TSTP Solution File: NUM860_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM860_1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 13:12:20 EDT 2022
% Result : Theorem 0.15s 0.40s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : NUM860_1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n028.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri Sep 2 15:36:22 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40 % SZS output start Proof
% 0.15/0.40 tff(summation_type, type, (
% 0.15/0.40 summation: $int > $int)).
% 0.15/0.40 tff(tptp_fun_Y_4_type, type, (
% 0.15/0.40 tptp_fun_Y_4: $int)).
% 0.15/0.40 tff(tptp_fun_Z_3_type, type, (
% 0.15/0.40 tptp_fun_Z_3: $int)).
% 0.15/0.40 tff(ub_type, type, (
% 0.15/0.40 ub: ( $int * $int * $int ) > $o)).
% 0.15/0.40 tff(tptp_fun_X_5_type, type, (
% 0.15/0.40 tptp_fun_X_5: $int)).
% 0.15/0.40 tff(max_type, type, (
% 0.15/0.40 max: ( $int * $int ) > $int)).
% 0.15/0.40 tff(model_max_type, type, (
% 0.15/0.40 model_max: ( $int * $int * $int ) > $o)).
% 0.15/0.40 tff(model_ub_type, type, (
% 0.15/0.40 model_ub: ( $int * $int * $int ) > $o)).
% 0.15/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.15/0.40 tptp_fun_Z_0: ( $int * $int * $int ) > $int)).
% 0.15/0.40 tff(tptp_fun_Z_2_type, type, (
% 0.15/0.40 tptp_fun_Z_2: ( $int * $int * $int ) > $int)).
% 0.15/0.40 tff(minsol_model_ub_type, type, (
% 0.15/0.40 minsol_model_ub: ( $int * $int * $int ) > $o)).
% 0.15/0.40 tff(tptp_fun_Z_1_type, type, (
% 0.15/0.40 tptp_fun_Z_1: ( $int * $int * $int ) > $int)).
% 0.15/0.40 tff(minsol_model_max_type, type, (
% 0.15/0.40 minsol_model_max: ( $int * $int * $int ) > $o)).
% 0.15/0.40 tff(1,assumption,(~(ub(X!5, Y!4, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0))), introduced(assumption)).
% 0.15/0.40 tff(2,plain,
% 0.15/0.40 (^[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))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(3,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.15/0.40 tff(4,plain,
% 0.15/0.40 (^[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))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(5,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.15/0.40 tff(6,plain,
% 0.15/0.40 (^[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))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(7,plain,
% 0.15/0.40 (![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)))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.15/0.40 tff(8,plain,
% 0.15/0.40 (^[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))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(9,plain,
% 0.15/0.40 (![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)))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.15/0.40 tff(10,plain,
% 0.15/0.40 (![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)))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(11,axiom,(![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ub')).
% 0.15/0.40 tff(12,plain,
% 0.15/0.40 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq(X, Z) & $lesseq(Y, Z)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.15/0.40 tff(13,plain,
% 0.15/0.40 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($lesseq($sum(X, $product(-1, Z)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.15/0.40 tff(14,plain,
% 0.15/0.40 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.15/0.40 tff(15,plain,(
% 0.15/0.40 ![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> ($greatereq($sum(Z, $product(-1, X)), 0) & $lesseq($sum(Y, $product(-1, Z)), 0)))),
% 0.15/0.40 inference(skolemize,[status(sab)],[14])).
% 0.15/0.40 tff(16,plain,
% 0.15/0.40 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.15/0.40 tff(17,plain,
% 0.15/0.40 (![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[16, 3])).
% 0.15/0.40 tff(18,plain,
% 0.15/0.40 (((~![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, Y!4) <=> $greatereq($sum(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, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0)))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(19,plain,
% 0.15/0.40 ((ub(X!5, Y!4, Y!4) <=> (~((~$lesseq($sum(Y!4, $product(-1, Y!4)), 0)) | (~$greatereq($sum(Y!4, $product(-1, X!5)), 0))))) <=> (ub(X!5, Y!4, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(20,plain,
% 0.15/0.40 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, Y!4) <=> (~((~$lesseq($sum(Y!4, $product(-1, Y!4)), 0)) | (~$greatereq($sum(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, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0)))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.15/0.40 tff(21,plain,
% 0.15/0.40 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, Y!4) <=> (~((~$lesseq($sum(Y!4, $product(-1, Y!4)), 0)) | (~$greatereq($sum(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, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0)))),
% 0.15/0.40 inference(transitivity,[status(thm)],[20, 18])).
% 0.15/0.40 tff(22,plain,
% 0.15/0.40 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, Y!4, Y!4) <=> (~((~$lesseq($sum(Y!4, $product(-1, Y!4)), 0)) | (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(23,plain,
% 0.15/0.40 ((~![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, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.15/0.40 tff(24,plain,
% 0.15/0.40 ($false),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[23, 17, 1])).
% 0.15/0.40 tff(25,plain,(ub(X!5, Y!4, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.40 tff(26,assumption,(~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.15/0.40 tff(27,plain,
% 0.15/0.40 ((~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)) | $lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.40 tff(28,plain,
% 0.15/0.40 (~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.15/0.40 tff(29,plain,
% 0.15/0.40 (^[X: $int, Y: $int] : refl(((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)) <=> ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(30,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)) <=> ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.15/0.40 tff(31,plain,
% 0.15/0.40 (^[X: $int, Y: $int] : rewrite(((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)) <=> ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(32,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)) <=> ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.15/0.40 tff(33,plain,
% 0.15/0.40 (^[X: $int, Y: $int] : rewrite(((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(34,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.15/0.40 tff(35,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(36,plain,
% 0.15/0.40 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ((~$lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(37,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X))) <=> ![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.15/0.40 tff(38,axiom,(![X: $int, Y: $int] : ((max(X, Y) = X) | (~$lesseq(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_1')).
% 0.15/0.40 tff(39,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.15/0.40 tff(40,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.15/0.40 tff(41,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$lesseq($sum(Y, $product(-1, X)), 0)) | ($sum(max(X, Y), $product(-1, X)) = 0))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.15/0.40 tff(42,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[41, 32])).
% 0.15/0.40 tff(43,plain,(
% 0.15/0.40 ![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.15/0.40 inference(skolemize,[status(sab)],[42])).
% 0.15/0.40 tff(44,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ((~$greatereq($sum(X, $product(-1, Y)), 0)) | ($sum(X, $product(-1, max(X, Y))) = 0))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[43, 30])).
% 0.15/0.40 tff(45,plain,
% 0.15/0.40 (((~![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, $product(-1, max(X!5, Y!4))) = 0))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(46,plain,
% 0.15/0.40 (((~$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))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(47,plain,
% 0.15/0.40 (((~![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)))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.15/0.40 tff(48,plain,
% 0.15/0.40 (((~![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))),
% 0.15/0.40 inference(transitivity,[status(thm)],[47, 45])).
% 0.15/0.40 tff(49,plain,
% 0.15/0.40 ((~![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))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(50,plain,
% 0.15/0.40 ((~![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, $product(-1, max(X!5, Y!4))) = 0)),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.15/0.40 tff(51,plain,
% 0.15/0.40 ((~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.15/0.40 tff(52,plain,
% 0.15/0.40 (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[51, 28])).
% 0.15/0.40 tff(53,plain,
% 0.15/0.40 (^[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)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(54,plain,
% 0.15/0.40 (![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))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.15/0.40 tff(55,plain,
% 0.15/0.40 (^[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)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(56,plain,
% 0.15/0.40 (![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))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.15/0.40 tff(57,plain,
% 0.15/0.40 (^[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)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(58,plain,
% 0.15/0.40 (![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))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.15/0.40 tff(59,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y))) <=> ![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y)))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(60,axiom,(![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','summation_monotone')).
% 0.15/0.40 tff(61,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ($lesseq(X, Y) <=> $lesseq(summation(X), summation(Y)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.15/0.40 tff(62,plain,
% 0.15/0.40 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $lesseq($sum(summation(X), $product(-1, summation(Y))), 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.15/0.41 tff(63,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.15/0.41 tff(64,plain,(
% 0.15/0.41 ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.15/0.41 inference(skolemize,[status(sab)],[63])).
% 0.15/0.41 tff(65,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) <=> $greatereq($sum(summation(Y), $product(-1, summation(X))), 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.15/0.41 tff(66,plain,
% 0.15/0.41 (((~![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, X!5)), 0) <=> $lesseq($sum(summation(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(Y!4, $product(-1, X!5)), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(67,plain,
% 0.15/0.41 (($lesseq($sum(Y!4, $product(-1, X!5)), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(Y!4))), 0)) <=> ($lesseq($sum(Y!4, $product(-1, X!5)), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(68,plain,
% 0.15/0.41 (((~![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, X!5)), 0) <=> $greatereq($sum(summation(X!5), $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, X!5)), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0)))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[67])).
% 0.15/0.41 tff(69,plain,
% 0.15/0.41 (((~![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, X!5)), 0) <=> $greatereq($sum(summation(X!5), $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, X!5)), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0)))),
% 0.15/0.41 inference(transitivity,[status(thm)],[68, 66])).
% 0.15/0.41 tff(70,plain,
% 0.15/0.41 ((~![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, X!5)), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(Y!4))), 0))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(71,plain,
% 0.15/0.41 ((~![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, X!5)), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.15/0.41 tff(72,plain,
% 0.15/0.41 ($lesseq($sum(Y!4, $product(-1, X!5)), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.15/0.41 tff(73,plain,
% 0.15/0.41 ((~($lesseq($sum(Y!4, $product(-1, X!5)), 0) <=> $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0))) | $lesseq($sum(Y!4, $product(-1, X!5)), 0) | (~$lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(74,plain,
% 0.15/0.41 ($lesseq($sum(Y!4, $product(-1, X!5)), 0) | (~$lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.15/0.41 tff(75,plain,
% 0.15/0.41 (~$lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[74, 52])).
% 0.15/0.41 tff(76,assumption,(~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.15/0.41 tff(77,plain,
% 0.15/0.41 ((~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)) | $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.41 tff(78,plain,
% 0.15/0.41 (~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.15/0.41 tff(79,plain,
% 0.15/0.41 (^[X: $int, Y: $int] : refl(((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(80,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.15/0.41 tff(81,plain,
% 0.15/0.41 (^[X: $int, Y: $int] : rewrite(((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(82,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.15/0.41 tff(83,plain,
% 0.15/0.41 (^[X: $int, Y: $int] : rewrite(((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(84,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.15/0.41 tff(85,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(86,plain,
% 0.15/0.41 (^[X: $int, Y: $int] : rewrite(((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ((~$lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(87,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y))) <=> ![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.15/0.41 tff(88,axiom,(![X: $int, Y: $int] : ((max(X, Y) = Y) | (~$lesseq(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_2')).
% 0.15/0.41 tff(89,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.15/0.41 tff(90,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.15/0.41 tff(91,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(max(X, Y), $product(-1, Y)) = 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[90, 84])).
% 0.15/0.41 tff(92,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[91, 82])).
% 0.15/0.41 tff(93,plain,(
% 0.15/0.41 ![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.15/0.41 inference(skolemize,[status(sab)],[92])).
% 0.15/0.41 tff(94,plain,
% 0.15/0.41 (![X: $int, Y: $int] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | ($sum(Y, $product(-1, max(X, Y))) = 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[93, 80])).
% 0.15/0.41 tff(95,plain,
% 0.15/0.41 (((~![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, $product(-1, max(X!5, Y!4))) = 0))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(96,plain,
% 0.15/0.41 (((~$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))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(97,plain,
% 0.15/0.41 (((~![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)))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[96])).
% 0.15/0.41 tff(98,plain,
% 0.15/0.41 (((~![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))),
% 0.15/0.41 inference(transitivity,[status(thm)],[97, 95])).
% 0.15/0.41 tff(99,plain,
% 0.15/0.41 ((~![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))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(100,plain,
% 0.15/0.41 ((~![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, $product(-1, max(X!5, Y!4))) = 0)),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.15/0.41 tff(101,plain,
% 0.15/0.41 ((~$greatereq($sum(Y!4, $product(-1, X!5)), 0)) | ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[100, 94])).
% 0.15/0.41 tff(102,plain,
% 0.15/0.41 (~$greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[101, 78])).
% 0.15/0.41 tff(103,plain,
% 0.15/0.41 ($greatereq($sum(Y!4, $product(-1, X!5)), 0) | $lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.41 tff(104,plain,
% 0.15/0.41 ($lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.15/0.41 tff(105,plain,
% 0.15/0.41 ($sum(X!5, $product(-1, max(X!5, Y!4))) = 0),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[51, 104])).
% 0.15/0.41 tff(106,plain,
% 0.15/0.41 ($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0) | (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.41 tff(107,plain,
% 0.15/0.41 (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[106, 104, 76])).
% 0.15/0.41 tff(108,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[27, 107, 105])).
% 0.15/0.41 tff(109,plain,($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.41 tff(110,plain,
% 0.15/0.41 ($greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[103, 52])).
% 0.15/0.41 tff(111,plain,
% 0.15/0.41 ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[101, 110])).
% 0.15/0.41 tff(112,plain,
% 0.15/0.41 ((~($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0)) | $greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.41 tff(113,plain,
% 0.15/0.41 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.15/0.41 tff(114,plain,
% 0.15/0.41 (Y!4 = max(X!5, Y!4)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[113, 109])).
% 0.15/0.41 tff(115,plain,
% 0.15/0.41 (summation(Y!4) = summation(max(X!5, Y!4))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[114])).
% 0.15/0.41 tff(116,plain,
% 0.15/0.41 ((~(summation(Y!4) = summation(max(X!5, Y!4)))) | $lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.41 tff(117,plain,
% 0.15/0.41 ($lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.15/0.41 tff(118,plain,
% 0.15/0.41 (((~![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), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(119,plain,
% 0.15/0.41 (($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))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(120,plain,
% 0.15/0.41 (((~![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)))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.15/0.41 tff(121,plain,
% 0.15/0.41 (((~![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)))),
% 0.15/0.41 inference(transitivity,[status(thm)],[120, 118])).
% 0.15/0.41 tff(122,plain,
% 0.15/0.41 ((~![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))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(123,plain,
% 0.15/0.41 ((~![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), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.15/0.41 tff(124,plain,
% 0.15/0.41 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) <=> $greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[123, 65])).
% 0.15/0.41 tff(125,plain,
% 0.15/0.41 ($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0) | $greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.41 tff(126,plain,
% 0.15/0.41 ($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[125, 26])).
% 0.15/0.41 tff(127,plain,
% 0.15/0.41 ((~($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), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(128,plain,
% 0.15/0.41 ((~($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(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.15/0.41 tff(129,plain,
% 0.15/0.41 ($greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[128, 124])).
% 0.15/0.41 tff(130,plain,
% 0.15/0.41 ((~$greatereq($sum(summation(X!5), $product(-1, summation(max(X!5, Y!4)))), 0)) | (~$lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)) | $lesseq($sum(summation(Y!4), $product(-1, summation(X!5))), 0)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.41 tff(131,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[130, 129, 117, 75])).
% 0.15/0.41 tff(132,plain,($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.41 tff(133,assumption,($greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.15/0.41 tff(134,assumption,($lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.15/0.41 tff(135,plain,
% 0.15/0.41 (X!5 = max(X!5, Y!4)),
% 0.15/0.41 inference(theory_lemma,[status(thm)],[133, 134])).
% 0.15/0.41 tff(136,plain,
% 0.15/0.41 (max(X!5, Y!4) = X!5),
% 0.15/0.41 inference(symmetry,[status(thm)],[135])).
% 0.15/0.41 tff(137,plain,
% 0.15/0.41 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> ub(X!5, Y!4, max(X!5, Y!4))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[136])).
% 0.15/0.41 tff(138,plain,
% 0.15/0.41 (ub(X!5, Y!4, max(X!5, Y!4)) <=> ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.15/0.41 inference(symmetry,[status(thm)],[137])).
% 0.15/0.41 tff(139,plain,
% 0.15/0.41 ((~ub(X!5, Y!4, max(X!5, Y!4))) <=> (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[138])).
% 0.15/0.41 tff(140,assumption,(~ub(X!5, Y!4, max(X!5, Y!4))), introduced(assumption)).
% 0.15/0.41 tff(141,plain,
% 0.15/0.41 (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.15/0.41 tff(142,plain,
% 0.15/0.41 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $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(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(143,plain,
% 0.15/0.41 ((ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0))))) <=> (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(144,plain,
% 0.15/0.41 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[143])).
% 0.15/0.41 tff(145,plain,
% 0.15/0.41 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)))),
% 0.15/0.41 inference(transitivity,[status(thm)],[144, 142])).
% 0.15/0.41 tff(146,plain,
% 0.15/0.41 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$greatereq($sum(max(X!5, Y!4), $product(-1, max(X!5, Y!4))), 0)))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(147,plain,
% 0.15/0.42 ((~![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, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.15/0.42 tff(148,plain,
% 0.15/0.42 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[147, 17])).
% 0.15/0.42 tff(149,assumption,($lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.15/0.42 tff(150,plain,
% 0.15/0.42 ((~(ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))) | ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(151,plain,
% 0.15/0.42 ((~(ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> $lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))) | ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.15/0.42 tff(152,plain,
% 0.15/0.42 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[151, 148])).
% 0.15/0.42 tff(153,plain,
% 0.15/0.42 ($false),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[152, 141])).
% 0.15/0.42 tff(154,plain,(ub(X!5, Y!4, max(X!5, Y!4)) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.42 tff(155,plain,
% 0.15/0.42 (ub(X!5, Y!4, max(X!5, Y!4)) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[154, 109])).
% 0.15/0.42 tff(156,plain,
% 0.15/0.42 (ub(X!5, Y!4, max(X!5, Y!4))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[155, 133, 132])).
% 0.15/0.42 tff(157,plain,
% 0.15/0.42 (((~![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)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(158,plain,
% 0.15/0.42 (($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))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(159,plain,
% 0.15/0.42 (((~![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)))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[158])).
% 0.15/0.42 tff(160,plain,
% 0.15/0.42 (((~![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)))),
% 0.15/0.42 inference(transitivity,[status(thm)],[159, 157])).
% 0.15/0.42 tff(161,plain,
% 0.15/0.42 ((~![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))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(162,plain,
% 0.15/0.42 ((~![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)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.15/0.42 tff(163,plain,
% 0.15/0.42 ($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)),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[162, 65])).
% 0.15/0.42 tff(164,plain,
% 0.15/0.42 ((~![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), $product(-1, max(X!5, Y!4))), 0)))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(165,plain,
% 0.15/0.42 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[164, 17])).
% 0.15/0.42 tff(166,plain,
% 0.15/0.42 (X!5 = max(X!5, Y!4)),
% 0.15/0.42 inference(theory_lemma,[status(thm)],[133, 132])).
% 0.15/0.42 tff(167,plain,
% 0.15/0.42 (max(X!5, Y!4) = X!5),
% 0.15/0.42 inference(symmetry,[status(thm)],[166])).
% 0.15/0.42 tff(168,plain,
% 0.15/0.42 (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)),
% 0.15/0.42 inference(monotonicity,[status(thm)],[167])).
% 0.15/0.42 tff(169,plain,
% 0.15/0.42 (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))),
% 0.15/0.42 inference(symmetry,[status(thm)],[168])).
% 0.15/0.42 tff(170,plain,
% 0.15/0.42 (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)))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[169])).
% 0.15/0.42 tff(171,plain,
% 0.15/0.42 (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))),
% 0.15/0.42 inference(symmetry,[status(thm)],[170])).
% 0.15/0.42 tff(172,plain,
% 0.15/0.42 (^[X: $int, Y: $int, N: $int] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(173,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[172])).
% 0.15/0.42 tff(174,plain,
% 0.15/0.42 (^[X: $int, Y: $int, N: $int] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(175,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[174])).
% 0.15/0.42 tff(176,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[175, 173])).
% 0.15/0.42 tff(177,plain,
% 0.15/0.42 (^[X: $int, Y: $int, N: $int] : trans(monotonicity(rewrite(((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))), rewrite((model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0)))) <=> (model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0))))) & (model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0))))) & (model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(178,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0))))) <=> ![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[177])).
% 0.15/0.42 tff(179,plain,
% 0.15/0.42 (^[X: $int, Y: $int, N: $int] : rewrite((model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(summation(Z), $product(-1, N)), 0))) <=> (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(180,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(summation(Z), $product(-1, N)), 0))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0)))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[179])).
% 0.15/0.42 tff(181,plain,
% 0.15/0.42 (^[X: $int, Y: $int, N: $int] : rewrite((model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq(summation(Z), N))) <=> (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(summation(Z), $product(-1, N)), 0))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(182,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq(summation(Z), N))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(summation(Z), $product(-1, N)), 0)))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[181])).
% 0.15/0.42 tff(183,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq(summation(Z), N))) <=> ![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq(summation(Z), N)))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(184,axiom,(![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq(summation(Z), N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_ub_3')).
% 0.15/0.42 tff(185,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq(summation(Z), N)))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.15/0.42 tff(186,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $lesseq($sum(summation(Z), $product(-1, N)), 0)))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[185, 182])).
% 0.15/0.42 tff(187,plain,
% 0.15/0.42 (![X: $int, Y: $int, N: $int] : (model_ub(X, Y, N) <=> ?[Z: $int] : (ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0)))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[186, 180])).
% 0.15/0.42 tff(188,plain,(
% 0.15/0.42 ![X: $int, Y: $int, N: $int] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & $greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0))) & (model_ub(X, Y, N) | ![Z: $int] : (~(ub(X, Y, Z) & $greatereq($sum(N, $product(-1, summation(Z))), 0)))))),
% 0.15/0.43 inference(skolemize,[status(sab)],[187])).
% 0.15/0.43 tff(189,plain,
% 0.15/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[188, 178])).
% 0.15/0.43 tff(190,plain,
% 0.15/0.43 (![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[189, 176])).
% 0.15/0.43 tff(191,plain,
% 0.15/0.43 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(192,plain,
% 0.15/0.43 ((~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0))))))) <=> (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(193,plain,
% 0.15/0.43 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[192])).
% 0.15/0.43 tff(194,plain,
% 0.15/0.43 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[193, 191])).
% 0.15/0.43 tff(195,plain,
% 0.15/0.43 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0)))))))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(196,plain,
% 0.15/0.43 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.15/0.43 tff(197,plain,
% 0.15/0.43 (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[196, 190])).
% 0.15/0.43 tff(198,plain,
% 0.15/0.43 (((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))) | ((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(199,plain,
% 0.15/0.43 ((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.15/0.43 tff(200,plain,
% 0.15/0.43 (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))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[167])).
% 0.15/0.43 tff(201,plain,
% 0.15/0.43 (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))),
% 0.15/0.43 inference(symmetry,[status(thm)],[200])).
% 0.15/0.43 tff(202,assumption,(model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.15/0.43 tff(203,plain,
% 0.15/0.43 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0))))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(204,plain,
% 0.15/0.44 ((~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(Z!3, $product(-1, summation(Z))), 0))))))) <=> (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0)))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(205,plain,
% 0.15/0.44 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(Z!3, $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0))))))))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[204])).
% 0.15/0.44 tff(206,plain,
% 0.15/0.44 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(Z!3, $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0))))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[205, 203])).
% 0.15/0.44 tff(207,plain,
% 0.15/0.44 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(Z!3, $product(-1, summation(Z))), 0)))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(208,plain,
% 0.15/0.44 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0)))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.15/0.44 tff(209,plain,
% 0.15/0.44 (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[208, 190])).
% 0.15/0.44 tff(210,plain,
% 0.15/0.44 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(summation(Z), $product(-1, Z!3)), 0)))))) | ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(211,plain,
% 0.15/0.44 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.15/0.44 tff(212,plain,
% 0.15/0.44 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))))) | (~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(213,plain,
% 0.15/0.44 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.15/0.44 tff(214,plain,
% 0.15/0.44 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[213, 202])).
% 0.15/0.44 tff(215,plain,
% 0.15/0.44 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))) | $greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(216,plain,
% 0.15/0.44 ($greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.15/0.44 tff(217,plain,
% 0.15/0.44 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0)))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(218,plain,
% 0.15/0.44 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[217, 17])).
% 0.15/0.44 tff(219,plain,
% 0.15/0.44 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[167])).
% 0.15/0.44 tff(220,plain,
% 0.15/0.44 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.44 inference(symmetry,[status(thm)],[219])).
% 0.15/0.44 tff(221,plain,
% 0.15/0.44 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))) | ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(222,plain,
% 0.15/0.44 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[221, 214])).
% 0.15/0.44 tff(223,plain,
% 0.15/0.44 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[222, 220])).
% 0.15/0.44 tff(224,plain,
% 0.15/0.44 ((~(ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0)))))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~$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), $product(-1, max(X!5, Y!4))), 0))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(225,plain,
% 0.15/0.44 (~((~$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), $product(-1, max(X!5, Y!4))), 0)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[224, 223, 218])).
% 0.15/0.44 tff(226,plain,
% 0.15/0.44 (((~$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, max(X!5, Y!4))), 0))) | $greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(227,plain,
% 0.15/0.44 ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.15/0.44 tff(228,assumption,(~($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)).
% 0.15/0.44 tff(229,plain,
% 0.15/0.44 (((~![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)), $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(230,plain,
% 0.15/0.44 (($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))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(231,plain,
% 0.15/0.44 (((~![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)))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[230])).
% 0.15/0.44 tff(232,plain,
% 0.15/0.44 (((~![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)))),
% 0.15/0.45 inference(transitivity,[status(thm)],[231, 229])).
% 0.15/0.45 tff(233,plain,
% 0.15/0.45 ((~![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))),
% 0.15/0.45 inference(quant_inst,[status(thm)],[])).
% 0.15/0.45 tff(234,plain,
% 0.15/0.45 ((~![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)), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.15/0.45 tff(235,plain,
% 0.15/0.45 ($false),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[234, 65, 228])).
% 0.15/0.45 tff(236,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)), $product(-1, summation(max(X!5, Y!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.45 tff(237,plain,
% 0.15/0.45 ((~($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)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(238,plain,
% 0.15/0.45 ((~$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)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.15/0.45 tff(239,plain,
% 0.15/0.45 ($greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[238, 227])).
% 0.15/0.45 tff(240,assumption,($greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)), introduced(assumption)).
% 0.15/0.45 tff(241,assumption,(~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.15/0.45 tff(242,assumption,($greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.15/0.45 tff(243,plain,
% 0.15/0.45 ($false),
% 0.15/0.45 inference(theory_lemma,[status(thm)],[242, 241, 240])).
% 0.15/0.45 tff(244,plain,((~$greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)) | $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.45 tff(245,plain,
% 0.15/0.45 ($greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[244, 239, 216])).
% 0.15/0.45 tff(246,assumption,(~(model_max(X!5, Y!4, Z!3) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))), introduced(assumption)).
% 0.15/0.45 tff(247,plain,
% 0.15/0.45 (^[X: $int, Y: $int, N: $int] : refl((model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0)) <=> (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0)))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(248,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[247])).
% 0.15/0.45 tff(249,plain,
% 0.15/0.45 (^[X: $int, Y: $int, N: $int] : rewrite((model_max(X, Y, N) <=> $lesseq($sum(summation(max(X, Y)), $product(-1, N)), 0)) <=> (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0)))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(250,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(summation(max(X, Y)), $product(-1, N)), 0)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[249])).
% 0.15/0.45 tff(251,plain,
% 0.15/0.45 (^[X: $int, Y: $int, N: $int] : rewrite((model_max(X, Y, N) <=> $lesseq(summation(max(X, Y)), N)) <=> (model_max(X, Y, N) <=> $lesseq($sum(summation(max(X, Y)), $product(-1, N)), 0)))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(252,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq(summation(max(X, Y)), N)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(summation(max(X, Y)), $product(-1, N)), 0))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[251])).
% 0.15/0.45 tff(253,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq(summation(max(X, Y)), N)) <=> ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq(summation(max(X, Y)), N))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(254,axiom,(![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq(summation(max(X, Y)), N))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_max_3')).
% 0.15/0.45 tff(255,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq(summation(max(X, Y)), N))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.15/0.45 tff(256,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $lesseq($sum(summation(max(X, Y)), $product(-1, N)), 0))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[255, 252])).
% 0.15/0.45 tff(257,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[256, 250])).
% 0.15/0.45 tff(258,plain,(
% 0.15/0.45 ![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))),
% 0.15/0.45 inference(skolemize,[status(sab)],[257])).
% 0.15/0.45 tff(259,plain,
% 0.15/0.45 (![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[258, 248])).
% 0.15/0.45 tff(260,plain,
% 0.15/0.45 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, Z!3) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.45 inference(quant_inst,[status(thm)],[])).
% 0.15/0.45 tff(261,plain,
% 0.15/0.45 ($false),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[260, 259, 246])).
% 0.15/0.45 tff(262,plain,(model_max(X!5, Y!4, Z!3) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.45 tff(263,plain,
% 0.15/0.45 ((~(model_max(X!5, Y!4, Z!3) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))) | model_max(X!5, Y!4, Z!3) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(264,plain,
% 0.15/0.45 (model_max(X!5, Y!4, Z!3) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.15/0.45 tff(265,plain,
% 0.15/0.45 (model_max(X!5, Y!4, Z!3)),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[264, 245])).
% 0.15/0.45 tff(266,assumption,(minsol_model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.15/0.45 tff(267,plain,
% 0.15/0.45 (^[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))))))))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(268,plain,
% 0.15/0.45 (![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)))))))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[267])).
% 0.15/0.45 tff(269,plain,
% 0.15/0.45 (^[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))))))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(270,plain,
% 0.15/0.45 (![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)))))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[269])).
% 0.15/0.45 tff(271,plain,
% 0.15/0.45 (^[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))))))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(272,plain,
% 0.15/0.45 (![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)))))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[271])).
% 0.15/0.45 tff(273,plain,
% 0.15/0.45 (![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)))))))),
% 0.15/0.45 inference(transitivity,[status(thm)],[272, 270])).
% 0.15/0.45 tff(274,plain,
% 0.15/0.45 (^[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)))))))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(275,plain,
% 0.15/0.45 (![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)))))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[274])).
% 0.15/0.45 tff(276,plain,
% 0.15/0.45 (^[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))))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(277,plain,
% 0.15/0.45 (![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)))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[276])).
% 0.15/0.45 tff(278,plain,
% 0.15/0.45 (^[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)))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(279,plain,
% 0.15/0.45 (![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))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[278])).
% 0.15/0.45 tff(280,plain,
% 0.15/0.45 (![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))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(281,plain,
% 0.15/0.45 (^[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)))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(282,plain,
% 0.15/0.45 (![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))))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[281])).
% 0.15/0.45 tff(283,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/sandbox/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.15/0.45 tff(284,plain,
% 0.15/0.45 (![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))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.15/0.45 tff(285,plain,
% 0.15/0.45 (![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))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.15/0.45 tff(286,plain,
% 0.15/0.45 (![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))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[285, 279])).
% 0.15/0.45 tff(287,plain,(
% 0.15/0.45 ![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))))))),
% 0.15/0.45 inference(skolemize,[status(sab)],[286])).
% 0.15/0.45 tff(288,plain,
% 0.15/0.45 (![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)))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[287, 277])).
% 0.15/0.45 tff(289,plain,
% 0.15/0.45 (![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)))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[288, 275])).
% 0.15/0.45 tff(290,plain,
% 0.15/0.45 (![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)))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[289, 273])).
% 0.15/0.45 tff(291,plain,
% 0.15/0.45 (![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)))))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[290, 268])).
% 0.15/0.45 tff(292,plain,
% 0.15/0.45 (((~![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))))))))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(293,plain,
% 0.15/0.45 ((~((~(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)))))))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(294,plain,
% 0.15/0.45 (((~![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))))))))))),
% 0.15/0.46 inference(monotonicity,[status(thm)],[293])).
% 0.15/0.46 tff(295,plain,
% 0.15/0.46 (((~![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))))))))))),
% 0.15/0.46 inference(transitivity,[status(thm)],[294, 292])).
% 0.15/0.46 tff(296,plain,
% 0.15/0.46 ((~![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)))))))))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(297,plain,
% 0.15/0.46 ((~![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)))))))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.15/0.46 tff(298,plain,
% 0.15/0.46 (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($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))))))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[297, 291])).
% 0.15/0.46 tff(299,plain,
% 0.15/0.46 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($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))))))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(300,plain,
% 0.15/0.46 ((~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)))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.15/0.46 tff(301,plain,
% 0.15/0.46 ((~((~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)))))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(302,plain,
% 0.15/0.46 ((~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)))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[301, 300])).
% 0.15/0.46 tff(303,plain,
% 0.15/0.46 (~((~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))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[302, 266])).
% 0.15/0.46 tff(304,plain,
% 0.15/0.46 (((~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))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(305,plain,
% 0.15/0.46 (![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.15/0.46 tff(306,assumption,(model_ub(X!5, Y!4, $sum(-1, Z!3))), introduced(assumption)).
% 0.15/0.46 tff(307,assumption,(![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))), introduced(assumption)).
% 0.15/0.46 tff(308,plain,
% 0.15/0.46 (((~![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))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(309,plain,
% 0.15/0.46 (((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | $false) <=> (~model_ub(X!5, Y!4, $sum(-1, Z!3)))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(310,plain,
% 0.15/0.46 ($greatereq(-1, 0) <=> $false),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(311,plain,
% 0.15/0.46 ($sum($sum(-1, Z!3), $product(-1, Z!3)) = -1),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(312,plain,
% 0.15/0.46 ($greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0) <=> $greatereq(-1, 0)),
% 0.15/0.46 inference(monotonicity,[status(thm)],[311])).
% 0.15/0.46 tff(313,plain,
% 0.15/0.46 ($greatereq($sum($sum(-1, Z!3), $product(-1, Z!3)), 0) <=> $false),
% 0.15/0.46 inference(transitivity,[status(thm)],[312, 310])).
% 0.15/0.46 tff(314,plain,
% 0.15/0.46 (((~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)),
% 0.15/0.46 inference(monotonicity,[status(thm)],[313])).
% 0.15/0.46 tff(315,plain,
% 0.15/0.46 (((~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)))),
% 0.15/0.46 inference(transitivity,[status(thm)],[314, 309])).
% 0.15/0.46 tff(316,plain,
% 0.15/0.46 (((~![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))))),
% 0.15/0.46 inference(monotonicity,[status(thm)],[315])).
% 0.15/0.46 tff(317,plain,
% 0.15/0.46 (((~![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))))),
% 0.15/0.46 inference(transitivity,[status(thm)],[316, 308])).
% 0.15/0.46 tff(318,plain,
% 0.15/0.46 ((~![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))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(319,plain,
% 0.15/0.46 ((~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | (~model_ub(X!5, Y!4, $sum(-1, Z!3)))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.15/0.46 tff(320,plain,
% 0.15/0.46 ($false),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[319, 307, 306])).
% 0.15/0.46 tff(321,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.46 tff(322,plain,
% 0.15/0.46 (~model_ub(X!5, Y!4, $sum(-1, Z!3))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[321, 305])).
% 0.15/0.46 tff(323,plain,
% 0.15/0.46 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(summation(Z), $product(-1, Z!3)), -1)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(summation(Z), $product(-1, Z!3)), -1))))))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(324,plain,
% 0.15/0.46 ((~((~((~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))), $product(-1, 1)), Y!4, X!5))) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(tptp_fun_Z_0($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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(Z))), 0))))))) <=> (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(summation(Z), $product(-1, Z!3)), -1)))))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(325,plain,
% 0.15/0.46 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, 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))), $product(-1, 1)), Y!4, X!5))) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(tptp_fun_Z_0($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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(summation(Z), $product(-1, Z!3)), -1))))))))),
% 0.15/0.46 inference(monotonicity,[status(thm)],[324])).
% 0.15/0.46 tff(326,plain,
% 0.15/0.46 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, 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))), $product(-1, 1)), Y!4, X!5))) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(tptp_fun_Z_0($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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(summation(Z), $product(-1, Z!3)), -1))))))))),
% 0.15/0.46 inference(transitivity,[status(thm)],[325, 323])).
% 0.15/0.46 tff(327,plain,
% 0.15/0.46 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, 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))), $product(-1, 1)), Y!4, X!5))) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(tptp_fun_Z_0($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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, summation(Z))), 0)))))))),
% 0.15/0.47 inference(quant_inst,[status(thm)],[])).
% 0.15/0.47 tff(328,plain,
% 0.15/0.47 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, $sum(-1, Z!3))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0($sum(-1, Z!3), Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(summation(Z), $product(-1, Z!3)), -1)))))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.15/0.47 tff(329,plain,
% 0.15/0.47 (~((~((~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))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(summation(Z), $product(-1, Z!3)), -1))))))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[328, 190])).
% 0.15/0.47 tff(330,plain,
% 0.15/0.47 (((~((~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))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0($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(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(summation(Z), $product(-1, Z!3)), -1))))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(331,plain,
% 0.15/0.47 (model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[330, 329])).
% 0.15/0.47 tff(332,plain,
% 0.15/0.47 ((~(model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($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(summation(Z), $product(-1, Z!3)), -1)))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(333,plain,
% 0.15/0.47 (model_ub(X!5, Y!4, $sum(-1, Z!3)) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[332, 331])).
% 0.15/0.47 tff(334,plain,
% 0.15/0.47 (![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[333, 322])).
% 0.15/0.47 tff(335,plain,
% 0.15/0.47 (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)),
% 0.15/0.47 inference(monotonicity,[status(thm)],[167])).
% 0.15/0.47 tff(336,plain,
% 0.15/0.47 (summation(max(max(X!5, Y!4), Y!4)) = summation(max(X!5, Y!4))),
% 0.15/0.47 inference(monotonicity,[status(thm)],[335])).
% 0.15/0.47 tff(337,plain,
% 0.15/0.47 (summation(max(X!5, Y!4)) = summation(max(max(X!5, Y!4), Y!4))),
% 0.15/0.47 inference(symmetry,[status(thm)],[336])).
% 0.15/0.47 tff(338,plain,
% 0.15/0.47 ((~(summation(max(X!5, Y!4)) = summation(max(max(X!5, Y!4), Y!4)))) | $lesseq($sum(summation(max(X!5, Y!4)), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.15/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.47 tff(339,plain,
% 0.15/0.47 ($lesseq($sum(summation(max(X!5, Y!4)), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[338, 337])).
% 0.15/0.47 tff(340,plain,
% 0.15/0.47 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0))),
% 0.15/0.47 inference(quant_inst,[status(thm)],[])).
% 0.15/0.47 tff(341,plain,
% 0.15/0.47 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[340, 259])).
% 0.15/0.47 tff(342,plain,
% 0.15/0.47 (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))),
% 0.15/0.47 inference(monotonicity,[status(thm)],[167])).
% 0.15/0.47 tff(343,plain,
% 0.15/0.47 (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))),
% 0.15/0.47 inference(symmetry,[status(thm)],[342])).
% 0.15/0.47 tff(344,assumption,(model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.15/0.47 tff(345,plain,
% 0.15/0.47 ((~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))) <=> ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(346,plain,
% 0.15/0.47 ((~![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)))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(347,axiom,(~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.15/0.47 tff(348,plain,
% 0.15/0.47 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.15/0.47 tff(349,plain,
% 0.15/0.47 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[348, 346])).
% 0.15/0.47 tff(350,plain,
% 0.15/0.47 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[349, 346])).
% 0.15/0.47 tff(351,plain,
% 0.15/0.47 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.15/0.47 tff(352,plain,
% 0.15/0.47 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[351, 346])).
% 0.15/0.47 tff(353,plain,
% 0.15/0.47 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[352, 346])).
% 0.15/0.47 tff(354,plain,
% 0.15/0.47 (~![X: $int, Y: $int, Z: $int] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[353, 346])).
% 0.15/0.47 tff(355,plain,(
% 0.15/0.47 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.15/0.47 inference(skolemize,[status(sab)],[354])).
% 0.15/0.47 tff(356,plain,
% 0.15/0.47 ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[355, 345])).
% 0.15/0.47 tff(357,plain,
% 0.15/0.47 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(358,plain,
% 0.15/0.47 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[357, 356])).
% 0.15/0.47 tff(359,plain,
% 0.15/0.47 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[358, 266])).
% 0.15/0.47 tff(360,plain,
% 0.15/0.47 (^[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))))))))))),
% 0.15/0.47 inference(bind,[status(th)],[])).
% 0.15/0.47 tff(361,plain,
% 0.15/0.47 (![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)))))))))),
% 0.15/0.47 inference(quant_intro,[status(thm)],[360])).
% 0.15/0.47 tff(362,plain,
% 0.15/0.47 (^[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))))))))))),
% 0.15/0.47 inference(bind,[status(th)],[])).
% 0.15/0.47 tff(363,plain,
% 0.15/0.47 (![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)))))))))),
% 0.15/0.47 inference(quant_intro,[status(thm)],[362])).
% 0.15/0.47 tff(364,plain,
% 0.15/0.47 (![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)))))))))),
% 0.15/0.47 inference(transitivity,[status(thm)],[363, 361])).
% 0.15/0.47 tff(365,plain,
% 0.15/0.47 (^[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)))))))))))),
% 0.15/0.47 inference(bind,[status(th)],[])).
% 0.15/0.47 tff(366,plain,
% 0.15/0.47 (![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)))))))))),
% 0.15/0.47 inference(quant_intro,[status(thm)],[365])).
% 0.15/0.47 tff(367,plain,
% 0.15/0.47 (^[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))))))),
% 0.15/0.47 inference(bind,[status(th)],[])).
% 0.15/0.47 tff(368,plain,
% 0.15/0.47 (![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)))))),
% 0.15/0.47 inference(quant_intro,[status(thm)],[367])).
% 0.15/0.47 tff(369,plain,
% 0.15/0.47 (^[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)))))),
% 0.15/0.47 inference(bind,[status(th)],[])).
% 0.15/0.47 tff(370,plain,
% 0.15/0.47 (![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))))),
% 0.15/0.47 inference(quant_intro,[status(thm)],[369])).
% 0.15/0.47 tff(371,plain,
% 0.15/0.47 (![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))))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(372,plain,
% 0.15/0.47 (^[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)))))),
% 0.15/0.47 inference(bind,[status(th)],[])).
% 0.15/0.47 tff(373,plain,
% 0.15/0.47 (![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))))),
% 0.15/0.47 inference(quant_intro,[status(thm)],[372])).
% 0.15/0.47 tff(374,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/sandbox/benchmark/theBenchmark.p','minsol_model_max')).
% 0.15/0.47 tff(375,plain,
% 0.15/0.47 (![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))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.15/0.47 tff(376,plain,
% 0.15/0.47 (![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))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[375, 371])).
% 0.15/0.47 tff(377,plain,
% 0.15/0.47 (![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))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[376, 370])).
% 0.15/0.47 tff(378,plain,(
% 0.15/0.47 ![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))))))),
% 0.15/0.47 inference(skolemize,[status(sab)],[377])).
% 0.15/0.47 tff(379,plain,
% 0.15/0.47 (![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)))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[378, 368])).
% 0.15/0.47 tff(380,plain,
% 0.15/0.47 (![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)))))))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[379, 366])).
% 0.15/0.47 tff(381,plain,
% 0.15/0.47 (![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)))))))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[380, 364])).
% 0.15/0.47 tff(382,plain,
% 0.15/0.47 (((~![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))))))))))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(383,plain,
% 0.15/0.48 ((~((~(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)))))))))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(384,plain,
% 0.15/0.48 (((~![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))))))))))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[383])).
% 0.15/0.48 tff(385,plain,
% 0.15/0.48 (((~![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))))))))))),
% 0.15/0.48 inference(transitivity,[status(thm)],[384, 382])).
% 0.15/0.48 tff(386,plain,
% 0.15/0.48 ((~![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)))))))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(387,plain,
% 0.15/0.48 ((~![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)))))))))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.15/0.48 tff(388,plain,
% 0.15/0.48 (~((~(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))))))))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[387, 381])).
% 0.15/0.48 tff(389,plain,
% 0.15/0.48 (((~(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))))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(390,plain,
% 0.15/0.48 (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)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[389, 388])).
% 0.15/0.48 tff(391,plain,
% 0.15/0.48 ((~(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)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(392,plain,
% 0.15/0.48 (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)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.15/0.48 tff(393,plain,
% 0.15/0.48 (~((~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))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[392, 359, 344])).
% 0.15/0.48 tff(394,plain,
% 0.15/0.48 (((~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))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(395,plain,
% 0.15/0.48 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.15/0.48 tff(396,plain,
% 0.15/0.48 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[395, 343])).
% 0.15/0.48 tff(397,plain,
% 0.15/0.48 ((~(model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, 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))) | $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(398,plain,
% 0.15/0.48 ($greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[397, 396, 341])).
% 0.15/0.48 tff(399,plain,
% 0.15/0.48 (((~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, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(400,plain,
% 0.15/0.48 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[399, 393])).
% 0.15/0.48 tff(401,plain,
% 0.15/0.48 ($greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)) | (~$greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 0.15/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.48 tff(402,plain,
% 0.15/0.48 ($greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[401, 400, 398, 339])).
% 0.15/0.48 tff(403,plain,
% 0.15/0.48 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(404,plain,
% 0.15/0.48 (((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), -1))) <=> ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(405,plain,
% 0.15/0.48 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[404])).
% 0.15/0.48 tff(406,plain,
% 0.15/0.48 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)))),
% 0.15/0.49 inference(transitivity,[status(thm)],[405, 403])).
% 0.15/0.49 tff(407,plain,
% 0.15/0.49 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), -1)))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(408,plain,
% 0.15/0.49 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.15/0.49 tff(409,plain,
% 0.15/0.49 ($false),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[408, 402, 334, 156])).
% 0.15/0.49 tff(410,plain,((~minsol_model_ub(X!5, Y!4, Z!3)) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)) | (~model_max(X!5, Y!4, Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.49 tff(411,plain,
% 0.15/0.49 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[410, 265, 133])).
% 0.15/0.49 tff(412,plain,
% 0.15/0.49 (((~(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))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(413,plain,
% 0.15/0.49 (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)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[412, 298])).
% 0.15/0.49 tff(414,plain,
% 0.15/0.49 ((~(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)))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(415,plain,
% 0.15/0.49 (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)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[414, 413])).
% 0.15/0.49 tff(416,plain,
% 0.15/0.49 (~((~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))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[415, 411, 202])).
% 0.15/0.49 tff(417,plain,
% 0.15/0.49 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)) | model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(418,plain,
% 0.15/0.49 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[417, 416])).
% 0.15/0.49 tff(419,plain,
% 0.15/0.49 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[418, 201])).
% 0.15/0.49 tff(420,plain,
% 0.15/0.49 ((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))))) | (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(421,plain,
% 0.15/0.49 (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[420, 419, 199])).
% 0.15/0.49 tff(422,plain,
% 0.15/0.49 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))) | ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(423,plain,
% 0.15/0.49 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[422, 421])).
% 0.15/0.49 tff(424,plain,
% 0.15/0.49 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[423, 171])).
% 0.15/0.49 tff(425,plain,
% 0.15/0.49 ((~(ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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), $product(-1, max(X!5, Y!4))), 0))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(426,plain,
% 0.15/0.49 (~((~$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), $product(-1, max(X!5, Y!4))), 0)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[425, 424, 165])).
% 0.15/0.49 tff(427,plain,
% 0.15/0.49 (((~$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), $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(428,plain,
% 0.15/0.49 ($greatereq($sum(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[427, 426])).
% 0.15/0.49 tff(429,plain,
% 0.15/0.49 ((~($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)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(430,plain,
% 0.15/0.49 ($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)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[429, 428, 163])).
% 0.15/0.49 tff(431,plain,
% 0.15/0.49 (((~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, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(432,plain,
% 0.15/0.49 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[431, 416])).
% 0.15/0.49 tff(433,plain,
% 0.15/0.49 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0))) | $greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(434,plain,
% 0.15/0.49 ($greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[433, 421])).
% 0.15/0.49 tff(435,plain,
% 0.15/0.49 (summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), 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)))),
% 0.15/0.49 inference(monotonicity,[status(thm)],[169])).
% 0.15/0.49 tff(436,plain,
% 0.15/0.49 ((~(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), 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))))) | $lesseq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)),
% 0.15/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.49 tff(437,plain,
% 0.15/0.49 ($lesseq($sum(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))), 0)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[436, 435])).
% 0.15/0.49 tff(438,plain,
% 0.15/0.49 ((~(summation(max(X!5, Y!4)) = summation(max(max(X!5, Y!4), Y!4)))) | $greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.15/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.49 tff(439,plain,
% 0.15/0.49 ($greatereq($sum(summation(max(X!5, Y!4)), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[438, 337])).
% 0.15/0.49 tff(440,plain,
% 0.15/0.49 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1)))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(441,plain,
% 0.15/0.49 ((model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0)) <=> (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(442,plain,
% 0.15/0.49 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1)))),
% 0.15/0.49 inference(monotonicity,[status(thm)],[441])).
% 0.15/0.49 tff(443,plain,
% 0.15/0.49 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1)))),
% 0.15/0.49 inference(transitivity,[status(thm)],[442, 440])).
% 0.15/0.49 tff(444,plain,
% 0.15/0.49 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 0))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(445,plain,
% 0.15/0.49 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.15/0.50 tff(446,plain,
% 0.15/0.50 (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[445, 259])).
% 0.15/0.50 tff(447,plain,
% 0.15/0.50 (model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> model_max(X!5, Y!4, $sum(-1, Z!3))),
% 0.15/0.50 inference(monotonicity,[status(thm)],[167])).
% 0.15/0.50 tff(448,plain,
% 0.15/0.50 (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3))),
% 0.15/0.50 inference(symmetry,[status(thm)],[447])).
% 0.15/0.50 tff(449,plain,
% 0.15/0.50 ((~model_max(X!5, Y!4, $sum(-1, Z!3))) <=> (~model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)))),
% 0.15/0.50 inference(monotonicity,[status(thm)],[448])).
% 0.15/0.50 tff(450,plain,
% 0.15/0.50 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(451,plain,
% 0.15/0.50 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[450, 356])).
% 0.15/0.50 tff(452,plain,
% 0.15/0.50 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[451, 411])).
% 0.15/0.50 tff(453,plain,
% 0.15/0.50 (((~(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))))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(454,plain,
% 0.15/0.50 ((~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)))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[453, 388])).
% 0.15/0.50 tff(455,plain,
% 0.15/0.50 ((~((~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)))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(456,plain,
% 0.15/0.50 ((~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)))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[455, 454])).
% 0.15/0.50 tff(457,plain,
% 0.15/0.50 (~((~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))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[456, 452])).
% 0.15/0.50 tff(458,plain,
% 0.15/0.50 (((~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))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(459,plain,
% 0.15/0.50 (![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[458, 457])).
% 0.15/0.50 tff(460,plain,
% 0.15/0.50 (((~![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))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(461,plain,
% 0.15/0.50 (((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $false) <=> (~model_max(X!5, Y!4, $sum(-1, Z!3)))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(462,plain,
% 0.15/0.50 ($sum(Z!3, -1) = $sum(-1, Z!3)),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(463,plain,
% 0.15/0.50 ($product(-1, 1) = -1),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(464,plain,
% 0.15/0.50 ($sum(0, Z!3) = Z!3),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(465,plain,
% 0.15/0.50 ($product(-1, $product(-1, Z!3)) = Z!3),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(466,plain,
% 0.15/0.50 ($sum(0, $product(-1, $product(-1, Z!3))) = $sum(0, Z!3)),
% 0.15/0.50 inference(monotonicity,[status(thm)],[465])).
% 0.15/0.50 tff(467,plain,
% 0.15/0.50 ($sum(0, $product(-1, $product(-1, Z!3))) = Z!3),
% 0.15/0.50 inference(transitivity,[status(thm)],[466, 464])).
% 0.15/0.50 tff(468,plain,
% 0.15/0.50 ($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)) = $sum(Z!3, -1)),
% 0.15/0.50 inference(monotonicity,[status(thm)],[467, 463])).
% 0.15/0.50 tff(469,plain,
% 0.15/0.50 ($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)) = $sum(-1, Z!3)),
% 0.15/0.50 inference(transitivity,[status(thm)],[468, 462])).
% 0.15/0.50 tff(470,plain,
% 0.15/0.50 ($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, Z!3)) = $sum($sum(-1, Z!3), $product(-1, Z!3))),
% 0.15/0.50 inference(monotonicity,[status(thm)],[469])).
% 0.15/0.50 tff(471,plain,
% 0.15/0.50 ($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, Z!3)) = -1),
% 0.15/0.50 inference(transitivity,[status(thm)],[470, 311])).
% 0.15/0.50 tff(472,plain,
% 0.15/0.50 ($greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, Z!3)), 0) <=> $greatereq(-1, 0)),
% 0.15/0.50 inference(monotonicity,[status(thm)],[471])).
% 0.15/0.50 tff(473,plain,
% 0.15/0.50 ($greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, Z!3)), 0) <=> $false),
% 0.15/0.50 inference(transitivity,[status(thm)],[472, 310])).
% 0.15/0.50 tff(474,plain,
% 0.15/0.50 ((~model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) <=> (~model_max(X!5, Y!4, $sum(-1, Z!3)))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(475,plain,
% 0.15/0.50 (((~model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | $greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, Z!3)), 0)) <=> ((~model_max(X!5, Y!4, $sum(-1, Z!3))) | $false)),
% 0.15/0.50 inference(monotonicity,[status(thm)],[474, 473])).
% 0.15/0.50 tff(476,plain,
% 0.15/0.50 (((~model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | $greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, Z!3)), 0)) <=> (~model_max(X!5, Y!4, $sum(-1, Z!3)))),
% 0.15/0.50 inference(transitivity,[status(thm)],[475, 461])).
% 0.15/0.50 tff(477,plain,
% 0.15/0.50 (((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | $greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $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))))),
% 0.15/0.50 inference(monotonicity,[status(thm)],[476])).
% 0.15/0.50 tff(478,plain,
% 0.15/0.50 (((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | $greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $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))))),
% 0.15/0.50 inference(transitivity,[status(thm)],[477, 460])).
% 0.15/0.50 tff(479,plain,
% 0.15/0.50 ((~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))) | ((~model_max(X!5, Y!4, $sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)))) | $greatereq($sum($sum($sum(0, $product(-1, $product(-1, Z!3))), $product(-1, 1)), $product(-1, Z!3)), 0))),
% 0.15/0.50 inference(quant_inst,[status(thm)],[])).
% 0.15/0.50 tff(480,plain,
% 0.15/0.50 ((~![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)))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.15/0.50 tff(481,plain,
% 0.15/0.50 (~model_max(X!5, Y!4, $sum(-1, Z!3))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[480, 459])).
% 0.15/0.50 tff(482,plain,
% 0.15/0.50 (~model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[481, 449])).
% 0.15/0.50 tff(483,plain,
% 0.15/0.50 ((~(model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1))) | model_max(max(X!5, Y!4), Y!4, $sum(-1, Z!3)) | (~$greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(484,plain,
% 0.15/0.50 (~$greatereq($sum(Z!3, $product(-1, summation(max(max(X!5, Y!4), Y!4)))), 1)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[483, 482, 446])).
% 0.15/0.50 tff(485,plain,
% 0.15/0.50 ($false),
% 0.15/0.50 inference(theory_lemma,[status(thm)],[484, 439, 437, 434, 432, 430])).
% 0.15/0.50 tff(486,plain,((~model_ub(X!5, Y!4, Z!3)) | (~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.50 tff(487,plain,
% 0.15/0.50 (~model_ub(X!5, Y!4, Z!3)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[486, 133])).
% 0.15/0.50 tff(488,plain,
% 0.15/0.50 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, 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(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(summation(Z), $product(-1, Z!3)), 0))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(489,plain,
% 0.15/0.50 (model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[488, 209])).
% 0.15/0.50 tff(490,plain,
% 0.15/0.50 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($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(summation(Z), $product(-1, Z!3)), 0)))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(491,plain,
% 0.15/0.50 (model_ub(X!5, Y!4, Z!3) | ![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[490, 489])).
% 0.15/0.50 tff(492,plain,
% 0.15/0.50 (![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[491, 487])).
% 0.15/0.50 tff(493,assumption,(ub(X!5, Y!4, max(X!5, Y!4))), introduced(assumption)).
% 0.15/0.50 tff(494,assumption,(![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))), introduced(assumption)).
% 0.15/0.50 tff(495,assumption,($greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)), introduced(assumption)).
% 0.15/0.50 tff(496,plain,
% 0.15/0.50 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(497,plain,
% 0.15/0.50 (((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), 0))) <=> ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(498,plain,
% 0.15/0.50 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))))),
% 0.15/0.50 inference(monotonicity,[status(thm)],[497])).
% 0.15/0.50 tff(499,plain,
% 0.15/0.50 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), 0)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)))),
% 0.15/0.50 inference(transitivity,[status(thm)],[498, 496])).
% 0.15/0.50 tff(500,plain,
% 0.15/0.51 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~$lesseq($sum(summation(max(X!5, Y!4)), $product(-1, Z!3)), 0)))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(501,plain,
% 0.15/0.51 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.15/0.51 tff(502,plain,
% 0.15/0.51 ($false),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[501, 495, 494, 493])).
% 0.15/0.51 tff(503,plain,((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)) | (~ub(X!5, Y!4, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.51 tff(504,plain,
% 0.15/0.51 (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[503, 492, 156])).
% 0.15/0.51 tff(505,plain,
% 0.15/0.51 ((~(model_max(X!5, Y!4, Z!3) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0))) | (~model_max(X!5, Y!4, Z!3)) | $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(506,plain,
% 0.15/0.51 ((~model_max(X!5, Y!4, Z!3)) | $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[505, 262])).
% 0.15/0.51 tff(507,plain,
% 0.15/0.51 (~model_max(X!5, Y!4, Z!3)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[506, 504])).
% 0.15/0.51 tff(508,plain,
% 0.15/0.51 (((~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)),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(509,plain,
% 0.15/0.51 ((~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)))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[508, 487])).
% 0.15/0.51 tff(510,plain,
% 0.15/0.51 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[302, 509])).
% 0.15/0.51 tff(511,plain,
% 0.15/0.51 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[451, 510])).
% 0.15/0.51 tff(512,plain,
% 0.15/0.51 (~((~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))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[456, 511])).
% 0.15/0.51 tff(513,plain,
% 0.15/0.51 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0)))) | model_max(X!5, Y!4, Z!3)),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(514,plain,
% 0.15/0.51 ($false),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[513, 512, 507])).
% 0.15/0.51 tff(515,plain,(~$greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.51 tff(516,plain,
% 0.15/0.51 ((~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)) | $greatereq($sum(X!5, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.51 tff(517,plain,
% 0.15/0.51 (~($sum(X!5, $product(-1, max(X!5, Y!4))) = 0)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[516, 515])).
% 0.15/0.51 tff(518,plain,
% 0.15/0.51 (~$lesseq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[51, 517])).
% 0.15/0.51 tff(519,plain,
% 0.15/0.51 ($greatereq($sum(Y!4, $product(-1, X!5)), 0)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[103, 518])).
% 0.15/0.51 tff(520,plain,
% 0.15/0.51 ((~(ub(X!5, Y!4, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0))) | ub(X!5, Y!4, Y!4) | (~$greatereq($sum(Y!4, $product(-1, X!5)), 0))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(521,plain,
% 0.15/0.51 ((~(ub(X!5, Y!4, Y!4) <=> $greatereq($sum(Y!4, $product(-1, X!5)), 0))) | ub(X!5, Y!4, Y!4)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[520, 519])).
% 0.15/0.51 tff(522,plain,
% 0.15/0.51 (ub(X!5, Y!4, Y!4)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[521, 25])).
% 0.15/0.51 tff(523,plain,
% 0.15/0.51 ((~![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)), $product(-1, summation(Y!4))), 0))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(524,plain,
% 0.15/0.51 ($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)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[523, 65])).
% 0.15/0.51 tff(525,plain,
% 0.15/0.51 (((~![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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))))),
% 0.15/0.51 inference(rewrite,[status(thm)],[])).
% 0.15/0.51 tff(526,plain,
% 0.15/0.51 ((ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($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)))))),
% 0.15/0.51 inference(rewrite,[status(thm)],[])).
% 0.15/0.51 tff(527,plain,
% 0.15/0.51 (((~![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))))))),
% 0.15/0.51 inference(monotonicity,[status(thm)],[526])).
% 0.15/0.51 tff(528,plain,
% 0.15/0.51 (((~![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))))))),
% 0.15/0.51 inference(transitivity,[status(thm)],[527, 525])).
% 0.15/0.51 tff(529,plain,
% 0.15/0.51 ((~![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)))))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(530,plain,
% 0.15/0.51 ((~![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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.15/0.51 tff(531,plain,
% 0.15/0.51 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$lesseq($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))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[530, 17])).
% 0.15/0.51 tff(532,plain,
% 0.15/0.51 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))))),
% 0.15/0.51 inference(rewrite,[status(thm)],[])).
% 0.15/0.51 tff(533,plain,
% 0.15/0.51 ((~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0))))))) <=> (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))))),
% 0.15/0.51 inference(rewrite,[status(thm)],[])).
% 0.15/0.51 tff(534,plain,
% 0.15/0.51 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))))),
% 0.15/0.52 inference(monotonicity,[status(thm)],[533])).
% 0.15/0.52 tff(535,plain,
% 0.15/0.52 (((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0)))))))) <=> ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))))),
% 0.15/0.52 inference(transitivity,[status(thm)],[534, 532])).
% 0.15/0.52 tff(536,plain,
% 0.15/0.52 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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: $int] : ((~ub(X!5, Y!4, Z)) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(Z))), 0)))))))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(537,plain,
% 0.15/0.52 ((~![X: $int, Y: $int, N: $int] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~$greatereq($sum(N, $product(-1, summation(tptp_fun_Z_0(N, Y, X)))), 0)))))) | (~(model_ub(X, Y, N) | ![Z: $int] : ((~ub(X, Y, Z)) | (~$greatereq($sum(N, $product(-1, summation(Z))), 0)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.15/0.52 tff(538,plain,
% 0.15/0.52 (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[537, 190])).
% 0.15/0.52 tff(539,plain,
% 0.15/0.52 (((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, 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(summation(Z), $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)))))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)))))),
% 0.15/0.52 inference(tautology,[status(thm)],[])).
% 0.15/0.52 tff(540,plain,
% 0.15/0.52 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[539, 538])).
% 0.15/0.52 tff(541,plain,
% 0.15/0.52 ($sum(Y!4, $product(-1, max(X!5, Y!4))) = 0),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[101, 519])).
% 0.15/0.52 tff(542,plain,
% 0.15/0.52 ($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[112, 541])).
% 0.15/0.52 tff(543,plain,
% 0.15/0.52 (~model_max(X!5, Y!4, Z!3)),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[506, 241])).
% 0.15/0.52 tff(544,plain,
% 0.15/0.52 ((~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)))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[513, 543])).
% 0.15/0.52 tff(545,plain,
% 0.15/0.52 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[456, 544])).
% 0.15/0.52 tff(546,plain,
% 0.15/0.52 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[451, 545])).
% 0.15/0.52 tff(547,plain,
% 0.15/0.52 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[302, 546])).
% 0.15/0.52 tff(548,plain,
% 0.15/0.52 (model_ub(X!5, Y!4, Z!3)),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[508, 547])).
% 0.15/0.52 tff(549,plain,
% 0.15/0.52 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[213, 548])).
% 0.15/0.52 tff(550,plain,
% 0.15/0.52 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[221, 549])).
% 0.15/0.52 tff(551,assumption,($greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.15/0.52 tff(552,plain,
% 0.15/0.52 (Y!4 = max(X!5, Y!4)),
% 0.15/0.52 inference(theory_lemma,[status(thm)],[551, 149])).
% 0.15/0.52 tff(553,plain,
% 0.15/0.52 (max(X!5, Y!4) = Y!4),
% 0.15/0.52 inference(symmetry,[status(thm)],[552])).
% 0.15/0.52 tff(554,plain,
% 0.15/0.52 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(monotonicity,[status(thm)],[553])).
% 0.15/0.52 tff(555,plain,
% 0.15/0.52 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(symmetry,[status(thm)],[554])).
% 0.15/0.52 tff(556,assumption,(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.15/0.52 tff(557,plain,
% 0.15/0.52 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.15/0.52 tff(558,plain,
% 0.15/0.52 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)))))) <=> ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0))))))),
% 0.15/0.52 inference(rewrite,[status(thm)],[])).
% 0.15/0.52 tff(559,plain,
% 0.15/0.52 ((ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, 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), $product(-1, X!5)), 0))))) <=> (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)))))),
% 0.15/0.52 inference(rewrite,[status(thm)],[])).
% 0.15/0.52 tff(560,plain,
% 0.15/0.52 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, 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, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0))))))),
% 0.15/0.52 inference(monotonicity,[status(thm)],[559])).
% 0.15/0.52 tff(561,plain,
% 0.15/0.52 (((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, 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, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0))))))),
% 0.15/0.52 inference(transitivity,[status(thm)],[560, 558])).
% 0.15/0.52 tff(562,plain,
% 0.15/0.52 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(max(X!5, 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)))))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(563,plain,
% 0.15/0.52 ((~![X: $int, Y: $int, Z: $int] : (ub(X, Y, Z) <=> (~((~$lesseq($sum(Y, $product(-1, Z)), 0)) | (~$greatereq($sum(Z, $product(-1, X)), 0)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.15/0.52 tff(564,plain,
% 0.15/0.52 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[563, 17])).
% 0.15/0.52 tff(565,assumption,(~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)), introduced(assumption)).
% 0.15/0.52 tff(566,plain,
% 0.15/0.52 (((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0))) | $greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(567,plain,
% 0.15/0.53 ((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[566, 565])).
% 0.15/0.53 tff(568,plain,
% 0.15/0.53 ((~(ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)))))) | (~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0))))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(569,plain,
% 0.15/0.53 ((~(ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~$lesseq($sum(X!5, $product(-1, tptp_fun_Z_0(Z!3, Y!4, X!5))), 0)) | (~$greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)))))) | (~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[568, 567])).
% 0.15/0.53 tff(570,plain,
% 0.15/0.53 (~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[569, 564])).
% 0.15/0.53 tff(571,plain,
% 0.15/0.53 ($false),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[570, 557])).
% 0.15/0.53 tff(572,plain,((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | (~$lesseq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.53 tff(573,plain,
% 0.15/0.53 ((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~$greatereq($sum(Y!4, $product(-1, max(X!5, Y!4))), 0)) | $greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[572, 109])).
% 0.15/0.53 tff(574,plain,
% 0.15/0.53 ($greatereq($sum(tptp_fun_Z_0(Z!3, Y!4, X!5), $product(-1, max(X!5, Y!4))), 0)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[573, 550, 542])).
% 0.15/0.53 tff(575,plain,
% 0.15/0.53 ($greatereq($sum(Z!3, $product(-1, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))), 0)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[215, 549])).
% 0.15/0.53 tff(576,plain,
% 0.15/0.53 (~$greatereq($sum(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[244, 575, 241])).
% 0.15/0.53 tff(577,plain,
% 0.15/0.53 ($false),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[238, 576, 574])).
% 0.15/0.53 tff(578,plain,($greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.53 tff(579,plain,
% 0.15/0.53 (Y!4 = max(X!5, Y!4)),
% 0.15/0.53 inference(theory_lemma,[status(thm)],[542, 109])).
% 0.15/0.53 tff(580,plain,
% 0.15/0.53 (ub(X!5, Y!4, Y!4) <=> ub(X!5, Y!4, max(X!5, Y!4))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[579])).
% 0.15/0.53 tff(581,plain,
% 0.15/0.53 (ub(X!5, Y!4, max(X!5, Y!4))),
% 0.15/0.53 inference(modus_ponens,[status(thm)],[522, 580])).
% 0.15/0.53 tff(582,plain,
% 0.15/0.53 (~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), 0)))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[503, 581, 578])).
% 0.15/0.53 tff(583,plain,
% 0.15/0.53 (model_ub(X!5, Y!4, Z!3)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[491, 582])).
% 0.15/0.53 tff(584,assumption,(~minsol_model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.15/0.53 tff(585,plain,
% 0.15/0.53 (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[415, 584, 583])).
% 0.15/0.53 tff(586,plain,
% 0.15/0.53 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[417, 585])).
% 0.15/0.53 tff(587,plain,
% 0.15/0.53 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)))))) | (~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(588,plain,
% 0.15/0.53 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)))))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[587, 586])).
% 0.15/0.53 tff(589,plain,
% 0.15/0.53 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[588, 540])).
% 0.15/0.53 tff(590,plain,
% 0.15/0.53 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))) | ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(591,plain,
% 0.15/0.53 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[590, 589])).
% 0.15/0.53 tff(592,plain,
% 0.15/0.53 ((~(ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(593,plain,
% 0.15/0.53 ((~(ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0))))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[592, 591])).
% 0.15/0.53 tff(594,plain,
% 0.15/0.53 (~((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[593, 531])).
% 0.15/0.53 tff(595,plain,
% 0.15/0.53 (((~$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, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(596,plain,
% 0.15/0.53 ($lesseq($sum(Y!4, $product(-1, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), 0)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[595, 594])).
% 0.15/0.53 tff(597,plain,
% 0.15/0.53 ((~($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)), $product(-1, summation(Y!4))), 0)),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(598,plain,
% 0.15/0.53 ($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)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[597, 596, 524])).
% 0.15/0.53 tff(599,plain,
% 0.15/0.53 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)))),
% 0.15/0.53 inference(rewrite,[status(thm)],[])).
% 0.15/0.53 tff(600,plain,
% 0.15/0.53 ((model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(X!5, Y!4)))), 0)) <=> (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))),
% 0.15/0.53 inference(rewrite,[status(thm)],[])).
% 0.15/0.53 tff(601,plain,
% 0.15/0.53 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[600])).
% 0.15/0.53 tff(602,plain,
% 0.15/0.53 (((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(X!5, Y!4)))), 0))) <=> ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)))),
% 0.15/0.53 inference(transitivity,[status(thm)],[601, 599])).
% 0.15/0.53 tff(603,plain,
% 0.15/0.53 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum($sum(-1, Z!3), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.53 inference(quant_inst,[status(thm)],[])).
% 0.15/0.53 tff(604,plain,
% 0.15/0.53 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))),
% 0.15/0.53 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.15/0.53 tff(605,plain,
% 0.15/0.53 (model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[604, 259])).
% 0.15/0.53 tff(606,plain,
% 0.15/0.53 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[451, 584])).
% 0.15/0.53 tff(607,plain,
% 0.15/0.53 (~((~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))))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[456, 606])).
% 0.15/0.53 tff(608,plain,
% 0.15/0.53 (![Z: $int] : ((~model_max(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[458, 607])).
% 0.15/0.53 tff(609,plain,
% 0.15/0.53 (~model_max(X!5, Y!4, $sum(-1, Z!3))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[480, 608])).
% 0.15/0.53 tff(610,plain,
% 0.15/0.53 ((~(model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))) | model_max(X!5, Y!4, $sum(-1, Z!3)) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(611,plain,
% 0.15/0.53 ((~(model_max(X!5, Y!4, $sum(-1, Z!3)) <=> $greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))) | (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[610, 609])).
% 0.15/0.53 tff(612,plain,
% 0.15/0.53 (~$greatereq($sum(Z!3, $product(-1, summation(max(X!5, Y!4)))), 1)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[611, 605])).
% 0.15/0.53 tff(613,plain,
% 0.15/0.53 (summation(Y!4) = summation(max(X!5, Y!4))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[579])).
% 0.15/0.54 tff(614,plain,
% 0.15/0.54 ((~(summation(Y!4) = summation(max(X!5, Y!4)))) | $greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.54 tff(615,plain,
% 0.15/0.54 ($greatereq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[614, 613])).
% 0.15/0.54 tff(616,plain,
% 0.15/0.54 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_2(Z!3, Y!4, X!5))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[431, 585])).
% 0.15/0.54 tff(617,plain,
% 0.15/0.54 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~$greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0))) | $greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(618,plain,
% 0.15/0.54 ($greatereq($sum(tptp_fun_Z_2(Z!3, Y!4, X!5), $product(-1, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[617, 589])).
% 0.15/0.54 tff(619,plain,
% 0.15/0.54 ($false),
% 0.15/0.54 inference(theory_lemma,[status(thm)],[618, 616, 615, 612, 598])).
% 0.15/0.54 tff(620,plain,(minsol_model_ub(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.54 tff(621,plain,
% 0.15/0.54 (~((~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))))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[302, 620])).
% 0.15/0.54 tff(622,plain,
% 0.15/0.54 (![Z: $int] : ((~model_ub(X!5, Y!4, Z)) | $greatereq($sum(Z, $product(-1, Z!3)), 0))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[304, 621])).
% 0.15/0.54 tff(623,plain,
% 0.15/0.54 (~model_ub(X!5, Y!4, $sum(-1, Z!3))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[321, 622])).
% 0.15/0.54 tff(624,plain,
% 0.15/0.54 (![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[333, 623])).
% 0.15/0.54 tff(625,plain,
% 0.15/0.54 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$greatereq($sum(Z!3, $product(-1, summation(Y!4))), 1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | (~ub(X!5, Y!4, Y!4)) | (~$greatereq($sum(Z!3, $product(-1, summation(Y!4))), 1)))),
% 0.15/0.54 inference(rewrite,[status(thm)],[])).
% 0.15/0.54 tff(626,plain,
% 0.15/0.54 (((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(summation(Y!4), $product(-1, Z!3)), -1))) <=> ((~ub(X!5, Y!4, Y!4)) | (~$greatereq($sum(Z!3, $product(-1, summation(Y!4))), 1)))),
% 0.15/0.54 inference(rewrite,[status(thm)],[])).
% 0.15/0.54 tff(627,plain,
% 0.15/0.54 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(summation(Y!4), $product(-1, Z!3)), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$greatereq($sum(Z!3, $product(-1, summation(Y!4))), 1))))),
% 0.15/0.54 inference(monotonicity,[status(thm)],[626])).
% 0.15/0.54 tff(628,plain,
% 0.15/0.54 (((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(summation(Y!4), $product(-1, Z!3)), -1)))) <=> ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | (~ub(X!5, Y!4, Y!4)) | (~$greatereq($sum(Z!3, $product(-1, summation(Y!4))), 1)))),
% 0.15/0.54 inference(transitivity,[status(thm)],[627, 625])).
% 0.15/0.54 tff(629,plain,
% 0.15/0.54 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | ((~ub(X!5, Y!4, Y!4)) | (~$lesseq($sum(summation(Y!4), $product(-1, Z!3)), -1)))),
% 0.15/0.54 inference(quant_inst,[status(thm)],[])).
% 0.15/0.54 tff(630,plain,
% 0.15/0.54 ((~![Z: $int] : ((~ub(X!5, Y!4, Z)) | (~$lesseq($sum(summation(Z), $product(-1, Z!3)), -1)))) | (~ub(X!5, Y!4, Y!4)) | (~$greatereq($sum(Z!3, $product(-1, summation(Y!4))), 1))),
% 0.15/0.54 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.15/0.54 tff(631,plain,
% 0.15/0.54 (~$greatereq($sum(Z!3, $product(-1, summation(Y!4))), 1)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[630, 624, 522])).
% 0.15/0.54 tff(632,plain,
% 0.15/0.54 (model_max(X!5, Y!4, Z!3)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[264, 578])).
% 0.15/0.54 tff(633,plain,
% 0.15/0.54 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[358, 620])).
% 0.15/0.54 tff(634,plain,
% 0.15/0.54 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[392, 633, 632])).
% 0.15/0.54 tff(635,plain,
% 0.15/0.54 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Z_1(Z!3, Y!4, X!5))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[399, 634])).
% 0.15/0.54 tff(636,plain,
% 0.15/0.54 ((~![X: $int, Y: $int, N: $int] : (model_max(X, Y, N) <=> $greatereq($sum(N, $product(-1, summation(max(X, Y)))), 0))) | (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(X!5, Y!4)))), 0))),
% 0.15/0.54 inference(quant_inst,[status(thm)],[])).
% 0.15/0.54 tff(637,plain,
% 0.15/0.54 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[636, 259])).
% 0.15/0.54 tff(638,plain,
% 0.15/0.54 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[394, 634])).
% 0.15/0.54 tff(639,plain,
% 0.15/0.54 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) | (~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(640,plain,
% 0.15/0.54 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(X!5, Y!4)))), 0))) | $greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[639, 638])).
% 0.15/0.54 tff(641,plain,
% 0.15/0.54 ($greatereq($sum(tptp_fun_Z_1(Z!3, Y!4, X!5), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[640, 637])).
% 0.15/0.54 tff(642,plain,
% 0.15/0.54 (max(X!5, Y!4) = Y!4),
% 0.15/0.54 inference(symmetry,[status(thm)],[579])).
% 0.15/0.54 tff(643,plain,
% 0.15/0.54 (summation(max(X!5, Y!4)) = summation(Y!4)),
% 0.15/0.54 inference(monotonicity,[status(thm)],[642])).
% 0.15/0.54 tff(644,plain,
% 0.15/0.54 (summation(Y!4) = summation(max(X!5, Y!4))),
% 0.15/0.54 inference(symmetry,[status(thm)],[643])).
% 0.15/0.54 tff(645,plain,
% 0.15/0.54 ($lesseq($sum(summation(Y!4), $product(-1, summation(max(X!5, Y!4)))), 0)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[116, 644])).
% 0.15/0.54 tff(646,plain,
% 0.15/0.54 ($false),
% 0.15/0.54 inference(theory_lemma,[status(thm)],[645, 641, 635, 631])).
% 0.15/0.54 % SZS output end Proof
%------------------------------------------------------------------------------