TSTP Solution File: NUM862_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM862_1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 0.50s 0.56s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM862_1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 15:50:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.50/0.56 % SZS status Theorem
% 0.50/0.56 % SZS output start Proof
% 0.50/0.56 tff(model_ub_type, type, (
% 0.50/0.56 model_ub: ( $int * $int * $int ) > $o)).
% 0.50/0.56 tff(tptp_fun_Z_3_type, type, (
% 0.50/0.56 tptp_fun_Z_3: $int)).
% 0.50/0.56 tff(tptp_fun_Y_4_type, type, (
% 0.50/0.56 tptp_fun_Y_4: $int)).
% 0.50/0.56 tff(tptp_fun_X_5_type, type, (
% 0.50/0.56 tptp_fun_X_5: $int)).
% 0.50/0.56 tff(summation_type, type, (
% 0.50/0.56 summation: $int > $int)).
% 0.50/0.56 tff(c_type, type, (
% 0.50/0.56 c: $int)).
% 0.50/0.56 tff(ub_type, type, (
% 0.50/0.56 ub: ( $int * $int * $int ) > $o)).
% 0.50/0.56 tff(tptp_fun_Z_0_type, type, (
% 0.50/0.56 tptp_fun_Z_0: ( $int * $int * $int ) > $int)).
% 0.50/0.56 tff(max_type, type, (
% 0.50/0.56 max: ( $int * $int ) > $int)).
% 0.50/0.56 tff(tptp_fun_Z_1_type, type, (
% 0.50/0.56 tptp_fun_Z_1: ( $int * $int * $int ) > $int)).
% 0.50/0.56 tff(model_max_type, type, (
% 0.50/0.56 model_max: ( $int * $int * $int ) > $o)).
% 0.50/0.56 tff(minsol_model_max_type, type, (
% 0.50/0.56 minsol_model_max: ( $int * $int * $int ) > $o)).
% 0.50/0.56 tff(tptp_fun_Z_2_type, type, (
% 0.50/0.56 tptp_fun_Z_2: ( $int * $int * $int ) > $int)).
% 0.50/0.56 tff(minsol_model_ub_type, type, (
% 0.50/0.56 minsol_model_ub: ( $int * $int * $int ) > $o)).
% 0.50/0.56 tff(1,plain,
% 0.50/0.56 (^[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), summation(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), summation(Z))), 0))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), summation(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), summation(Z))), 0))))))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(2,plain,
% 0.50/0.56 (![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), summation(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), summation(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), summation(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), summation(Z))), 0)))))))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.50/0.56 tff(3,plain,
% 0.50/0.56 (^[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), summation(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), summation(Z))), 0))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), summation(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), summation(Z))), 0))))))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(4,plain,
% 0.50/0.56 (![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), summation(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), summation(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), summation(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), summation(Z))), 0)))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[3])).
% 0.50/0.57 tff(5,plain,
% 0.50/0.57 (![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), summation(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), summation(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), summation(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), summation(Z))), 0)))))))),
% 0.50/0.57 inference(transitivity,[status(thm)],[4, 2])).
% 0.50/0.57 tff(6,plain,
% 0.50/0.57 (^[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), summation(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), summation(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), summation(Z))), 0)))) <=> (model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$lesseq($sum(c, $sum($product(-1, N), summation(Z))), 0))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $lesseq($sum(c, $sum($product(-1, N), summation(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), summation(Z))), 0))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), summation(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), summation(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), summation(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), summation(Z))), 0))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), summation(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), summation(Z))), 0)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $lesseq($sum(c, $sum($product(-1, N), summation(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), summation(Z))), 0))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$lesseq($sum(c, $sum($product(-1, N), summation(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), summation(Z))), 0)))))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(7,plain,
% 0.50/0.57 (![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), summation(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), summation(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), summation(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), summation(Z))), 0)))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[6])).
% 0.50/0.57 tff(8,plain,
% 0.50/0.57 (^[X: $int, Y: $int, N: $int] : rewrite((model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(summation(Z), $product(-1, N))), 0))) <=> (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), summation(Z))), 0))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(9,plain,
% 0.50/0.57 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(summation(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), summation(Z))), 0)))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[8])).
% 0.50/0.57 tff(10,plain,
% 0.50/0.57 (^[X: $int, Y: $int, N: $int] : rewrite((model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, summation(Z)), N))) <=> (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(summation(Z), $product(-1, N))), 0))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(11,plain,
% 0.50/0.57 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, summation(Z)), N))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(summation(Z), $product(-1, N))), 0)))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[10])).
% 0.50/0.57 tff(12,plain,
% 0.50/0.57 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, summation(Z)), N))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, summation(Z)), N)))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(13,axiom,(![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, summation(Z)), N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_ub_5')).
% 0.50/0.57 tff(14,plain,
% 0.50/0.57 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, summation(Z)), N)))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.50/0.57 tff(15,plain,
% 0.50/0.57 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum(summation(Z), $product(-1, N))), 0)))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.50/0.57 tff(16,plain,
% 0.50/0.57 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(c, $sum($product(-1, N), summation(Z))), 0)))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.50/0.57 tff(17,plain,(
% 0.50/0.57 ![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), summation(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), summation(Z))), 0)))))),
% 0.50/0.57 inference(skolemize,[status(sab)],[16])).
% 0.50/0.57 tff(18,plain,
% 0.50/0.57 (![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), summation(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), summation(Z))), 0)))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.50/0.57 tff(19,plain,
% 0.50/0.57 (![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), summation(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), summation(Z))), 0)))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.50/0.57 tff(20,plain,
% 0.50/0.57 (((~![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), summation(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), summation(Z))), 0)))))))) | (~((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5)))), -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), summation(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), summation(Z))), 0)))))))) | (~((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5)))), -1)))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(21,plain,
% 0.50/0.57 ((~((~((~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))), $product(-1, 1))), summation(tptp_fun_Z_0($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))), summation(Z))), 0))))))) <=> (~((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5)))), -1))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(22,plain,
% 0.50/0.57 (((~![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), summation(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), summation(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))), $product(-1, 1))), summation(tptp_fun_Z_0($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))), summation(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), summation(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), summation(Z))), 0)))))))) | (~((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5)))), -1)))))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[21])).
% 0.50/0.57 tff(23,plain,
% 0.50/0.57 (((~![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), summation(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), summation(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))), $product(-1, 1))), summation(tptp_fun_Z_0($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))), summation(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), summation(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), summation(Z))), 0)))))))) | (~((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5)))), -1)))))))))),
% 0.53/0.57 inference(transitivity,[status(thm)],[22, 20])).
% 0.53/0.57 tff(24,plain,
% 0.53/0.57 ((~![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), summation(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), summation(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))), $product(-1, 1))), summation(tptp_fun_Z_0($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))), summation(Z))), 0)))))))),
% 0.53/0.57 inference(quant_inst,[status(thm)],[])).
% 0.53/0.57 tff(25,plain,
% 0.53/0.57 ((~![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), summation(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), summation(Z))), 0)))))))) | (~((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5)))), -1))))))))),
% 0.53/0.57 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.53/0.57 tff(26,plain,
% 0.53/0.57 (~((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5)))), -1)))))))),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.53/0.57 tff(27,plain,
% 0.53/0.57 (((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1))))) | (~((~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), summation(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(summation(Z), $product(-1, Z!3))), -1))))),
% 0.53/0.57 inference(tautology,[status(thm)],[])).
% 0.53/0.57 tff(28,plain,
% 0.53/0.57 (model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.53/0.57 tff(29,assumption,(~$lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.53/0.57 tff(30,plain,
% 0.53/0.57 (^[X: $int, Y: $int] : refl(($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0)) <=> ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0)))),
% 0.53/0.57 inference(bind,[status(th)],[])).
% 0.53/0.57 tff(31,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0)) <=> ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.53/0.57 inference(quant_intro,[status(thm)],[30])).
% 0.53/0.57 tff(32,plain,
% 0.53/0.57 (^[X: $int, Y: $int] : rewrite(($lesseq($sum(X, $product(-1, Y)), 0) <=> $lesseq($sum(summation(X), $product(-1, summation(Y))), 0)) <=> ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0)))),
% 0.53/0.57 inference(bind,[status(th)],[])).
% 0.53/0.57 tff(33,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $lesseq($sum(summation(X), $product(-1, summation(Y))), 0)) <=> ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.53/0.57 inference(quant_intro,[status(thm)],[32])).
% 0.53/0.57 tff(34,plain,
% 0.53/0.57 (^[X: $int, Y: $int] : rewrite(($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y))) <=> ($lesseq($sum(X, $product(-1, Y)), 0) <=> $lesseq($sum(summation(X), $product(-1, summation(Y))), 0)))),
% 0.53/0.57 inference(bind,[status(th)],[])).
% 0.53/0.57 tff(35,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y))) <=> ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $lesseq($sum(summation(X), $product(-1, summation(Y))), 0))),
% 0.53/0.57 inference(quant_intro,[status(thm)],[34])).
% 0.53/0.57 tff(36,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y))) <=> ![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y)))),
% 0.53/0.57 inference(rewrite,[status(thm)],[])).
% 0.53/0.57 tff(37,axiom,(![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','summation_monotone')).
% 0.53/0.57 tff(38,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y)))),
% 0.53/0.57 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.53/0.57 tff(39,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $lesseq($sum(summation(X), $product(-1, summation(Y))), 0))),
% 0.53/0.57 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.53/0.57 tff(40,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.53/0.57 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.53/0.57 tff(41,plain,(
% 0.53/0.57 ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.53/0.57 inference(skolemize,[status(sab)],[40])).
% 0.53/0.57 tff(42,plain,
% 0.53/0.57 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.53/0.57 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.53/0.57 tff(43,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(rewrite,[status(thm)],[])).
% 0.53/0.57 tff(44,plain,
% 0.53/0.57 (($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(Y!4))), 0)) <=> ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(rewrite,[status(thm)],[])).
% 0.53/0.57 tff(45,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(Y!4))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(monotonicity,[status(thm)],[44])).
% 0.53/0.57 tff(46,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(Y!4))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(transitivity,[status(thm)],[45, 43])).
% 0.53/0.57 tff(47,plain,
% 0.53/0.57 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(Y!4))), 0))),
% 0.53/0.57 inference(quant_inst,[status(thm)],[])).
% 0.53/0.57 tff(48,plain,
% 0.53/0.57 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.53/0.57 tff(49,plain,
% 0.53/0.57 ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[48, 42])).
% 0.53/0.57 tff(50,plain,
% 0.53/0.57 ((~($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.57 inference(tautology,[status(thm)],[])).
% 0.53/0.57 tff(51,plain,
% 0.53/0.57 ((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.53/0.57 tff(52,plain,
% 0.53/0.57 (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[51, 29])).
% 0.53/0.57 tff(53,plain,
% 0.53/0.57 ((~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)) | $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.57 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.57 tff(54,plain,
% 0.53/0.57 (~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.53/0.57 tff(55,plain,
% 0.53/0.57 ($lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0) | $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.57 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.57 tff(56,plain,
% 0.53/0.57 ($greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[55, 29])).
% 0.53/0.57 tff(57,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(rewrite,[status(thm)],[])).
% 0.53/0.57 tff(58,plain,
% 0.53/0.57 (($lesseq($sum(max(X!5, Y!4), $product(-1, Y!4)), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)) <=> ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(rewrite,[status(thm)],[])).
% 0.53/0.57 tff(59,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, Y!4)), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(monotonicity,[status(thm)],[58])).
% 0.53/0.57 tff(60,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, Y!4)), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(transitivity,[status(thm)],[59, 57])).
% 0.53/0.57 tff(61,plain,
% 0.53/0.57 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, Y!4)), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(quant_inst,[status(thm)],[])).
% 0.53/0.57 tff(62,plain,
% 0.53/0.57 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.53/0.57 tff(63,plain,
% 0.53/0.57 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[62, 42])).
% 0.53/0.57 tff(64,plain,
% 0.53/0.57 ((~($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) | $greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) | (~$greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(tautology,[status(thm)],[])).
% 0.53/0.57 tff(65,plain,
% 0.53/0.57 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) | (~$greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.53/0.57 tff(66,plain,
% 0.53/0.57 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.57 inference(unit_resolution,[status(thm)],[65, 56])).
% 0.53/0.57 tff(67,assumption,(~$lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.53/0.57 tff(68,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(rewrite,[status(thm)],[])).
% 0.53/0.57 tff(69,plain,
% 0.53/0.57 (($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(X!5))), 0)) <=> ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.57 inference(rewrite,[status(thm)],[])).
% 0.53/0.57 tff(70,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(X!5))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.57 inference(monotonicity,[status(thm)],[69])).
% 0.53/0.57 tff(71,plain,
% 0.53/0.57 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(X!5))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.58 inference(transitivity,[status(thm)],[70, 68])).
% 0.53/0.58 tff(72,plain,
% 0.53/0.58 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(X!5))), 0))),
% 0.53/0.58 inference(quant_inst,[status(thm)],[])).
% 0.53/0.58 tff(73,plain,
% 0.53/0.58 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.53/0.58 tff(74,plain,
% 0.53/0.58 ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[73, 42])).
% 0.53/0.58 tff(75,plain,
% 0.53/0.58 ((~($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.58 inference(tautology,[status(thm)],[])).
% 0.53/0.58 tff(76,plain,
% 0.53/0.58 ((~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.53/0.58 tff(77,plain,
% 0.53/0.58 (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[76, 67])).
% 0.53/0.58 tff(78,plain,
% 0.53/0.58 ((~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)) | $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.58 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.58 tff(79,plain,
% 0.53/0.58 (~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.53/0.58 tff(80,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : refl(((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)) <=> ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(81,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)) <=> ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[80])).
% 0.53/0.58 tff(82,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : rewrite(((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)) <=> ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(83,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)) <=> ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[82])).
% 0.53/0.58 tff(84,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : rewrite(((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(85,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[84])).
% 0.53/0.58 tff(86,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(87,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ((~$lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(88,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[87])).
% 0.53/0.58 tff(89,axiom,(![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_1')).
% 0.53/0.58 tff(90,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.53/0.58 tff(91,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.53/0.58 tff(92,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.53/0.58 tff(93,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[92, 83])).
% 0.53/0.58 tff(94,plain,(
% 0.53/0.58 ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(skolemize,[status(sab)],[93])).
% 0.53/0.58 tff(95,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[94, 81])).
% 0.53/0.58 tff(96,plain,
% 0.53/0.58 (((~![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, $product(-1, max(X!5, Y!4))) = 0))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(97,plain,
% 0.53/0.58 (((~$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))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(98,plain,
% 0.53/0.58 (((~![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)))),
% 0.53/0.58 inference(monotonicity,[status(thm)],[97])).
% 0.53/0.58 tff(99,plain,
% 0.53/0.58 (((~![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))),
% 0.53/0.58 inference(transitivity,[status(thm)],[98, 96])).
% 0.53/0.58 tff(100,plain,
% 0.53/0.58 ((~![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))),
% 0.53/0.58 inference(quant_inst,[status(thm)],[])).
% 0.53/0.58 tff(101,plain,
% 0.53/0.58 ((~![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, $product(-1, max(X!5, Y!4))) = 0)),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.53/0.58 tff(102,plain,
% 0.53/0.58 ((~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[101, 95])).
% 0.53/0.58 tff(103,plain,
% 0.53/0.58 (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[102, 79])).
% 0.53/0.58 tff(104,plain,
% 0.53/0.58 ($greatereq($sum(Y!4, $product(-1, X!5)), 0) | $lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.53/0.58 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.58 tff(105,plain,
% 0.53/0.58 ($greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.53/0.58 tff(106,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : refl(((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(107,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[106])).
% 0.53/0.58 tff(108,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : rewrite(((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(109,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[108])).
% 0.53/0.58 tff(110,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : rewrite(((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(111,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[110])).
% 0.53/0.58 tff(112,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(113,plain,
% 0.53/0.58 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ((~$lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(114,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[113])).
% 0.53/0.58 tff(115,axiom,(![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_2')).
% 0.53/0.58 tff(116,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.53/0.58 tff(117,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.53/0.58 tff(118,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[117, 111])).
% 0.53/0.58 tff(119,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[118, 109])).
% 0.53/0.58 tff(120,plain,(
% 0.53/0.58 ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(skolemize,[status(sab)],[119])).
% 0.53/0.58 tff(121,plain,
% 0.53/0.58 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[120, 107])).
% 0.53/0.58 tff(122,plain,
% 0.53/0.58 (((~![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, $product(-1, max(X!5, Y!4))) = 0))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(123,plain,
% 0.53/0.58 (((~$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))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(124,plain,
% 0.53/0.58 (((~![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)))),
% 0.53/0.58 inference(monotonicity,[status(thm)],[123])).
% 0.53/0.58 tff(125,plain,
% 0.53/0.58 (((~![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))),
% 0.53/0.58 inference(transitivity,[status(thm)],[124, 122])).
% 0.53/0.58 tff(126,plain,
% 0.53/0.58 ((~![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))),
% 0.53/0.58 inference(quant_inst,[status(thm)],[])).
% 0.53/0.58 tff(127,plain,
% 0.53/0.58 ((~![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, $product(-1, max(X!5, Y!4))) = 0)),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.53/0.58 tff(128,plain,
% 0.53/0.58 ((~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[127, 121])).
% 0.53/0.58 tff(129,plain,
% 0.53/0.58 ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[128, 105])).
% 0.53/0.58 tff(130,plain,
% 0.53/0.58 ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[53, 129])).
% 0.53/0.58 tff(131,plain,
% 0.53/0.58 ($lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0) | $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.58 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.58 tff(132,plain,
% 0.53/0.58 ($greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[131, 67])).
% 0.53/0.58 tff(133,plain,
% 0.53/0.58 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(134,plain,
% 0.53/0.58 (($lesseq($sum(max(X!5, Y!4), $product(-1, X!5)), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)) <=> ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(135,plain,
% 0.53/0.58 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, X!5)), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.58 inference(monotonicity,[status(thm)],[134])).
% 0.53/0.58 tff(136,plain,
% 0.53/0.58 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, X!5)), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.58 inference(transitivity,[status(thm)],[135, 133])).
% 0.53/0.58 tff(137,plain,
% 0.53/0.58 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, X!5)), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(quant_inst,[status(thm)],[])).
% 0.53/0.58 tff(138,plain,
% 0.53/0.58 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.53/0.58 tff(139,plain,
% 0.53/0.58 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[138, 42])).
% 0.53/0.58 tff(140,plain,
% 0.53/0.58 ((~($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) | $greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) | (~$greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(tautology,[status(thm)],[])).
% 0.53/0.58 tff(141,plain,
% 0.53/0.58 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) | (~$greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.53/0.58 tff(142,plain,
% 0.53/0.58 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[141, 132])).
% 0.53/0.58 tff(143,plain,
% 0.53/0.58 ($false),
% 0.53/0.58 inference(theory_lemma,[status(thm)],[142, 130, 103])).
% 0.53/0.58 tff(144,plain,($lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.58 tff(145,plain,
% 0.53/0.58 ((~($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) | $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) | (~$lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(tautology,[status(thm)],[])).
% 0.53/0.58 tff(146,plain,
% 0.53/0.58 ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) | (~$lesseq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[145, 74])).
% 0.53/0.58 tff(147,plain,
% 0.53/0.58 ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[146, 144])).
% 0.53/0.58 tff(148,plain,
% 0.53/0.58 ((~$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, $product(-1, max(X!5, Y!4))), 0))),
% 0.53/0.58 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.58 tff(149,plain,
% 0.53/0.58 ((~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.53/0.58 tff(150,plain,
% 0.53/0.58 ($greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[149, 66])).
% 0.53/0.58 tff(151,plain,
% 0.53/0.58 ($false),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[128, 150, 54])).
% 0.53/0.58 tff(152,plain,($lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.58 tff(153,plain,
% 0.53/0.58 ((~($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) | $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) | (~$lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(tautology,[status(thm)],[])).
% 0.53/0.58 tff(154,plain,
% 0.53/0.58 ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) | (~$lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[153, 49])).
% 0.53/0.58 tff(155,plain,
% 0.53/0.58 ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[154, 152])).
% 0.53/0.58 tff(156,plain,
% 0.53/0.58 ((~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 0.53/0.58 inference(tautology,[status(thm)],[])).
% 0.53/0.58 tff(157,plain,
% 0.53/0.58 ((~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[156, 147])).
% 0.53/0.58 tff(158,plain,
% 0.53/0.58 (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[157, 155])).
% 0.53/0.58 tff(159,assumption,(~(ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))))), introduced(assumption)).
% 0.53/0.58 tff(160,plain,
% 0.53/0.58 (^[X: $int, Y: $int, Z: $int] : refl((ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))) <=> (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(161,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[160])).
% 0.53/0.58 tff(162,plain,
% 0.53/0.58 (^[X: $int, Y: $int, Z: $int] : rewrite((ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(163,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[162])).
% 0.53/0.58 tff(164,plain,
% 0.53/0.58 (^[X: $int, Y: $int, Z: $int] : rewrite((ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(165,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[164])).
% 0.53/0.58 tff(166,plain,
% 0.53/0.58 (^[X: $int, Y: $int, Z: $int] : rewrite((ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z))) <=> (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(167,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[166])).
% 0.53/0.58 tff(168,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z))) <=> ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(169,axiom,(![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ub')).
% 0.53/0.58 tff(170,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.53/0.58 tff(171,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[170, 167])).
% 0.53/0.58 tff(172,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[171, 165])).
% 0.53/0.58 tff(173,plain,(
% 0.53/0.58 ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.53/0.58 inference(skolemize,[status(sab)],[172])).
% 0.53/0.58 tff(174,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[173, 163])).
% 0.53/0.58 tff(175,plain,
% 0.53/0.58 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[174, 161])).
% 0.53/0.58 tff(176,plain,
% 0.53/0.58 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$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, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(177,plain,
% 0.53/0.58 ((ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, X!5)), 0))))) <=> (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(178,plain,
% 0.53/0.58 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(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, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))))))),
% 0.53/0.58 inference(monotonicity,[status(thm)],[177])).
% 0.53/0.58 tff(179,plain,
% 0.53/0.58 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(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, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))))))),
% 0.53/0.58 inference(transitivity,[status(thm)],[178, 176])).
% 0.53/0.58 tff(180,plain,
% 0.53/0.58 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, X!5)), 0)))))),
% 0.53/0.58 inference(quant_inst,[status(thm)],[])).
% 0.53/0.58 tff(181,plain,
% 0.53/0.58 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.53/0.58 tff(182,plain,
% 0.53/0.58 ($false),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[181, 175, 159])).
% 0.53/0.58 tff(183,plain,(ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.58 tff(184,plain,
% 0.53/0.58 ((~(ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))))) | ub(X!5, Y!4, max(X!5, Y!4)) | ((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))),
% 0.53/0.58 inference(tautology,[status(thm)],[])).
% 0.53/0.58 tff(185,plain,
% 0.53/0.58 (ub(X!5, Y!4, max(X!5, Y!4)) | ((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.53/0.58 tff(186,plain,
% 0.53/0.58 (ub(X!5, Y!4, max(X!5, Y!4))),
% 0.53/0.58 inference(unit_resolution,[status(thm)],[185, 158])).
% 0.53/0.58 tff(187,assumption,($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.53/0.58 tff(188,assumption,(~minsol_model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.53/0.58 tff(189,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)).
% 0.53/0.58 tff(190,plain,
% 0.53/0.58 (^[X: $int, Y: $int, N: $int] : refl((~((~(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))))))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(191,plain,
% 0.53/0.58 (![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))))))))) <=> ![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)))))))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[190])).
% 0.53/0.58 tff(192,plain,
% 0.53/0.58 (^[X: $int, Y: $int, N: $int] : 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)) | (~![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))))))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(193,plain,
% 0.53/0.58 (![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))))))))) <=> ![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)))))))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[192])).
% 0.53/0.58 tff(194,plain,
% 0.53/0.58 (![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))))))))) <=> ![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)))))))))),
% 0.53/0.58 inference(transitivity,[status(thm)],[193, 191])).
% 0.53/0.58 tff(195,plain,
% 0.53/0.58 (^[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)) | (~((~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) & ![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)))))))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(196,plain,
% 0.53/0.58 (![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)))))))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[195])).
% 0.53/0.58 tff(197,plain,
% 0.53/0.58 (^[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))))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(198,plain,
% 0.53/0.58 (![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)))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[197])).
% 0.53/0.58 tff(199,plain,
% 0.53/0.58 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))) <=> (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(200,plain,
% 0.53/0.58 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[199])).
% 0.53/0.58 tff(201,plain,
% 0.53/0.58 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.58 inference(rewrite,[status(thm)],[])).
% 0.53/0.58 tff(202,plain,
% 0.53/0.58 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : (model_max(X, Y, Z) => $lesseq(N, Z)))) <=> (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z)))))),
% 0.53/0.58 inference(bind,[status(th)],[])).
% 0.53/0.58 tff(203,plain,
% 0.53/0.58 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : (model_max(X, Y, Z) => $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.58 inference(quant_intro,[status(thm)],[202])).
% 0.53/0.58 tff(204,axiom,(![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : (model_max(X, Y, Z) => $lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_max')).
% 0.53/0.58 tff(205,plain,
% 0.53/0.58 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.58 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.53/0.58 tff(206,plain,
% 0.53/0.58 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.53/0.59 tff(207,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $int] : ((~model_max(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[206, 200])).
% 0.53/0.59 tff(208,plain,(
% 0.53/0.59 ![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))))))),
% 0.53/0.59 inference(skolemize,[status(sab)],[207])).
% 0.53/0.59 tff(209,plain,
% 0.53/0.59 (![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)))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[208, 198])).
% 0.53/0.59 tff(210,plain,
% 0.53/0.59 (![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)))))))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[209, 196])).
% 0.53/0.59 tff(211,plain,
% 0.53/0.59 (![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)))))))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[210, 194])).
% 0.53/0.59 tff(212,plain,
% 0.53/0.59 (((~![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))))))))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(213,plain,
% 0.53/0.59 ((~((~(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)))))))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(214,plain,
% 0.53/0.59 (((~![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))))))))))),
% 0.53/0.59 inference(monotonicity,[status(thm)],[213])).
% 0.53/0.59 tff(215,plain,
% 0.53/0.59 (((~![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))))))))))),
% 0.53/0.59 inference(transitivity,[status(thm)],[214, 212])).
% 0.53/0.59 tff(216,plain,
% 0.53/0.59 ((~![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)))))))))),
% 0.53/0.59 inference(quant_inst,[status(thm)],[])).
% 0.53/0.59 tff(217,plain,
% 0.53/0.59 ((~![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)))))))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.53/0.59 tff(218,plain,
% 0.53/0.59 (~((~(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))))))))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[217, 211])).
% 0.53/0.59 tff(219,plain,
% 0.53/0.59 (((~(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))))),
% 0.53/0.59 inference(tautology,[status(thm)],[])).
% 0.53/0.59 tff(220,plain,
% 0.53/0.59 (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)))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.53/0.59 tff(221,plain,
% 0.53/0.59 ((~(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)))),
% 0.53/0.59 inference(tautology,[status(thm)],[])).
% 0.53/0.59 tff(222,plain,
% 0.53/0.59 (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)))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.53/0.59 tff(223,plain,
% 0.53/0.59 (~model_max(X!5, Y!4, Z!3)),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[222, 188, 189])).
% 0.53/0.59 tff(224,assumption,(~(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))), introduced(assumption)).
% 0.53/0.59 tff(225,plain,
% 0.53/0.59 (^[X: $int, Y: $int, N: $int] : refl((model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0)) <=> (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0)))),
% 0.53/0.59 inference(bind,[status(th)],[])).
% 0.53/0.59 tff(226,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))),
% 0.53/0.59 inference(quant_intro,[status(thm)],[225])).
% 0.53/0.59 tff(227,plain,
% 0.53/0.59 (^[X: $int, Y: $int, N: $int] : rewrite((model_max(X, Y, N) <=> $lesseq($sum(c, $sum(summation(max(X, Y)), $product(-1, N))), 0)) <=> (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0)))),
% 0.53/0.59 inference(bind,[status(th)],[])).
% 0.53/0.59 tff(228,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(summation(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), summation(max(X, Y)))), 0))),
% 0.53/0.59 inference(quant_intro,[status(thm)],[227])).
% 0.53/0.59 tff(229,plain,
% 0.53/0.59 (^[X: $int, Y: $int, N: $int] : rewrite((model_max(X, Y, N) <=> $lesseq($sum(c, summation(max(X, Y))), N)) <=> (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(summation(max(X, Y)), $product(-1, N))), 0)))),
% 0.53/0.59 inference(bind,[status(th)],[])).
% 0.53/0.59 tff(230,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, summation(max(X, Y))), N)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(summation(max(X, Y)), $product(-1, N))), 0))),
% 0.53/0.59 inference(quant_intro,[status(thm)],[229])).
% 0.53/0.59 tff(231,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, summation(max(X, Y))), N)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, summation(max(X, Y))), N))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(232,axiom,(![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, summation(max(X, Y))), N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_max_5')).
% 0.53/0.59 tff(233,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, summation(max(X, Y))), N))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.53/0.59 tff(234,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum(summation(max(X, Y)), $product(-1, N))), 0))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[233, 230])).
% 0.53/0.59 tff(235,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[234, 228])).
% 0.53/0.59 tff(236,plain,(
% 0.53/0.59 ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))),
% 0.53/0.59 inference(skolemize,[status(sab)],[235])).
% 0.53/0.59 tff(237,plain,
% 0.53/0.59 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[236, 226])).
% 0.53/0.59 tff(238,plain,
% 0.53/0.59 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))),
% 0.53/0.59 inference(quant_inst,[status(thm)],[])).
% 0.53/0.59 tff(239,plain,
% 0.53/0.59 ($false),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[238, 237, 224])).
% 0.53/0.59 tff(240,plain,(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.59 tff(241,plain,
% 0.53/0.59 ((~(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))) | model_max(X!5, Y!4, Z!3) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))),
% 0.53/0.59 inference(tautology,[status(thm)],[])).
% 0.53/0.59 tff(242,plain,
% 0.53/0.59 (model_max(X!5, Y!4, Z!3) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.53/0.59 tff(243,plain,
% 0.53/0.59 (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[242, 223])).
% 0.53/0.59 tff(244,plain,
% 0.53/0.59 (((~![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), summation(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), summation(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), summation(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(summation(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), summation(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), summation(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), summation(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(summation(Z), $product(-1, Z!3))), 0))))))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(245,plain,
% 0.53/0.59 ((~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(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), summation(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), summation(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(summation(Z), $product(-1, Z!3))), 0)))))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(246,plain,
% 0.53/0.59 (((~![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), summation(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), summation(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), summation(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), summation(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), summation(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), summation(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), summation(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(summation(Z), $product(-1, Z!3))), 0))))))))),
% 0.53/0.59 inference(monotonicity,[status(thm)],[245])).
% 0.53/0.59 tff(247,plain,
% 0.53/0.59 (((~![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), summation(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), summation(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), summation(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), summation(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), summation(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), summation(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), summation(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(summation(Z), $product(-1, Z!3))), 0))))))))),
% 0.53/0.59 inference(transitivity,[status(thm)],[246, 244])).
% 0.53/0.59 tff(248,plain,
% 0.53/0.59 ((~![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), summation(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), summation(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), summation(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), summation(Z))), 0)))))))),
% 0.53/0.59 inference(quant_inst,[status(thm)],[])).
% 0.53/0.59 tff(249,plain,
% 0.53/0.59 ((~![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), summation(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), summation(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), summation(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(summation(Z), $product(-1, Z!3))), 0)))))))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.53/0.59 tff(250,plain,
% 0.53/0.59 (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(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(summation(Z), $product(-1, Z!3))), 0))))))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[249, 19])).
% 0.53/0.59 tff(251,plain,
% 0.53/0.59 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(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(summation(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), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))))),
% 0.53/0.59 inference(tautology,[status(thm)],[])).
% 0.53/0.59 tff(252,plain,
% 0.53/0.59 ((~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), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))))),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.53/0.59 tff(253,plain,
% 0.53/0.59 ((~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))) <=> ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(254,plain,
% 0.53/0.59 ((~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))) <=> (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z)))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(255,axiom,(~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.53/0.59 tff(256,plain,
% 0.53/0.59 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.53/0.59 tff(257,plain,
% 0.53/0.59 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[256, 254])).
% 0.53/0.59 tff(258,plain,
% 0.53/0.59 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[257, 254])).
% 0.53/0.59 tff(259,plain,
% 0.53/0.59 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.53/0.59 tff(260,plain,
% 0.53/0.59 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[259, 254])).
% 0.53/0.59 tff(261,plain,
% 0.53/0.59 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[260, 254])).
% 0.53/0.59 tff(262,plain,
% 0.53/0.59 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[261, 254])).
% 0.53/0.59 tff(263,plain,(
% 0.53/0.59 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.53/0.59 inference(skolemize,[status(sab)],[262])).
% 0.53/0.59 tff(264,plain,
% 0.53/0.59 ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)),
% 0.53/0.59 inference(modus_ponens,[status(thm)],[263, 253])).
% 0.53/0.59 tff(265,plain,
% 0.53/0.59 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 0.53/0.59 inference(tautology,[status(thm)],[])).
% 0.53/0.59 tff(266,plain,
% 0.53/0.59 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.53/0.59 tff(267,plain,
% 0.53/0.59 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.53/0.59 inference(unit_resolution,[status(thm)],[266, 188])).
% 0.53/0.59 tff(268,plain,
% 0.53/0.59 (^[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))))))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(269,plain,
% 0.53/0.60 (![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)))))))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[268])).
% 0.53/0.60 tff(270,plain,
% 0.53/0.60 (^[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))))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(271,plain,
% 0.53/0.60 (![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)))))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[270])).
% 0.53/0.60 tff(272,plain,
% 0.53/0.60 (^[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))))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(273,plain,
% 0.53/0.60 (![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)))))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[272])).
% 0.53/0.60 tff(274,plain,
% 0.53/0.60 (![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)))))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[273, 271])).
% 0.53/0.60 tff(275,plain,
% 0.53/0.60 (^[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)))))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(276,plain,
% 0.53/0.60 (![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)))))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[275])).
% 0.53/0.60 tff(277,plain,
% 0.53/0.60 (^[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))))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(278,plain,
% 0.53/0.60 (![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)))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[277])).
% 0.53/0.60 tff(279,plain,
% 0.53/0.60 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))) <=> (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0)))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(280,plain,
% 0.53/0.60 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[279])).
% 0.53/0.60 tff(281,plain,
% 0.53/0.60 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(282,plain,
% 0.53/0.60 (^[X: $int, Y: $int, N: $int] : rewrite((minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : (model_ub(X, Y, Z) => $lesseq(N, Z)))) <=> (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z)))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(283,plain,
% 0.53/0.60 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : (model_ub(X, Y, Z) => $lesseq(N, Z)))) <=> ![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[282])).
% 0.53/0.60 tff(284,axiom,(![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : (model_ub(X, Y, Z) => $lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.53/0.60 tff(285,plain,
% 0.53/0.60 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.53/0.60 tff(286,plain,
% 0.53/0.60 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq(N, Z))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.53/0.60 tff(287,plain,
% 0.53/0.60 (![X: $int, Y: $int, N: $int] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $int] : ((~model_ub(X, Y, Z)) | $lesseq($sum(N, $product(-1, Z)), 0))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[286, 280])).
% 0.53/0.60 tff(288,plain,(
% 0.53/0.60 ![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))))))),
% 0.53/0.60 inference(skolemize,[status(sab)],[287])).
% 0.53/0.60 tff(289,plain,
% 0.53/0.60 (![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)))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[288, 278])).
% 0.53/0.60 tff(290,plain,
% 0.53/0.60 (![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)))))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[289, 276])).
% 0.53/0.60 tff(291,plain,
% 0.53/0.60 (![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)))))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[290, 274])).
% 0.53/0.60 tff(292,plain,
% 0.53/0.60 (![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)))))))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[291, 269])).
% 0.53/0.60 tff(293,plain,
% 0.53/0.60 (((~![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))))))))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(294,plain,
% 0.53/0.60 ((~((~(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)))))))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(295,plain,
% 0.53/0.60 (((~![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))))))))))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[294])).
% 0.53/0.60 tff(296,plain,
% 0.53/0.60 (((~![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))))))))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[295, 293])).
% 0.53/0.60 tff(297,plain,
% 0.53/0.60 ((~![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)))))))))),
% 0.53/0.60 inference(quant_inst,[status(thm)],[])).
% 0.53/0.60 tff(298,plain,
% 0.53/0.60 ((~![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)))))))))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.53/0.60 tff(299,plain,
% 0.53/0.60 (~((~(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))))))))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[298, 292])).
% 0.53/0.60 tff(300,plain,
% 0.53/0.60 (((~(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))))))),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(301,plain,
% 0.53/0.60 ((~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)))))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[300, 299])).
% 0.53/0.60 tff(302,plain,
% 0.53/0.60 ((~((~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)))))),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(303,plain,
% 0.53/0.60 ((~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)))))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.53/0.60 tff(304,plain,
% 0.53/0.60 (~((~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))))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[303, 267])).
% 0.53/0.60 tff(305,plain,
% 0.53/0.60 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))) | model_ub(X!5, Y!4, Z!3)),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(306,plain,
% 0.53/0.60 (model_ub(X!5, Y!4, Z!3)),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[305, 304])).
% 0.53/0.60 tff(307,plain,
% 0.53/0.60 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(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), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))))),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(308,plain,
% 0.53/0.60 ((~((~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), summation(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), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[307, 306])).
% 0.53/0.60 tff(309,plain,
% 0.53/0.60 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[308, 252])).
% 0.53/0.60 tff(310,plain,
% 0.53/0.60 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))) | $lesseq($sum(c, $sum($product(-1, Z!3), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(311,plain,
% 0.53/0.60 ($lesseq($sum(c, $sum($product(-1, Z!3), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.53/0.60 tff(312,assumption,($lesseq($sum(c, $sum($product(-1, Z!3), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)), introduced(assumption)).
% 0.53/0.60 tff(313,assumption,(~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.53/0.60 tff(314,assumption,($greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.53/0.60 tff(315,plain,
% 0.53/0.60 ($false),
% 0.53/0.60 inference(theory_lemma,[status(thm)],[314, 313, 312])).
% 0.53/0.60 tff(316,plain,((~$greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)) | $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.60 tff(317,plain,
% 0.53/0.60 (~$greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[316, 311, 243])).
% 0.53/0.60 tff(318,assumption,(~($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))), introduced(assumption)).
% 0.53/0.60 tff(319,plain,
% 0.53/0.60 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(320,plain,
% 0.53/0.60 (($lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)) <=> ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(321,plain,
% 0.53/0.60 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[320])).
% 0.53/0.60 tff(322,plain,
% 0.53/0.60 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.60 inference(transitivity,[status(thm)],[321, 319])).
% 0.53/0.60 tff(323,plain,
% 0.53/0.60 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($lesseq($sum(max(X!5, Y!4), $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.60 inference(quant_inst,[status(thm)],[])).
% 0.53/0.60 tff(324,plain,
% 0.53/0.60 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.53/0.60 tff(325,plain,
% 0.53/0.60 ($false),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[324, 42, 318])).
% 0.53/0.60 tff(326,plain,($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.60 tff(327,plain,
% 0.53/0.60 ((~($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.60 inference(tautology,[status(thm)],[])).
% 0.53/0.60 tff(328,plain,
% 0.53/0.60 ((~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[327, 326])).
% 0.53/0.60 tff(329,plain,
% 0.53/0.60 (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[328, 317])).
% 0.53/0.60 tff(330,plain,
% 0.53/0.60 (((~![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, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(331,plain,
% 0.53/0.60 ((ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$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)))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(332,plain,
% 0.53/0.61 (((~![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))))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[331])).
% 0.53/0.61 tff(333,plain,
% 0.53/0.61 (((~![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))))))),
% 0.53/0.61 inference(transitivity,[status(thm)],[332, 330])).
% 0.53/0.61 tff(334,plain,
% 0.53/0.61 ((~![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)))))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(335,plain,
% 0.53/0.61 ((~![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, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.53/0.61 tff(336,plain,
% 0.53/0.61 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[335, 175])).
% 0.53/0.61 tff(337,plain,
% 0.53/0.61 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(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))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(338,plain,
% 0.53/0.61 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[337, 309])).
% 0.53/0.61 tff(339,plain,
% 0.53/0.61 ((~(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, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(340,plain,
% 0.53/0.61 ((~(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))))) | (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[339, 338])).
% 0.53/0.61 tff(341,plain,
% 0.53/0.61 (~((~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[340, 336])).
% 0.53/0.61 tff(342,plain,
% 0.53/0.61 (((~$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, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(343,plain,
% 0.53/0.61 ($lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[342, 341])).
% 0.53/0.61 tff(344,plain,
% 0.53/0.61 (((~$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, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(345,plain,
% 0.53/0.61 ($lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[344, 341])).
% 0.53/0.61 tff(346,assumption,($lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)), introduced(assumption)).
% 0.53/0.61 tff(347,assumption,(~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.53/0.61 tff(348,plain,
% 0.53/0.61 ($false),
% 0.53/0.61 inference(theory_lemma,[status(thm)],[187, 347, 346])).
% 0.53/0.61 tff(349,plain,((~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.61 tff(350,plain,
% 0.53/0.61 (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[349, 347, 346])).
% 0.53/0.61 tff(351,plain,
% 0.53/0.61 ((~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)) | $greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.61 tff(352,plain,
% 0.53/0.61 (~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[351, 350])).
% 0.53/0.61 tff(353,plain,
% 0.53/0.61 (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[102, 352])).
% 0.53/0.61 tff(354,plain,
% 0.53/0.61 ($greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[104, 353])).
% 0.53/0.61 tff(355,plain,
% 0.53/0.61 ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[128, 354])).
% 0.53/0.61 tff(356,plain,
% 0.53/0.61 ((~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)) | $greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.61 tff(357,plain,
% 0.53/0.61 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[356, 355])).
% 0.53/0.61 tff(358,assumption,($lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)), introduced(assumption)).
% 0.53/0.61 tff(359,plain,
% 0.53/0.61 ($false),
% 0.53/0.61 inference(theory_lemma,[status(thm)],[358, 347, 357])).
% 0.53/0.61 tff(360,plain,($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0) | (~$lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.61 tff(361,plain,
% 0.53/0.61 ($false),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[360, 345, 343, 329])).
% 0.53/0.61 tff(362,plain,(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)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.61 tff(363,plain,
% 0.53/0.61 (~((~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))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[362, 188])).
% 0.53/0.61 tff(364,plain,
% 0.53/0.61 (((~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))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(365,plain,
% 0.53/0.61 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[364, 363])).
% 0.53/0.61 tff(366,plain,
% 0.53/0.61 (((~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, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(367,plain,
% 0.53/0.61 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[366, 363])).
% 0.53/0.61 tff(368,plain,
% 0.53/0.61 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), 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)), summation(max(max(X!5, Y!4), Y!4)))), 0))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(369,plain,
% 0.53/0.61 (model_max(max(X!5, Y!4), 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)), summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[368, 237])).
% 0.53/0.61 tff(370,plain,
% 0.53/0.61 (X!5 = max(X!5, Y!4)),
% 0.53/0.61 inference(theory_lemma,[status(thm)],[187, 147])).
% 0.53/0.61 tff(371,plain,
% 0.53/0.61 (max(X!5, Y!4) = X!5),
% 0.53/0.61 inference(symmetry,[status(thm)],[370])).
% 0.53/0.61 tff(372,plain,
% 0.53/0.61 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[371])).
% 0.53/0.61 tff(373,plain,
% 0.53/0.61 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.53/0.61 inference(symmetry,[status(thm)],[372])).
% 0.53/0.61 tff(374,assumption,(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.53/0.61 tff(375,plain,
% 0.53/0.61 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.53/0.61 tff(376,plain,
% 0.53/0.61 ((~(model_max(max(X!5, Y!4), 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)), summation(max(max(X!5, Y!4), Y!4)))), 0))) | (~model_max(max(X!5, Y!4), 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)), summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(377,plain,
% 0.53/0.61 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[376, 375, 369])).
% 0.53/0.61 tff(378,assumption,(~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)), introduced(assumption)).
% 0.53/0.61 tff(379,plain,
% 0.53/0.61 (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)),
% 0.53/0.61 inference(monotonicity,[status(thm)],[371])).
% 0.53/0.61 tff(380,plain,
% 0.53/0.61 (summation(max(max(X!5, Y!4), Y!4)) = summation(max(X!5, Y!4))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[379])).
% 0.53/0.61 tff(381,plain,
% 0.53/0.61 (summation(max(X!5, Y!4)) = summation(max(max(X!5, Y!4), Y!4))),
% 0.53/0.61 inference(symmetry,[status(thm)],[380])).
% 0.53/0.61 tff(382,plain,
% 0.53/0.61 ((~(summation(max(X!5, Y!4)) = summation(max(max(X!5, Y!4), Y!4)))) | $lesseq($sum(summation(max(X!5, Y!4)), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.53/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.53/0.61 tff(383,plain,
% 0.53/0.61 ($lesseq($sum(summation(max(X!5, Y!4)), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[382, 381])).
% 0.53/0.61 tff(384,assumption,(~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)), introduced(assumption)).
% 0.53/0.61 tff(385,plain,
% 0.53/0.61 ($false),
% 0.53/0.61 inference(theory_lemma,[status(thm)],[384, 383, 378, 377])).
% 0.53/0.61 tff(386,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), summation(max(X!5, Y!4)))), -1) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.61 tff(387,plain,
% 0.53/0.61 ($lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[386, 367, 187, 365])).
% 0.53/0.61 tff(388,assumption,(![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))), introduced(assumption)).
% 0.53/0.61 tff(389,assumption,($lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)), introduced(assumption)).
% 0.53/0.61 tff(390,plain,
% 0.53/0.61 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(391,plain,
% 0.53/0.61 (((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), -1))) <=> ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(392,plain,
% 0.53/0.61 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[391])).
% 0.53/0.61 tff(393,plain,
% 0.53/0.61 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)))),
% 0.53/0.61 inference(transitivity,[status(thm)],[392, 390])).
% 0.53/0.61 tff(394,plain,
% 0.53/0.61 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), -1)))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(395,plain,
% 0.53/0.61 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.53/0.61 tff(396,plain,
% 0.53/0.61 ($false),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[395, 389, 186, 388])).
% 0.53/0.61 tff(397,plain,((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.61 tff(398,plain,
% 0.53/0.61 (~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[397, 387])).
% 0.53/0.61 tff(399,plain,
% 0.53/0.61 ((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(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(summation(Z), $product(-1, Z!3))), -1)))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(400,plain,
% 0.53/0.61 (model_ub(X!5, Y!4, $sum(-1, Z!3))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[399, 398, 28])).
% 0.53/0.61 tff(401,plain,
% 0.53/0.61 (((~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))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(402,plain,
% 0.53/0.61 (![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[401, 304])).
% 0.53/0.61 tff(403,plain,
% 0.53/0.61 (((~![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))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(404,plain,
% 0.53/0.61 (((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $false) <=> (~model_ub(X!5, Y!4, $sum(-1, Z!3)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(405,plain,
% 0.53/0.61 ($greatereq(-1, 0) <=> $false),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(406,plain,
% 0.53/0.61 ($sum($sum(-1, Z!3), $product(-1, Z!3)) = -1),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(407,plain,
% 0.53/0.61 ($greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0) <=> $greatereq(-1, 0)),
% 0.53/0.61 inference(monotonicity,[status(thm)],[406])).
% 0.53/0.61 tff(408,plain,
% 0.53/0.61 ($greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0) <=> $false),
% 0.53/0.61 inference(transitivity,[status(thm)],[407, 405])).
% 0.53/0.61 tff(409,plain,
% 0.53/0.61 (((~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)),
% 0.53/0.61 inference(monotonicity,[status(thm)],[408])).
% 0.53/0.61 tff(410,plain,
% 0.53/0.61 (((~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)))),
% 0.53/0.61 inference(transitivity,[status(thm)],[409, 404])).
% 0.53/0.61 tff(411,plain,
% 0.53/0.61 (((~![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))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[410])).
% 0.53/0.61 tff(412,plain,
% 0.53/0.61 (((~![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))))),
% 0.53/0.61 inference(transitivity,[status(thm)],[411, 403])).
% 0.53/0.61 tff(413,plain,
% 0.53/0.61 ((~![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))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(414,plain,
% 0.53/0.61 ((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_ub(X!5, Y!4, $sum(-1, Z!3)))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.53/0.61 tff(415,plain,
% 0.53/0.61 ($false),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[414, 402, 400])).
% 0.53/0.61 tff(416,plain,(minsol_model_max(X!5, Y!4, Z!3) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.61 tff(417,plain,
% 0.53/0.61 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[416, 187])).
% 0.53/0.61 tff(418,plain,
% 0.53/0.61 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(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(summation(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(summation(Z), $product(-1, Z!3))), 0))))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(419,plain,
% 0.53/0.61 (model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[418, 250])).
% 0.53/0.61 tff(420,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)).
% 0.53/0.61 tff(421,assumption,(minsol_model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.53/0.61 tff(422,plain,
% 0.53/0.61 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(423,plain,
% 0.53/0.61 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[422, 264])).
% 0.53/0.61 tff(424,plain,
% 0.53/0.61 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[423, 421])).
% 0.53/0.62 tff(425,plain,
% 0.53/0.62 (((~(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))))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(426,plain,
% 0.53/0.62 (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)))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[425, 299])).
% 0.53/0.62 tff(427,plain,
% 0.53/0.62 ((~(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)))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(428,plain,
% 0.53/0.62 (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)))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[427, 426])).
% 0.53/0.62 tff(429,plain,
% 0.53/0.62 (~model_ub(X!5, Y!4, Z!3)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[428, 424, 420])).
% 0.53/0.62 tff(430,plain,
% 0.53/0.62 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(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(summation(Z), $product(-1, Z!3))), 0)))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(431,plain,
% 0.53/0.62 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0))))) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[430, 429])).
% 0.53/0.62 tff(432,plain,
% 0.53/0.62 (![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[431, 419])).
% 0.53/0.62 tff(433,assumption,(ub(X!5, Y!4, max(X!5, Y!4))), introduced(assumption)).
% 0.53/0.62 tff(434,plain,
% 0.53/0.62 (((~(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))))))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(435,plain,
% 0.53/0.62 ((~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)))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[434, 218])).
% 0.53/0.62 tff(436,plain,
% 0.53/0.62 ((~((~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)))))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(437,plain,
% 0.53/0.62 ((~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)))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[436, 435])).
% 0.53/0.62 tff(438,plain,
% 0.53/0.62 (~((~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))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[437, 421])).
% 0.53/0.62 tff(439,plain,
% 0.53/0.62 (((~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)),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(440,plain,
% 0.53/0.62 (model_max(X!5, Y!4, Z!3)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[439, 438])).
% 0.53/0.62 tff(441,plain,
% 0.53/0.62 ((~(model_max(X!5, Y!4, Z!3) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))) | (~model_max(X!5, Y!4, Z!3)) | $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(442,plain,
% 0.53/0.62 ((~model_max(X!5, Y!4, Z!3)) | $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[441, 240])).
% 0.53/0.62 tff(443,plain,
% 0.53/0.62 ($lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[442, 440])).
% 0.53/0.62 tff(444,plain,
% 0.53/0.62 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(445,plain,
% 0.53/0.62 (((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), 0))) <=> ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(446,plain,
% 0.53/0.62 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[445])).
% 0.53/0.62 tff(447,plain,
% 0.53/0.62 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.62 inference(transitivity,[status(thm)],[446, 444])).
% 0.53/0.62 tff(448,plain,
% 0.53/0.62 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum(summation(max(X!5, Y!4)), $product(-1, Z!3))), 0)))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(449,plain,
% 0.53/0.62 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), 0)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), 0))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.53/0.62 tff(450,plain,
% 0.53/0.62 ($false),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[449, 443, 433, 432])).
% 0.53/0.62 tff(451,plain,((~minsol_model_max(X!5, Y!4, Z!3)) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.62 tff(452,plain,
% 0.53/0.62 (~((~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))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[451, 417, 186])).
% 0.53/0.62 tff(453,plain,
% 0.53/0.62 (((~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, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(454,plain,
% 0.53/0.62 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[453, 452])).
% 0.53/0.62 tff(455,plain,
% 0.53/0.62 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(456,plain,
% 0.53/0.62 (($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(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)) <=> ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(457,plain,
% 0.53/0.62 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[456])).
% 0.53/0.62 tff(458,plain,
% 0.53/0.62 (((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.53/0.62 inference(transitivity,[status(thm)],[457, 455])).
% 0.53/0.62 tff(459,plain,
% 0.53/0.62 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(460,plain,
% 0.53/0.62 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.53/0.62 tff(461,plain,
% 0.53/0.62 ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[460, 42])).
% 0.53/0.62 tff(462,plain,
% 0.53/0.62 (((~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))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(463,plain,
% 0.53/0.62 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[462, 452])).
% 0.53/0.62 tff(464,plain,
% 0.53/0.62 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[371])).
% 0.53/0.62 tff(465,plain,
% 0.53/0.62 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.53/0.62 inference(symmetry,[status(thm)],[464])).
% 0.53/0.62 tff(466,assumption,(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.53/0.62 tff(467,plain,
% 0.53/0.62 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.53/0.62 tff(468,plain,
% 0.53/0.62 (((~![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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(469,plain,
% 0.53/0.62 ((~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(Z))), 0))))))) <=> (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(470,plain,
% 0.53/0.63 (((~![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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[469])).
% 0.53/0.63 tff(471,plain,
% 0.53/0.63 (((~![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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[470, 468])).
% 0.53/0.63 tff(472,plain,
% 0.53/0.63 ((~![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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(Z))), 0)))))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(473,plain,
% 0.53/0.63 ((~![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), summation(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), summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.53/0.63 tff(474,plain,
% 0.53/0.63 (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[473, 19])).
% 0.53/0.63 tff(475,plain,
% 0.53/0.63 (((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))) | ((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(476,plain,
% 0.53/0.63 ((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[475, 474])).
% 0.53/0.63 tff(477,assumption,(~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), introduced(assumption)).
% 0.53/0.63 tff(478,plain,
% 0.53/0.63 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))) | ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(479,plain,
% 0.53/0.63 ((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[478, 477])).
% 0.53/0.63 tff(480,plain,
% 0.53/0.63 ((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))))),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(481,plain,
% 0.59/0.63 ((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[480, 479])).
% 0.59/0.63 tff(482,plain,
% 0.59/0.63 (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[481, 476])).
% 0.59/0.63 tff(483,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[482, 467])).
% 0.59/0.63 tff(484,plain,((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.63 tff(485,plain,
% 0.59/0.63 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[484, 463, 187])).
% 0.59/0.63 tff(486,plain,
% 0.59/0.63 (tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)),
% 0.59/0.63 inference(monotonicity,[status(thm)],[371])).
% 0.59/0.63 tff(487,plain,
% 0.59/0.63 (tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))),
% 0.59/0.63 inference(symmetry,[status(thm)],[486])).
% 0.59/0.63 tff(488,plain,
% 0.59/0.63 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[487])).
% 0.59/0.63 tff(489,plain,
% 0.59/0.63 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))) <=> ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.59/0.63 inference(symmetry,[status(thm)],[488])).
% 0.59/0.63 tff(490,assumption,(ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), introduced(assumption)).
% 0.59/0.63 tff(491,plain,
% 0.59/0.63 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.59/0.63 tff(492,plain,
% 0.59/0.63 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0)))))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(493,plain,
% 0.59/0.63 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0))))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[492, 175])).
% 0.59/0.63 tff(494,assumption,(~$greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.59/0.63 tff(495,plain,
% 0.59/0.63 (((~$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, max(X!5, Y!4))), 0))) | $greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(496,plain,
% 0.59/0.63 ((~$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), $product(-1, max(X!5, Y!4))), 0))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[495, 494])).
% 0.59/0.63 tff(497,plain,
% 0.59/0.63 ((~(ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0)))))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~$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), $product(-1, max(X!5, Y!4))), 0))))),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(498,plain,
% 0.59/0.63 ((~(ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0)))))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[497, 496])).
% 0.59/0.63 tff(499,plain,
% 0.59/0.63 (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[498, 493])).
% 0.59/0.63 tff(500,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[499, 491])).
% 0.59/0.63 tff(501,plain,((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.63 tff(502,plain,
% 0.59/0.63 ($greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[501, 485, 187])).
% 0.59/0.63 tff(503,plain,
% 0.59/0.63 ((~($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) | (~$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)) | $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(504,plain,
% 0.59/0.63 ((~($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0))) | $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[503, 502])).
% 0.59/0.63 tff(505,plain,
% 0.59/0.63 ($greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[504, 461])).
% 0.59/0.63 tff(506,plain,
% 0.59/0.63 (~((~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))))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[437, 417])).
% 0.59/0.63 tff(507,plain,
% 0.59/0.63 (((~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))),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(508,plain,
% 0.59/0.63 (![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[507, 506])).
% 0.59/0.63 tff(509,plain,
% 0.59/0.63 (((~![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))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(510,plain,
% 0.59/0.64 (((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $false) <=> (~model_max(X!5, Y!4, $sum(-1, Z!3)))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(511,plain,
% 0.59/0.64 (((~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)),
% 0.59/0.64 inference(monotonicity,[status(thm)],[408])).
% 0.59/0.64 tff(512,plain,
% 0.59/0.64 (((~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)))),
% 0.59/0.64 inference(transitivity,[status(thm)],[511, 510])).
% 0.59/0.64 tff(513,plain,
% 0.59/0.64 (((~![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))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[512])).
% 0.59/0.64 tff(514,plain,
% 0.59/0.64 (((~![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))))),
% 0.59/0.64 inference(transitivity,[status(thm)],[513, 509])).
% 0.59/0.64 tff(515,plain,
% 0.59/0.64 ((~![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))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(516,plain,
% 0.59/0.64 ((~![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)))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.59/0.64 tff(517,plain,
% 0.59/0.64 (~model_max(X!5, Y!4, $sum(-1, Z!3))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[516, 508])).
% 0.59/0.64 tff(518,plain,
% 0.59/0.64 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(519,plain,
% 0.59/0.64 ((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))), summation(max(X!5, Y!4)))), 0)) <=> (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(520,plain,
% 0.59/0.64 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(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))), summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[519])).
% 0.59/0.64 tff(521,plain,
% 0.59/0.64 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(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))), summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)))),
% 0.59/0.64 inference(transitivity,[status(thm)],[520, 518])).
% 0.59/0.64 tff(522,plain,
% 0.59/0.64 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(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))), summation(max(X!5, Y!4)))), 0))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(523,plain,
% 0.59/0.64 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.59/0.64 tff(524,plain,
% 0.59/0.64 (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[523, 237])).
% 0.59/0.64 tff(525,plain,
% 0.59/0.64 ((~(model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))) | model_max(X!5, Y!4, $sum(-1, Z!3)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))),
% 0.59/0.64 inference(tautology,[status(thm)],[])).
% 0.59/0.64 tff(526,plain,
% 0.59/0.64 (model_max(X!5, Y!4, $sum(-1, Z!3)) | (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[525, 524])).
% 0.59/0.64 tff(527,plain,
% 0.59/0.64 (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[526, 517])).
% 0.59/0.64 tff(528,plain,
% 0.59/0.64 (((~![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), summation(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), summation(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)), summation(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(summation(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), summation(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), summation(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)), summation(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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(529,plain,
% 0.59/0.64 ((~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(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)), summation(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)), summation(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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(530,plain,
% 0.59/0.64 (((~![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), summation(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), summation(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)), summation(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)), summation(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), summation(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), summation(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)), summation(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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[529])).
% 0.59/0.64 tff(531,plain,
% 0.59/0.64 (((~![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), summation(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), summation(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)), summation(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)), summation(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), summation(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), summation(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)), summation(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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))))),
% 0.59/0.64 inference(transitivity,[status(thm)],[530, 528])).
% 0.59/0.64 tff(532,plain,
% 0.59/0.64 ((~![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), summation(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), summation(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)), summation(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)), summation(Z))), 0)))))))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(533,plain,
% 0.59/0.64 ((~![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), summation(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), summation(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)), summation(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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0)))))))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.59/0.64 tff(534,plain,
% 0.59/0.64 (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)))), 0))))))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[533, 19])).
% 0.59/0.64 tff(535,plain,
% 0.59/0.64 (((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(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(summation(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)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)))))),
% 0.59/0.64 inference(tautology,[status(thm)],[])).
% 0.59/0.64 tff(536,plain,
% 0.59/0.64 ((~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)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[535, 534])).
% 0.59/0.64 tff(537,plain,
% 0.59/0.64 ((~((~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)), summation(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)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))))),
% 0.59/0.64 inference(tautology,[status(thm)],[])).
% 0.59/0.64 tff(538,plain,
% 0.59/0.64 ((~((~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)), summation(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(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[537, 463])).
% 0.59/0.64 tff(539,plain,
% 0.59/0.64 (~((~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)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[538, 536])).
% 0.59/0.64 tff(540,plain,
% 0.59/0.64 (((~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)), summation(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)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 0.59/0.64 inference(tautology,[status(thm)],[])).
% 0.59/0.64 tff(541,plain,
% 0.59/0.64 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[540, 539])).
% 0.59/0.64 tff(542,plain,
% 0.59/0.64 ($false),
% 0.59/0.64 inference(theory_lemma,[status(thm)],[541, 527, 505, 454])).
% 0.59/0.64 tff(543,plain,(~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.64 tff(544,plain,
% 0.59/0.64 (~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[351, 543])).
% 0.59/0.64 tff(545,plain,
% 0.59/0.64 (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[102, 544])).
% 0.59/0.64 tff(546,plain,
% 0.59/0.64 ($greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[104, 545])).
% 0.59/0.64 tff(547,plain,
% 0.59/0.64 ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[128, 546])).
% 0.59/0.64 tff(548,plain,
% 0.59/0.64 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[356, 547])).
% 0.59/0.64 tff(549,plain,
% 0.59/0.64 ((~($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0))) | (~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.59/0.64 inference(tautology,[status(thm)],[])).
% 0.59/0.64 tff(550,plain,
% 0.59/0.64 ((~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[549, 63])).
% 0.59/0.64 tff(551,plain,
% 0.59/0.64 ($greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[550, 548])).
% 0.59/0.64 tff(552,plain,
% 0.59/0.64 (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[451, 421, 433])).
% 0.59/0.64 tff(553,plain,
% 0.59/0.64 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[453, 552])).
% 0.59/0.64 tff(554,assumption,($greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.59/0.64 tff(555,plain,
% 0.59/0.64 (![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[507, 438])).
% 0.59/0.64 tff(556,plain,
% 0.59/0.64 (~model_max(X!5, Y!4, $sum(-1, Z!3))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[516, 555])).
% 0.59/0.64 tff(557,plain,
% 0.59/0.64 (~$lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[526, 556])).
% 0.59/0.64 tff(558,plain,
% 0.59/0.64 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[462, 552])).
% 0.59/0.64 tff(559,plain,
% 0.59/0.64 ((~((~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)), summation(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(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[537, 558])).
% 0.59/0.64 tff(560,plain,
% 0.59/0.64 (~((~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)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[559, 536])).
% 0.59/0.65 tff(561,plain,
% 0.59/0.65 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[540, 560])).
% 0.59/0.65 tff(562,plain,
% 0.59/0.65 ((~![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))) | ($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) <=> $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(Y!4))), 0))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(563,plain,
% 0.59/0.65 ($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(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(Y!4))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[562, 42])).
% 0.59/0.65 tff(564,plain,
% 0.59/0.65 (((~![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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(565,plain,
% 0.59/0.65 ((ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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)))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(566,plain,
% 0.59/0.65 (((~![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))))))),
% 0.59/0.65 inference(monotonicity,[status(thm)],[565])).
% 0.59/0.65 tff(567,plain,
% 0.59/0.65 (((~![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))))))),
% 0.59/0.65 inference(transitivity,[status(thm)],[566, 564])).
% 0.59/0.65 tff(568,plain,
% 0.59/0.65 ((~![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)))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(569,plain,
% 0.59/0.65 ((~![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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.59/0.65 tff(570,plain,
% 0.59/0.65 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[569, 175])).
% 0.59/0.65 tff(571,plain,
% 0.59/0.65 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5)), summation(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))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(572,plain,
% 0.59/0.65 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[571, 560])).
% 0.59/0.65 tff(573,plain,
% 0.59/0.65 ((~(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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(574,plain,
% 0.59/0.65 ((~(ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[573, 572])).
% 0.59/0.65 tff(575,plain,
% 0.59/0.65 (~((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[574, 570])).
% 0.59/0.65 tff(576,plain,
% 0.59/0.65 (((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(577,plain,
% 0.59/0.65 ($lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[576, 575])).
% 0.59/0.65 tff(578,plain,
% 0.59/0.65 ((~($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(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(Y!4))), 0))) | (~$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)) | $greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(Y!4))), 0)),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(579,plain,
% 0.59/0.65 ($greatereq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(Y!4))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[578, 577, 563])).
% 0.59/0.65 tff(580,plain,
% 0.59/0.65 ($false),
% 0.59/0.65 inference(theory_lemma,[status(thm)],[579, 561, 557, 554, 553])).
% 0.59/0.65 tff(581,plain,((~minsol_model_max(X!5, Y!4, Z!3)) | (~$greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)) | (~ub(X!5, Y!4, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.65 tff(582,plain,
% 0.59/0.65 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[581, 551, 186])).
% 0.59/0.65 tff(583,plain,
% 0.59/0.65 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[362, 582])).
% 0.59/0.65 tff(584,plain,
% 0.59/0.65 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[366, 583])).
% 0.59/0.65 tff(585,plain,
% 0.59/0.65 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(c, $sum($product(-1, N), summation(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)), summation(max(X!5, Y!4)))), 0))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(586,plain,
% 0.59/0.65 (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)), summation(max(X!5, Y!4)))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[585, 237])).
% 0.59/0.65 tff(587,plain,
% 0.59/0.65 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[364, 583])).
% 0.59/0.65 tff(588,plain,
% 0.59/0.65 ((~(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)), summation(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)), summation(max(X!5, Y!4)))), 0)),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(589,plain,
% 0.59/0.65 ((~(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)), summation(max(X!5, Y!4)))), 0))) | $lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[588, 587])).
% 0.59/0.65 tff(590,plain,
% 0.59/0.65 ($lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))), 0)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[589, 586])).
% 0.59/0.65 tff(591,plain,
% 0.59/0.65 ($lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1) | (~$lesseq($sum(c, $sum($product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))), 0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 0.59/0.65 inference(theory_lemma,[status(thm)],[])).
% 0.59/0.65 tff(592,plain,
% 0.59/0.65 ($lesseq($sum(c, $sum($product(-1, Z!3), summation(max(X!5, Y!4)))), -1)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[591, 590, 584])).
% 0.59/0.65 tff(593,plain,
% 0.59/0.65 (~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(c, $sum(summation(Z), $product(-1, Z!3))), -1)))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[397, 592])).
% 0.59/0.65 tff(594,plain,
% 0.59/0.65 (model_ub(X!5, Y!4, $sum(-1, Z!3))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[399, 593, 28])).
% 0.59/0.65 tff(595,plain,
% 0.59/0.65 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[266, 582])).
% 0.59/0.65 tff(596,plain,
% 0.59/0.65 (~((~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))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[303, 595])).
% 0.59/0.65 tff(597,plain,
% 0.59/0.65 (![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[401, 596])).
% 0.59/0.65 tff(598,plain,
% 0.59/0.65 ($false),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[414, 597, 594])).
% 0.59/0.65 % SZS output end Proof
%------------------------------------------------------------------------------