%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM861+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:22:16 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM861+1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:03:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(tptp_fun_Z_3_type, type, (
% 0.19/0.44 tptp_fun_Z_3: $i)).
% 0.19/0.44 tff(max_type, type, (
% 0.19/0.44 max: ( $i * $i ) > $i)).
% 0.19/0.44 tff(sum_type, type, (
% 0.19/0.44 sum: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_Y_4_type, type, (
% 0.19/0.44 tptp_fun_Y_4: $i)).
% 0.19/0.44 tff(tptp_fun_X_5_type, type, (
% 0.19/0.44 tptp_fun_X_5: $i)).
% 0.19/0.44 tff(c_type, type, (
% 0.19/0.44 c: $i)).
% 0.19/0.44 tff(lesseq_type, type, (
% 0.19/0.44 lesseq: ( $i * $i ) > $o)).
% 0.19/0.44 tff(model_max_type, type, (
% 0.19/0.44 model_max: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(minsol_model_max_type, type, (
% 0.19/0.44 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_Z_1_type, type, (
% 0.19/0.44 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.44 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.19/0.44 tff(ub_type, type, (
% 0.19/0.44 ub: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(model_ub_type, type, (
% 0.19/0.44 model_ub: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(minsol_model_ub_type, type, (
% 0.19/0.44 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_Z_2_type, type, (
% 0.19/0.44 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)) <=> (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_max_4')).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.44 tff(6,plain,(
% 0.19/0.44 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.19/0.44 inference(skolemize,[status(sab)],[5])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), Z!3))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.44 tff(10,assumption,(lesseq(Y!4, X!5)), introduced(assumption)).
% 0.19/0.44 tff(11,assumption,(~(max(X!5, Y!4) = X!5)), introduced(assumption)).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = X) | (~lesseq(Y, X))) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.44 tff(17,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_1')).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.44 tff(20,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.44 inference(skolemize,[status(sab)],[19])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[24, 21, 11, 10])).
% 0.19/0.44 tff(26,plain,((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (max(X!5, Y!4) = X!5),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[26, 10])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (X!5 = max(X!5, Y!4)),
% 0.19/0.44 inference(symmetry,[status(thm)],[27])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (sum(c, X!5) = sum(c, max(X!5, Y!4))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.44 inference(symmetry,[status(thm)],[30])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[32, 7])).
% 0.19/0.44 tff(34,assumption,(~minsol_model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[35, 7])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(40,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lesseq_total')).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.44 tff(42,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.44 inference(skolemize,[status(sab)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 ((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))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 ((~![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))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.45 tff(56,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_2')).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.45 tff(59,plain,(
% 0.19/0.45 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.45 inference(skolemize,[status(sab)],[58])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 ((~![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))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 ((~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))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (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)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[64, 50])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[65])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[67])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 ((lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[71, 69])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[74, 43])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, 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), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[77, 76, 36])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (^[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)) | (~((~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))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (![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)))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (^[X: $i, Y: $i, N: $i] : refl((~((~((~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)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (![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))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (^[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)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (![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))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (![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))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (^[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)) | (~![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)))))) <=> (~((~((~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))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (![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))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (^[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)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (![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))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.46 tff(93,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')).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.46 tff(96,plain,(
% 0.19/0.46 ![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)))))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[95])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (![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))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (![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))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (![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))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[98, 85])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (![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)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[99, 80])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (((~![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))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 ((~((~(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)) | (~((~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)))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (((~![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))))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (((~![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))))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 ((~![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)))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 ((~![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)))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | 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))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[106, 100])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | 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))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 ((~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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | 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))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | 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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (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(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[112, 7])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.19/0.47 inference(symmetry,[status(thm)],[114])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 ((~(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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(118,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')).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[119, 117])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.19/0.47 tff(123,plain,(
% 0.19/0.47 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.19/0.47 inference(skolemize,[status(sab)],[122])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 ((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)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[126, 34])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (^[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))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (![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)))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[133, 131])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (^[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))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (^[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)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[137])).
% 0.19/0.48 tff(139,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(140,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(141,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.48 tff(142,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')).
% 0.19/0.48 tff(143,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.19/0.48 tff(145,plain,(
% 0.19/0.48 ![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)))))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[144])).
% 0.19/0.48 tff(146,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[147, 134])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 (![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)))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[148, 129])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 ((~![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)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (~((~(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))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 (((~(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))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(153,plain,
% 0.19/0.48 ((~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)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.19/0.48 tff(154,plain,
% 0.19/0.48 ((~((~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)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(155,plain,
% 0.19/0.48 ((~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)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.19/0.48 tff(156,plain,
% 0.19/0.48 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[155, 127])).
% 0.19/0.48 tff(157,plain,
% 0.19/0.48 (((~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)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(158,plain,
% 0.19/0.48 (model_ub(X!5, Y!4, Z!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.19/0.48 tff(159,assumption,((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))), introduced(assumption)).
% 0.19/0.48 tff(160,plain,
% 0.19/0.48 (^[X: $i, Y: $i, N: $i] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(161,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[160])).
% 0.19/0.48 tff(162,plain,
% 0.19/0.48 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(163,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[162])).
% 0.19/0.48 tff(164,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[163, 161])).
% 0.19/0.48 tff(165,plain,
% 0.19/0.48 (^[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(sum(c, tptp_fun_Z_0(N, Y, X)), N))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))), rewrite((model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N)))) <=> (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(166,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[165])).
% 0.19/0.48 tff(167,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N))) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(168,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_ub_4')).
% 0.19/0.48 tff(169,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.48 tff(170,plain,(
% 0.19/0.48 ![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N)))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[169])).
% 0.19/0.48 tff(171,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.19/0.48 tff(173,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(174,plain,
% 0.19/0.48 ((~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, 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(sum(c, Z), Z!3))))))) <=> (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.48 tff(176,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[175, 173])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, Z), Z!3)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(178,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.48 tff(179,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[178, 172, 159])).
% 0.19/0.48 tff(180,plain,(~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(181,plain,
% 0.19/0.48 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(182,plain,
% 0.19/0.48 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.19/0.48 tff(183,plain,
% 0.19/0.48 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(184,plain,
% 0.19/0.48 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.19/0.48 tff(185,plain,
% 0.19/0.48 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[184, 158])).
% 0.19/0.48 tff(186,plain,
% 0.19/0.48 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(187,plain,
% 0.19/0.48 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.19/0.48 tff(188,plain,
% 0.19/0.48 (lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[187, 115])).
% 0.19/0.48 tff(189,plain,
% 0.19/0.48 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, 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(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(190,plain,
% 0.19/0.48 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[189, 188, 113])).
% 0.19/0.48 tff(191,plain,
% 0.19/0.48 (((~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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(192,plain,
% 0.19/0.48 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[191, 156])).
% 0.19/0.49 tff(193,plain,
% 0.19/0.49 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, 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))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(194,plain,
% 0.19/0.49 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[193, 185])).
% 0.19/0.49 tff(195,plain,
% 0.19/0.49 (sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)) = sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[66])).
% 0.19/0.49 tff(196,plain,
% 0.19/0.49 (lesseq(sum(c, 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(sum(c, 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)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[195])).
% 0.19/0.49 tff(197,plain,
% 0.19/0.49 (lesseq(sum(c, 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(sum(c, 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)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[196])).
% 0.19/0.49 tff(198,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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(sum(c, 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))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (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(sum(c, 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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[198, 7])).
% 0.19/0.49 tff(200,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)).
% 0.19/0.49 tff(201,plain,
% 0.19/0.49 (((~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)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 (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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.19/0.49 tff(203,plain,
% 0.19/0.49 ((~(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(sum(c, 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(sum(c, 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)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 ((~(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(sum(c, 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(sum(c, 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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.19/0.49 tff(205,plain,
% 0.19/0.49 (lesseq(sum(c, 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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[204, 199])).
% 0.19/0.49 tff(206,plain,
% 0.19/0.49 (lesseq(sum(c, 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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[205, 197])).
% 0.19/0.49 tff(207,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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)))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(208,plain,
% 0.19/0.49 ((~((~((~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(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, 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))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(209,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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)))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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)))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[209, 207])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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)))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(212,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.49 tff(213,plain,
% 0.19/0.49 (~((~(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(sum(c, 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(sum(c, 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)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[212, 172])).
% 0.19/0.49 tff(214,plain,
% 0.19/0.49 (((~(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(sum(c, 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(sum(c, 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(sum(c, 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))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(215,plain,
% 0.19/0.49 (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(sum(c, 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)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.19/0.49 tff(216,plain,
% 0.19/0.49 (((~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))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 (~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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[216, 200])).
% 0.19/0.49 tff(218,assumption,(![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.19/0.50 tff(219,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(220,plain,
% 0.19/0.50 ((~![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))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(221,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.19/0.50 tff(222,plain,
% 0.19/0.50 (~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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[221, 218, 217])).
% 0.19/0.50 tff(223,plain,
% 0.19/0.50 ((~(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(sum(c, 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(sum(c, 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)))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(224,plain,
% 0.19/0.50 ((~(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(sum(c, 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(sum(c, 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)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.19/0.50 tff(225,plain,
% 0.19/0.50 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[224, 215])).
% 0.19/0.50 tff(226,assumption,(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.19/0.50 tff(227,plain,
% 0.19/0.50 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, 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)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(228,plain,
% 0.19/0.50 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, 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)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(229,plain,
% 0.19/0.50 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.19/0.50 tff(230,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[229, 226, 225, 206])).
% 0.19/0.50 tff(231,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,[]))).
% 0.19/0.50 tff(232,plain,
% 0.19/0.50 ((~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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[231, 194, 192])).
% 0.19/0.50 tff(233,plain,
% 0.19/0.50 ((~((~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)))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(234,plain,
% 0.19/0.50 ((~((~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)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.19/0.50 tff(235,plain,
% 0.19/0.50 (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)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[234, 190, 111])).
% 0.19/0.50 tff(236,plain,
% 0.19/0.50 ((~((~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)))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(237,plain,
% 0.19/0.50 (~((~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))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[236, 235, 109])).
% 0.19/0.50 tff(238,plain,
% 0.19/0.50 (((~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))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(239,plain,
% 0.19/0.50 (![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))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.19/0.50 tff(240,plain,
% 0.19/0.50 (((~![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), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, sum(c, 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), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(241,plain,
% 0.19/0.50 ((~![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), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(242,plain,
% 0.19/0.50 ((~![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), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.50 tff(243,plain,
% 0.19/0.50 (lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[242, 239, 78])).
% 0.19/0.50 tff(244,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(245,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(246,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.50 tff(247,plain,
% 0.19/0.50 ((~lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[246, 21])).
% 0.19/0.50 tff(248,plain,
% 0.19/0.50 (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[247, 243])).
% 0.19/0.50 tff(249,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(250,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(251,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.19/0.50 tff(252,plain,
% 0.19/0.50 (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[251, 60, 187])).
% 0.19/0.50 tff(253,plain,
% 0.19/0.50 (Z!3 = max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.19/0.50 inference(symmetry,[status(thm)],[252])).
% 0.19/0.50 tff(254,plain,
% 0.19/0.50 (Z!3 = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.50 inference(transitivity,[status(thm)],[253, 248])).
% 0.19/0.50 tff(255,plain,
% 0.19/0.50 (lesseq(sum(c, max(X!5, Y!4)), Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[254])).
% 0.19/0.50 tff(256,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(257,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[256])).
% 0.19/0.50 tff(258,plain,
% 0.19/0.50 (^[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)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(259,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[258])).
% 0.19/0.50 tff(260,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(261,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')).
% 0.19/0.50 tff(262,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.19/0.50 tff(263,plain,(
% 0.19/0.50 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[262])).
% 0.19/0.50 tff(264,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.19/0.50 tff(265,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.19/0.50 tff(266,plain,
% 0.19/0.50 ((~![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))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(267,plain,
% 0.19/0.50 (~(((~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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.19/0.50 tff(268,plain,
% 0.19/0.50 ((((~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)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(269,plain,
% 0.19/0.50 ((((~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)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[268, 194])).
% 0.19/0.50 tff(270,plain,
% 0.19/0.50 (~((~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))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[269, 267])).
% 0.19/0.50 tff(271,plain,
% 0.19/0.50 (((~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))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(272,plain,
% 0.19/0.51 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.19/0.51 tff(273,plain,
% 0.19/0.51 (((~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)))) | lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(274,plain,
% 0.19/0.51 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[273, 270])).
% 0.19/0.51 tff(275,assumption,(lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.19/0.51 tff(276,assumption,(~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.19/0.51 tff(277,assumption,(max(X!5, Y!4) = X!5), introduced(assumption)).
% 0.19/0.51 tff(278,plain,
% 0.19/0.51 (X!5 = max(X!5, Y!4)),
% 0.19/0.51 inference(symmetry,[status(thm)],[277])).
% 0.19/0.51 tff(279,plain,
% 0.19/0.51 (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))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[278])).
% 0.19/0.51 tff(280,plain,
% 0.19/0.51 (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))),
% 0.19/0.51 inference(symmetry,[status(thm)],[279])).
% 0.19/0.51 tff(281,plain,
% 0.19/0.51 ((~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)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[280])).
% 0.19/0.51 tff(282,plain,
% 0.19/0.51 (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[276, 281])).
% 0.19/0.51 tff(283,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[275, 282])).
% 0.19/0.51 tff(284,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,[]))).
% 0.19/0.51 tff(285,plain,
% 0.19/0.51 (~(max(X!5, Y!4) = X!5)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[284, 276, 275])).
% 0.19/0.51 tff(286,plain,
% 0.19/0.51 ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.19/0.51 tff(287,plain,
% 0.19/0.51 (~lesseq(Y!4, X!5)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[286, 285])).
% 0.19/0.51 tff(288,plain,
% 0.19/0.51 (((~![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))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(289,plain,
% 0.19/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(290,plain,
% 0.19/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.51 tff(291,plain,
% 0.19/0.51 (lesseq(X!5, Y!4)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[290, 43, 287])).
% 0.19/0.51 tff(292,plain,
% 0.19/0.51 (((~![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))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(293,plain,
% 0.19/0.51 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(294,plain,
% 0.19/0.51 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.19/0.51 tff(295,plain,
% 0.19/0.51 ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[294, 60])).
% 0.19/0.51 tff(296,plain,
% 0.19/0.51 (max(X!5, Y!4) = Y!4),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[295, 291])).
% 0.19/0.51 tff(297,plain,
% 0.19/0.51 (Y!4 = max(X!5, Y!4)),
% 0.19/0.51 inference(symmetry,[status(thm)],[296])).
% 0.19/0.51 tff(298,plain,
% 0.19/0.51 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[297])).
% 0.19/0.51 tff(299,plain,
% 0.19/0.51 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(symmetry,[status(thm)],[298])).
% 0.19/0.51 tff(300,plain,
% 0.19/0.51 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.51 tff(301,plain,
% 0.19/0.51 (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[276, 300])).
% 0.19/0.51 tff(302,assumption,(lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.19/0.51 tff(303,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.19/0.51 tff(304,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,[]))).
% 0.19/0.51 tff(305,plain,
% 0.19/0.51 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[304, 274, 272])).
% 0.19/0.51 tff(306,assumption,(~lesseq(sum(c, max(X!5, Y!4)), Z!3)), introduced(assumption)).
% 0.19/0.51 tff(307,assumption,(lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)), introduced(assumption)).
% 0.19/0.51 tff(308,plain,
% 0.19/0.51 (^[X: $i, Y: $i, Z: $i] : refl((lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(309,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[308])).
% 0.19/0.51 tff(310,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(311,axiom,(![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sum_monotone_1')).
% 0.19/0.51 tff(312,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.19/0.51 tff(313,plain,(
% 0.19/0.51 ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[312])).
% 0.19/0.51 tff(314,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.19/0.51 tff(315,plain,
% 0.19/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(316,plain,
% 0.19/0.51 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.19/0.51 tff(317,assumption,(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.19/0.51 tff(318,plain,
% 0.19/0.51 ((~(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, 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(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(319,plain,
% 0.19/0.51 ((~(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.19/0.51 tff(320,plain,
% 0.19/0.51 (lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[319, 316])).
% 0.19/0.51 tff(321,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(322,plain,
% 0.19/0.51 (^[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)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(323,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[322])).
% 0.19/0.51 tff(324,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(325,plain,
% 0.19/0.51 (^[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)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(326,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[325])).
% 0.19/0.51 tff(327,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')).
% 0.19/0.51 tff(328,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.19/0.51 tff(329,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.19/0.51 tff(330,plain,(
% 0.19/0.51 ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.19/0.51 inference(skolemize,[status(sab)],[329])).
% 0.19/0.51 tff(331,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[330, 323])).
% 0.19/0.51 tff(332,plain,
% 0.19/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[331, 321])).
% 0.19/0.51 tff(333,plain,
% 0.19/0.51 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(334,plain,
% 0.19/0.51 ((lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(335,plain,
% 0.19/0.51 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[334])).
% 0.19/0.51 tff(336,plain,
% 0.19/0.51 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[335, 333])).
% 0.19/0.51 tff(337,plain,
% 0.19/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(338,plain,
% 0.19/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.19/0.51 tff(339,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[338, 332, 320, 307, 306])).
% 0.19/0.51 tff(340,plain,(lesseq(sum(c, max(X!5, Y!4)), Z!3) | (~lesseq(sum(c, 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,[]))).
% 0.19/0.51 tff(341,plain,
% 0.19/0.51 (lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[340, 305, 187])).
% 0.19/0.51 tff(342,plain,
% 0.19/0.51 (lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[341, 255])).
% 0.19/0.51 tff(343,assumption,(max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3), introduced(assumption)).
% 0.19/0.51 tff(344,assumption,(max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.19/0.51 tff(345,plain,
% 0.19/0.51 (sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.19/0.51 inference(symmetry,[status(thm)],[344])).
% 0.19/0.51 tff(346,plain,
% 0.19/0.51 (sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)) = Z!3),
% 0.19/0.51 inference(transitivity,[status(thm)],[345, 343])).
% 0.19/0.51 tff(347,plain,
% 0.19/0.51 (model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> model_max(X!5, Y!4, Z!3)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[346])).
% 0.19/0.51 tff(348,plain,
% 0.19/0.51 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[347])).
% 0.19/0.51 tff(349,plain,
% 0.19/0.51 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[348])).
% 0.19/0.51 tff(350,assumption,(~model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.19/0.51 tff(351,plain,
% 0.19/0.51 (~model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.19/0.51 tff(352,plain,
% 0.19/0.51 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(353,plain,
% 0.19/0.51 (model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[352, 7])).
% 0.19/0.51 tff(354,assumption,(lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))), introduced(assumption)).
% 0.19/0.51 tff(355,plain,
% 0.19/0.51 ((~(model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))) | model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(356,plain,
% 0.19/0.51 ((~(model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))) | model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[355, 354])).
% 0.19/0.51 tff(357,plain,
% 0.19/0.51 (model_max(X!5, Y!4, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[356, 353])).
% 0.19/0.51 tff(358,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[357, 351])).
% 0.19/0.51 tff(359,plain,(model_max(X!5, Y!4, Z!3) | (~(max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3)) | (~(max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(360,plain,
% 0.19/0.52 (model_max(X!5, Y!4, Z!3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[359, 342, 252, 248])).
% 0.19/0.52 tff(361,plain,
% 0.19/0.52 ((~![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)))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(362,plain,
% 0.19/0.52 (~((~(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))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[361, 100])).
% 0.19/0.52 tff(363,plain,
% 0.19/0.52 (((~(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)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(364,plain,
% 0.19/0.52 (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))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[363, 362])).
% 0.19/0.52 tff(365,plain,
% 0.19/0.52 ((~(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))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(366,plain,
% 0.19/0.52 (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))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[365, 364])).
% 0.19/0.52 tff(367,plain,
% 0.19/0.52 (~((~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)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[366, 360, 34])).
% 0.19/0.52 tff(368,plain,
% 0.19/0.52 (((~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))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(369,plain,
% 0.19/0.52 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[368, 367])).
% 0.19/0.52 tff(370,plain,
% 0.19/0.52 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, 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(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(371,plain,
% 0.19/0.52 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[370, 369])).
% 0.19/0.52 tff(372,plain,
% 0.19/0.52 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[371, 33])).
% 0.19/0.52 tff(373,plain,
% 0.19/0.52 (lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[372, 31])).
% 0.19/0.52 tff(374,plain,
% 0.19/0.52 (((~![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))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(375,plain,
% 0.19/0.52 ((lesseq(X!5, X!5) | lesseq(X!5, X!5)) <=> lesseq(X!5, X!5)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(376,plain,
% 0.19/0.52 (((~![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))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[375])).
% 0.19/0.52 tff(377,plain,
% 0.19/0.52 (((~![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))),
% 0.19/0.52 inference(transitivity,[status(thm)],[376, 374])).
% 0.19/0.52 tff(378,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(379,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.19/0.52 tff(380,plain,
% 0.19/0.52 (lesseq(X!5, X!5)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[379, 43])).
% 0.19/0.52 tff(381,plain,
% 0.19/0.52 ((~((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5)))) | (~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(382,plain,
% 0.19/0.52 (~((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[381, 380, 10])).
% 0.19/0.52 tff(383,assumption,(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)), introduced(assumption)).
% 0.19/0.52 tff(384,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(385,plain,
% 0.19/0.52 ((~(((~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)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(386,plain,
% 0.19/0.52 ((((~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))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(387,plain,
% 0.19/0.52 ((~(((~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)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[386])).
% 0.19/0.52 tff(388,plain,
% 0.19/0.52 ((~(((~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)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[387, 385])).
% 0.19/0.52 tff(389,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[388])).
% 0.19/0.52 tff(390,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[389, 384])).
% 0.19/0.52 tff(391,plain,
% 0.19/0.52 ((~![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)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(392,plain,
% 0.19/0.52 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.19/0.52 tff(393,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[392, 265, 383])).
% 0.19/0.52 tff(394,plain,(~(((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) <=> ub(X!5, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(395,plain,
% 0.19/0.52 ((((~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)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(396,plain,
% 0.19/0.52 (((~lesseq(X!5, X!5)) | (~lesseq(Y!4, X!5))) | ub(X!5, Y!4, X!5)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[395, 394])).
% 0.19/0.52 tff(397,plain,
% 0.19/0.52 (ub(X!5, Y!4, X!5)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[396, 382])).
% 0.19/0.52 tff(398,plain,
% 0.19/0.52 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(399,plain,
% 0.19/0.52 (~((~((~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(sum(c, 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(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[398, 172])).
% 0.19/0.52 tff(400,plain,
% 0.19/0.52 (((~((~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(sum(c, 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(sum(c, 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(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(401,plain,
% 0.19/0.52 (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(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[400, 399])).
% 0.19/0.52 tff(402,plain,
% 0.19/0.52 (((~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)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(403,plain,
% 0.19/0.52 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[402, 367])).
% 0.19/0.52 tff(404,plain,
% 0.19/0.52 (((~![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)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(405,plain,
% 0.19/0.52 ((~![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)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(406,plain,
% 0.19/0.52 ((~![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))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.19/0.52 tff(407,plain,
% 0.19/0.52 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[406, 403, 192])).
% 0.19/0.52 tff(408,plain,
% 0.19/0.52 ((~(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(sum(c, 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(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(409,plain,
% 0.19/0.52 ((~(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(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[408, 407])).
% 0.19/0.52 tff(410,plain,
% 0.19/0.52 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[409, 401])).
% 0.19/0.52 tff(411,plain,
% 0.19/0.52 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(412,plain,
% 0.19/0.52 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(413,plain,
% 0.19/0.52 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.19/0.52 tff(414,plain,
% 0.19/0.52 ((~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[413, 410])).
% 0.19/0.52 tff(415,plain,
% 0.19/0.52 (~lesseq(sum(c, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[414, 397])).
% 0.19/0.52 tff(416,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[415, 373])).
% 0.19/0.52 tff(417,plain,(minsol_model_max(X!5, Y!4, Z!3) | (~lesseq(Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(418,plain,
% 0.19/0.52 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[417, 10])).
% 0.19/0.52 tff(419,plain,
% 0.19/0.52 (((~(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))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(420,plain,
% 0.19/0.52 ((~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)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[419, 362])).
% 0.19/0.52 tff(421,plain,
% 0.19/0.52 ((~((~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)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(422,plain,
% 0.19/0.52 ((~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)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[421, 420])).
% 0.19/0.52 tff(423,plain,
% 0.19/0.52 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[422, 418])).
% 0.19/0.52 tff(424,plain,
% 0.19/0.52 (((~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)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(425,plain,
% 0.19/0.52 (model_max(X!5, Y!4, Z!3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[424, 423])).
% 0.19/0.52 tff(426,plain,
% 0.19/0.52 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), Z!3))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(427,plain,
% 0.19/0.52 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), Z!3))) | lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[426, 425])).
% 0.19/0.52 tff(428,plain,
% 0.19/0.52 (lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[427, 9])).
% 0.19/0.52 tff(429,assumption,(~(max(sum(c, max(X!5, Y!4)), Z!3) = Z!3)), introduced(assumption)).
% 0.19/0.52 tff(430,assumption,(lesseq(sum(c, max(X!5, Y!4)), Z!3)), introduced(assumption)).
% 0.19/0.52 tff(431,plain,
% 0.19/0.52 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (max(sum(c, max(X!5, Y!4)), Z!3) = Z!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (max(sum(c, max(X!5, Y!4)), Z!3) = Z!3))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(432,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (max(sum(c, max(X!5, Y!4)), Z!3) = Z!3))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(433,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (max(sum(c, max(X!5, Y!4)), Z!3) = Z!3)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.19/0.52 tff(434,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[433, 60, 430, 429])).
% 0.19/0.52 tff(435,plain,((~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (max(sum(c, max(X!5, Y!4)), Z!3) = Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(436,plain,
% 0.19/0.52 (max(sum(c, max(X!5, Y!4)), Z!3) = Z!3),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[435, 428])).
% 0.19/0.52 tff(437,plain,
% 0.19/0.52 (((~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))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(438,plain,
% 0.19/0.52 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[437, 423])).
% 0.19/0.52 tff(439,plain,
% 0.19/0.52 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(X!5, Y!4, sum(c, max(X!5, Y!4))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(440,plain,
% 0.19/0.52 (model_max(X!5, Y!4, sum(c, max(X!5, Y!4))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[439, 7])).
% 0.19/0.52 tff(441,plain,
% 0.19/0.52 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(442,plain,
% 0.19/0.52 ((lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4)))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(443,plain,
% 0.19/0.52 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[442])).
% 0.19/0.53 tff(444,plain,
% 0.19/0.53 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[443, 441])).
% 0.19/0.53 tff(445,plain,
% 0.19/0.53 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(446,plain,
% 0.19/0.53 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.19/0.53 tff(447,plain,
% 0.19/0.53 (lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[446, 43])).
% 0.19/0.53 tff(448,plain,
% 0.19/0.53 ((~(model_max(X!5, Y!4, sum(c, max(X!5, Y!4))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))) | model_max(X!5, Y!4, sum(c, max(X!5, Y!4))) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(449,plain,
% 0.19/0.53 (model_max(X!5, Y!4, sum(c, max(X!5, Y!4)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[448, 447, 440])).
% 0.19/0.53 tff(450,assumption,(~lesseq(Z!3, sum(c, max(X!5, Y!4)))), introduced(assumption)).
% 0.19/0.53 tff(451,assumption,(![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.19/0.53 tff(452,plain,
% 0.19/0.53 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, sum(c, max(X!5, Y!4)))) | lesseq(Z!3, sum(c, max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, sum(c, max(X!5, Y!4)))) | lesseq(Z!3, sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(453,plain,
% 0.19/0.53 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, sum(c, max(X!5, Y!4)))) | lesseq(Z!3, sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(454,plain,
% 0.19/0.53 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, sum(c, max(X!5, Y!4)))) | lesseq(Z!3, sum(c, max(X!5, Y!4)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.19/0.53 tff(455,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[454, 451, 450, 449])).
% 0.19/0.53 tff(456,plain,((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | lesseq(Z!3, sum(c, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(457,plain,
% 0.19/0.53 (lesseq(Z!3, sum(c, max(X!5, Y!4)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[456, 438])).
% 0.19/0.53 tff(458,assumption,(lesseq(Z!3, sum(c, max(X!5, Y!4)))), introduced(assumption)).
% 0.19/0.53 tff(459,assumption,(~(max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4)))), introduced(assumption)).
% 0.19/0.53 tff(460,plain,
% 0.19/0.53 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(461,plain,
% 0.19/0.53 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(462,plain,
% 0.19/0.53 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.19/0.53 tff(463,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[462, 21, 459, 458])).
% 0.19/0.53 tff(464,plain,((~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(465,plain,
% 0.19/0.53 (max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[464, 457])).
% 0.19/0.53 tff(466,plain,
% 0.19/0.53 ((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))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(467,plain,
% 0.19/0.53 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[466, 124])).
% 0.19/0.53 tff(468,plain,
% 0.19/0.53 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[467, 418])).
% 0.19/0.53 tff(469,plain,
% 0.19/0.53 (((~![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))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(470,plain,
% 0.19/0.53 ((~![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))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(471,plain,
% 0.19/0.53 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.19/0.53 tff(472,plain,
% 0.19/0.53 (lesseq(Z!3, Z!3)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[471, 425, 438])).
% 0.19/0.53 tff(473,assumption,(max(sum(c, max(X!5, Y!4)), Z!3) = Z!3), introduced(assumption)).
% 0.19/0.53 tff(474,assumption,(max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4))), introduced(assumption)).
% 0.19/0.53 tff(475,plain,
% 0.19/0.53 (sum(c, max(X!5, Y!4)) = max(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.53 inference(symmetry,[status(thm)],[474])).
% 0.19/0.53 tff(476,plain,
% 0.19/0.53 (sum(c, X!5) = sum(c, max(X!5, Y!4))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[278])).
% 0.19/0.53 tff(477,plain,
% 0.19/0.53 (sum(c, X!5) = Z!3),
% 0.19/0.53 inference(transitivity,[status(thm)],[476, 475, 473])).
% 0.19/0.53 tff(478,plain,
% 0.19/0.53 (lesseq(sum(c, X!5), Z!3) <=> lesseq(Z!3, Z!3)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[477])).
% 0.19/0.53 tff(479,plain,
% 0.19/0.53 (lesseq(Z!3, Z!3) <=> lesseq(sum(c, X!5), Z!3)),
% 0.19/0.53 inference(symmetry,[status(thm)],[478])).
% 0.19/0.53 tff(480,assumption,(lesseq(Z!3, Z!3)), introduced(assumption)).
% 0.19/0.53 tff(481,plain,
% 0.19/0.53 (lesseq(sum(c, X!5), Z!3)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.19/0.53 tff(482,assumption,(~lesseq(sum(c, X!5), Z!3)), introduced(assumption)).
% 0.19/0.53 tff(483,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[482, 481])).
% 0.19/0.53 tff(484,plain,(lesseq(sum(c, X!5), Z!3) | (~lesseq(Z!3, Z!3)) | (~(max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4)))) | (~(max(sum(c, max(X!5, Y!4)), Z!3) = Z!3)) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(485,plain,
% 0.19/0.53 (lesseq(sum(c, X!5), Z!3)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[484, 472, 465, 436, 27])).
% 0.19/0.53 tff(486,assumption,(lesseq(sum(c, X!5), Z!3)), introduced(assumption)).
% 0.19/0.53 tff(487,assumption,(![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))), introduced(assumption)).
% 0.19/0.53 tff(488,assumption,(ub(X!5, Y!4, X!5)), introduced(assumption)).
% 0.19/0.53 tff(489,plain,
% 0.19/0.53 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), Z!3)))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), Z!3)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(490,plain,
% 0.19/0.53 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | ((~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), Z!3)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(491,plain,
% 0.19/0.53 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), Z!3))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.19/0.53 tff(492,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[491, 488, 487, 486])).
% 0.19/0.53 tff(493,plain,((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | (~ub(X!5, Y!4, X!5)) | (~lesseq(sum(c, X!5), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(494,plain,
% 0.19/0.53 (~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[493, 397, 485])).
% 0.19/0.53 tff(495,plain,
% 0.19/0.53 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, Z), Z!3))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(496,plain,
% 0.19/0.53 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[495, 180])).
% 0.19/0.53 tff(497,plain,
% 0.19/0.53 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3))))) | model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(498,plain,
% 0.19/0.53 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[497, 496])).
% 0.19/0.53 tff(499,plain,
% 0.19/0.53 (model_ub(X!5, Y!4, Z!3)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[498, 494])).
% 0.19/0.53 tff(500,plain,
% 0.19/0.53 (((~(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)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(501,plain,
% 0.19/0.53 (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))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[500, 151])).
% 0.19/0.53 tff(502,plain,
% 0.19/0.53 ((~(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))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(503,plain,
% 0.19/0.53 (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))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[502, 501])).
% 0.19/0.53 tff(504,plain,
% 0.19/0.53 (~((~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)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[503, 499, 468])).
% 0.19/0.53 tff(505,plain,
% 0.19/0.53 (((~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)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(506,plain,
% 0.19/0.53 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[505, 504])).
% 0.19/0.53 tff(507,plain,
% 0.19/0.53 (((~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))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(508,plain,
% 0.19/0.53 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[507, 504])).
% 0.19/0.53 tff(509,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(sum(c, 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(sum(c, 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)).
% 0.19/0.53 tff(510,plain,
% 0.19/0.53 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(511,plain,
% 0.19/0.53 ((~((~((~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(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, 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)))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(512,plain,
% 0.19/0.53 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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))))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[511])).
% 0.19/0.53 tff(513,plain,
% 0.19/0.53 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, 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))))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[512, 510])).
% 0.19/0.53 tff(514,plain,
% 0.19/0.53 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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(sum(c, 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(sum(c, Z), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(515,plain,
% 0.19/0.53 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.19/0.54 tff(516,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[515, 172, 509])).
% 0.19/0.54 tff(517,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(sum(c, 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(sum(c, 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,[]))).
% 0.19/0.54 tff(518,plain,
% 0.19/0.54 (((~(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(sum(c, 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(sum(c, 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(sum(c, 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))))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(519,plain,
% 0.19/0.54 ((~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(sum(c, 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)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[518, 517])).
% 0.19/0.54 tff(520,plain,
% 0.19/0.54 ((~((~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(sum(c, 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(sum(c, 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)))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(521,plain,
% 0.19/0.54 ((~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(sum(c, 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)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[520, 519])).
% 0.19/0.54 tff(522,plain,
% 0.19/0.54 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[521, 508])).
% 0.19/0.54 tff(523,plain,
% 0.19/0.54 (sum(c, max(X!5, Y!4)) = sum(c, X!5)),
% 0.19/0.54 inference(symmetry,[status(thm)],[476])).
% 0.19/0.54 tff(524,plain,
% 0.19/0.54 (Z!3 = max(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.54 inference(symmetry,[status(thm)],[473])).
% 0.19/0.54 tff(525,plain,
% 0.19/0.54 (Z!3 = sum(c, X!5)),
% 0.19/0.54 inference(transitivity,[status(thm)],[524, 474, 523])).
% 0.19/0.54 tff(526,plain,
% 0.19/0.54 (lesseq(Z!3, sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(sum(c, X!5), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[525])).
% 0.19/0.54 tff(527,plain,
% 0.19/0.54 (lesseq(sum(c, X!5), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(Z!3, sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.54 inference(symmetry,[status(thm)],[526])).
% 0.19/0.54 tff(528,plain,
% 0.19/0.54 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(sum(c, X!5), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(529,plain,
% 0.19/0.54 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(sum(c, X!5), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[528, 314])).
% 0.19/0.54 tff(530,plain,
% 0.19/0.54 ((~![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))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(531,plain,
% 0.19/0.54 (~(((~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)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[530, 265])).
% 0.19/0.54 tff(532,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(sum(c, 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)).
% 0.19/0.54 tff(533,plain,
% 0.19/0.54 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(534,plain,
% 0.19/0.54 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[533, 532])).
% 0.19/0.54 tff(535,plain,
% 0.19/0.54 ((((~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)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(536,plain,
% 0.19/0.54 ((((~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)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[535, 534])).
% 0.19/0.54 tff(537,plain,
% 0.19/0.54 (~((~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))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[536, 531])).
% 0.19/0.54 tff(538,plain,
% 0.19/0.54 (((~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))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(539,plain,
% 0.19/0.54 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[538, 537])).
% 0.19/0.54 tff(540,plain,
% 0.19/0.54 ((~(lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(sum(c, X!5), sum(c, 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(sum(c, X!5), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(541,plain,
% 0.19/0.54 (lesseq(sum(c, X!5), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[540, 539, 529])).
% 0.19/0.54 tff(542,plain,
% 0.19/0.54 (lesseq(Z!3, sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[541, 527])).
% 0.19/0.54 tff(543,plain,
% 0.19/0.54 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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(sum(c, 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))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(544,plain,
% 0.19/0.54 (lesseq(sum(c, 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))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[543, 532])).
% 0.19/0.54 tff(545,assumption,(~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.19/0.54 tff(546,plain,
% 0.19/0.54 (((~![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(sum(c, 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, sum(c, 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(sum(c, 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, sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(547,plain,
% 0.19/0.54 ((~![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(sum(c, 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, sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(548,plain,
% 0.19/0.54 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.19/0.54 tff(549,plain,
% 0.19/0.54 (~lesseq(Z!3, sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[548, 332, 545, 544])).
% 0.19/0.54 tff(550,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[549, 542])).
% 0.19/0.54 tff(551,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(sum(c, 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(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4)))) | (~(max(sum(c, 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,[]))).
% 0.19/0.54 tff(552,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[551, 522, 506, 27, 465, 436])).
% 0.19/0.54 tff(553,plain,(~lesseq(Y!4, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(554,assumption,(~lesseq(Y!4, X!5)), introduced(assumption)).
% 0.19/0.54 tff(555,assumption,(~(max(X!5, Y!4) = Y!4)), introduced(assumption)).
% 0.19/0.54 tff(556,plain,
% 0.19/0.54 (~lesseq(X!5, Y!4)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[294, 60, 555])).
% 0.19/0.54 tff(557,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[290, 43, 554, 556])).
% 0.19/0.54 tff(558,plain,(lesseq(Y!4, X!5) | (max(X!5, Y!4) = Y!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(559,plain,
% 0.19/0.54 (max(X!5, Y!4) = Y!4),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[558, 554])).
% 0.19/0.54 tff(560,plain,
% 0.19/0.54 (Y!4 = max(X!5, Y!4)),
% 0.19/0.54 inference(symmetry,[status(thm)],[559])).
% 0.19/0.54 tff(561,plain,
% 0.19/0.54 (sum(c, Y!4) = sum(c, max(X!5, Y!4))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[560])).
% 0.19/0.54 tff(562,plain,
% 0.19/0.54 (lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[561])).
% 0.19/0.54 tff(563,plain,
% 0.19/0.54 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.54 inference(symmetry,[status(thm)],[562])).
% 0.19/0.54 tff(564,plain,
% 0.19/0.54 (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[178, 172])).
% 0.19/0.54 tff(565,plain,
% 0.19/0.54 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[181, 564])).
% 0.19/0.54 tff(566,plain,
% 0.19/0.54 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, 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(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[183, 158])).
% 0.19/0.54 tff(567,plain,
% 0.19/0.54 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[566, 565])).
% 0.19/0.54 tff(568,plain,
% 0.19/0.54 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[186, 567])).
% 0.19/0.54 tff(569,plain,
% 0.19/0.54 (lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[568, 115])).
% 0.19/0.55 tff(570,plain,
% 0.19/0.55 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[189, 569, 113])).
% 0.19/0.55 tff(571,plain,
% 0.19/0.55 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[193, 567])).
% 0.19/0.55 tff(572,plain,
% 0.19/0.55 ((~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)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[231, 571, 192])).
% 0.19/0.55 tff(573,plain,
% 0.19/0.55 ((~((~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)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[233, 572])).
% 0.19/0.55 tff(574,plain,
% 0.19/0.55 (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)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[573, 570, 111])).
% 0.19/0.55 tff(575,plain,
% 0.19/0.55 (~((~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))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[236, 574, 109])).
% 0.19/0.55 tff(576,plain,
% 0.19/0.55 (![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))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[238, 575])).
% 0.19/0.55 tff(577,plain,
% 0.19/0.55 (lesseq(Z!3, sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[242, 576, 78])).
% 0.19/0.55 tff(578,plain,
% 0.19/0.55 (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[247, 577])).
% 0.19/0.55 tff(579,plain,
% 0.19/0.55 (max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) = Z!3),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[251, 60, 568])).
% 0.19/0.55 tff(580,plain,
% 0.19/0.55 (Z!3 = max(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.19/0.55 inference(symmetry,[status(thm)],[579])).
% 0.19/0.55 tff(581,plain,
% 0.19/0.55 (Z!3 = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(transitivity,[status(thm)],[580, 578])).
% 0.19/0.55 tff(582,plain,
% 0.19/0.55 (lesseq(sum(c, max(X!5, Y!4)), Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[581])).
% 0.19/0.55 tff(583,plain,
% 0.19/0.55 ((((~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)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[268, 571])).
% 0.19/0.55 tff(584,plain,
% 0.19/0.55 (~((~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))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[583, 267])).
% 0.19/0.55 tff(585,plain,
% 0.19/0.55 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[271, 584])).
% 0.19/0.55 tff(586,plain,
% 0.19/0.55 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[273, 584])).
% 0.19/0.55 tff(587,plain,
% 0.19/0.55 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[304, 586, 585])).
% 0.19/0.55 tff(588,plain,
% 0.19/0.55 (lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[340, 587, 568])).
% 0.19/0.55 tff(589,plain,
% 0.19/0.55 (lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[588, 582])).
% 0.19/0.55 tff(590,plain,
% 0.19/0.55 (model_max(X!5, Y!4, Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[359, 579, 578, 589])).
% 0.19/0.55 tff(591,plain,
% 0.19/0.55 (~((~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)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[366, 590, 34])).
% 0.19/0.55 tff(592,plain,
% 0.19/0.55 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[368, 591])).
% 0.19/0.55 tff(593,plain,
% 0.19/0.55 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[370, 592])).
% 0.19/0.55 tff(594,plain,
% 0.19/0.55 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[593, 33])).
% 0.19/0.55 tff(595,plain,
% 0.19/0.55 (lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[594, 563])).
% 0.19/0.55 tff(596,plain,
% 0.19/0.55 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[402, 591])).
% 0.19/0.55 tff(597,plain,
% 0.19/0.55 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[406, 596, 192])).
% 0.19/0.55 tff(598,plain,
% 0.19/0.55 ((~(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(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[408, 597])).
% 0.19/0.55 tff(599,plain,
% 0.19/0.55 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[598, 401])).
% 0.19/0.55 tff(600,plain,
% 0.19/0.55 (lesseq(X!5, Y!4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[290, 43, 554])).
% 0.19/0.55 tff(601,plain,
% 0.19/0.55 (((~![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))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(602,plain,
% 0.19/0.55 ((lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(603,plain,
% 0.19/0.55 (((~![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))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[602])).
% 0.19/0.55 tff(604,plain,
% 0.19/0.55 (((~![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))),
% 0.19/0.55 inference(transitivity,[status(thm)],[603, 601])).
% 0.19/0.55 tff(605,plain,
% 0.19/0.55 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(606,plain,
% 0.19/0.55 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.19/0.55 tff(607,plain,
% 0.19/0.55 (lesseq(Y!4, Y!4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[606, 43])).
% 0.19/0.55 tff(608,plain,
% 0.19/0.55 ((~((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4)))) | (~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(609,plain,
% 0.19/0.55 (~((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[608, 607, 600])).
% 0.19/0.55 tff(610,assumption,(((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) <=> ub(X!5, Y!4, Y!4)), introduced(assumption)).
% 0.19/0.55 tff(611,plain,
% 0.19/0.55 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) <=> ub(X!5, Y!4, Y!4)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(612,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[611, 265, 610])).
% 0.19/0.55 tff(613,plain,(~(((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) <=> ub(X!5, Y!4, Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(614,plain,
% 0.19/0.55 ((((~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)),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(615,plain,
% 0.19/0.55 (((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4))) | ub(X!5, Y!4, Y!4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[614, 613])).
% 0.19/0.55 tff(616,plain,
% 0.19/0.55 (ub(X!5, Y!4, Y!4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[615, 609])).
% 0.19/0.55 tff(617,plain,
% 0.19/0.55 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(618,plain,
% 0.19/0.55 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(619,plain,
% 0.19/0.55 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.19/0.55 tff(620,plain,
% 0.19/0.55 (~lesseq(sum(c, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[619, 616, 599])).
% 0.19/0.55 tff(621,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[620, 595])).
% 0.19/0.55 tff(622,plain,(minsol_model_max(X!5, Y!4, Z!3) | lesseq(Y!4, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(623,plain,
% 0.19/0.55 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[622, 553])).
% 0.19/0.55 tff(624,plain,
% 0.19/0.55 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[422, 623])).
% 0.19/0.55 tff(625,plain,
% 0.19/0.55 (model_max(X!5, Y!4, Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[424, 624])).
% 0.19/0.55 tff(626,plain,
% 0.19/0.55 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), Z!3))) | lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[426, 625])).
% 0.19/0.55 tff(627,plain,
% 0.19/0.55 (lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[626, 9])).
% 0.19/0.55 tff(628,plain,
% 0.19/0.55 (max(sum(c, max(X!5, Y!4)), Z!3) = Z!3),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[435, 627])).
% 0.19/0.55 tff(629,plain,
% 0.19/0.55 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[437, 624])).
% 0.19/0.55 tff(630,plain,
% 0.19/0.55 (lesseq(Z!3, sum(c, max(X!5, Y!4)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[456, 629])).
% 0.19/0.55 tff(631,plain,
% 0.19/0.55 (max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[464, 630])).
% 0.19/0.55 tff(632,plain,
% 0.19/0.55 (max(X!5, Y!4) = Y!4),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[558, 553])).
% 0.19/0.55 tff(633,plain,
% 0.19/0.55 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[467, 623])).
% 0.19/0.55 tff(634,plain,
% 0.19/0.55 (lesseq(Z!3, Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[471, 625, 629])).
% 0.19/0.55 tff(635,assumption,(max(X!5, Y!4) = Y!4), introduced(assumption)).
% 0.19/0.55 tff(636,plain,
% 0.19/0.55 (Y!4 = max(X!5, Y!4)),
% 0.19/0.55 inference(symmetry,[status(thm)],[635])).
% 0.19/0.55 tff(637,plain,
% 0.19/0.55 (sum(c, Y!4) = sum(c, max(X!5, Y!4))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[636])).
% 0.19/0.55 tff(638,plain,
% 0.19/0.55 (sum(c, Y!4) = Z!3),
% 0.19/0.55 inference(transitivity,[status(thm)],[637, 475, 473])).
% 0.19/0.55 tff(639,plain,
% 0.19/0.55 (lesseq(sum(c, Y!4), Z!3) <=> lesseq(Z!3, Z!3)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[638])).
% 0.19/0.55 tff(640,plain,
% 0.19/0.55 (lesseq(Z!3, Z!3) <=> lesseq(sum(c, Y!4), Z!3)),
% 0.19/0.55 inference(symmetry,[status(thm)],[639])).
% 0.19/0.55 tff(641,plain,
% 0.19/0.55 (lesseq(sum(c, Y!4), Z!3)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[480, 640])).
% 0.19/0.55 tff(642,assumption,(~lesseq(sum(c, Y!4), Z!3)), introduced(assumption)).
% 0.19/0.55 tff(643,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[642, 641])).
% 0.19/0.55 tff(644,plain,(lesseq(sum(c, Y!4), Z!3) | (~lesseq(Z!3, Z!3)) | (~(max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4)))) | (~(max(sum(c, max(X!5, Y!4)), Z!3) = Z!3)) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(645,plain,
% 0.19/0.55 (lesseq(sum(c, Y!4), Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[644, 628, 632, 631, 634])).
% 0.19/0.55 tff(646,plain,
% 0.19/0.55 (lesseq(X!5, Y!4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[290, 43, 553])).
% 0.19/0.55 tff(647,plain,
% 0.19/0.55 (~((~lesseq(Y!4, Y!4)) | (~lesseq(X!5, Y!4)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[608, 607, 646])).
% 0.19/0.55 tff(648,plain,
% 0.19/0.55 (ub(X!5, Y!4, Y!4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[615, 647])).
% 0.19/0.55 tff(649,assumption,(lesseq(sum(c, Y!4), Z!3)), introduced(assumption)).
% 0.19/0.55 tff(650,assumption,(ub(X!5, Y!4, Y!4)), introduced(assumption)).
% 0.19/0.55 tff(651,plain,
% 0.19/0.55 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), Z!3)))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), Z!3)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(652,plain,
% 0.19/0.55 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | ((~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), Z!3)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(653,plain,
% 0.19/0.55 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), Z!3))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.19/0.55 tff(654,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[653, 650, 649, 487])).
% 0.19/0.55 tff(655,plain,((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))) | (~ub(X!5, Y!4, Y!4)) | (~lesseq(sum(c, Y!4), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(656,plain,
% 0.19/0.55 (~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), Z!3)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[655, 648, 645])).
% 0.19/0.55 tff(657,plain,
% 0.19/0.55 (model_ub(X!5, Y!4, Z!3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[498, 656])).
% 0.19/0.55 tff(658,plain,
% 0.19/0.55 (~((~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)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[503, 657, 633])).
% 0.19/0.55 tff(659,plain,
% 0.19/0.55 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[505, 658])).
% 0.19/0.55 tff(660,plain,
% 0.19/0.55 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[507, 658])).
% 0.19/0.55 tff(661,plain,
% 0.19/0.55 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[521, 660])).
% 0.19/0.55 tff(662,plain,
% 0.19/0.55 (sum(c, max(X!5, Y!4)) = sum(c, Y!4)),
% 0.19/0.55 inference(symmetry,[status(thm)],[637])).
% 0.19/0.55 tff(663,plain,
% 0.19/0.55 (lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(sum(c, Y!4), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[662])).
% 0.19/0.55 tff(664,plain,
% 0.19/0.55 (lesseq(sum(c, Y!4), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.55 inference(symmetry,[status(thm)],[663])).
% 0.19/0.55 tff(665,plain,
% 0.19/0.55 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(sum(c, Y!4), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(666,plain,
% 0.19/0.55 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(sum(c, Y!4), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[665, 314])).
% 0.19/0.55 tff(667,plain,
% 0.19/0.55 (((~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))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(668,plain,
% 0.19/0.55 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[667, 537])).
% 0.19/0.55 tff(669,plain,
% 0.19/0.55 ((~(lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(sum(c, Y!4), sum(c, 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(sum(c, Y!4), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(670,plain,
% 0.19/0.55 (lesseq(sum(c, Y!4), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[669, 668, 666])).
% 0.19/0.55 tff(671,plain,
% 0.19/0.55 (lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[670, 664])).
% 0.19/0.55 tff(672,plain,
% 0.19/0.55 (sum(c, max(X!5, Y!4)) = Z!3),
% 0.19/0.55 inference(transitivity,[status(thm)],[475, 473])).
% 0.19/0.55 tff(673,plain,
% 0.19/0.55 (lesseq(sum(c, 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))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[672])).
% 0.19/0.55 tff(674,plain,
% 0.19/0.55 (lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(symmetry,[status(thm)],[673])).
% 0.19/0.55 tff(675,plain,
% 0.19/0.55 ((~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[674])).
% 0.19/0.55 tff(676,plain,
% 0.19/0.55 (~lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[545, 675])).
% 0.19/0.55 tff(677,plain,
% 0.19/0.55 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, 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(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, 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(sum(c, 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(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(678,plain,
% 0.19/0.55 ((lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, 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(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) <=> ((~lesseq(sum(c, 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(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(679,plain,
% 0.19/0.55 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, 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(sum(c, max(X!5, Y!4)), sum(c, 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(sum(c, 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(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[678])).
% 0.19/0.56 tff(680,plain,
% 0.19/0.56 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, 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(sum(c, max(X!5, Y!4)), sum(c, 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(sum(c, 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(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[679, 677])).
% 0.19/0.56 tff(681,plain,
% 0.19/0.56 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, 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(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(682,plain,
% 0.19/0.56 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.19/0.56 tff(683,plain,
% 0.19/0.56 (~lesseq(sum(c, max(X!5, Y!4)), sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[682, 332, 676, 544])).
% 0.19/0.56 tff(684,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[683, 671])).
% 0.19/0.56 tff(685,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(sum(c, 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(sum(c, max(X!5, Y!4)), Z!3) = Z!3)) | (~(max(sum(c, max(X!5, Y!4)), Z!3) = sum(c, max(X!5, Y!4))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(686,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[685, 661, 659, 632, 631, 628])).
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56 % E exiting
%------------------------------------------------------------------------------