TSTP Solution File: NUM861_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM861_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 13:12:21 EDT 2022
% Result : Theorem 1.27s 1.06s
% Output : Proof 1.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM861_1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 15:37:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.27/1.06 % SZS status Theorem
% 1.27/1.06 % SZS output start Proof
% 1.27/1.06 tff(max_type, type, (
% 1.27/1.06 max: ( $int * $int ) > $int)).
% 1.27/1.06 tff(tptp_fun_Y_4_type, type, (
% 1.27/1.06 tptp_fun_Y_4: $int)).
% 1.27/1.06 tff(tptp_fun_X_5_type, type, (
% 1.27/1.06 tptp_fun_X_5: $int)).
% 1.27/1.06 tff(tptp_fun_Z_3_type, type, (
% 1.27/1.06 tptp_fun_Z_3: $int)).
% 1.27/1.06 tff(c_type, type, (
% 1.27/1.06 c: $int)).
% 1.27/1.06 tff(minsol_model_max_type, type, (
% 1.27/1.06 minsol_model_max: ( $int * $int * $int ) > $o)).
% 1.27/1.06 tff(tptp_fun_Z_1_type, type, (
% 1.27/1.06 tptp_fun_Z_1: ( $int * $int * $int ) > $int)).
% 1.27/1.06 tff(model_max_type, type, (
% 1.27/1.06 model_max: ( $int * $int * $int ) > $o)).
% 1.27/1.06 tff(tptp_fun_Z_0_type, type, (
% 1.27/1.06 tptp_fun_Z_0: ( $int * $int * $int ) > $int)).
% 1.27/1.06 tff(ub_type, type, (
% 1.27/1.06 ub: ( $int * $int * $int ) > $o)).
% 1.27/1.06 tff(model_ub_type, type, (
% 1.27/1.06 model_ub: ( $int * $int * $int ) > $o)).
% 1.27/1.06 tff(minsol_model_ub_type, type, (
% 1.27/1.06 minsol_model_ub: ( $int * $int * $int ) > $o)).
% 1.27/1.06 tff(tptp_fun_Z_2_type, type, (
% 1.27/1.06 tptp_fun_Z_2: ( $int * $int * $int ) > $int)).
% 1.27/1.06 tff(1,assumption,(~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)), introduced(assumption)).
% 1.27/1.06 tff(2,assumption,(~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))), introduced(assumption)).
% 1.27/1.06 tff(3,plain,
% 1.27/1.06 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))),
% 1.27/1.06 inference(tautology,[status(thm)],[])).
% 1.27/1.06 tff(4,plain,
% 1.27/1.06 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 1.27/1.06 inference(unit_resolution,[status(thm)],[3, 2])).
% 1.27/1.06 tff(5,plain,
% 1.27/1.06 (^[X: $int, Y: $int, N: $int] : refl((model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0)) <=> (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0)))),
% 1.27/1.06 inference(bind,[status(th)],[])).
% 1.27/1.06 tff(6,plain,
% 1.27/1.06 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))),
% 1.27/1.06 inference(quant_intro,[status(thm)],[5])).
% 1.27/1.06 tff(7,plain,
% 1.27/1.06 (^[X: $int, Y: $int, N: $int] : rewrite((model_max(X, Y, N) <=> $lesseq($sum(c, $sum(max(X, Y), $product(-1, N))), 0)) <=> (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0)))),
% 1.27/1.06 inference(bind,[status(th)],[])).
% 1.27/1.06 tff(8,plain,
% 1.27/1.06 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(max(X, Y), $product(-1, N))), 0)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))),
% 1.27/1.06 inference(quant_intro,[status(thm)],[7])).
% 1.27/1.06 tff(9,plain,
% 1.27/1.06 (^[X: $int, Y: $int, N: $int] : rewrite((model_max(X, Y, N) <=> $lesseq($sum(c, max(X, Y)), N)) <=> (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(max(X, Y), $product(-1, N))), 0)))),
% 1.27/1.06 inference(bind,[status(th)],[])).
% 1.27/1.06 tff(10,plain,
% 1.27/1.06 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, max(X, Y)), N)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(max(X, Y), $product(-1, N))), 0))),
% 1.27/1.06 inference(quant_intro,[status(thm)],[9])).
% 1.27/1.06 tff(11,plain,
% 1.27/1.06 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, max(X, Y)), N)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, max(X, Y)), N))),
% 1.27/1.06 inference(rewrite,[status(thm)],[])).
% 1.27/1.06 tff(12,axiom,(![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, max(X, Y)), N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_max_4')).
% 1.27/1.06 tff(13,plain,
% 1.27/1.06 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, max(X, Y)), N))),
% 1.27/1.06 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.27/1.06 tff(14,plain,
% 1.27/1.06 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(max(X, Y), $product(-1, N))), 0))),
% 1.27/1.06 inference(modus_ponens,[status(thm)],[13, 10])).
% 1.27/1.06 tff(15,plain,
% 1.27/1.06 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))),
% 1.27/1.06 inference(modus_ponens,[status(thm)],[14, 8])).
% 1.27/1.07 tff(16,plain,(
% 1.27/1.07 ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))),
% 1.27/1.07 inference(skolemize,[status(sab)],[15])).
% 1.27/1.07 tff(17,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[16, 6])).
% 1.27/1.07 tff(18,plain,
% 1.27/1.07 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), max(X!5, Y!4))), 0))),
% 1.27/1.07 inference(quant_inst,[status(thm)],[])).
% 1.27/1.07 tff(19,plain,
% 1.27/1.07 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), max(X!5, Y!4))), 0)),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[18, 17])).
% 1.27/1.07 tff(20,plain,
% 1.27/1.07 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)) | model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 1.27/1.07 inference(tautology,[status(thm)],[])).
% 1.27/1.07 tff(21,plain,
% 1.27/1.07 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[20, 2])).
% 1.27/1.07 tff(22,plain,
% 1.27/1.07 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), max(X!5, Y!4))), 0))) | (~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), max(X!5, Y!4))), 0)),
% 1.27/1.07 inference(tautology,[status(thm)],[])).
% 1.27/1.07 tff(23,plain,
% 1.27/1.07 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), max(X!5, Y!4))), 0))) | $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), max(X!5, Y!4))), 0)),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.27/1.07 tff(24,plain,
% 1.27/1.07 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), max(X!5, Y!4))), 0)),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[23, 19])).
% 1.27/1.07 tff(25,plain,
% 1.27/1.07 ($false),
% 1.27/1.07 inference(theory_lemma,[status(thm)],[24, 1, 4])).
% 1.27/1.07 tff(26,plain,(((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)) | $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.07 tff(27,plain,
% 1.27/1.07 ((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[26, 1])).
% 1.27/1.07 tff(28,plain,
% 1.27/1.07 (^[X: $int, Y: $int, N: $int] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(29,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[28])).
% 1.27/1.07 tff(30,plain,
% 1.27/1.07 (^[X: $int, Y: $int, N: $int] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(31,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[30])).
% 1.27/1.07 tff(32,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))),
% 1.27/1.07 inference(transitivity,[status(thm)],[31, 29])).
% 1.27/1.07 tff(33,plain,
% 1.27/1.07 (^[X: $int, Y: $int, N: $int] : trans(monotonicity(rewrite(((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))), rewrite((model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0)))) <=> (model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0))))) & (model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0))))) & (model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(34,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[33])).
% 1.27/1.07 tff(35,plain,
% 1.27/1.07 (^[X: $int, Y: $int, N: $int] : rewrite((model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(Z, $product(-1, N))), 0))) <=> (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(36,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(Z, $product(-1, N))), 0))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0)))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[35])).
% 1.27/1.07 tff(37,plain,
% 1.27/1.07 (^[X: $int, Y: $int, N: $int] : rewrite((model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, Z), N))) <=> (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(Z, $product(-1, N))), 0))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(38,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, Z), N))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(Z, $product(-1, N))), 0)))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[37])).
% 1.27/1.07 tff(39,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, Z), N))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, Z), N)))),
% 1.27/1.07 inference(rewrite,[status(thm)],[])).
% 1.27/1.07 tff(40,axiom,(![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, Z), N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_ub_4')).
% 1.27/1.07 tff(41,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, Z), N)))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.27/1.07 tff(42,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(Z, $product(-1, N))), 0)))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[41, 38])).
% 1.27/1.07 tff(43,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0)))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[42, 36])).
% 1.27/1.07 tff(44,plain,(
% 1.27/1.07 ![X: $int, Y: $int, N: $int] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))),
% 1.27/1.07 inference(skolemize,[status(sab)],[43])).
% 1.27/1.07 tff(45,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[44, 34])).
% 1.27/1.07 tff(46,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[45, 32])).
% 1.27/1.07 tff(47,plain,
% 1.27/1.07 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0))))))))),
% 1.27/1.07 inference(rewrite,[status(thm)],[])).
% 1.27/1.07 tff(48,plain,
% 1.27/1.07 ((~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Z)), 0))))))) <=> (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))))))),
% 1.27/1.07 inference(rewrite,[status(thm)],[])).
% 1.27/1.07 tff(49,plain,
% 1.27/1.07 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Z)), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0))))))))),
% 1.27/1.07 inference(monotonicity,[status(thm)],[48])).
% 1.27/1.07 tff(50,plain,
% 1.27/1.07 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Z)), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0))))))))),
% 1.27/1.07 inference(transitivity,[status(thm)],[49, 47])).
% 1.27/1.07 tff(51,plain,
% 1.27/1.07 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Z)), 0)))))))),
% 1.27/1.07 inference(quant_inst,[status(thm)],[])).
% 1.27/1.07 tff(52,plain,
% 1.27/1.07 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.27/1.07 tff(53,plain,
% 1.27/1.07 (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0))))))),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[52, 46])).
% 1.27/1.07 tff(54,plain,
% 1.27/1.07 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))))) | ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))),
% 1.27/1.07 inference(tautology,[status(thm)],[])).
% 1.27/1.07 tff(55,plain,
% 1.27/1.07 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[54, 53])).
% 1.27/1.07 tff(56,assumption,(~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0)), introduced(assumption)).
% 1.27/1.07 tff(57,assumption,(~(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0))), introduced(assumption)).
% 1.27/1.07 tff(58,plain,
% 1.27/1.07 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0))),
% 1.27/1.07 inference(quant_inst,[status(thm)],[])).
% 1.27/1.07 tff(59,plain,
% 1.27/1.07 ($false),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[58, 17, 57])).
% 1.27/1.07 tff(60,plain,(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.07 tff(61,plain,
% 1.27/1.07 ((~(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0))) | (~model_max(X!5, Y!4, Z!3)) | $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0)),
% 1.27/1.07 inference(tautology,[status(thm)],[])).
% 1.27/1.07 tff(62,plain,
% 1.27/1.07 ((~model_max(X!5, Y!4, Z!3)) | $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0)),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[61, 60])).
% 1.27/1.07 tff(63,plain,
% 1.27/1.07 (~model_max(X!5, Y!4, Z!3)),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[62, 56])).
% 1.27/1.07 tff(64,plain,
% 1.27/1.07 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))) | model_max(X!5, Y!4, Z!3)),
% 1.27/1.07 inference(tautology,[status(thm)],[])).
% 1.27/1.07 tff(65,plain,
% 1.27/1.07 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))),
% 1.27/1.07 inference(unit_resolution,[status(thm)],[64, 63])).
% 1.27/1.07 tff(66,plain,
% 1.27/1.07 (^[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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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))))))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(67,plain,
% 1.27/1.07 (![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_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_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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)))))))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[66])).
% 1.27/1.07 tff(68,plain,
% 1.27/1.07 (^[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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(69,plain,
% 1.27/1.07 (![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_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_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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[68])).
% 1.27/1.07 tff(70,plain,
% 1.27/1.07 (^[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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(71,plain,
% 1.27/1.07 (![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_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_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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[70])).
% 1.27/1.07 tff(72,plain,
% 1.27/1.07 (![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_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_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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 1.27/1.07 inference(transitivity,[status(thm)],[71, 69])).
% 1.27/1.07 tff(73,plain,
% 1.27/1.07 (^[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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))) <=> (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(74,plain,
% 1.27/1.07 (![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_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_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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[73])).
% 1.27/1.07 tff(75,plain,
% 1.27/1.07 (^[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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(76,plain,
% 1.27/1.07 (![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_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_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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[75])).
% 1.27/1.07 tff(77,plain,
% 1.27/1.07 (^[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)))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(78,plain,
% 1.27/1.07 (![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))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[77])).
% 1.27/1.07 tff(79,plain,
% 1.27/1.07 (![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))))),
% 1.27/1.07 inference(rewrite,[status(thm)],[])).
% 1.27/1.07 tff(80,plain,
% 1.27/1.07 (^[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)))))),
% 1.27/1.07 inference(bind,[status(th)],[])).
% 1.27/1.07 tff(81,plain,
% 1.27/1.07 (![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))))),
% 1.27/1.07 inference(quant_intro,[status(thm)],[80])).
% 1.27/1.07 tff(82,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')).
% 1.27/1.07 tff(83,plain,
% 1.27/1.07 (![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))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.27/1.07 tff(84,plain,
% 1.27/1.07 (![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))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.27/1.07 tff(85,plain,
% 1.27/1.07 (![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))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[84, 78])).
% 1.27/1.07 tff(86,plain,(
% 1.27/1.07 ![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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0))))))),
% 1.27/1.07 inference(skolemize,[status(sab)],[85])).
% 1.27/1.07 tff(87,plain,
% 1.27/1.07 (![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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[86, 76])).
% 1.27/1.07 tff(88,plain,
% 1.27/1.07 (![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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[87, 74])).
% 1.27/1.07 tff(89,plain,
% 1.27/1.07 (![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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(N, Y, X))), 0)))))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[88, 72])).
% 1.27/1.07 tff(90,plain,
% 1.27/1.07 (![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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)))))))))),
% 1.27/1.07 inference(modus_ponens,[status(thm)],[89, 67])).
% 1.27/1.07 tff(91,plain,
% 1.27/1.07 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))))),
% 1.27/1.07 inference(rewrite,[status(thm)],[])).
% 1.27/1.07 tff(92,plain,
% 1.27/1.07 ((~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $product(-1, Z)), 0))))))))) <=> (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))))),
% 1.27/1.07 inference(rewrite,[status(thm)],[])).
% 1.27/1.07 tff(93,plain,
% 1.27/1.07 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))))),
% 1.27/1.07 inference(monotonicity,[status(thm)],[92])).
% 1.27/1.07 tff(94,plain,
% 1.27/1.07 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $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_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))))),
% 1.27/1.07 inference(transitivity,[status(thm)],[93, 91])).
% 1.27/1.07 tff(95,plain,
% 1.27/1.07 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $product(-1, Z)), 0)))))))))),
% 1.27/1.07 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(96,plain,
% 1.27/1.08 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_1(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!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.27/1.08 tff(97,plain,
% 1.27/1.08 (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[96, 90])).
% 1.27/1.08 tff(98,plain,
% 1.27/1.08 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))) | ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))),
% 1.27/1.08 inference(tautology,[status(thm)],[])).
% 1.27/1.08 tff(99,plain,
% 1.27/1.08 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[98, 97])).
% 1.27/1.08 tff(100,plain,
% 1.27/1.08 ((~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))),
% 1.27/1.08 inference(tautology,[status(thm)],[])).
% 1.27/1.08 tff(101,plain,
% 1.27/1.08 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[100, 99])).
% 1.27/1.08 tff(102,plain,
% 1.27/1.08 (~minsol_model_max(X!5, Y!4, Z!3)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[101, 65])).
% 1.27/1.08 tff(103,plain,
% 1.27/1.08 ((~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))) <=> ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(104,plain,
% 1.27/1.08 ((~![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)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(105,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')).
% 1.27/1.08 tff(106,plain,
% 1.27/1.08 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.27/1.08 tff(107,plain,
% 1.27/1.08 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[106, 104])).
% 1.27/1.08 tff(108,plain,
% 1.27/1.08 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[107, 104])).
% 1.27/1.08 tff(109,plain,
% 1.27/1.08 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[108, 104])).
% 1.27/1.08 tff(110,plain,
% 1.27/1.08 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[109, 104])).
% 1.27/1.08 tff(111,plain,
% 1.27/1.08 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[110, 104])).
% 1.27/1.08 tff(112,plain,
% 1.27/1.08 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[111, 104])).
% 1.27/1.08 tff(113,plain,(
% 1.27/1.08 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 1.27/1.08 inference(skolemize,[status(sab)],[112])).
% 1.27/1.08 tff(114,plain,
% 1.27/1.08 ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[113, 103])).
% 1.27/1.08 tff(115,plain,
% 1.27/1.08 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 1.27/1.08 inference(tautology,[status(thm)],[])).
% 1.27/1.08 tff(116,plain,
% 1.27/1.08 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[115, 114])).
% 1.27/1.08 tff(117,plain,
% 1.27/1.08 (minsol_model_ub(X!5, Y!4, Z!3)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[116, 102])).
% 1.27/1.08 tff(118,plain,
% 1.27/1.08 (^[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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0))))))) <=> (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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))))))))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(119,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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)))))))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[118])).
% 1.27/1.08 tff(120,plain,
% 1.27/1.08 (^[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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0))))))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(121,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[120])).
% 1.27/1.08 tff(122,plain,
% 1.27/1.08 (^[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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0))))))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(123,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[122])).
% 1.27/1.08 tff(124,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))))),
% 1.27/1.08 inference(transitivity,[status(thm)],[123, 121])).
% 1.27/1.08 tff(125,plain,
% 1.27/1.08 (^[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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))) <=> (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(126,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[125])).
% 1.27/1.08 tff(127,plain,
% 1.27/1.08 (^[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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0))))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(128,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[127])).
% 1.27/1.08 tff(129,plain,
% 1.27/1.08 (^[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)))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(130,plain,
% 1.27/1.08 (![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))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[129])).
% 1.27/1.08 tff(131,plain,
% 1.27/1.08 (![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))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(132,plain,
% 1.27/1.08 (^[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)))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(133,plain,
% 1.27/1.08 (![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))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[132])).
% 1.27/1.08 tff(134,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')).
% 1.27/1.08 tff(135,plain,
% 1.27/1.08 (![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))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.27/1.08 tff(136,plain,
% 1.27/1.08 (![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))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[135, 131])).
% 1.27/1.08 tff(137,plain,
% 1.27/1.08 (![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))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[136, 130])).
% 1.27/1.08 tff(138,plain,(
% 1.27/1.08 ![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0))))))),
% 1.27/1.08 inference(skolemize,[status(sab)],[137])).
% 1.27/1.08 tff(139,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[138, 128])).
% 1.27/1.08 tff(140,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[139, 126])).
% 1.27/1.08 tff(141,plain,
% 1.27/1.08 (![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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(N, Y, X))), 0)))))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[140, 124])).
% 1.27/1.08 tff(142,plain,
% 1.27/1.08 (![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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)))))))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[141, 119])).
% 1.27/1.08 tff(143,plain,
% 1.27/1.08 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(144,plain,
% 1.27/1.08 ((~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $product(-1, Z)), 0))))))))) <=> (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(145,plain,
% 1.27/1.08 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))))),
% 1.27/1.08 inference(monotonicity,[status(thm)],[144])).
% 1.27/1.08 tff(146,plain,
% 1.27/1.08 (((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $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_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))))),
% 1.27/1.08 inference(transitivity,[status(thm)],[145, 143])).
% 1.27/1.08 tff(147,plain,
% 1.27/1.08 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $lesseq($sum(Z!3, $product(-1, Z)), 0)))))))))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(148,plain,
% 1.27/1.08 ((~![X: $int, Y: $int, N: $int] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | $lesseq($sum(N, $product(-1, tptp_fun_Z_2(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!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.27/1.08 tff(149,plain,
% 1.27/1.08 (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[148, 142])).
% 1.27/1.08 tff(150,plain,
% 1.27/1.08 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))) | ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))),
% 1.27/1.08 inference(tautology,[status(thm)],[])).
% 1.27/1.08 tff(151,plain,
% 1.27/1.08 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[150, 149])).
% 1.27/1.08 tff(152,plain,
% 1.27/1.08 ((~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))))) | (~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))),
% 1.27/1.08 inference(tautology,[status(thm)],[])).
% 1.27/1.08 tff(153,plain,
% 1.27/1.08 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[152, 151])).
% 1.27/1.08 tff(154,plain,
% 1.27/1.08 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[153, 117])).
% 1.35/1.08 tff(155,plain,
% 1.35/1.08 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))) | model_ub(X!5, Y!4, Z!3)),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(156,plain,
% 1.35/1.08 (model_ub(X!5, Y!4, Z!3)),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[155, 154])).
% 1.35/1.08 tff(157,plain,
% 1.35/1.08 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(158,plain,
% 1.35/1.08 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[157, 156])).
% 1.35/1.08 tff(159,plain,
% 1.35/1.08 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[158, 55])).
% 1.35/1.08 tff(160,plain,
% 1.35/1.08 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))) | $lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(161,plain,
% 1.35/1.08 ($lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[160, 159])).
% 1.35/1.08 tff(162,plain,
% 1.35/1.08 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))) | ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(163,plain,
% 1.35/1.08 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[162, 159])).
% 1.35/1.08 tff(164,assumption,(~(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))), introduced(assumption)).
% 1.35/1.08 tff(165,plain,
% 1.35/1.08 (^[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))))))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(166,plain,
% 1.35/1.08 (![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)))))),
% 1.35/1.08 inference(quant_intro,[status(thm)],[165])).
% 1.35/1.08 tff(167,plain,
% 1.35/1.08 (^[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))))))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(168,plain,
% 1.35/1.08 (![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)))))),
% 1.35/1.08 inference(quant_intro,[status(thm)],[167])).
% 1.35/1.08 tff(169,plain,
% 1.35/1.08 (^[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))))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(170,plain,
% 1.35/1.08 (![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)))),
% 1.35/1.08 inference(quant_intro,[status(thm)],[169])).
% 1.35/1.08 tff(171,plain,
% 1.35/1.08 (^[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))))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(172,plain,
% 1.35/1.08 (![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)))),
% 1.35/1.08 inference(quant_intro,[status(thm)],[171])).
% 1.35/1.08 tff(173,plain,
% 1.35/1.08 (![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)))),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(174,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')).
% 1.35/1.08 tff(175,plain,
% 1.35/1.08 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.35/1.08 tff(176,plain,
% 1.35/1.08 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[175, 172])).
% 1.35/1.08 tff(177,plain,
% 1.35/1.08 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[176, 170])).
% 1.35/1.08 tff(178,plain,(
% 1.35/1.08 ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 1.35/1.08 inference(skolemize,[status(sab)],[177])).
% 1.35/1.08 tff(179,plain,
% 1.35/1.08 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[178, 168])).
% 1.35/1.08 tff(180,plain,
% 1.35/1.08 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[179, 166])).
% 1.35/1.08 tff(181,plain,
% 1.35/1.08 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))))),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(182,plain,
% 1.35/1.08 ((ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, X!5)), 0))))) <=> (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(183,plain,
% 1.35/1.08 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, X!5)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))))),
% 1.35/1.08 inference(monotonicity,[status(thm)],[182])).
% 1.35/1.08 tff(184,plain,
% 1.35/1.08 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, X!5)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))))),
% 1.35/1.08 inference(transitivity,[status(thm)],[183, 181])).
% 1.35/1.08 tff(185,plain,
% 1.35/1.08 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, X!5)), 0)))))),
% 1.35/1.08 inference(quant_inst,[status(thm)],[])).
% 1.35/1.08 tff(186,plain,
% 1.35/1.08 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.35/1.08 tff(187,plain,
% 1.35/1.08 ($false),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[186, 180, 164])).
% 1.35/1.08 tff(188,plain,(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.08 tff(189,plain,
% 1.35/1.08 ((~(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(190,plain,
% 1.35/1.08 ((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[189, 188])).
% 1.35/1.08 tff(191,plain,
% 1.35/1.08 (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[190, 163])).
% 1.35/1.08 tff(192,plain,
% 1.35/1.08 (((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))) | $lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(193,plain,
% 1.35/1.08 ($lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[192, 191])).
% 1.35/1.08 tff(194,plain,
% 1.35/1.08 (((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))) | $lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(195,plain,
% 1.35/1.08 ($lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[194, 191])).
% 1.35/1.08 tff(196,assumption,($lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)), introduced(assumption)).
% 1.35/1.08 tff(197,assumption,($lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)), introduced(assumption)).
% 1.35/1.09 tff(198,assumption,($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 1.35/1.09 tff(199,plain,
% 1.35/1.09 ($false),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[197, 198, 56, 196])).
% 1.35/1.09 tff(200,plain,((~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0) | (~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.09 tff(201,plain,
% 1.35/1.09 (~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[200, 56, 197, 196])).
% 1.35/1.09 tff(202,plain,
% 1.35/1.09 ((~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)) | $greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(203,plain,
% 1.35/1.09 (~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[202, 201])).
% 1.35/1.09 tff(204,plain,
% 1.35/1.09 (^[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)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(205,plain,
% 1.35/1.09 (![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))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[204])).
% 1.35/1.09 tff(206,plain,
% 1.35/1.09 (^[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)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(207,plain,
% 1.35/1.09 (![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))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[206])).
% 1.35/1.09 tff(208,plain,
% 1.35/1.09 (^[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)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(209,plain,
% 1.35/1.09 (![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))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[208])).
% 1.35/1.09 tff(210,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(211,plain,
% 1.35/1.09 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ((~$lesseq(X, Y)) | (max(X, Y) = Y)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(212,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[211])).
% 1.35/1.09 tff(213,axiom,(![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_2')).
% 1.35/1.09 tff(214,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.35/1.09 tff(215,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[214, 210])).
% 1.35/1.09 tff(216,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[215, 209])).
% 1.35/1.09 tff(217,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[216, 207])).
% 1.35/1.09 tff(218,plain,(
% 1.35/1.09 ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 1.35/1.09 inference(skolemize,[status(sab)],[217])).
% 1.35/1.09 tff(219,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[218, 205])).
% 1.35/1.09 tff(220,plain,
% 1.35/1.09 (((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(221,plain,
% 1.35/1.09 (((~$lesseq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)) <=> ((~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(222,plain,
% 1.35/1.09 (((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[221])).
% 1.35/1.09 tff(223,plain,
% 1.35/1.09 (((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(transitivity,[status(thm)],[222, 220])).
% 1.35/1.09 tff(224,plain,
% 1.35/1.09 ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(225,plain,
% 1.35/1.09 ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.35/1.09 tff(226,plain,
% 1.35/1.09 ((~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[225, 219])).
% 1.35/1.09 tff(227,plain,
% 1.35/1.09 (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[226, 203])).
% 1.35/1.09 tff(228,plain,
% 1.35/1.09 ($greatereq($sum(Y!4, $product(-1, X!5)), 0) | $lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(229,plain,
% 1.35/1.09 ($lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[228, 227])).
% 1.35/1.09 tff(230,plain,
% 1.35/1.09 (^[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)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(231,plain,
% 1.35/1.09 (![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))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[230])).
% 1.35/1.09 tff(232,plain,
% 1.35/1.09 (^[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)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(233,plain,
% 1.35/1.09 (![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))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[232])).
% 1.35/1.09 tff(234,plain,
% 1.35/1.09 (^[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)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(235,plain,
% 1.35/1.09 (![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))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[234])).
% 1.35/1.09 tff(236,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(237,plain,
% 1.35/1.09 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ((~$lesseq(Y, X)) | (max(X, Y) = X)))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(238,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[237])).
% 1.35/1.09 tff(239,axiom,(![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_1')).
% 1.35/1.09 tff(240,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.35/1.09 tff(241,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[240, 236])).
% 1.35/1.09 tff(242,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[241, 235])).
% 1.35/1.09 tff(243,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[242, 233])).
% 1.35/1.09 tff(244,plain,(
% 1.35/1.09 ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 1.35/1.09 inference(skolemize,[status(sab)],[243])).
% 1.35/1.09 tff(245,plain,
% 1.35/1.09 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[244, 231])).
% 1.35/1.09 tff(246,plain,
% 1.35/1.09 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(247,plain,
% 1.35/1.09 (((~$greatereq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)) <=> ((~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(248,plain,
% 1.35/1.09 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[247])).
% 1.35/1.09 tff(249,plain,
% 1.35/1.09 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(transitivity,[status(thm)],[248, 246])).
% 1.35/1.09 tff(250,plain,
% 1.35/1.09 ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum(X!5, $product(-1, Y!4)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(251,plain,
% 1.35/1.09 ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.35/1.09 tff(252,plain,
% 1.35/1.09 ((~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[251, 245])).
% 1.35/1.09 tff(253,plain,
% 1.35/1.09 ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[252, 229])).
% 1.35/1.09 tff(254,plain,
% 1.35/1.09 ((~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)) | $greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(255,plain,
% 1.35/1.09 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[254, 253])).
% 1.35/1.09 tff(256,assumption,($lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)), introduced(assumption)).
% 1.35/1.09 tff(257,plain,
% 1.35/1.09 ($false),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[256, 197, 56, 255])).
% 1.35/1.09 tff(258,plain,($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.09 tff(259,plain,
% 1.35/1.09 ($false),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[258, 195, 193, 56, 161])).
% 1.35/1.09 tff(260,plain,($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.09 tff(261,plain,
% 1.35/1.09 ((~(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0))) | model_max(X!5, Y!4, Z!3) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(262,plain,
% 1.35/1.09 (model_max(X!5, Y!4, Z!3) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[261, 60])).
% 1.35/1.09 tff(263,plain,
% 1.35/1.09 (model_max(X!5, Y!4, Z!3)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[262, 260])).
% 1.35/1.09 tff(264,plain,
% 1.35/1.09 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))) | (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(265,plain,
% 1.35/1.09 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[264, 97])).
% 1.35/1.09 tff(266,plain,
% 1.35/1.09 ((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))))) | minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(267,plain,
% 1.35/1.09 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[266, 265])).
% 1.35/1.09 tff(268,plain,
% 1.35/1.09 (minsol_model_max(X!5, Y!4, Z!3) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[267, 263])).
% 1.35/1.09 tff(269,plain,
% 1.35/1.09 (minsol_model_max(X!5, Y!4, Z!3)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[268, 27])).
% 1.35/1.09 tff(270,assumption,(~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 1.35/1.09 tff(271,plain,
% 1.35/1.09 ((~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)) | $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(272,plain,
% 1.35/1.09 (~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[271, 270])).
% 1.35/1.09 tff(273,plain,
% 1.35/1.09 (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[252, 272])).
% 1.35/1.09 tff(274,assumption,(~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 1.35/1.09 tff(275,plain,
% 1.35/1.09 ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) | $greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(276,plain,
% 1.35/1.09 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[275, 274])).
% 1.35/1.09 tff(277,plain,
% 1.35/1.09 ((~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)) | $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(278,plain,
% 1.35/1.09 (~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[277, 274])).
% 1.35/1.09 tff(279,plain,
% 1.35/1.09 (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[226, 278])).
% 1.35/1.09 tff(280,plain,
% 1.35/1.09 ((~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(Y!4, $product(-1, X!5)), 0) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(281,plain,
% 1.35/1.09 (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[280, 279, 276])).
% 1.35/1.09 tff(282,plain,
% 1.35/1.09 ($lesseq($sum(Y!4, $product(-1, X!5)), 0) | $greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(283,plain,
% 1.35/1.09 ($lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[282, 279])).
% 1.35/1.09 tff(284,plain,
% 1.35/1.09 ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[252, 283])).
% 1.35/1.09 tff(285,plain,
% 1.35/1.09 ($false),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[271, 284, 281])).
% 1.35/1.09 tff(286,plain,($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.09 tff(287,plain,
% 1.35/1.09 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) | $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(288,plain,
% 1.35/1.09 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[287, 270])).
% 1.35/1.09 tff(289,plain,
% 1.35/1.09 ($false),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[288, 286, 273])).
% 1.35/1.09 tff(290,plain,($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.09 tff(291,assumption,(Y!4 = max(X!5, Y!4)), introduced(assumption)).
% 1.35/1.09 tff(292,plain,
% 1.35/1.09 (max(X!5, Y!4) = Y!4),
% 1.35/1.09 inference(symmetry,[status(thm)],[291])).
% 1.35/1.09 tff(293,plain,
% 1.35/1.09 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> ub(X!5, Y!4, Y!4)),
% 1.35/1.09 inference(monotonicity,[status(thm)],[292, 292])).
% 1.35/1.09 tff(294,plain,
% 1.35/1.09 (ub(X!5, Y!4, Y!4) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 1.35/1.09 inference(symmetry,[status(thm)],[293])).
% 1.35/1.09 tff(295,plain,
% 1.35/1.09 ((~ub(X!5, Y!4, Y!4)) <=> (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[294])).
% 1.35/1.09 tff(296,assumption,(~ub(X!5, Y!4, Y!4)), introduced(assumption)).
% 1.35/1.09 tff(297,plain,
% 1.35/1.09 (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.35/1.09 tff(298,plain,
% 1.35/1.09 (((~![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!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!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!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(299,plain,
% 1.35/1.09 ((ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, X!5)), 0))))) <=> (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(300,plain,
% 1.35/1.09 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, X!5)), 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!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[299])).
% 1.35/1.09 tff(301,plain,
% 1.35/1.09 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, X!5)), 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!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))),
% 1.35/1.09 inference(transitivity,[status(thm)],[300, 298])).
% 1.35/1.09 tff(302,plain,
% 1.35/1.09 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, X!5)), 0)))))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(303,plain,
% 1.35/1.09 ((~![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!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[302, 301])).
% 1.35/1.09 tff(304,plain,
% 1.35/1.09 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[303, 180])).
% 1.35/1.09 tff(305,plain,
% 1.35/1.09 ((~(ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))) | ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(306,plain,
% 1.35/1.09 ((~(ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))) | ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[305, 290])).
% 1.35/1.09 tff(307,plain,
% 1.35/1.09 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[306, 304])).
% 1.35/1.09 tff(308,plain,
% 1.35/1.09 ($false),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[307, 297])).
% 1.35/1.09 tff(309,plain,(ub(X!5, Y!4, Y!4) | (~(Y!4 = max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.09 tff(310,plain,
% 1.35/1.09 (ub(X!5, Y!4, Y!4)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[309, 291])).
% 1.35/1.09 tff(311,plain,
% 1.35/1.09 ($lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0)) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.09 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.09 tff(312,plain,
% 1.35/1.09 ($lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[311, 286, 260])).
% 1.35/1.09 tff(313,plain,
% 1.35/1.09 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(314,plain,
% 1.35/1.09 (((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), 0))) <=> ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(315,plain,
% 1.35/1.09 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0))))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[314])).
% 1.35/1.09 tff(316,plain,
% 1.35/1.09 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0)))),
% 1.35/1.09 inference(transitivity,[status(thm)],[315, 313])).
% 1.35/1.09 tff(317,plain,
% 1.35/1.09 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), 0)))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(318,plain,
% 1.35/1.09 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), 0))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[317, 316])).
% 1.35/1.09 tff(319,plain,
% 1.35/1.09 (~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[318, 310, 312])).
% 1.35/1.09 tff(320,plain,
% 1.35/1.09 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))))) | (model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0))))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(321,plain,
% 1.35/1.09 (model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[320, 53])).
% 1.35/1.09 tff(322,plain,
% 1.35/1.09 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0))))) | model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(323,plain,
% 1.35/1.09 (model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[322, 321])).
% 1.35/1.09 tff(324,plain,
% 1.35/1.09 (model_ub(X!5, Y!4, Z!3)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[323, 319])).
% 1.35/1.09 tff(325,plain,
% 1.35/1.09 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(326,plain,
% 1.35/1.09 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[325, 114])).
% 1.35/1.09 tff(327,plain,
% 1.35/1.09 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[326, 269])).
% 1.35/1.09 tff(328,plain,
% 1.35/1.09 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))))))) | (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(329,plain,
% 1.35/1.10 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[328, 149])).
% 1.35/1.10 tff(330,plain,
% 1.35/1.10 ((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))) | minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(331,plain,
% 1.35/1.10 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[330, 329])).
% 1.35/1.10 tff(332,plain,
% 1.35/1.10 (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[331, 327, 324])).
% 1.35/1.10 tff(333,plain,
% 1.35/1.10 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(334,plain,
% 1.35/1.10 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[333, 332])).
% 1.35/1.10 tff(335,plain,
% 1.35/1.10 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)) | model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(336,plain,
% 1.35/1.10 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[335, 332])).
% 1.35/1.10 tff(337,assumption,((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))), introduced(assumption)).
% 1.35/1.10 tff(338,plain,
% 1.35/1.10 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(339,plain,
% 1.35/1.10 ((~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), Z)), 0))))))) <=> (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(340,plain,
% 1.35/1.10 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), Z)), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[339])).
% 1.35/1.10 tff(341,plain,
% 1.35/1.10 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), Z)), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 1.35/1.10 inference(transitivity,[status(thm)],[340, 338])).
% 1.35/1.10 tff(342,plain,
% 1.35/1.10 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), Z)), 0)))))))),
% 1.35/1.10 inference(quant_inst,[status(thm)],[])).
% 1.35/1.10 tff(343,plain,
% 1.35/1.10 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.35/1.10 tff(344,plain,
% 1.35/1.10 ($false),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[343, 46, 337])).
% 1.35/1.10 tff(345,plain,(~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.10 tff(346,plain,
% 1.35/1.10 (((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(347,plain,
% 1.35/1.10 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[346, 345])).
% 1.35/1.10 tff(348,plain,
% 1.35/1.10 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(349,plain,
% 1.35/1.10 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[348, 347])).
% 1.35/1.10 tff(350,plain,
% 1.35/1.10 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[349, 336])).
% 1.35/1.10 tff(351,plain,
% 1.35/1.10 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))) | $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(352,plain,
% 1.35/1.10 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[351, 350])).
% 1.35/1.10 tff(353,plain,
% 1.35/1.10 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(354,plain,
% 1.35/1.10 (($false | ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)) <=> ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(355,plain,
% 1.35/1.10 (($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) = 0) <=> ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(356,plain,
% 1.35/1.10 ((~$true) <=> $false),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(357,plain,
% 1.35/1.10 ($greatereq(0, 0) <=> $true),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(358,plain,
% 1.35/1.10 ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum($product(-1, c), $sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) = 0),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(359,plain,
% 1.35/1.10 ($sum($product(-1, c), $sum($product(-1, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) = $sum($product(-1, c), $sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(360,plain,
% 1.35/1.10 ($product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) = $sum($product(-1, c), $sum($product(-1, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(361,plain,
% 1.35/1.10 ($product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) = $sum($product(-1, c), $sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 1.35/1.10 inference(transitivity,[status(thm)],[360, 359])).
% 1.35/1.10 tff(362,plain,
% 1.35/1.10 ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) = $sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum($product(-1, c), $sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[361])).
% 1.35/1.10 tff(363,plain,
% 1.35/1.10 ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) = 0),
% 1.35/1.10 inference(transitivity,[status(thm)],[362, 358])).
% 1.35/1.10 tff(364,plain,
% 1.35/1.10 ($greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0) <=> $greatereq(0, 0)),
% 1.35/1.10 inference(monotonicity,[status(thm)],[363])).
% 1.35/1.10 tff(365,plain,
% 1.35/1.10 ($greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0) <=> $true),
% 1.35/1.10 inference(transitivity,[status(thm)],[364, 357])).
% 1.35/1.10 tff(366,plain,
% 1.35/1.10 ((~$greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0)) <=> (~$true)),
% 1.35/1.10 inference(monotonicity,[status(thm)],[365])).
% 1.35/1.10 tff(367,plain,
% 1.35/1.10 ((~$greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0)) <=> $false),
% 1.35/1.10 inference(transitivity,[status(thm)],[366, 356])).
% 1.35/1.10 tff(368,plain,
% 1.35/1.10 (((~$greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0)) | ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) = 0)) <=> ($false | ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[367, 355])).
% 1.35/1.11 tff(369,plain,
% 1.35/1.11 (((~$greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0)) | ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) = 0)) <=> ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)),
% 1.35/1.11 inference(transitivity,[status(thm)],[368, 354])).
% 1.35/1.11 tff(370,plain,
% 1.35/1.11 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0)) | ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[369])).
% 1.35/1.11 tff(371,plain,
% 1.35/1.11 (((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0)) | ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0))),
% 1.35/1.11 inference(transitivity,[status(thm)],[370, 353])).
% 1.35/1.11 tff(372,plain,
% 1.35/1.11 ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ((~$greatereq($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))), 0)) | ($sum($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))) = 0))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(373,plain,
% 1.35/1.11 ((~![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))) | ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.35/1.11 tff(374,plain,
% 1.35/1.11 ($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[373, 245])).
% 1.35/1.11 tff(375,plain,
% 1.35/1.11 ((~($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)) | $greatereq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))), 0)),
% 1.35/1.11 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.11 tff(376,plain,
% 1.35/1.11 ($greatereq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))), 0)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[375, 374])).
% 1.35/1.11 tff(377,plain,
% 1.35/1.11 ((~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))), 0)) | $lesseq(max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 1.35/1.11 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.11 tff(378,plain,
% 1.35/1.11 ((~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | $lesseq(max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[377, 376])).
% 1.35/1.11 tff(379,plain,
% 1.35/1.11 ($lesseq(max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[378, 352])).
% 1.35/1.11 tff(380,plain,
% 1.35/1.11 ((~($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))) = 0)) | $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))), 0)),
% 1.35/1.11 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.11 tff(381,plain,
% 1.35/1.11 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), $sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), $sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))))), 0)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[380, 374])).
% 1.35/1.11 tff(382,plain,
% 1.35/1.11 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(383,plain,
% 1.35/1.11 ((ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0))))) <=> (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(384,plain,
% 1.35/1.11 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[383])).
% 1.35/1.11 tff(385,plain,
% 1.35/1.11 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 1.35/1.11 inference(transitivity,[status(thm)],[384, 382])).
% 1.35/1.11 tff(386,plain,
% 1.35/1.11 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0)))))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(387,plain,
% 1.35/1.11 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.35/1.11 tff(388,plain,
% 1.35/1.11 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[387, 180])).
% 1.35/1.11 tff(389,plain,
% 1.35/1.11 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[292])).
% 1.35/1.11 tff(390,plain,
% 1.35/1.11 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 1.35/1.11 inference(symmetry,[status(thm)],[389])).
% 1.35/1.11 tff(391,plain,
% 1.35/1.11 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))) | ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 1.35/1.11 inference(tautology,[status(thm)],[])).
% 1.35/1.11 tff(392,plain,
% 1.35/1.11 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[391, 350])).
% 1.35/1.11 tff(393,plain,
% 1.35/1.11 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[392, 390])).
% 1.35/1.11 tff(394,plain,
% 1.35/1.11 ((~(ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.11 inference(tautology,[status(thm)],[])).
% 1.35/1.11 tff(395,plain,
% 1.35/1.11 (~((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[394, 393, 388])).
% 1.35/1.11 tff(396,plain,
% 1.35/1.11 (((~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))) | $greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.11 inference(tautology,[status(thm)],[])).
% 1.35/1.11 tff(397,plain,
% 1.35/1.11 ($greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[396, 395])).
% 1.35/1.11 tff(398,plain,
% 1.35/1.11 ($false),
% 1.35/1.11 inference(theory_lemma,[status(thm)],[397, 1, 381, 379, 334])).
% 1.35/1.11 tff(399,plain,($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1) | (~(Y!4 = max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.11 tff(400,plain,
% 1.35/1.11 ($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[399, 291])).
% 1.35/1.11 tff(401,assumption,($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)), introduced(assumption)).
% 1.35/1.11 tff(402,assumption,(~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1)), introduced(assumption)).
% 1.35/1.11 tff(403,plain,
% 1.35/1.11 ($false),
% 1.35/1.11 inference(theory_lemma,[status(thm)],[402, 401, 286])).
% 1.35/1.11 tff(404,plain,($lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.11 tff(405,plain,
% 1.35/1.11 ($lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[404, 400])).
% 1.35/1.11 tff(406,plain,
% 1.35/1.11 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(407,plain,
% 1.35/1.11 (((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), -1))) <=> ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(408,plain,
% 1.35/1.11 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[407])).
% 1.35/1.11 tff(409,plain,
% 1.35/1.11 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1)))),
% 1.35/1.11 inference(transitivity,[status(thm)],[408, 406])).
% 1.35/1.11 tff(410,plain,
% 1.35/1.11 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum(Y!4, $product(-1, Z!3))), -1)))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(411,plain,
% 1.35/1.11 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), Y!4)), -1))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.35/1.11 tff(412,plain,
% 1.35/1.11 (~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[411, 405, 310])).
% 1.35/1.11 tff(413,plain,
% 1.35/1.11 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1))))))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(414,plain,
% 1.35/1.11 ((~((~((~model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), Z)), 0))))))) <=> (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(415,plain,
% 1.35/1.11 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), Z)), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1))))))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[414])).
% 1.35/1.11 tff(416,plain,
% 1.35/1.11 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), Z)), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1))))))))),
% 1.35/1.12 inference(transitivity,[status(thm)],[415, 413])).
% 1.35/1.12 tff(417,plain,
% 1.35/1.12 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), tptp_fun_Z_0($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), Y!4, X!5))), 0)))))) | (~(model_ub(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), Z)), 0)))))))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(418,plain,
% 1.35/1.12 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), tptp_fun_Z_0(N, Y, X))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), Z)), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))))))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.35/1.12 tff(419,plain,
% 1.35/1.12 (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1))))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[418, 46])).
% 1.35/1.12 tff(420,plain,
% 1.35/1.12 (((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))), -1)))))) | (~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))))) | (model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1))))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(421,plain,
% 1.35/1.12 (model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[420, 419])).
% 1.35/1.12 tff(422,plain,
% 1.35/1.12 ((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1))))) | model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(423,plain,
% 1.35/1.12 (model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[422, 421])).
% 1.35/1.12 tff(424,plain,
% 1.35/1.12 (model_ub(X!5, Y!4, $sum(-1, Z!3))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[423, 412])).
% 1.35/1.12 tff(425,plain,
% 1.35/1.12 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(426,plain,
% 1.35/1.12 ((model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) <=> $lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), max(X!5, Y!4))), 0)) <=> (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(427,plain,
% 1.35/1.12 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) <=> $lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), max(X!5, Y!4))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[426])).
% 1.35/1.12 tff(428,plain,
% 1.35/1.12 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) <=> $lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), max(X!5, Y!4))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[427, 425])).
% 1.35/1.12 tff(429,plain,
% 1.35/1.12 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))) <=> $lesseq($sum(c, $sum($product(-1, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1))), max(X!5, Y!4))), 0))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(430,plain,
% 1.35/1.12 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), max(X, Y))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.35/1.12 tff(431,plain,
% 1.35/1.12 (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[430, 17])).
% 1.35/1.12 tff(432,plain,
% 1.35/1.12 ((~(model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1))) | model_max(X!5, Y!4, $sum(-1, Z!3)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(433,plain,
% 1.35/1.12 (model_max(X!5, Y!4, $sum(-1, Z!3)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[432, 431])).
% 1.35/1.12 tff(434,plain,
% 1.35/1.12 (model_max(X!5, Y!4, $sum(-1, Z!3))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[433, 400])).
% 1.35/1.12 tff(435,assumption,(model_max(X!5, Y!4, $sum(-1, Z!3))), introduced(assumption)).
% 1.35/1.12 tff(436,assumption,(![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))), introduced(assumption)).
% 1.35/1.12 tff(437,plain,
% 1.35/1.12 (((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_max(X!5, Y!4, $sum(-1, Z!3)))) <=> ((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_max(X!5, Y!4, $sum(-1, Z!3))))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(438,plain,
% 1.35/1.12 (((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $false) <=> (~model_max(X!5, Y!4, $sum(-1, Z!3)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(439,plain,
% 1.35/1.12 ($greatereq(-1, 0) <=> $false),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(440,plain,
% 1.35/1.12 ($sum($sum(-1, Z!3), $product(-1, Z!3)) = -1),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(441,plain,
% 1.35/1.12 ($greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0) <=> $greatereq(-1, 0)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[440])).
% 1.35/1.12 tff(442,plain,
% 1.35/1.12 ($greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0) <=> $false),
% 1.35/1.12 inference(transitivity,[status(thm)],[441, 439])).
% 1.35/1.12 tff(443,plain,
% 1.35/1.12 (((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0)) <=> ((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $false)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[442])).
% 1.35/1.12 tff(444,plain,
% 1.35/1.12 (((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0)) <=> (~model_max(X!5, Y!4, $sum(-1, Z!3)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[443, 438])).
% 1.35/1.12 tff(445,plain,
% 1.35/1.12 (((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0))) <=> ((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_max(X!5, Y!4, $sum(-1, Z!3))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[444])).
% 1.35/1.12 tff(446,plain,
% 1.35/1.12 (((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0))) <=> ((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_max(X!5, Y!4, $sum(-1, Z!3))))),
% 1.35/1.12 inference(transitivity,[status(thm)],[445, 437])).
% 1.35/1.12 tff(447,plain,
% 1.35/1.12 ((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(448,plain,
% 1.35/1.12 ((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_max(X!5, Y!4, $sum(-1, Z!3)))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.35/1.12 tff(449,plain,
% 1.35/1.12 ($false),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[448, 436, 435])).
% 1.35/1.12 tff(450,plain,((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_max(X!5, Y!4, $sum(-1, Z!3)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.12 tff(451,plain,
% 1.35/1.12 (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[450, 434])).
% 1.35/1.12 tff(452,plain,
% 1.35/1.12 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))) | ![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(453,plain,
% 1.35/1.12 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[452, 451])).
% 1.35/1.12 tff(454,plain,
% 1.35/1.12 (~minsol_model_max(X!5, Y!4, Z!3)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[101, 453])).
% 1.35/1.12 tff(455,plain,
% 1.35/1.12 (minsol_model_ub(X!5, Y!4, Z!3)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[116, 454])).
% 1.35/1.12 tff(456,plain,
% 1.35/1.12 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[153, 455])).
% 1.35/1.12 tff(457,plain,
% 1.35/1.12 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))) | ![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(458,plain,
% 1.35/1.12 (![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[457, 456])).
% 1.35/1.12 tff(459,plain,
% 1.35/1.12 (((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_ub(X!5, Y!4, $sum(-1, Z!3)))) <=> ((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_ub(X!5, Y!4, $sum(-1, Z!3))))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(460,plain,
% 1.35/1.12 (((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $false) <=> (~model_ub(X!5, Y!4, $sum(-1, Z!3)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(461,plain,
% 1.35/1.12 (((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0)) <=> ((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $false)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[442])).
% 1.35/1.12 tff(462,plain,
% 1.35/1.12 (((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0)) <=> (~model_ub(X!5, Y!4, $sum(-1, Z!3)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[461, 460])).
% 1.35/1.12 tff(463,plain,
% 1.35/1.12 (((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0))) <=> ((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_ub(X!5, Y!4, $sum(-1, Z!3))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[462])).
% 1.35/1.12 tff(464,plain,
% 1.35/1.12 (((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0))) <=> ((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_ub(X!5, Y!4, $sum(-1, Z!3))))),
% 1.35/1.12 inference(transitivity,[status(thm)],[463, 459])).
% 1.35/1.12 tff(465,plain,
% 1.35/1.12 ((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(466,plain,
% 1.35/1.12 ((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_ub(X!5, Y!4, $sum(-1, Z!3)))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[465, 464])).
% 1.35/1.12 tff(467,plain,
% 1.35/1.12 ($false),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[466, 458, 424])).
% 1.35/1.12 tff(468,plain,(~(Y!4 = max(X!5, Y!4))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.12 tff(469,plain,
% 1.35/1.12 ((Y!4 = max(X!5, Y!4)) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.12 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.12 tff(470,plain,
% 1.35/1.12 ((Y!4 = max(X!5, Y!4)) | (~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[469, 286])).
% 1.35/1.12 tff(471,plain,
% 1.35/1.12 (~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[470, 468])).
% 1.35/1.12 tff(472,plain,
% 1.35/1.12 (~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[202, 471])).
% 1.35/1.12 tff(473,plain,
% 1.35/1.12 (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[226, 472])).
% 1.35/1.12 tff(474,plain,
% 1.35/1.12 ($lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[282, 473])).
% 1.35/1.12 tff(475,plain,
% 1.35/1.12 ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[252, 474])).
% 1.35/1.12 tff(476,plain,
% 1.35/1.12 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[254, 475])).
% 1.35/1.12 tff(477,assumption,(~($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0)), introduced(assumption)).
% 1.35/1.12 tff(478,plain,
% 1.35/1.12 (((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | ($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0))) <=> ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | ($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(479,plain,
% 1.35/1.12 ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | ((~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | ($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(480,plain,
% 1.35/1.12 ((~![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | ($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.35/1.12 tff(481,plain,
% 1.35/1.12 ($false),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[480, 219, 290, 477])).
% 1.35/1.12 tff(482,plain,($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0), inference(lemma,lemma(discharge,[]))).
% 1.35/1.12 tff(483,plain,
% 1.35/1.12 ((~($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0)) | $lesseq($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))), 0)),
% 1.35/1.12 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.12 tff(484,plain,
% 1.35/1.12 ($lesseq($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[483, 482])).
% 1.35/1.12 tff(485,plain,
% 1.35/1.12 ((~($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))) = 0)) | $greatereq($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))), 0)),
% 1.35/1.12 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.12 tff(486,plain,
% 1.35/1.12 ($greatereq($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[485, 482])).
% 1.35/1.12 tff(487,plain,
% 1.35/1.12 (X!5 = max(X!5, max(X!5, Y!4))),
% 1.35/1.12 inference(theory_lemma,[status(thm)],[486, 484, 476, 290])).
% 1.35/1.12 tff(488,plain,
% 1.35/1.12 (max(X!5, max(X!5, Y!4)) = X!5),
% 1.35/1.12 inference(symmetry,[status(thm)],[487])).
% 1.35/1.12 tff(489,plain,
% 1.35/1.12 (ub(X!5, Y!4, max(X!5, max(X!5, Y!4))) <=> ub(X!5, Y!4, X!5)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[488])).
% 1.35/1.12 tff(490,plain,
% 1.35/1.12 (ub(X!5, Y!4, X!5) <=> ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))),
% 1.35/1.12 inference(symmetry,[status(thm)],[489])).
% 1.35/1.12 tff(491,plain,
% 1.35/1.12 ($lesseq($sum(Y!4, $product(-1, $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))))), 0) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.12 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.12 tff(492,plain,
% 1.35/1.12 ($lesseq($sum(Y!4, $product(-1, $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))))), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[491, 290])).
% 1.35/1.12 tff(493,plain,
% 1.35/1.12 ($greatereq($sum(Y!4, $product(-1, $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))))), 0) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 1.35/1.12 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.12 tff(494,plain,
% 1.35/1.12 ($greatereq($sum(Y!4, $product(-1, $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))))), 0)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[493, 476])).
% 1.35/1.12 tff(495,plain,
% 1.35/1.12 ((Y!4 = $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4)))) | (~$lesseq($sum(Y!4, $product(-1, $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))))), 0)) | (~$greatereq($sum(Y!4, $product(-1, $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))))), 0))),
% 1.35/1.12 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.12 tff(496,plain,
% 1.35/1.12 (Y!4 = $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[495, 494, 492])).
% 1.35/1.12 tff(497,plain,
% 1.35/1.12 ($sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))) = Y!4),
% 1.35/1.12 inference(symmetry,[status(thm)],[496])).
% 1.35/1.12 tff(498,plain,
% 1.35/1.12 (ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> ub(X!5, Y!4, X!5)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[488, 497, 488])).
% 1.35/1.12 tff(499,plain,
% 1.35/1.12 (ub(X!5, Y!4, X!5) <=> ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4)))),
% 1.35/1.12 inference(symmetry,[status(thm)],[498])).
% 1.35/1.12 tff(500,plain,
% 1.35/1.12 ((~ub(X!5, Y!4, X!5)) <=> (~ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[499])).
% 1.35/1.12 tff(501,assumption,(~ub(X!5, Y!4, X!5)), introduced(assumption)).
% 1.35/1.12 tff(502,plain,
% 1.35/1.12 (~ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4)))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.35/1.12 tff(503,plain,
% 1.35/1.12 (((~![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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(504,plain,
% 1.35/1.12 ((ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> (~((~$lesseq($sum($sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), $product(-1, max(X!5, max(X!5, Y!4)))), 0)) | (~$greatereq($sum(max(X!5, max(X!5, Y!4)), $product(-1, max(X!5, max(X!5, Y!4)))), 0))))) <=> (ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(505,plain,
% 1.35/1.12 (((~![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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> (~((~$lesseq($sum($sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), $product(-1, max(X!5, max(X!5, Y!4)))), 0)) | (~$greatereq($sum(max(X!5, max(X!5, Y!4)), $product(-1, max(X!5, max(X!5, Y!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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0)))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[504])).
% 1.35/1.12 tff(506,plain,
% 1.35/1.12 (((~![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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> (~((~$lesseq($sum($sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), $product(-1, max(X!5, max(X!5, Y!4)))), 0)) | (~$greatereq($sum(max(X!5, max(X!5, Y!4)), $product(-1, max(X!5, max(X!5, Y!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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[505, 503])).
% 1.35/1.12 tff(507,plain,
% 1.35/1.12 ((~![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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> (~((~$lesseq($sum($sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), $product(-1, max(X!5, max(X!5, Y!4)))), 0)) | (~$greatereq($sum(max(X!5, max(X!5, Y!4)), $product(-1, max(X!5, max(X!5, Y!4)))), 0)))))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(508,plain,
% 1.35/1.13 ((~![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(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.35/1.13 tff(509,plain,
% 1.35/1.13 (ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[508, 180])).
% 1.35/1.13 tff(510,plain,
% 1.35/1.13 ($lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0) | (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | (~$lesseq($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))), 0))),
% 1.35/1.13 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.13 tff(511,plain,
% 1.35/1.13 ($lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[510, 484, 474])).
% 1.35/1.13 tff(512,plain,
% 1.35/1.13 ((~(ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0))) | ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) | (~$lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0))),
% 1.35/1.13 inference(tautology,[status(thm)],[])).
% 1.35/1.13 tff(513,plain,
% 1.35/1.13 ((~(ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4))) <=> $lesseq($sum(Y!4, $sum($product(-1, X!5), $sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))))), 0))) | ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4)))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[512, 511])).
% 1.35/1.13 tff(514,plain,
% 1.35/1.13 (ub(max(X!5, max(X!5, Y!4)), $sum(Y!4, $sum($product(-1, X!5), max(X!5, Y!4))), max(X!5, max(X!5, Y!4)))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[513, 509])).
% 1.35/1.13 tff(515,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[514, 502])).
% 1.35/1.13 tff(516,plain,(ub(X!5, Y!4, X!5)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(517,plain,
% 1.35/1.13 (ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[516, 490])).
% 1.35/1.13 tff(518,assumption,(~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))), introduced(assumption)).
% 1.35/1.13 tff(519,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[518, 517])).
% 1.35/1.13 tff(520,plain,(ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(521,plain,
% 1.35/1.13 ($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, max(X!5, max(X!5, Y!4)))), 0))),
% 1.35/1.13 inference(theory_lemma,[status(thm)],[])).
% 1.35/1.13 tff(522,plain,
% 1.35/1.13 ($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[521, 486, 260])).
% 1.35/1.13 tff(523,assumption,(![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))), introduced(assumption)).
% 1.35/1.13 tff(524,plain,
% 1.35/1.13 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(525,plain,
% 1.35/1.13 (((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), 0))) <=> ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(526,plain,
% 1.35/1.13 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[525])).
% 1.35/1.13 tff(527,plain,
% 1.35/1.13 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[526, 524])).
% 1.35/1.13 tff(528,plain,
% 1.35/1.13 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), 0)))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(529,plain,
% 1.35/1.13 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), 0))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.35/1.13 tff(530,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[529, 523, 522, 520])).
% 1.35/1.13 tff(531,plain,(~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), 0)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(532,plain,
% 1.35/1.13 (model_ub(X!5, Y!4, Z!3)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[323, 531])).
% 1.35/1.13 tff(533,assumption,(~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))), introduced(assumption)).
% 1.35/1.13 tff(534,plain,
% 1.35/1.13 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[333, 533])).
% 1.35/1.13 tff(535,plain,
% 1.35/1.13 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[335, 533])).
% 1.35/1.13 tff(536,plain,
% 1.35/1.13 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[349, 535])).
% 1.35/1.13 tff(537,plain,
% 1.35/1.13 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(538,plain,
% 1.35/1.13 ((ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0))))) <=> (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(539,plain,
% 1.35/1.13 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[538])).
% 1.35/1.13 tff(540,plain,
% 1.35/1.13 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 1.35/1.13 inference(transitivity,[status(thm)],[539, 537])).
% 1.35/1.13 tff(541,plain,
% 1.35/1.13 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, X!5)), 0)))))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(542,plain,
% 1.35/1.13 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.35/1.13 tff(543,plain,
% 1.35/1.13 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[542, 180])).
% 1.35/1.13 tff(544,assumption,(~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))), introduced(assumption)).
% 1.35/1.13 tff(545,plain,
% 1.35/1.13 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[391, 544])).
% 1.35/1.13 tff(546,plain,
% 1.35/1.13 ((~(ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.13 inference(tautology,[status(thm)],[])).
% 1.35/1.13 tff(547,plain,
% 1.35/1.13 ((~(ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))) | (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[546, 545])).
% 1.35/1.13 tff(548,plain,
% 1.35/1.13 (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[547, 543])).
% 1.35/1.13 tff(549,plain,
% 1.35/1.13 (((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))) | $lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 1.35/1.13 inference(tautology,[status(thm)],[])).
% 1.35/1.13 tff(550,plain,
% 1.35/1.13 ($lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[549, 548])).
% 1.35/1.13 tff(551,plain,
% 1.35/1.13 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[351, 544])).
% 1.35/1.13 tff(552,assumption,($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 1.35/1.13 tff(553,assumption,(~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)), introduced(assumption)).
% 1.35/1.13 tff(554,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(theory_lemma,[status(thm)],[1, 553, 552, 551, 550])).
% 1.35/1.13 tff(555,plain,(((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))) | $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(556,plain,
% 1.35/1.13 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))) | $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[555, 476])).
% 1.35/1.13 tff(557,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[556, 536, 534, 1])).
% 1.35/1.13 tff(558,plain,(((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)) | $lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(559,plain,
% 1.35/1.13 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[558, 1])).
% 1.35/1.13 tff(560,plain,
% 1.35/1.13 (minsol_model_ub(X!5, Y!4, Z!3)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[331, 559, 532])).
% 1.35/1.13 tff(561,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[326, 560, 269])).
% 1.35/1.13 tff(562,plain,($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, Y!4))), -1)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(563,assumption,(model_ub(X!5, Y!4, $sum(-1, Z!3))), introduced(assumption)).
% 1.35/1.13 tff(564,plain,
% 1.35/1.13 (model_max(X!5, Y!4, $sum(-1, Z!3))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[433, 562])).
% 1.35/1.13 tff(565,plain,
% 1.35/1.13 (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[450, 564])).
% 1.35/1.13 tff(566,plain,
% 1.35/1.13 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[452, 565])).
% 1.35/1.13 tff(567,plain,
% 1.35/1.13 (~minsol_model_max(X!5, Y!4, Z!3)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[101, 566])).
% 1.35/1.13 tff(568,plain,
% 1.35/1.13 (minsol_model_ub(X!5, Y!4, Z!3)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[116, 567])).
% 1.35/1.13 tff(569,plain,
% 1.35/1.13 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[153, 568])).
% 1.35/1.13 tff(570,plain,
% 1.35/1.13 (![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[457, 569])).
% 1.35/1.13 tff(571,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[466, 570, 563])).
% 1.35/1.13 tff(572,plain,(~model_ub(X!5, Y!4, $sum(-1, Z!3))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(573,plain,
% 1.35/1.13 (![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[423, 572])).
% 1.35/1.13 tff(574,assumption,($lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1)), introduced(assumption)).
% 1.35/1.13 tff(575,assumption,(![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))), introduced(assumption)).
% 1.35/1.13 tff(576,plain,
% 1.35/1.13 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(577,plain,
% 1.35/1.13 (((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), -1))) <=> ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(578,plain,
% 1.35/1.13 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[577])).
% 1.35/1.13 tff(579,plain,
% 1.35/1.13 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[578, 576])).
% 1.35/1.13 tff(580,plain,
% 1.35/1.13 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum(max(X!5, max(X!5, Y!4)), $product(-1, Z!3))), -1)))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(581,plain,
% 1.35/1.13 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, max(X!5, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.35/1.13 tff(582,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[581, 575, 520, 574])).
% 1.35/1.13 tff(583,plain,((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(Z, $product(-1, Z!3))), -1)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(584,plain,
% 1.35/1.13 (~$lesseq($sum(c, $sum($product(-1, Z!3), max(X!5, max(X!5, Y!4)))), -1)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[583, 573])).
% 1.35/1.13 tff(585,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(theory_lemma,[status(thm)],[584, 486, 562])).
% 1.35/1.13 % SZS output end Proof
%------------------------------------------------------------------------------