Y!4, Z!3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[356, 339, 249, 245])).
% 0.18/0.49 tff(358,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(359,plain,
% 0.18/0.49 (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[358, 97])).
% 0.18/0.49 tff(360,plain,
% 0.18/0.49 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(361,plain,
% 0.18/0.49 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[360, 359])).
% 0.18/0.49 tff(362,plain,
% 0.18/0.49 ((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(363,plain,
% 0.18/0.49 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[362, 361])).
% 0.18/0.49 tff(364,plain,
% 0.18/0.49 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[363, 357, 34])).
% 0.18/0.49 tff(365,plain,
% 0.18/0.49 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) | model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(366,plain,
% 0.18/0.49 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[365, 364])).
% 0.18/0.49 tff(367,plain,
% 0.18/0.49 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | (~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(368,plain,
% 0.18/0.49 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[367, 366])).
% 0.18/0.49 tff(369,plain,
% 0.18/0.49 (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[368, 33])).
% 0.18/0.49 tff(370,plain,
% 0.18/0.49 (lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[369, 31])).
% 0.18/0.49 tff(371,plain,
% 0.18/0.49 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(372,plain,
% 0.18/0.49 ((lesseq(X!5, X!5) | lesseq(X!5, X!5)) <=> lesseq(X!5, X!5)),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(373,plain,
% 0.18/0.49 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[372])).
% 0.18/0.49 tff(374,plain,
% 0.18/0.49 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.18/0.49 inference(transitivity,[status(thm)],[373, 371])).
% 0.18/0.49 tff(375,plain,
% 0.18/0.49 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(376,plain,
% 0.18/0.49 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.18/0.49 tff(377,plain,
% 0.18/0.49 (lesseq(X!5, X!5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[376, 43])).
% 0.18/0.49 tff(378,plain,
% 0.18/0.49 ((~((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5)))) | (~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(379,plain,
% 0.18/0.49 (~((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[378, 377, 10])).
% 0.18/0.49 tff(380,assumption,(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)), introduced(assumption)).
% 0.18/0.49 tff(381,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(382,plain,
% 0.18/0.49 ((~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5))) <=> (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(383,plain,
% 0.18/0.49 ((((~lesseq(Y!4, X!5)) | (~lesseq(X!5, X!5))) <=> ub(X!5, Y!4, X!5)) <=> (((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(384,plain,
% 0.18/0.49 ((~(((~lesseq(Y!4, X!5)) | (~lesseq(X!5, X!5))) <=> ub(X!5, Y!4, X!5))) <=> (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[383])).
% 0.18/0.49 tff(385,plain,
% 0.18/0.49 ((~(((~lesseq(Y!4, X!5)) | (~lesseq(X!5, X!5))) <=> ub(X!5, Y!4, X!5))) <=> (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[384, 382])).
% 0.18/0.49 tff(386,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, X!5)) | (~lesseq(X!5, X!5))) <=> ub(X!5, Y!4, X!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[385])).
% 0.18/0.49 tff(387,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, X!5)) | (~lesseq(X!5, X!5))) <=> ub(X!5, Y!4, X!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[386, 381])).
% 0.18/0.49 tff(388,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, X!5)) | (~lesseq(X!5, X!5))) <=> ub(X!5, Y!4, X!5)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(389,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.18/0.49 tff(390,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[389, 262, 380])).
% 0.18/0.49 tff(391,plain,(~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(392,plain,
% 0.18/0.49 ((((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)) | ((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) | ub(X!5, Y!4, X!5)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(393,plain,
% 0.18/0.49 (((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) | ub(X!5, Y!4, X!5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[392, 391])).
% 0.18/0.49 tff(394,plain,
% 0.18/0.49 (ub(X!5, Y!4, X!5)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[393, 379])).
% 0.18/0.49 tff(395,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(396,plain,
% 0.18/0.49 (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[395, 169])).
% 0.18/0.49 tff(397,plain,
% 0.18/0.49 (((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(398,plain,
% 0.18/0.49 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[397, 396])).
% 0.18/0.49 tff(399,plain,
% 0.18/0.49 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(400,plain,
% 0.18/0.49 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[399, 364])).
% 0.18/0.49 tff(401,plain,
% 0.18/0.49 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(402,plain,
% 0.18/0.49 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(403,plain,
% 0.18/0.49 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.18/0.49 tff(404,plain,
% 0.18/0.49 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[403, 400, 189])).
% 0.18/0.49 tff(405,plain,
% 0.18/0.49 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(406,plain,
% 0.18/0.49 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[405, 404])).
% 0.18/0.49 tff(407,plain,
% 0.18/0.49 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[406, 398])).
% 0.18/0.49 tff(408,plain,
% 0.18/0.49 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(409,plain,
% 0.18/0.49 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(410,plain,
% 0.18/0.49 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.18/0.49 tff(411,plain,
% 0.18/0.49 ((~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[410, 407])).
% 0.18/0.49 tff(412,plain,
% 0.18/0.49 (~lesseq(summation(X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[411, 394])).
% 0.18/0.49 tff(413,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[412, 370])).
% 0.18/0.49 tff(414,plain,(minsol_model_max(X!5, Y!4, Z!3) | (~lesseq(Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(415,plain,
% 0.18/0.49 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[414, 10])).
% 0.18/0.49 tff(416,plain,
% 0.18/0.49 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(417,plain,
% 0.18/0.49 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[416, 359])).
% 0.18/0.49 tff(418,plain,
% 0.18/0.49 ((~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(419,plain,
% 0.18/0.49 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[418, 417])).
% 0.18/0.49 tff(420,plain,
% 0.18/0.49 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[419, 415])).
% 0.18/0.49 tff(421,plain,
% 0.18/0.49 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | model_max(X!5, Y!4, Z!3)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(422,plain,
% 0.18/0.49 (model_max(X!5, Y!4, Z!3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[421, 420])).
% 0.18/0.49 tff(423,plain,
% 0.18/0.49 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(summation(max(X!5, Y!4)), Z!3))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(424,plain,
% 0.18/0.49 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(summation(max(X!5, Y!4)), Z!3))) | lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[423, 422])).
% 0.18/0.49 tff(425,plain,
% 0.18/0.49 (lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[424, 9])).
% 0.18/0.49 tff(426,assumption,(~(max(summation(max(X!5, Y!4)), Z!3) = Z!3)), introduced(assumption)).
% 0.18/0.49 tff(427,assumption,(lesseq(summation(max(X!5, Y!4)), Z!3)), introduced(assumption)).
% 0.18/0.49 tff(428,plain,
% 0.18/0.49 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(summation(max(X!5, Y!4)), Z!3)) | (max(summation(max(X!5, Y!4)), Z!3) = Z!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(summation(max(X!5, Y!4)), Z!3)) | (max(summation(max(X!5, Y!4)), Z!3) = Z!3))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(429,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(summation(max(X!5, Y!4)), Z!3)) | (max(summation(max(X!5, Y!4)), Z!3) = Z!3))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(430,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(summation(max(X!5, Y!4)), Z!3)) | (max(summation(max(X!5, Y!4)), Z!3) = Z!3)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.18/0.50 tff(431,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[430, 60, 427, 426])).
% 0.18/0.50 tff(432,plain,((~lesseq(summation(max(X!5, Y!4)), Z!3)) | (max(summation(max(X!5, Y!4)), Z!3) = Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(433,plain,
% 0.18/0.50 (max(summation(max(X!5, Y!4)), Z!3) = Z!3),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[432, 425])).
% 0.18/0.50 tff(434,plain,
% 0.18/0.50 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | ![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(435,plain,
% 0.18/0.50 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[434, 420])).
% 0.18/0.50 tff(436,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(summation(max(X, Y)), N))) | (model_max(X!5, Y!4, summation(max(X!5, Y!4))) <=> lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(437,plain,
% 0.18/0.50 (model_max(X!5, Y!4, summation(max(X!5, Y!4))) <=> lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[436, 7])).
% 0.18/0.50 tff(438,plain,
% 0.18/0.50 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(439,plain,
% 0.18/0.50 ((lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4)))) <=> lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(440,plain,
% 0.18/0.50 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[439])).
% 0.18/0.50 tff(441,plain,
% 0.18/0.50 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[440, 438])).
% 0.18/0.50 tff(442,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(443,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.18/0.50 tff(444,plain,
% 0.18/0.50 (lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[443, 43])).
% 0.18/0.50 tff(445,plain,
% 0.18/0.50 ((~(model_max(X!5, Y!4, summation(max(X!5, Y!4))) <=> lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))) | model_max(X!5, Y!4, summation(max(X!5, Y!4))) | (~lesseq(summation(max(X!5, Y!4)), summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(446,plain,
% 0.18/0.50 (model_max(X!5, Y!4, summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[445, 444, 437])).
% 0.18/0.50 tff(447,assumption,(~lesseq(Z!3, summation(max(X!5, Y!4)))), introduced(assumption)).
% 0.18/0.50 tff(448,assumption,(![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.18/0.50 tff(449,plain,
% 0.18/0.50 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, summation(max(X!5, Y!4)))) | lesseq(Z!3, summation(max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, summation(max(X!5, Y!4)))) | lesseq(Z!3, summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(450,plain,
% 0.18/0.50 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, summation(max(X!5, Y!4)))) | lesseq(Z!3, summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(451,plain,
% 0.18/0.50 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, summation(max(X!5, Y!4)))) | lesseq(Z!3, summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.18/0.50 tff(452,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[451, 448, 447, 446])).
% 0.18/0.50 tff(453,plain,((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | lesseq(Z!3, summation(max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(454,plain,
% 0.18/0.50 (lesseq(Z!3, summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[453, 435])).
% 0.18/0.50 tff(455,assumption,(lesseq(Z!3, summation(max(X!5, Y!4)))), introduced(assumption)).
% 0.18/0.50 tff(456,assumption,(~(max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4)))), introduced(assumption)).
% 0.18/0.50 tff(457,plain,
% 0.18/0.50 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, summation(max(X!5, Y!4)))) | (max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, summation(max(X!5, Y!4)))) | (max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(458,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, summation(max(X!5, Y!4)))) | (max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(459,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, summation(max(X!5, Y!4)))) | (max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.18/0.50 tff(460,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[459, 21, 456, 455])).
% 0.18/0.50 tff(461,plain,((~lesseq(Z!3, summation(max(X!5, Y!4)))) | (max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(462,plain,
% 0.18/0.50 (max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[461, 454])).
% 0.18/0.50 tff(463,plain,
% 0.18/0.50 ((minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3)) | (~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(464,plain,
% 0.18/0.50 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[463, 121])).
% 0.18/0.50 tff(465,plain,
% 0.18/0.50 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[464, 415])).
% 0.18/0.50 tff(466,plain,
% 0.18/0.50 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(467,plain,
% 0.18/0.50 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(468,plain,
% 0.18/0.50 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.18/0.50 tff(469,plain,
% 0.18/0.50 (lesseq(Z!3, Z!3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[468, 422, 435])).
% 0.18/0.50 tff(470,assumption,(max(summation(max(X!5, Y!4)), Z!3) = Z!3), introduced(assumption)).
% 0.18/0.50 tff(471,assumption,(max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4))), introduced(assumption)).
% 0.18/0.50 tff(472,plain,
% 0.18/0.50 (summation(max(X!5, Y!4)) = max(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.50 inference(symmetry,[status(thm)],[471])).
% 0.18/0.50 tff(473,plain,
% 0.18/0.50 (summation(X!5) = summation(max(X!5, Y!4))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[275])).
% 0.18/0.50 tff(474,plain,
% 0.18/0.50 (summation(X!5) = Z!3),
% 0.18/0.50 inference(transitivity,[status(thm)],[473, 472, 470])).
% 0.18/0.50 tff(475,plain,
% 0.18/0.50 (lesseq(summation(X!5), Z!3) <=> lesseq(Z!3, Z!3)),
% 0.18/0.50 inference(monotonicity,[status(thm)],[474])).
% 0.18/0.50 tff(476,plain,
% 0.18/0.50 (lesseq(Z!3, Z!3) <=> lesseq(summation(X!5), Z!3)),
% 0.18/0.50 inference(symmetry,[status(thm)],[475])).
% 0.18/0.50 tff(477,assumption,(lesseq(Z!3, Z!3)), introduced(assumption)).
% 0.18/0.50 tff(478,plain,
% 0.18/0.50 (lesseq(summation(X!5), Z!3)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.18/0.50 tff(479,assumption,(~lesseq(summation(X!5), Z!3)), introduced(assumption)).
% 0.18/0.50 tff(480,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[479, 478])).
% 0.18/0.50 tff(481,plain,(lesseq(summation(X!5), Z!3) | (~lesseq(Z!3, Z!3)) | (~(max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4)))) | (~(max(summation(max(X!5, Y!4)), Z!3) = Z!3)) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(482,plain,
% 0.18/0.50 (lesseq(summation(X!5), Z!3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[481, 469, 462, 433, 27])).
% 0.18/0.50 tff(483,assumption,(lesseq(summation(X!5), Z!3)), introduced(assumption)).
% 0.18/0.50 tff(484,assumption,(![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))), introduced(assumption)).
% 0.18/0.50 tff(485,assumption,(ub(X!5, Y!4, X!5)), introduced(assumption)).
% 0.18/0.50 tff(486,plain,
% 0.18/0.50 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), Z!3)))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), Z!3)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(487,plain,
% 0.18/0.50 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), Z!3)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(488,plain,
% 0.18/0.50 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), Z!3))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.18/0.50 tff(489,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[488, 485, 484, 483])).
% 0.18/0.50 tff(490,plain,((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(summation(X!5), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(491,plain,
% 0.18/0.50 (~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[490, 394, 482])).
% 0.18/0.50 tff(492,plain,
% 0.18/0.50 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))) | (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(493,plain,
% 0.18/0.50 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[492, 177])).
% 0.18/0.50 tff(494,plain,
% 0.18/0.50 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(495,plain,
% 0.18/0.50 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[494, 493])).
% 0.18/0.50 tff(496,plain,
% 0.18/0.50 (model_ub(X!5, Y!4, Z!3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[495, 491])).
% 0.18/0.50 tff(497,plain,
% 0.18/0.50 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(498,plain,
% 0.18/0.50 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[497, 148])).
% 0.18/0.50 tff(499,plain,
% 0.18/0.50 ((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(500,plain,
% 0.18/0.50 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[499, 498])).
% 0.18/0.50 tff(501,plain,
% 0.18/0.50 (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[500, 496, 465])).
% 0.18/0.50 tff(502,plain,
% 0.18/0.50 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(503,plain,
% 0.18/0.50 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[502, 501])).
% 0.18/0.50 tff(504,plain,
% 0.18/0.50 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) | model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(505,plain,
% 0.18/0.50 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[504, 501])).
% 0.18/0.50 tff(506,assumption,((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))), introduced(assumption)).
% 0.18/0.50 tff(507,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(508,plain,
% 0.18/0.50 ((~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))) <=> (~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(509,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[508])).
% 0.18/0.50 tff(510,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[509, 507])).
% 0.18/0.50 tff(511,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(512,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(summation(tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(summation(Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.18/0.50 tff(513,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[512, 169, 506])).
% 0.18/0.50 tff(514,plain,(~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(515,plain,
% 0.18/0.50 (((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(516,plain,
% 0.18/0.50 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[515, 514])).
% 0.18/0.50 tff(517,plain,
% 0.18/0.50 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(518,plain,
% 0.18/0.50 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[517, 516])).
% 0.18/0.50 tff(519,plain,
% 0.18/0.50 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[518, 505])).
% 0.18/0.50 tff(520,plain,
% 0.18/0.50 (summation(max(X!5, Y!4)) = summation(X!5)),
% 0.18/0.50 inference(symmetry,[status(thm)],[473])).
% 0.18/0.50 tff(521,plain,
% 0.18/0.50 (Z!3 = max(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.50 inference(symmetry,[status(thm)],[470])).
% 0.18/0.50 tff(522,plain,
% 0.18/0.50 (Z!3 = summation(X!5)),
% 0.18/0.50 inference(transitivity,[status(thm)],[521, 471, 520])).
% 0.18/0.50 tff(523,plain,
% 0.18/0.50 (lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(summation(X!5), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[522])).
% 0.18/0.50 tff(524,plain,
% 0.18/0.50 (lesseq(summation(X!5), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.50 inference(symmetry,[status(thm)],[523])).
% 0.18/0.51 tff(525,plain,
% 0.18/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(summation(X!5), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(526,plain,
% 0.18/0.51 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(summation(X!5), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[525, 311])).
% 0.18/0.51 tff(527,plain,
% 0.18/0.51 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(528,plain,
% 0.18/0.51 (~(((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[527, 262])).
% 0.18/0.51 tff(529,assumption,(~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))), introduced(assumption)).
% 0.18/0.51 tff(530,plain,
% 0.18/0.51 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(531,plain,
% 0.18/0.51 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[530, 529])).
% 0.18/0.51 tff(532,plain,
% 0.18/0.51 ((((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(533,plain,
% 0.18/0.51 ((((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[532, 531])).
% 0.18/0.51 tff(534,plain,
% 0.18/0.51 (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[533, 528])).
% 0.18/0.51 tff(535,plain,
% 0.18/0.51 (((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(536,plain,
% 0.18/0.51 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[535, 534])).
% 0.18/0.51 tff(537,plain,
% 0.18/0.51 ((~(lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(summation(X!5), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | lesseq(summation(X!5), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(538,plain,
% 0.18/0.51 (lesseq(summation(X!5), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[537, 536, 526])).
% 0.18/0.51 tff(539,plain,
% 0.18/0.51 (lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[538, 524])).
% 0.18/0.51 tff(540,plain,
% 0.18/0.51 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(541,plain,
% 0.18/0.51 (lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[540, 529])).
% 0.18/0.51 tff(542,assumption,(~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.18/0.51 tff(543,plain,
% 0.18/0.51 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(544,plain,
% 0.18/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(545,plain,
% 0.18/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.18/0.51 tff(546,plain,
% 0.18/0.51 (~lesseq(Z!3, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[545, 329, 542, 541])).
% 0.18/0.51 tff(547,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[546, 539])).
% 0.18/0.51 tff(548,plain,(((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | (~(max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4)))) | (~(max(summation(max(X!5, Y!4)), Z!3) = Z!3)) | (~(max(X!5, Y!4) = X!5)) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(549,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[548, 519, 503, 27, 462, 433])).
% 0.18/0.51 tff(550,plain,(~lesseq(Y!4, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(551,assumption,(~lesseq(Y!4, X!5)), introduced(assumption)).
% 0.18/0.51 tff(552,assumption,(~(max(X!5, Y!4) = Y!4)), introduced(assumption)).
% 0.18/0.51 tff(553,plain,
% 0.18/0.51 (~lesseq(X!5, Y!4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[291, 60, 552])).
% 0.18/0.51 tff(554,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[287, 43, 551, 553])).
% 0.18/0.51 tff(555,plain,(lesseq(Y!4, X!5) | (max(X!5, Y!4) = Y!4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(556,plain,
% 0.18/0.51 (max(X!5, Y!4) = Y!4),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[555, 551])).
% 0.18/0.51 tff(557,plain,
% 0.18/0.51 (Y!4 = max(X!5, Y!4)),
% 0.18/0.51 inference(symmetry,[status(thm)],[556])).
% 0.18/0.51 tff(558,plain,
% 0.18/0.51 (summation(Y!4) = summation(max(X!5, Y!4))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[557])).
% 0.18/0.51 tff(559,plain,
% 0.18/0.51 (lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[558])).
% 0.18/0.51 tff(560,plain,
% 0.18/0.51 (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(symmetry,[status(thm)],[559])).
% 0.18/0.51 tff(561,plain,
% 0.18/0.51 (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[175, 169])).
% 0.18/0.51 tff(562,plain,
% 0.18/0.51 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[178, 561])).
% 0.18/0.51 tff(563,plain,
% 0.18/0.51 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[180, 155])).
% 0.18/0.51 tff(564,plain,
% 0.18/0.51 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[563, 562])).
% 0.18/0.51 tff(565,plain,
% 0.18/0.51 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[183, 564])).
% 0.18/0.51 tff(566,plain,
% 0.18/0.51 (lesseq(summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[565, 112])).
% 0.18/0.51 tff(567,plain,
% 0.18/0.51 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[186, 566, 110])).
% 0.18/0.51 tff(568,plain,
% 0.18/0.51 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[190, 564])).
% 0.18/0.51 tff(569,plain,
% 0.18/0.51 ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[228, 568, 189])).
% 0.18/0.51 tff(570,plain,
% 0.18/0.51 ((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[230, 569])).
% 0.18/0.51 tff(571,plain,
% 0.18/0.51 (minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[570, 567, 108])).
% 0.18/0.51 tff(572,plain,
% 0.18/0.51 (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[233, 571, 106])).
% 0.18/0.51 tff(573,plain,
% 0.18/0.51 (![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z)) | lesseq(Z!3, Z))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[235, 572])).
% 0.18/0.51 tff(574,plain,
% 0.18/0.51 (lesseq(Z!3, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[239, 573, 78])).
% 0.18/0.51 tff(575,plain,
% 0.18/0.51 (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[244, 574])).
% 0.18/0.51 tff(576,plain,
% 0.18/0.51 (max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[248, 60, 565])).
% 0.18/0.51 tff(577,plain,
% 0.18/0.51 (Z!3 = max(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.18/0.51 inference(symmetry,[status(thm)],[576])).
% 0.18/0.51 tff(578,plain,
% 0.18/0.51 (Z!3 = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(transitivity,[status(thm)],[577, 575])).
% 0.18/0.51 tff(579,plain,
% 0.18/0.51 (lesseq(summation(max(X!5, Y!4)), Z!3) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[578])).
% 0.18/0.51 tff(580,plain,
% 0.18/0.51 ((((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[265, 568])).
% 0.18/0.51 tff(581,plain,
% 0.18/0.51 (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[580, 264])).
% 0.18/0.51 tff(582,plain,
% 0.18/0.51 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[268, 581])).
% 0.18/0.51 tff(583,plain,
% 0.18/0.51 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[270, 581])).
% 0.18/0.51 tff(584,plain,
% 0.18/0.51 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[301, 583, 582])).
% 0.18/0.51 tff(585,plain,
% 0.18/0.51 (lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[337, 584, 565])).
% 0.18/0.51 tff(586,plain,
% 0.18/0.51 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[585, 579])).
% 0.18/0.51 tff(587,plain,
% 0.18/0.51 (model_max(X!5, Y!4, Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[356, 576, 575, 586])).
% 0.18/0.51 tff(588,plain,
% 0.18/0.51 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[363, 587, 34])).
% 0.18/0.51 tff(589,plain,
% 0.18/0.51 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[365, 588])).
% 0.18/0.51 tff(590,plain,
% 0.18/0.51 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[367, 589])).
% 0.18/0.51 tff(591,plain,
% 0.18/0.51 (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[590, 33])).
% 0.18/0.51 tff(592,plain,
% 0.18/0.51 (lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[591, 560])).
% 0.18/0.51 tff(593,plain,
% 0.18/0.51 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[399, 588])).
% 0.18/0.51 tff(594,plain,
% 0.18/0.51 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[403, 593, 189])).
% 0.18/0.51 tff(595,plain,
% 0.18/0.51 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[405, 594])).
% 0.18/0.51 tff(596,plain,
% 0.18/0.51 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[595, 398])).
% 0.18/0.51 tff(597,plain,
% 0.18/0.51 (lesseq(X!5, Y!4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[287, 43, 551])).
% 0.18/0.51 tff(598,plain,
% 0.18/0.51 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(599,plain,
% 0.18/0.51 ((lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(600,plain,
% 0.18/0.51 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[599])).
% 0.18/0.51 tff(601,plain,
% 0.18/0.51 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.18/0.51 inference(transitivity,[status(thm)],[600, 598])).
% 0.18/0.51 tff(602,plain,
% 0.18/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(603,plain,
% 0.18/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.18/0.51 tff(604,plain,
% 0.18/0.51 (lesseq(Y!4, Y!4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[603, 43])).
% 0.18/0.51 tff(605,plain,
% 0.18/0.51 ((~((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4)))) | (~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(606,plain,
% 0.18/0.51 (~((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[605, 604, 597])).
% 0.18/0.51 tff(607,assumption,(((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) <=> ub(X!5, Y!4, Y!4)), introduced(assumption)).
% 0.18/0.51 tff(608,plain,
% 0.18/0.51 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) <=> ub(X!5, Y!4, Y!4)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(609,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[608, 262, 607])).
% 0.18/0.51 tff(610,plain,(~(((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) <=> ub(X!5, Y!4, Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(611,plain,
% 0.18/0.51 ((((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) <=> ub(X!5, Y!4, Y!4)) | ((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) | ub(X!5, Y!4, Y!4)),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(612,plain,
% 0.18/0.51 (((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) | ub(X!5, Y!4, Y!4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[611, 610])).
% 0.18/0.51 tff(613,plain,
% 0.18/0.51 (ub(X!5, Y!4, Y!4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[612, 606])).
% 0.18/0.51 tff(614,plain,
% 0.18/0.51 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(615,plain,
% 0.18/0.51 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(616,plain,
% 0.18/0.51 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.18/0.51 tff(617,plain,
% 0.18/0.51 (~lesseq(summation(Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[616, 613, 596])).
% 0.18/0.51 tff(618,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[617, 592])).
% 0.18/0.51 tff(619,plain,(minsol_model_max(X!5, Y!4, Z!3) | lesseq(Y!4, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(620,plain,
% 0.18/0.51 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[619, 550])).
% 0.18/0.51 tff(621,plain,
% 0.18/0.51 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[419, 620])).
% 0.18/0.51 tff(622,plain,
% 0.18/0.51 (model_max(X!5, Y!4, Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[421, 621])).
% 0.18/0.51 tff(623,plain,
% 0.18/0.51 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(summation(max(X!5, Y!4)), Z!3))) | lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[423, 622])).
% 0.18/0.51 tff(624,plain,
% 0.18/0.51 (lesseq(summation(max(X!5, Y!4)), Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[623, 9])).
% 0.18/0.51 tff(625,plain,
% 0.18/0.51 (max(summation(max(X!5, Y!4)), Z!3) = Z!3),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[432, 624])).
% 0.18/0.51 tff(626,plain,
% 0.18/0.51 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[434, 621])).
% 0.18/0.51 tff(627,plain,
% 0.18/0.51 (lesseq(Z!3, summation(max(X!5, Y!4)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[453, 626])).
% 0.18/0.51 tff(628,plain,
% 0.18/0.51 (max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[461, 627])).
% 0.18/0.51 tff(629,plain,
% 0.18/0.51 (max(X!5, Y!4) = Y!4),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[555, 550])).
% 0.18/0.51 tff(630,plain,
% 0.18/0.51 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[464, 620])).
% 0.18/0.51 tff(631,plain,
% 0.18/0.51 (lesseq(Z!3, Z!3)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[468, 622, 626])).
% 0.18/0.51 tff(632,assumption,(max(X!5, Y!4) = Y!4), introduced(assumption)).
% 0.18/0.51 tff(633,plain,
% 0.18/0.51 (Y!4 = max(X!5, Y!4)),
% 0.18/0.51 inference(symmetry,[status(thm)],[632])).
% 0.18/0.51 tff(634,plain,
% 0.18/0.51 (summation(Y!4) = summation(max(X!5, Y!4))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[633])).
% 0.18/0.51 tff(635,plain,
% 0.18/0.51 (summation(Y!4) = Z!3),
% 0.18/0.51 inference(transitivity,[status(thm)],[634, 472, 470])).
% 0.18/0.51 tff(636,plain,
% 0.18/0.51 (lesseq(summation(Y!4), Z!3) <=> lesseq(Z!3, Z!3)),
% 0.18/0.51 inference(monotonicity,[status(thm)],[635])).
% 0.18/0.51 tff(637,plain,
% 0.18/0.51 (lesseq(Z!3, Z!3) <=> lesseq(summation(Y!4), Z!3)),
% 0.18/0.51 inference(symmetry,[status(thm)],[636])).
% 0.18/0.51 tff(638,plain,
% 0.18/0.51 (lesseq(summation(Y!4), Z!3)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[477, 637])).
% 0.18/0.51 tff(639,assumption,(~lesseq(summation(Y!4), Z!3)), introduced(assumption)).
% 0.18/0.51 tff(640,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[639, 638])).
% 0.18/0.51 tff(641,plain,(lesseq(summation(Y!4), Z!3) | (~lesseq(Z!3, Z!3)) | (~(max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4)))) | (~(max(summation(max(X!5, Y!4)), Z!3) = Z!3)) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.52 tff(642,plain,
% 0.18/0.52 (lesseq(summation(Y!4), Z!3)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[641, 625, 629, 628, 631])).
% 0.18/0.52 tff(643,plain,
% 0.18/0.52 (lesseq(X!5, Y!4)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[287, 43, 550])).
% 0.18/0.52 tff(644,plain,
% 0.18/0.52 (~((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[605, 604, 643])).
% 0.18/0.52 tff(645,plain,
% 0.18/0.52 (ub(X!5, Y!4, Y!4)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[612, 644])).
% 0.18/0.52 tff(646,assumption,(lesseq(summation(Y!4), Z!3)), introduced(assumption)).
% 0.18/0.52 tff(647,assumption,(ub(X!5, Y!4, Y!4)), introduced(assumption)).
% 0.18/0.52 tff(648,plain,
% 0.18/0.52 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), Z!3)))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), Z!3)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(649,plain,
% 0.18/0.52 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), Z!3)))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(650,plain,
% 0.18/0.52 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), Z!3))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.18/0.52 tff(651,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[650, 647, 646, 484])).
% 0.18/0.52 tff(652,plain,((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(summation(Y!4), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.52 tff(653,plain,
% 0.18/0.52 (~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(summation(Z), Z!3)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[652, 645, 642])).
% 0.18/0.52 tff(654,plain,
% 0.18/0.52 (model_ub(X!5, Y!4, Z!3)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[495, 653])).
% 0.18/0.52 tff(655,plain,
% 0.18/0.52 (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[500, 654, 630])).
% 0.18/0.52 tff(656,plain,
% 0.18/0.52 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[502, 655])).
% 0.18/0.52 tff(657,plain,
% 0.18/0.52 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[504, 655])).
% 0.18/0.52 tff(658,plain,
% 0.18/0.52 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[518, 657])).
% 0.18/0.52 tff(659,plain,
% 0.18/0.52 (summation(max(X!5, Y!4)) = summation(Y!4)),
% 0.18/0.52 inference(symmetry,[status(thm)],[634])).
% 0.18/0.52 tff(660,plain,
% 0.18/0.52 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(summation(Y!4), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[659])).
% 0.18/0.52 tff(661,plain,
% 0.18/0.52 (lesseq(summation(Y!4), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.52 inference(symmetry,[status(thm)],[660])).
% 0.18/0.52 tff(662,plain,
% 0.18/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(summation(Y!4), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(663,plain,
% 0.18/0.52 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(summation(Y!4), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[662, 311])).
% 0.18/0.52 tff(664,plain,
% 0.18/0.52 (((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(665,plain,
% 0.18/0.52 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[664, 534])).
% 0.18/0.52 tff(666,plain,
% 0.18/0.52 ((~(lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(summation(Y!4), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) | (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | lesseq(summation(Y!4), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(667,plain,
% 0.18/0.52 (lesseq(summation(Y!4), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[666, 665, 663])).
% 0.18/0.52 tff(668,plain,
% 0.18/0.52 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[667, 661])).
% 0.18/0.52 tff(669,plain,
% 0.18/0.52 (summation(max(X!5, Y!4)) = Z!3),
% 0.18/0.52 inference(transitivity,[status(thm)],[472, 470])).
% 0.18/0.52 tff(670,plain,
% 0.18/0.52 (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[669])).
% 0.18/0.52 tff(671,plain,
% 0.18/0.52 (lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.52 inference(symmetry,[status(thm)],[670])).
% 0.18/0.52 tff(672,plain,
% 0.18/0.52 ((~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[671])).
% 0.18/0.52 tff(673,plain,
% 0.18/0.52 (~lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[542, 672])).
% 0.18/0.52 tff(674,plain,
% 0.18/0.52 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(675,plain,
% 0.18/0.52 ((lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) <=> ((~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(676,plain,
% 0.18/0.52 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))),
% 0.35/0.52 inference(monotonicity,[status(thm)],[675])).
% 0.35/0.52 tff(677,plain,
% 0.35/0.52 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.35/0.52 inference(transitivity,[status(thm)],[676, 674])).
% 0.35/0.52 tff(678,plain,
% 0.35/0.52 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(679,plain,
% 0.35/0.52 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[678, 677])).
% 0.35/0.52 tff(680,plain,
% 0.35/0.52 (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[679, 329, 673, 541])).
% 0.35/0.52 tff(681,plain,
% 0.35/0.52 ($false),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[680, 668])).
% 0.35/0.52 tff(682,plain,(((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | (~(max(X!5, Y!4) = Y!4)) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~(max(summation(max(X!5, Y!4)), Z!3) = Z!3)) | (~(max(summation(max(X!5, Y!4)), Z!3) = summation(max(X!5, Y!4))))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.52 tff(683,plain,
% 0.35/0.52 ($false),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[682, 658, 656, 629, 628, 625])).
% 0.35/0.52 % SZS output end Proof
% 0.35/0.52 % E exiting
%------------------------------------------------------------------------------