TSTP Solution File: NUM858_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM858_1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Sun Sep 18 13:12:19 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM858_1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 15:34:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(ub_type, type, (
% 0.19/0.40 ub: ( $int * $int * $int ) > $o)).
% 0.19/0.40 tff(tptp_fun_Z_2_type, type, (
% 0.19/0.40 tptp_fun_Z_2: $int)).
% 0.19/0.40 tff(tptp_fun_X_4_type, type, (
% 0.19/0.40 tptp_fun_X_4: $int)).
% 0.19/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.40 tptp_fun_Y_3: $int)).
% 0.19/0.40 tff(max_type, type, (
% 0.19/0.40 max: ( $int * $int ) > $int)).
% 0.19/0.40 tff(model_ub_type, type, (
% 0.19/0.40 model_ub: ( $int * $int * $int ) > $o)).
% 0.19/0.40 tff(minsol_model_ub_type, type, (
% 0.19/0.40 minsol_model_ub: ( $int * $int * $int ) > $o)).
% 0.19/0.40 tff(minsol_model_max_type, type, (
% 0.19/0.40 minsol_model_max: ( $int * $int * $int ) > $o)).
% 0.19/0.40 tff(model_max_type, type, (
% 0.19/0.40 model_max: ( $int * $int * $int ) > $o)).
% 0.19/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.40 tptp_fun_Z_0: ( $int * $int * $int ) > $int)).
% 0.19/0.40 tff(tptp_fun_Z_1_type, type, (
% 0.19/0.40 tptp_fun_Z_1: ( $int * $int * $int ) > $int)).
% 0.19/0.40 tff(1,assumption,(~$lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0)) | $lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (~($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.40 tff(4,assumption,(~$lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 ((~($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)) | $lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (^[X: $int, Y: $int] : refl(((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)) <=> ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)) <=> ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (^[X: $int, Y: $int] : rewrite(((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)) <=> ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)) <=> ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[X: $int, Y: $int] : rewrite(((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ((~$lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.40 tff(16,axiom,(![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_1')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 10])).
% 0.19/0.41 tff(21,plain,(
% 0.19/0.41 ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(skolemize,[status(sab)],[20])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 8])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (((~$greatereq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)) <=> ((~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(transitivity,[status(thm)],[25, 23])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 ((~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (~$lesseq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[29, 6])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ($greatereq($sum(Y!3, $product(-1, X!4)), 0) | $lesseq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ($greatereq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (^[X: $int, Y: $int] : refl(((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (^[X: $int, Y: $int] : rewrite(((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (^[X: $int, Y: $int] : rewrite(((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ((~$lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.41 tff(42,axiom,(![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_2')).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 36])).
% 0.19/0.41 tff(47,plain,(
% 0.19/0.41 ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(skolemize,[status(sab)],[46])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 34])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$greatereq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (((~$lesseq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0)) <=> ((~$greatereq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$greatereq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!4, $product(-1, Y!3)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$greatereq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~$greatereq($sum(Y!3, $product(-1, X!4)), 0)) | ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[54, 48])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[55, 32])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ($lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0) | (~$lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)) | (~$greatereq($sum(Y!3, $product(-1, X!4)), 0))),
% 0.19/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (~$lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 32, 4])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[2, 58, 56])).
% 0.19/0.41 tff(60,plain,($lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ($lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0) | (~$lesseq($sum(Y!3, $product(-1, X!4)), 0)) | (~$lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0))),
% 0.19/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (~$lesseq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 1, 60])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ($greatereq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[55, 63, 3])).
% 0.19/0.41 tff(65,plain,($lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(66,assumption,(~(ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))), introduced(assumption)).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (^[X: $int, Y: $int, Z: $int] : refl((ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))) <=> (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (^[X: $int, Y: $int, Z: $int] : rewrite((ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (^[X: $int, Y: $int, Z: $int] : rewrite((ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (^[X: $int, Y: $int, Z: $int] : rewrite((ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z))) <=> (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,axiom,(![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ub')).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 72])).
% 0.19/0.41 tff(80,plain,(
% 0.19/0.41 ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[79])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 68])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((ub(X!4, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0))))) <=> (ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[88, 82, 66])).
% 0.19/0.41 tff(90,plain,(ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(91,assumption,(~(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))), introduced(assumption)).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (^[X: $int, Y: $int, N: $int] : refl((model_ub(X, Y, N) <=> ub(X, Y, N)) <=> (model_ub(X, Y, N) <=> ub(X, Y, N)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N)) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N)) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(95,axiom,(![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_ub_1')).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.41 tff(97,plain,(
% 0.19/0.41 ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.41 inference(skolemize,[status(sab)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[99, 98, 91])).
% 0.19/0.41 tff(101,plain,(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(102,assumption,(~$greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((~($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)) | $greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (~($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.41 tff(105,assumption,(~(model_max(X!4, Y!3, Z!2) <=> ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0))), introduced(assumption)).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (^[X: $int, Y: $int, N: $int] : refl((model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0)) <=> (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (^[X: $int, Y: $int, N: $int] : rewrite((model_max(X, Y, N) <=> (N = max(X, Y))) <=> (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> (N = max(X, Y))) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> (N = max(X, Y))) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> (N = max(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(111,axiom,(![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> (N = max(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_max_1')).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> (N = max(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.19/0.41 tff(114,plain,(
% 0.19/0.41 ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(skolemize,[status(sab)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0))) | (model_max(X!4, Y!3, Z!2) <=> ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[116, 115, 105])).
% 0.19/0.41 tff(118,plain,(model_max(X!4, Y!3, Z!2) <=> ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~(model_max(X!4, Y!3, Z!2) <=> ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0))) | (~model_max(X!4, Y!3, Z!2)) | ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ((~model_max(X!4, Y!3, Z!2)) | ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (~model_max(X!4, Y!3, Z!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[120, 104])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))) | model_max(X!4, Y!3, Z!2)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (^[X: $int, Y: $int, N: $int] : rewrite((~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (^[X: $int, Y: $int, N: $int] : refl((~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))) <=> (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (^[X: $int, Y: $int, N: $int] : rewrite((~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))) <=> (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (^[X: $int, Y: $int, N: $int] : trans(monotonicity(rewrite(((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) <=> ((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))), rewrite((minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))) <=> (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) <=> (((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))), rewrite((((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) <=> (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) <=> (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (^[X: $int, Y: $int, N: $int] : rewrite((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))) <=> (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))) <=> ![X: $int, Y: $int, N: $int] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[133])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))) <=> (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : (model_max(X, Y, Z) => $lesseq(N, Z)))) <=> (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : (model_max(X, Y, Z) => $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.42 tff(140,axiom,(![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : (model_max(X, Y, Z) => $lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_max')).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[142, 136])).
% 0.19/0.42 tff(144,plain,(
% 0.19/0.42 ![X: $int, Y: $int, N: $int] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[143])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[145, 132])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[146, 130])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 (![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[147, 125])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 ((~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0))))))))) <=> (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0)))))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[150])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0)))))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[151, 149])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_0(N, Y, X))), 0))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[154, 148])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))) | ((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 ((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 ((~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))) | (~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 ((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (~minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[159, 123])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 ((~(minsol_model_ub(X!4, Y!3, Z!2) <=> minsol_model_max(X!4, Y!3, Z!2))) <=> ((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 ((~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))) <=> (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(163,axiom,(~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[164, 162])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[165, 162])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[167, 162])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[168, 162])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.19/0.43 tff(171,plain,(
% 0.19/0.43 ~(minsol_model_ub(X!4, Y!3, Z!2) <=> minsol_model_max(X!4, Y!3, Z!2))),
% 0.19/0.43 inference(skolemize,[status(sab)],[170])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 ((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (minsol_model_ub(X!4, Y!3, Z!2) | minsol_model_max(X!4, Y!3, Z!2) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (minsol_model_ub(X!4, Y!3, Z!2) | minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 (minsol_model_ub(X!4, Y!3, Z!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[174, 160])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (^[X: $int, Y: $int, N: $int] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (^[X: $int, Y: $int, N: $int] : refl((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (^[X: $int, Y: $int, N: $int] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[181, 179])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (^[X: $int, Y: $int, N: $int] : trans(monotonicity(rewrite(((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) <=> ((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))), rewrite((minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))) <=> (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) <=> (((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))), rewrite((((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[183])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (^[X: $int, Y: $int, N: $int] : rewrite((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))) <=> (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))) <=> ![X: $int, Y: $int, N: $int] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))) <=> (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : (model_ub(X, Y, Z) => $lesseq(N, Z)))) <=> (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : (model_ub(X, Y, Z) => $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[190])).
% 0.19/0.43 tff(192,axiom,(![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : (model_ub(X, Y, Z) => $lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[194, 188])).
% 0.19/0.43 tff(196,plain,(
% 0.19/0.43 ![X: $int, Y: $int, N: $int] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[195])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[196, 186])).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[197, 184])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[198, 182])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[199, 177])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 ((~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0))))))))) <=> (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0)))))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[202])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0)))))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[203, 201])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $lesseq($sum(Z!2, $product(-1, Z)), 0)))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(206,plain,
% 0.19/0.44 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))))))) | (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.19/0.44 tff(207,plain,
% 0.19/0.44 (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[206, 200])).
% 0.19/0.44 tff(208,plain,
% 0.19/0.44 (((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))) | ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(209,plain,
% 0.19/0.44 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.19/0.44 tff(210,plain,
% 0.19/0.44 ((~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))))) | (~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(211,plain,
% 0.19/0.44 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.19/0.44 tff(212,plain,
% 0.19/0.44 (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[211, 175])).
% 0.19/0.44 tff(213,plain,
% 0.19/0.44 (((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))) | model_ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(214,plain,
% 0.19/0.44 (model_ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.19/0.44 tff(215,plain,
% 0.19/0.44 ((~(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))) | (~model_ub(X!4, Y!3, Z!2)) | ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(216,plain,
% 0.19/0.44 (ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[215, 214, 101])).
% 0.19/0.44 tff(217,assumption,($greatereq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.44 tff(218,plain,
% 0.19/0.44 ($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0) | (~$greatereq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0))),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(219,plain,
% 0.19/0.44 (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[218, 102, 217])).
% 0.19/0.44 tff(220,plain,
% 0.19/0.44 (((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))) | $greatereq($sum(Z!2, $product(-1, X!4)), 0)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(221,plain,
% 0.19/0.44 ((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.19/0.44 tff(222,plain,
% 0.19/0.44 ((~(ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))) | (~ub(X!4, Y!3, Z!2)) | (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(223,plain,
% 0.19/0.44 (~ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[222, 221, 90])).
% 0.19/0.44 tff(224,plain,
% 0.19/0.44 (~model_ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[215, 223, 101])).
% 0.19/0.44 tff(225,plain,
% 0.19/0.44 ((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[213, 224])).
% 0.19/0.44 tff(226,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[211, 225, 175])).
% 0.19/0.44 tff(227,plain,($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0) | (~$greatereq($sum(X!4, $product(-1, max(X!4, Y!3))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(228,plain,
% 0.19/0.44 (~$greatereq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[227, 102])).
% 0.19/0.44 tff(229,plain,
% 0.19/0.44 ((~($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)) | $greatereq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(230,plain,
% 0.19/0.44 (~($sum(X!4, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.19/0.44 tff(231,plain,
% 0.19/0.44 (~$lesseq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[29, 230])).
% 0.19/0.44 tff(232,plain,
% 0.19/0.44 ($greatereq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[31, 231])).
% 0.19/0.44 tff(233,plain,
% 0.19/0.44 ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[55, 232])).
% 0.19/0.44 tff(234,plain,
% 0.19/0.44 ((~($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0)) | $greatereq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(235,plain,
% 0.19/0.44 ($greatereq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.19/0.44 tff(236,plain,
% 0.19/0.44 ($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)) | (~$greatereq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0))),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(237,plain,
% 0.19/0.44 (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[236, 235, 102])).
% 0.19/0.44 tff(238,plain,
% 0.19/0.44 (((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))) | $greatereq($sum(Z!2, $product(-1, Y!3)), 0)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(239,plain,
% 0.19/0.44 ((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.19/0.44 tff(240,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[222, 239, 216, 90])).
% 0.19/0.44 tff(241,plain,($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(242,plain,
% 0.19/0.44 ($greatereq($sum(Z!2, $product(-1, X!4)), 0) | (~$lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)) | (~$greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0))),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(243,plain,
% 0.19/0.44 ($greatereq($sum(Z!2, $product(-1, X!4)), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[242, 241, 60])).
% 0.19/0.44 tff(244,plain,
% 0.19/0.44 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> ($sum(N, $product(-1, max(X, Y))) = 0))) | (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(245,plain,
% 0.19/0.44 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[244, 115])).
% 0.19/0.44 tff(246,assumption,(~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))), introduced(assumption)).
% 0.19/0.44 tff(247,plain,
% 0.19/0.44 (((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)) | model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(248,plain,
% 0.19/0.44 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.19/0.44 tff(249,plain,
% 0.19/0.44 ((~(model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0))) | (~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(250,plain,
% 0.19/0.44 ((~(model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0))) | ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.19/0.44 tff(251,plain,
% 0.19/0.44 ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[250, 245])).
% 0.19/0.44 tff(252,plain,
% 0.19/0.44 ((~($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0)) | $greatereq($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(253,plain,
% 0.19/0.44 ($greatereq($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.19/0.44 tff(254,assumption,($lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.44 tff(255,assumption,(~$lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.44 tff(256,plain,
% 0.19/0.44 ($lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0) | (~$lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)) | $greatereq($sum(Z!2, $product(-1, X!4)), 1)),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(257,plain,
% 0.19/0.44 ($greatereq($sum(Z!2, $product(-1, X!4)), 1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[256, 255, 254])).
% 0.19/0.44 tff(258,assumption,($lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.44 tff(259,plain,
% 0.19/0.44 ($greatereq($sum(Z!2, $product(-1, Y!3)), 1) | $lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0) | (~$lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0))),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(260,plain,
% 0.19/0.44 ($greatereq($sum(Z!2, $product(-1, Y!3)), 1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[259, 255, 258])).
% 0.19/0.44 tff(261,plain,
% 0.19/0.44 ((~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(262,plain,
% 0.19/0.44 (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[261, 260, 257])).
% 0.19/0.44 tff(263,plain,
% 0.19/0.44 ((~($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)) | $lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(264,plain,
% 0.19/0.44 (~($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[263, 255])).
% 0.19/0.44 tff(265,plain,
% 0.19/0.44 (~model_max(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[119, 264, 118])).
% 0.19/0.44 tff(266,plain,
% 0.19/0.44 ((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[122, 265])).
% 0.19/0.44 tff(267,plain,
% 0.19/0.44 (~minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[159, 266])).
% 0.19/0.45 tff(268,plain,
% 0.19/0.45 (minsol_model_ub(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[174, 267])).
% 0.19/0.45 tff(269,plain,
% 0.19/0.45 (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[211, 268])).
% 0.19/0.45 tff(270,plain,
% 0.19/0.45 (((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))) | ![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(271,plain,
% 0.19/0.45 (![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[270, 269])).
% 0.19/0.45 tff(272,plain,
% 0.19/0.45 (((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | (~model_ub(X!4, Y!3, $sum(-1, Z!2)))) <=> ((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | (~model_ub(X!4, Y!3, $sum(-1, Z!2))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(273,plain,
% 0.19/0.45 (((~model_ub(X!4, Y!3, $sum(-1, Z!2))) | $false) <=> (~model_ub(X!4, Y!3, $sum(-1, Z!2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(274,plain,
% 0.19/0.45 ($greatereq(-1, 0) <=> $false),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(275,plain,
% 0.19/0.45 ($sum($sum(-1, Z!2), $product(-1, Z!2)) = -1),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(276,plain,
% 0.19/0.45 ($greatereq($sum($sum(-1, Z!2), $product(-1, Z!2)), 0) <=> $greatereq(-1, 0)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[275])).
% 0.19/0.45 tff(277,plain,
% 0.19/0.45 ($greatereq($sum($sum(-1, Z!2), $product(-1, Z!2)), 0) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[276, 274])).
% 0.19/0.45 tff(278,plain,
% 0.19/0.45 (((~model_ub(X!4, Y!3, $sum(-1, Z!2))) | $greatereq($sum($sum(-1, Z!2), $product(-1, Z!2)), 0)) <=> ((~model_ub(X!4, Y!3, $sum(-1, Z!2))) | $false)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[277])).
% 0.19/0.45 tff(279,plain,
% 0.19/0.45 (((~model_ub(X!4, Y!3, $sum(-1, Z!2))) | $greatereq($sum($sum(-1, Z!2), $product(-1, Z!2)), 0)) <=> (~model_ub(X!4, Y!3, $sum(-1, Z!2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[278, 273])).
% 0.19/0.45 tff(280,plain,
% 0.19/0.45 (((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | ((~model_ub(X!4, Y!3, $sum(-1, Z!2))) | $greatereq($sum($sum(-1, Z!2), $product(-1, Z!2)), 0))) <=> ((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | (~model_ub(X!4, Y!3, $sum(-1, Z!2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[279])).
% 0.19/0.45 tff(281,plain,
% 0.19/0.45 (((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | ((~model_ub(X!4, Y!3, $sum(-1, Z!2))) | $greatereq($sum($sum(-1, Z!2), $product(-1, Z!2)), 0))) <=> ((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | (~model_ub(X!4, Y!3, $sum(-1, Z!2))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[280, 272])).
% 0.19/0.45 tff(282,plain,
% 0.19/0.45 ((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | ((~model_ub(X!4, Y!3, $sum(-1, Z!2))) | $greatereq($sum($sum(-1, Z!2), $product(-1, Z!2)), 0))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(283,plain,
% 0.19/0.45 ((~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))) | (~model_ub(X!4, Y!3, $sum(-1, Z!2)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.19/0.45 tff(284,plain,
% 0.19/0.45 (~model_ub(X!4, Y!3, $sum(-1, Z!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[283, 271])).
% 0.19/0.45 tff(285,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2)))) <=> ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(286,plain,
% 0.19/0.45 ((model_ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1))) <=> ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1)))) <=> (model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(287,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1))) <=> ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1))))) <=> ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[286])).
% 0.19/0.45 tff(288,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1))) <=> ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1))))) <=> ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[287, 285])).
% 0.19/0.45 tff(289,plain,
% 0.19/0.45 ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1))) <=> ub(X!4, Y!3, $sum($sum(0, $product(-1, $product(-1, Z!2))), $product(-1, 1))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(290,plain,
% 0.19/0.45 ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.45 tff(291,plain,
% 0.19/0.45 (model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[290, 98])).
% 0.19/0.45 tff(292,plain,
% 0.19/0.45 ((~(model_ub(X!4, Y!3, $sum(-1, Z!2)) <=> ub(X!4, Y!3, $sum(-1, Z!2)))) | model_ub(X!4, Y!3, $sum(-1, Z!2)) | (~ub(X!4, Y!3, $sum(-1, Z!2)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(293,plain,
% 0.19/0.45 (model_ub(X!4, Y!3, $sum(-1, Z!2)) | (~ub(X!4, Y!3, $sum(-1, Z!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.19/0.45 tff(294,plain,
% 0.19/0.45 (~ub(X!4, Y!3, $sum(-1, Z!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[293, 284])).
% 0.19/0.45 tff(295,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(296,plain,
% 0.19/0.45 ((ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$lesseq($sum(Y!3, $product(-1, $sum(-1, Z!2))), 0)) | (~$greatereq($sum($sum(-1, Z!2), $product(-1, X!4)), 0))))) <=> (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(297,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$lesseq($sum(Y!3, $product(-1, $sum(-1, Z!2))), 0)) | (~$greatereq($sum($sum(-1, Z!2), $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[296])).
% 0.19/0.45 tff(298,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$lesseq($sum(Y!3, $product(-1, $sum(-1, Z!2))), 0)) | (~$greatereq($sum($sum(-1, Z!2), $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[297, 295])).
% 0.19/0.45 tff(299,plain,
% 0.19/0.45 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$lesseq($sum(Y!3, $product(-1, $sum(-1, Z!2))), 0)) | (~$greatereq($sum($sum(-1, Z!2), $product(-1, X!4)), 0)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(300,plain,
% 0.19/0.45 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.19/0.45 tff(301,plain,
% 0.19/0.45 (ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[300, 82])).
% 0.19/0.45 tff(302,plain,
% 0.19/0.45 ((~(ub(X!4, Y!3, $sum(-1, Z!2)) <=> (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))))) | ub(X!4, Y!3, $sum(-1, Z!2)) | ((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(303,plain,
% 0.19/0.45 (ub(X!4, Y!3, $sum(-1, Z!2)) | ((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.19/0.45 tff(304,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[303, 294, 262])).
% 0.19/0.45 tff(305,plain,($lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0) | (~$lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)) | (~$lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(306,plain,
% 0.19/0.45 ($lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[305, 65, 60])).
% 0.19/0.45 tff(307,plain,
% 0.19/0.45 (((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(308,plain,
% 0.19/0.45 (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[307, 246])).
% 0.19/0.45 tff(309,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[308, 306, 253])).
% 0.19/0.45 tff(310,plain,((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(311,plain,
% 0.19/0.45 (($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0) | (~$lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)) | (~$greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0))),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(312,plain,
% 0.19/0.45 ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[311, 241, 306])).
% 0.19/0.45 tff(313,plain,
% 0.19/0.45 ((~(model_max(X!4, Y!3, Z!2) <=> ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0))) | model_max(X!4, Y!3, Z!2) | (~($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(314,plain,
% 0.19/0.45 (model_max(X!4, Y!3, Z!2) | (~($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[313, 118])).
% 0.19/0.45 tff(315,plain,
% 0.19/0.45 (model_max(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[314, 312])).
% 0.19/0.45 tff(316,plain,
% 0.19/0.45 (((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))) | (minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(317,plain,
% 0.19/0.45 (minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[316, 155])).
% 0.19/0.45 tff(318,plain,
% 0.19/0.45 ((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))))) | minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(319,plain,
% 0.19/0.45 (minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.19/0.45 tff(320,plain,
% 0.19/0.45 (minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[319, 315, 310])).
% 0.19/0.45 tff(321,plain,
% 0.19/0.45 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~minsol_model_max(X!4, Y!3, Z!2)) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(322,plain,
% 0.19/0.45 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~minsol_model_max(X!4, Y!3, Z!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[321, 172])).
% 0.19/0.45 tff(323,plain,
% 0.19/0.45 (~minsol_model_ub(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[322, 320])).
% 0.19/0.45 tff(324,assumption,(~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)), introduced(assumption)).
% 0.19/0.45 tff(325,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(326,plain,
% 0.19/0.45 ((ub(X!4, Z!2, Z!2) <=> (~((~$lesseq($sum(Z!2, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0))))) <=> (ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(327,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> (~((~$lesseq($sum(Z!2, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[326])).
% 0.19/0.45 tff(328,plain,
% 0.19/0.45 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> (~((~$lesseq($sum(Z!2, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[327, 325])).
% 0.19/0.45 tff(329,plain,
% 0.19/0.45 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> (~((~$lesseq($sum(Z!2, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(330,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.46 tff(331,plain,
% 0.19/0.46 (ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[330, 82])).
% 0.19/0.46 tff(332,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Z!2, Z!2) <=> ub(X!4, Z!2, Z!2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(333,plain,
% 0.19/0.46 (model_ub(X!4, Z!2, Z!2) <=> ub(X!4, Z!2, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[332, 98])).
% 0.19/0.46 tff(334,assumption,(~$greatereq($sum(Y!3, $product(-1, X!4)), 0)), introduced(assumption)).
% 0.19/0.46 tff(335,plain,
% 0.19/0.46 ($lesseq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[31, 334])).
% 0.19/0.46 tff(336,plain,
% 0.19/0.46 ($sum(X!4, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[29, 335])).
% 0.19/0.46 tff(337,plain,
% 0.19/0.46 ($lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[5, 336])).
% 0.19/0.46 tff(338,assumption,($lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.46 tff(339,plain,
% 0.19/0.46 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(340,plain,
% 0.19/0.46 ((ub(Z!2, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Z!2)), 0))))) <=> (ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(341,plain,
% 0.19/0.46 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Z!2)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[340])).
% 0.19/0.46 tff(342,plain,
% 0.19/0.46 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Z!2)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[341, 339])).
% 0.19/0.46 tff(343,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> (~((~$lesseq($sum(Y!3, $product(-1, Z!2)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Z!2)), 0)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(344,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.19/0.46 tff(345,plain,
% 0.19/0.46 (ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[344, 82])).
% 0.19/0.46 tff(346,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(Z!2, Y!3, Z!2) <=> ub(Z!2, Y!3, Z!2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(347,plain,
% 0.19/0.46 (model_ub(Z!2, Y!3, Z!2) <=> ub(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[346, 98])).
% 0.19/0.46 tff(348,assumption,(~minsol_model_ub(X!4, Y!3, Z!2)), introduced(assumption)).
% 0.19/0.46 tff(349,plain,
% 0.19/0.46 (minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[174, 348])).
% 0.19/0.46 tff(350,plain,
% 0.19/0.46 (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[159, 349])).
% 0.19/0.46 tff(351,plain,
% 0.19/0.46 (model_max(X!4, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[122, 350])).
% 0.19/0.46 tff(352,plain,
% 0.19/0.46 ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[119, 351, 118])).
% 0.19/0.46 tff(353,plain,
% 0.19/0.46 ($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[103, 352])).
% 0.19/0.46 tff(354,plain,
% 0.19/0.46 ($greatereq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[229, 336])).
% 0.19/0.46 tff(355,plain,
% 0.19/0.46 (Z!2 = X!4),
% 0.19/0.46 inference(theory_lemma,[status(thm)],[354, 337, 353, 338])).
% 0.19/0.46 tff(356,plain,
% 0.19/0.46 (model_ub(Z!2, Y!3, Z!2) <=> model_ub(X!4, Y!3, Z!2)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[355])).
% 0.19/0.46 tff(357,plain,
% 0.19/0.46 (model_ub(X!4, Y!3, Z!2) <=> model_ub(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(symmetry,[status(thm)],[356])).
% 0.19/0.46 tff(358,plain,
% 0.19/0.46 ((~model_ub(X!4, Y!3, Z!2)) <=> (~model_ub(Z!2, Y!3, Z!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[357])).
% 0.19/0.46 tff(359,plain,
% 0.19/0.46 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(360,plain,
% 0.19/0.46 ((ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, Z!2)), 0))))) <=> (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(361,plain,
% 0.19/0.46 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, Z!2)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[360])).
% 0.19/0.46 tff(362,plain,
% 0.19/0.46 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, Z!2)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[361, 359])).
% 0.19/0.46 tff(363,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, Z!2)), 0)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(364,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.19/0.46 tff(365,plain,
% 0.19/0.46 (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[364, 82])).
% 0.19/0.46 tff(366,plain,
% 0.19/0.46 ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(367,plain,
% 0.19/0.46 (model_ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[366, 98])).
% 0.19/0.46 tff(368,assumption,($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)), introduced(assumption)).
% 0.19/0.46 tff(369,plain,
% 0.19/0.46 (Z!2 = X!4),
% 0.19/0.46 inference(theory_lemma,[status(thm)],[217, 254, 368, 338])).
% 0.19/0.46 tff(370,plain,
% 0.19/0.46 (model_ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[369])).
% 0.19/0.46 tff(371,plain,
% 0.19/0.46 (model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(symmetry,[status(thm)],[370])).
% 0.19/0.46 tff(372,assumption,(model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))), introduced(assumption)).
% 0.19/0.46 tff(373,plain,
% 0.19/0.46 (model_ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.19/0.46 tff(374,plain,
% 0.19/0.46 ((~(model_ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)))) | (~model_ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(375,plain,
% 0.19/0.46 (ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[374, 373, 367])).
% 0.19/0.46 tff(376,plain,
% 0.19/0.46 (((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(377,plain,
% 0.19/0.46 ((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[376, 324])).
% 0.19/0.46 tff(378,plain,
% 0.19/0.46 ((~(ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))) | (~ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(379,plain,
% 0.19/0.46 ((~(ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Y!3, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))) | (~ub(Z!2, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[378, 377])).
% 0.19/0.46 tff(380,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[379, 375, 365])).
% 0.19/0.46 tff(381,plain,((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0) | (~$greatereq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)) | (~$lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)) | (~$greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)) | (~$lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(382,plain,
% 0.19/0.46 (~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[381, 353, 354, 337, 324, 338])).
% 0.19/0.46 tff(383,plain,
% 0.19/0.46 (((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(384,plain,
% 0.19/0.46 ((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[383, 382])).
% 0.19/0.46 tff(385,plain,
% 0.19/0.46 (((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))))))) | (minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(386,plain,
% 0.19/0.46 (minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[385, 207])).
% 0.19/0.46 tff(387,plain,
% 0.19/0.46 ((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))) | minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(388,plain,
% 0.19/0.46 (minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[387, 386])).
% 0.19/0.46 tff(389,plain,
% 0.19/0.46 (~model_ub(X!4, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[388, 384, 348])).
% 0.19/0.46 tff(390,plain,
% 0.19/0.46 (~model_ub(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[389, 358])).
% 0.19/0.46 tff(391,plain,
% 0.19/0.46 ((~(model_ub(Z!2, Y!3, Z!2) <=> ub(Z!2, Y!3, Z!2))) | model_ub(Z!2, Y!3, Z!2) | (~ub(Z!2, Y!3, Z!2))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(392,plain,
% 0.19/0.46 (~ub(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[391, 390, 347])).
% 0.19/0.46 tff(393,plain,
% 0.19/0.46 ($greatereq($sum(Z!2, $product(-1, Y!3)), 1) | $greatereq($sum(Y!3, $product(-1, X!4)), 0) | (~$lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)) | (~$greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0))),
% 0.19/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.46 tff(394,plain,
% 0.19/0.46 ($greatereq($sum(Z!2, $product(-1, Y!3)), 1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[393, 353, 337, 334])).
% 0.19/0.46 tff(395,plain,
% 0.19/0.46 ($greatereq($sum(Z!2, $product(-1, Y!3)), 0) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 1))),
% 0.19/0.46 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.46 tff(396,plain,
% 0.19/0.46 ($greatereq($sum(Z!2, $product(-1, Y!3)), 0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[395, 394])).
% 0.19/0.46 tff(397,plain,
% 0.19/0.46 ((~(ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0))) | ub(Z!2, Y!3, Z!2) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(398,plain,
% 0.19/0.47 ((~(ub(Z!2, Y!3, Z!2) <=> $greatereq($sum(Z!2, $product(-1, Y!3)), 0))) | ub(Z!2, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[397, 396])).
% 0.19/0.47 tff(399,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[398, 392, 345])).
% 0.19/0.47 tff(400,plain,(minsol_model_ub(X!4, Y!3, Z!2) | (~$lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0) | $greatereq($sum(Y!3, $product(-1, X!4)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(401,plain,
% 0.19/0.47 (minsol_model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[400, 338, 324, 334])).
% 0.19/0.47 tff(402,plain,
% 0.19/0.47 (~minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[322, 401])).
% 0.19/0.47 tff(403,plain,
% 0.19/0.47 (ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[88, 82])).
% 0.19/0.47 tff(404,plain,
% 0.19/0.47 (model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.47 tff(405,plain,
% 0.19/0.47 (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[211, 401])).
% 0.19/0.47 tff(406,plain,
% 0.19/0.47 (model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[213, 405])).
% 0.19/0.47 tff(407,plain,
% 0.19/0.47 ((~(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))) | ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[215, 406])).
% 0.19/0.47 tff(408,plain,
% 0.19/0.47 (ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[407, 404])).
% 0.19/0.47 tff(409,plain,
% 0.19/0.47 ((~(ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))) | (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 408])).
% 0.19/0.47 tff(410,plain,
% 0.19/0.47 (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[409, 403])).
% 0.19/0.47 tff(411,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, X!4)), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[220, 410])).
% 0.19/0.47 tff(412,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[218, 411, 354])).
% 0.19/0.47 tff(413,plain,
% 0.19/0.47 ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[311, 412, 338])).
% 0.19/0.47 tff(414,plain,
% 0.19/0.47 (model_max(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[313, 413, 118])).
% 0.19/0.47 tff(415,plain,
% 0.19/0.47 (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[319, 414, 402])).
% 0.19/0.47 tff(416,plain,
% 0.19/0.47 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[247, 415])).
% 0.19/0.47 tff(417,plain,
% 0.19/0.47 ((~(model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0))) | ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[249, 416])).
% 0.19/0.47 tff(418,plain,
% 0.19/0.47 ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[417, 245])).
% 0.19/0.47 tff(419,plain,
% 0.19/0.47 ($greatereq($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[252, 418])).
% 0.19/0.47 tff(420,plain,
% 0.19/0.47 (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[307, 415])).
% 0.19/0.47 tff(421,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(theory_lemma,[status(thm)],[420, 338, 419])).
% 0.19/0.47 tff(422,plain,((~$lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0) | $greatereq($sum(Y!3, $product(-1, X!4)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(423,plain,
% 0.19/0.47 (~$lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[422, 334, 324])).
% 0.19/0.47 tff(424,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0) | $lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.47 tff(425,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[424, 423])).
% 0.19/0.47 tff(426,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, Y!3)), 1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[393, 425, 337, 334])).
% 0.19/0.47 tff(427,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, X!4)), 1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[256, 423, 337])).
% 0.19/0.47 tff(428,plain,
% 0.19/0.47 (~((~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[261, 427, 426])).
% 0.19/0.47 tff(429,plain,
% 0.19/0.47 (ub(X!4, Y!3, $sum(-1, Z!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[303, 428])).
% 0.19/0.47 tff(430,plain,
% 0.19/0.47 (model_ub(X!4, Y!3, $sum(-1, Z!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[293, 429])).
% 0.19/0.47 tff(431,plain,
% 0.19/0.47 (~($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[263, 423])).
% 0.19/0.47 tff(432,plain,
% 0.19/0.47 (~model_max(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[119, 431, 118])).
% 0.19/0.47 tff(433,plain,
% 0.19/0.47 ((~model_max(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_max(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[122, 432])).
% 0.19/0.47 tff(434,plain,
% 0.19/0.47 (~minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[159, 433])).
% 0.19/0.47 tff(435,plain,
% 0.19/0.47 (minsol_model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[174, 434])).
% 0.19/0.47 tff(436,plain,
% 0.19/0.47 (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[211, 435])).
% 0.19/0.47 tff(437,plain,
% 0.19/0.47 (![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[270, 436])).
% 0.19/0.47 tff(438,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[283, 437, 430])).
% 0.19/0.47 tff(439,plain,($greatereq($sum(Y!3, $product(-1, X!4)), 0) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(440,plain,
% 0.19/0.47 ($greatereq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[439, 324])).
% 0.19/0.47 tff(441,plain,
% 0.19/0.47 ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[55, 440])).
% 0.19/0.47 tff(442,plain,
% 0.19/0.47 ($lesseq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[2, 441])).
% 0.19/0.47 tff(443,plain,
% 0.19/0.47 ($greatereq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[234, 441])).
% 0.19/0.47 tff(444,plain,
% 0.19/0.47 ($lesseq($sum(X!4, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[57, 442, 440])).
% 0.19/0.47 tff(445,plain,
% 0.19/0.47 ($lesseq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[305, 442, 444])).
% 0.19/0.47 tff(446,plain,
% 0.19/0.47 (Z!2 = Y!3),
% 0.19/0.47 inference(theory_lemma,[status(thm)],[353, 445, 443, 442])).
% 0.19/0.47 tff(447,plain,
% 0.19/0.47 (model_ub(X!4, Z!2, Z!2) <=> model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[446])).
% 0.19/0.47 tff(448,plain,
% 0.19/0.47 (model_ub(X!4, Y!3, Z!2) <=> model_ub(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(symmetry,[status(thm)],[447])).
% 0.19/0.47 tff(449,plain,
% 0.19/0.47 ((~model_ub(X!4, Y!3, Z!2)) <=> (~model_ub(X!4, Z!2, Z!2))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[448])).
% 0.19/0.47 tff(450,plain,
% 0.19/0.47 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(451,plain,
% 0.19/0.47 ((ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, X!4)), 0))))) <=> (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(452,plain,
% 0.19/0.47 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[451])).
% 0.19/0.47 tff(453,plain,
% 0.19/0.47 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, X!4)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[452, 450])).
% 0.19/0.47 tff(454,plain,
% 0.19/0.47 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!2, Y!3, X!4), $product(-1, X!4)), 0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(455,plain,
% 0.19/0.47 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.19/0.47 tff(456,plain,
% 0.19/0.47 (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[455, 82])).
% 0.19/0.47 tff(457,plain,
% 0.19/0.47 ((~![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(458,plain,
% 0.19/0.47 (model_ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[457, 98])).
% 0.19/0.47 tff(459,plain,
% 0.19/0.47 (Z!2 = Y!3),
% 0.19/0.47 inference(theory_lemma,[status(thm)],[368, 445, 443, 442])).
% 0.19/0.47 tff(460,plain,
% 0.19/0.47 (model_ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[459])).
% 0.19/0.47 tff(461,plain,
% 0.19/0.47 (model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(symmetry,[status(thm)],[460])).
% 0.19/0.47 tff(462,plain,
% 0.19/0.47 (model_ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[372, 461])).
% 0.19/0.47 tff(463,plain,
% 0.19/0.47 ((~(model_ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))) | (~model_ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))) | ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(464,plain,
% 0.19/0.47 (ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[463, 462, 458])).
% 0.19/0.47 tff(465,plain,
% 0.19/0.47 (((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(466,plain,
% 0.19/0.47 ((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[465, 324])).
% 0.19/0.47 tff(467,plain,
% 0.19/0.47 ((~(ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))) | (~ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(468,plain,
% 0.19/0.47 ((~(ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(X!4, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)))))) | (~ub(X!4, Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[467, 466])).
% 0.19/0.47 tff(469,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[468, 464, 456])).
% 0.19/0.47 tff(470,plain,((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0) | (~$greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(471,plain,
% 0.19/0.47 (~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[470, 353, 324])).
% 0.19/0.47 tff(472,plain,
% 0.19/0.47 ((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[383, 471])).
% 0.19/0.47 tff(473,plain,
% 0.19/0.47 (~model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[388, 472, 348])).
% 0.19/0.47 tff(474,plain,
% 0.19/0.47 (~model_ub(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[473, 449])).
% 0.19/0.47 tff(475,plain,
% 0.19/0.47 ((~(model_ub(X!4, Z!2, Z!2) <=> ub(X!4, Z!2, Z!2))) | model_ub(X!4, Z!2, Z!2) | (~ub(X!4, Z!2, Z!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(476,plain,
% 0.19/0.47 (~ub(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[475, 474, 333])).
% 0.19/0.47 tff(477,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, X!4)), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[242, 353, 444])).
% 0.19/0.47 tff(478,plain,
% 0.19/0.47 ((~(ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0))) | ub(X!4, Z!2, Z!2) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(479,plain,
% 0.19/0.47 ((~(ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0))) | ub(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[478, 477])).
% 0.19/0.47 tff(480,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[479, 476, 331])).
% 0.19/0.47 tff(481,plain,(minsol_model_ub(X!4, Y!3, Z!2) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(482,plain,
% 0.19/0.47 (minsol_model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[481, 324])).
% 0.19/0.47 tff(483,plain,
% 0.19/0.47 (~minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[322, 482])).
% 0.19/0.47 tff(484,plain,
% 0.19/0.47 (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $int] : ((~model_ub(X!4, Y!3, Z)) | $greatereq($sum(Z, $product(-1, Z!2)), 0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[211, 482])).
% 0.19/0.47 tff(485,plain,
% 0.19/0.47 (model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[213, 484])).
% 0.19/0.47 tff(486,plain,
% 0.19/0.47 ((~(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))) | ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[215, 485])).
% 0.19/0.47 tff(487,plain,
% 0.19/0.47 (ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[486, 404])).
% 0.19/0.47 tff(488,plain,
% 0.19/0.47 ((~(ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))) | (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 487])).
% 0.19/0.47 tff(489,plain,
% 0.19/0.47 (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[488, 403])).
% 0.19/0.47 tff(490,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, Y!3)), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[238, 489])).
% 0.19/0.47 tff(491,plain,
% 0.19/0.47 ($greatereq($sum(Z!2, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[236, 443, 490])).
% 0.19/0.47 tff(492,plain,
% 0.19/0.47 ($sum(Z!2, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[311, 491, 445])).
% 0.19/0.47 tff(493,plain,
% 0.19/0.47 (model_max(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[313, 492, 118])).
% 0.19/0.47 tff(494,plain,
% 0.19/0.47 (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[319, 493, 483])).
% 0.19/0.47 tff(495,plain,
% 0.19/0.47 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[247, 494])).
% 0.19/0.47 tff(496,plain,
% 0.19/0.47 ((~(model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0))) | ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[249, 495])).
% 0.19/0.47 tff(497,plain,
% 0.19/0.47 ($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[496, 245])).
% 0.19/0.47 tff(498,plain,
% 0.19/0.47 ($greatereq($sum(tptp_fun_Z_0(Z!2, Y!3, X!4), $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[252, 497])).
% 0.19/0.47 tff(499,plain,
% 0.19/0.47 (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_0(Z!2, Y!3, X!4))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[307, 494])).
% 0.19/0.47 tff(500,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(theory_lemma,[status(thm)],[499, 445, 498])).
% 0.19/0.47 tff(501,plain,($lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(502,plain,
% 0.19/0.47 (((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)) | (~$lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(503,plain,
% 0.19/0.47 ((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | $lesseq($sum(Z!2, $product(-1, tptp_fun_Z_1(Z!2, Y!3, X!4))), 0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[502, 501])).
% 0.19/0.47 tff(504,plain,
% 0.19/0.47 (minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[388, 503])).
% 0.19/0.47 tff(505,plain,
% 0.19/0.47 (~model_ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[504, 323])).
% 0.19/0.47 tff(506,plain,
% 0.19/0.47 ((~(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))) | model_ub(X!4, Y!3, Z!2) | (~ub(X!4, Y!3, Z!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(507,plain,
% 0.19/0.47 (~ub(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[506, 505, 101])).
% 0.19/0.47 tff(508,plain,
% 0.19/0.47 ((~(ub(X!4, Y!3, Z!2) <=> (~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))))) | ub(X!4, Y!3, Z!2) | ((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(509,plain,
% 0.19/0.47 ((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[508, 507, 90])).
% 0.19/0.48 tff(510,plain,
% 0.19/0.48 ((~((~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)))) | (~$greatereq($sum(Z!2, $product(-1, X!4)), 0)) | (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(511,plain,
% 0.19/0.48 (~$greatereq($sum(Z!2, $product(-1, Y!3)), 0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[510, 509, 243])).
% 0.19/0.48 tff(512,plain,
% 0.19/0.48 (~$greatereq($sum(Z!2, $product(-1, Y!3)), 1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[395, 511])).
% 0.19/0.48 tff(513,plain,
% 0.19/0.48 ($greatereq($sum(Y!3, $product(-1, X!4)), 0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[393, 512, 60, 241])).
% 0.19/0.48 tff(514,plain,
% 0.19/0.48 ($sum(Y!3, $product(-1, max(X!4, Y!3))) = 0),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[55, 513])).
% 0.19/0.48 tff(515,plain,
% 0.19/0.48 ($greatereq($sum(Y!3, $product(-1, max(X!4, Y!3))), 0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[234, 514])).
% 0.19/0.48 tff(516,plain,
% 0.19/0.48 (Z!2 = Y!3),
% 0.19/0.48 inference(theory_lemma,[status(thm)],[241, 306, 515, 65])).
% 0.19/0.48 tff(517,plain,
% 0.19/0.48 (ub(X!4, Z!2, Z!2) <=> ub(X!4, Y!3, Z!2)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[516])).
% 0.19/0.48 tff(518,plain,
% 0.19/0.48 (ub(X!4, Y!3, Z!2) <=> ub(X!4, Z!2, Z!2)),
% 0.19/0.48 inference(symmetry,[status(thm)],[517])).
% 0.19/0.48 tff(519,plain,
% 0.19/0.48 ((~ub(X!4, Y!3, Z!2)) <=> (~ub(X!4, Z!2, Z!2))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[518])).
% 0.19/0.48 tff(520,plain,
% 0.19/0.48 (~ub(X!4, Z!2, Z!2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[507, 519])).
% 0.19/0.48 tff(521,plain,
% 0.19/0.48 ((~(ub(X!4, Z!2, Z!2) <=> $greatereq($sum(Z!2, $product(-1, X!4)), 0))) | ub(X!4, Z!2, Z!2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[478, 243])).
% 0.19/0.48 tff(522,plain,
% 0.19/0.48 (ub(X!4, Z!2, Z!2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[521, 331])).
% 0.19/0.48 tff(523,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[522, 520])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------