TSTP Solution File: NUM862+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM862+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:12:21 EDT 2022
% Result : Theorem 0.15s 0.40s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM862+1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n014.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Sep 2 15:28:31 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -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(lesseq_type, type, (
% 0.15/0.40 lesseq: ( $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_Z_3_type, type, (
% 0.15/0.40 tptp_fun_Z_3: $i)).
% 0.15/0.40 tff(sum_type, type, (
% 0.15/0.40 sum: ( $i * $i ) > $i)).
% 0.15/0.40 tff(summation_type, type, (
% 0.15/0.40 summation: $i > $i)).
% 0.15/0.40 tff(max_type, type, (
% 0.15/0.40 max: ( $i * $i ) > $i)).
% 0.15/0.40 tff(tptp_fun_Y_4_type, type, (
% 0.15/0.40 tptp_fun_Y_4: $i)).
% 0.15/0.40 tff(tptp_fun_X_5_type, type, (
% 0.15/0.40 tptp_fun_X_5: $i)).
% 0.15/0.40 tff(c_type, type, (
% 0.15/0.40 c: $i)).
% 0.15/0.40 tff(model_max_type, type, (
% 0.15/0.40 model_max: ( $i * $i * $i ) > $o)).
% 0.15/0.40 tff(ub_type, type, (
% 0.15/0.40 ub: ( $i * $i * $i ) > $o)).
% 0.15/0.40 tff(model_ub_type, type, (
% 0.15/0.40 model_ub: ( $i * $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.15/0.40 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.15/0.40 tff(minsol_model_ub_type, type, (
% 0.15/0.40 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.15/0.40 tff(minsol_model_max_type, type, (
% 0.15/0.40 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_Z_1_type, type, (
% 0.15/0.40 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.15/0.40 tff(tptp_fun_Z_2_type, type, (
% 0.15/0.40 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 0.15/0.40 tff(1,assumption,((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))), introduced(assumption)).
% 0.15/0.40 tff(2,assumption,(lesseq(Y!4, X!5)), introduced(assumption)).
% 0.15/0.40 tff(3,plain,
% 0.15/0.40 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(4,plain,
% 0.15/0.40 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.15/0.40 tff(5,plain,
% 0.15/0.40 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(6,plain,
% 0.15/0.40 (^[X: $i, Y: $i] : 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(7,plain,
% 0.15/0.40 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.15/0.40 tff(8,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_1')).
% 0.15/0.40 tff(9,plain,
% 0.15/0.40 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.15/0.40 tff(10,plain,
% 0.15/0.40 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.15/0.40 tff(11,plain,(
% 0.15/0.40 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(skolemize,[status(sab)],[10])).
% 0.15/0.40 tff(12,plain,
% 0.15/0.40 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.15/0.40 tff(13,plain,
% 0.15/0.40 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(14,plain,
% 0.15/0.40 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(15,plain,
% 0.15/0.40 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.15/0.40 tff(16,plain,
% 0.15/0.40 ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.15/0.40 tff(17,plain,
% 0.15/0.40 (max(X!5, Y!4) = X!5),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[16, 2])).
% 0.15/0.40 tff(18,plain,
% 0.15/0.40 (X!5 = max(X!5, Y!4)),
% 0.15/0.40 inference(symmetry,[status(thm)],[17])).
% 0.15/0.40 tff(19,plain,
% 0.15/0.40 (lesseq(X!5, X!5) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.15/0.40 tff(20,plain,
% 0.15/0.40 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, X!5)),
% 0.15/0.40 inference(symmetry,[status(thm)],[19])).
% 0.15/0.40 tff(21,plain,
% 0.15/0.40 ((~lesseq(X!5, max(X!5, Y!4))) <=> (~lesseq(X!5, X!5))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.15/0.40 tff(22,plain,
% 0.15/0.40 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, X!5)),
% 0.15/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.15/0.40 tff(23,plain,
% 0.15/0.40 (lesseq(Y!4, X!5) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.15/0.41 inference(symmetry,[status(thm)],[22])).
% 0.15/0.41 tff(24,plain,
% 0.15/0.41 (lesseq(Y!4, max(X!5, Y!4))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[2, 23])).
% 0.15/0.41 tff(25,plain,
% 0.15/0.41 ((~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(26,plain,
% 0.15/0.41 (~lesseq(X!5, max(X!5, Y!4))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[25, 24, 1])).
% 0.15/0.41 tff(27,plain,
% 0.15/0.41 (~lesseq(X!5, X!5)),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.15/0.41 tff(28,plain,
% 0.15/0.41 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(29,plain,
% 0.15/0.41 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.15/0.41 tff(30,plain,
% 0.15/0.41 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(31,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lesseq_total')).
% 0.15/0.41 tff(32,plain,
% 0.15/0.41 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.15/0.41 tff(33,plain,(
% 0.15/0.41 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.15/0.41 inference(skolemize,[status(sab)],[32])).
% 0.15/0.41 tff(34,plain,
% 0.15/0.41 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.15/0.41 tff(35,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(36,plain,
% 0.15/0.41 ((lesseq(X!5, X!5) | lesseq(X!5, X!5)) <=> lesseq(X!5, X!5)),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(37,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[36])).
% 0.15/0.41 tff(38,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.15/0.41 inference(transitivity,[status(thm)],[37, 35])).
% 0.15/0.41 tff(39,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(40,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.15/0.41 tff(41,plain,
% 0.15/0.41 (lesseq(X!5, X!5)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.15/0.41 tff(42,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[41, 27])).
% 0.15/0.41 tff(43,plain,((~lesseq(Y!4, X!5)) | (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.41 tff(44,plain,
% 0.15/0.41 (~lesseq(Y!4, X!5)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[43, 1])).
% 0.15/0.41 tff(45,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(46,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(47,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5)),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.15/0.41 tff(48,plain,
% 0.15/0.41 (lesseq(X!5, Y!4)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[47, 34, 44])).
% 0.15/0.41 tff(49,plain,
% 0.15/0.41 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(50,plain,
% 0.15/0.41 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.15/0.41 tff(51,plain,
% 0.15/0.41 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(52,plain,
% 0.15/0.41 (^[X: $i, Y: $i] : 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(53,plain,
% 0.15/0.41 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.15/0.41 tff(54,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_2')).
% 0.15/0.41 tff(55,plain,
% 0.15/0.41 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.15/0.41 tff(56,plain,
% 0.15/0.41 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.15/0.41 tff(57,plain,(
% 0.15/0.41 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(skolemize,[status(sab)],[56])).
% 0.15/0.41 tff(58,plain,
% 0.15/0.41 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.15/0.41 tff(59,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(60,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(61,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.15/0.41 tff(62,plain,
% 0.15/0.41 ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.15/0.41 tff(63,plain,
% 0.15/0.41 (max(X!5, Y!4) = Y!4),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[62, 48])).
% 0.15/0.41 tff(64,plain,
% 0.15/0.41 (Y!4 = max(X!5, Y!4)),
% 0.15/0.41 inference(symmetry,[status(thm)],[63])).
% 0.15/0.41 tff(65,plain,
% 0.15/0.41 (lesseq(Y!4, Y!4) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[64])).
% 0.15/0.41 tff(66,plain,
% 0.15/0.41 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.15/0.41 inference(symmetry,[status(thm)],[65])).
% 0.15/0.41 tff(67,plain,
% 0.15/0.41 ((~lesseq(Y!4, max(X!5, Y!4))) <=> (~lesseq(Y!4, Y!4))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[66])).
% 0.15/0.41 tff(68,plain,
% 0.15/0.41 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, Y!4)),
% 0.15/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.15/0.41 tff(69,plain,
% 0.15/0.41 (lesseq(X!5, Y!4) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.15/0.41 inference(symmetry,[status(thm)],[68])).
% 0.15/0.41 tff(70,plain,
% 0.15/0.41 (lesseq(X!5, max(X!5, Y!4))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[48, 69])).
% 0.15/0.41 tff(71,plain,
% 0.15/0.41 (~lesseq(Y!4, max(X!5, Y!4))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[25, 70, 1])).
% 0.15/0.41 tff(72,plain,
% 0.15/0.41 (~lesseq(Y!4, Y!4)),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.15/0.41 tff(73,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(74,plain,
% 0.15/0.41 ((lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(75,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.15/0.41 tff(76,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.15/0.41 inference(transitivity,[status(thm)],[75, 73])).
% 0.15/0.41 tff(77,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(78,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.15/0.41 tff(79,plain,
% 0.15/0.41 (lesseq(Y!4, Y!4)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[78, 34])).
% 0.15/0.41 tff(80,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[79, 72])).
% 0.15/0.41 tff(81,plain,(~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.41 tff(82,plain,
% 0.15/0.41 (((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) | lesseq(X!5, max(X!5, Y!4))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(83,plain,
% 0.15/0.41 (lesseq(X!5, max(X!5, Y!4))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.15/0.41 tff(84,plain,
% 0.15/0.41 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(85,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(86,plain,
% 0.15/0.41 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.15/0.41 tff(87,plain,
% 0.15/0.41 (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[86, 58, 83])).
% 0.15/0.41 tff(88,plain,
% 0.15/0.41 (summation(max(X!5, max(X!5, Y!4))) = summation(max(X!5, Y!4))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[87])).
% 0.15/0.41 tff(89,plain,
% 0.15/0.41 (sum(c, summation(max(X!5, max(X!5, Y!4)))) = sum(c, summation(max(X!5, Y!4)))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.15/0.41 tff(90,plain,
% 0.15/0.41 (sum(c, summation(max(X!5, Y!4))) = sum(c, summation(max(X!5, max(X!5, Y!4))))),
% 0.15/0.41 inference(symmetry,[status(thm)],[89])).
% 0.15/0.41 tff(91,plain,
% 0.15/0.41 (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3)),
% 0.15/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.15/0.41 tff(92,plain,
% 0.15/0.41 (lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.15/0.41 inference(symmetry,[status(thm)],[91])).
% 0.15/0.41 tff(93,plain,
% 0.15/0.41 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)) <=> (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(94,plain,
% 0.15/0.41 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[93])).
% 0.15/0.41 tff(95,plain,
% 0.15/0.41 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(96,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_max_5')).
% 0.15/0.41 tff(97,plain,
% 0.15/0.41 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.15/0.41 tff(98,plain,(
% 0.15/0.41 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.15/0.41 inference(skolemize,[status(sab)],[97])).
% 0.15/0.41 tff(99,plain,
% 0.15/0.41 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.15/0.41 tff(100,plain,
% 0.15/0.41 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(101,plain,
% 0.15/0.41 (model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3)),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.15/0.41 tff(102,plain,
% 0.15/0.41 (^[X: $i, Y: $i, N: $i] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(103,plain,
% 0.15/0.41 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.15/0.41 tff(104,plain,
% 0.15/0.41 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(105,plain,
% 0.15/0.41 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[104])).
% 0.15/0.41 tff(106,plain,
% 0.15/0.41 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.15/0.41 tff(107,plain,
% 0.15/0.41 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))), rewrite((model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))) <=> (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(108,plain,
% 0.15/0.42 (![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.15/0.42 tff(109,plain,
% 0.15/0.42 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(110,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_ub_5')).
% 0.15/0.42 tff(111,plain,
% 0.15/0.42 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.15/0.42 tff(112,plain,(
% 0.15/0.42 ![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))))),
% 0.15/0.42 inference(skolemize,[status(sab)],[111])).
% 0.15/0.42 tff(113,plain,
% 0.15/0.42 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.15/0.42 tff(114,plain,
% 0.15/0.42 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.15/0.42 tff(115,plain,
% 0.15/0.42 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(116,plain,
% 0.15/0.42 ((~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))))) <=> (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(117,plain,
% 0.15/0.42 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[116])).
% 0.15/0.42 tff(118,plain,
% 0.15/0.42 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[117, 115])).
% 0.15/0.42 tff(119,plain,
% 0.15/0.42 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(120,plain,
% 0.15/0.42 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.15/0.43 tff(121,plain,
% 0.15/0.43 (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[120, 114])).
% 0.15/0.43 tff(122,plain,
% 0.15/0.43 (((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))))))) | (model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(123,plain,
% 0.15/0.43 (model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.15/0.43 tff(124,assumption,(max(X!5, Y!4) = X!5), introduced(assumption)).
% 0.15/0.43 tff(125,plain,
% 0.15/0.43 (model_ub(max(X!5, Y!4), Y!4, Z!3) <=> model_ub(X!5, Y!4, Z!3)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[124])).
% 0.15/0.43 tff(126,plain,
% 0.15/0.43 (model_ub(X!5, Y!4, Z!3) <=> model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.15/0.43 inference(symmetry,[status(thm)],[125])).
% 0.15/0.43 tff(127,plain,
% 0.15/0.43 ((~model_ub(X!5, Y!4, Z!3)) <=> (~model_ub(max(X!5, Y!4), Y!4, Z!3))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[126])).
% 0.15/0.43 tff(128,plain,
% 0.15/0.43 (((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) | lesseq(Y!4, max(X!5, Y!4))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(129,plain,
% 0.15/0.43 (lesseq(Y!4, max(X!5, Y!4))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[128, 81])).
% 0.15/0.43 tff(130,plain,
% 0.15/0.43 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(131,plain,
% 0.15/0.43 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(132,plain,
% 0.15/0.43 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.15/0.43 tff(133,plain,
% 0.15/0.43 (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[132, 12, 129])).
% 0.15/0.43 tff(134,plain,
% 0.15/0.43 (summation(max(max(X!5, Y!4), Y!4)) = summation(max(X!5, Y!4))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[133])).
% 0.15/0.43 tff(135,plain,
% 0.15/0.43 (sum(c, summation(max(max(X!5, Y!4), Y!4))) = sum(c, summation(max(X!5, Y!4)))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[134])).
% 0.15/0.43 tff(136,plain,
% 0.15/0.43 (sum(c, summation(max(X!5, Y!4))) = sum(c, summation(max(max(X!5, Y!4), Y!4)))),
% 0.15/0.43 inference(symmetry,[status(thm)],[135])).
% 0.15/0.43 tff(137,plain,
% 0.15/0.43 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.15/0.43 tff(138,plain,
% 0.15/0.43 (lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.43 inference(symmetry,[status(thm)],[137])).
% 0.15/0.43 tff(139,plain,
% 0.15/0.43 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(140,plain,
% 0.15/0.43 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[139, 99])).
% 0.15/0.43 tff(141,plain,
% 0.15/0.43 (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))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[124])).
% 0.15/0.43 tff(142,plain,
% 0.15/0.43 (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))),
% 0.15/0.43 inference(symmetry,[status(thm)],[141])).
% 0.15/0.43 tff(143,plain,
% 0.15/0.43 (^[X: $i, Y: $i, Z: $i] : refl((lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(144,plain,
% 0.15/0.43 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[143])).
% 0.15/0.43 tff(145,plain,
% 0.15/0.43 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(146,axiom,(![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sum_monotone_1')).
% 0.15/0.43 tff(147,plain,
% 0.15/0.43 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.15/0.43 tff(148,plain,(
% 0.15/0.43 ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.15/0.43 inference(skolemize,[status(sab)],[147])).
% 0.15/0.43 tff(149,plain,
% 0.15/0.43 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.15/0.43 tff(150,plain,
% 0.15/0.43 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(151,plain,
% 0.15/0.43 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.15/0.43 tff(152,plain,
% 0.15/0.43 (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.15/0.43 tff(153,plain,
% 0.15/0.43 (lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.15/0.43 inference(symmetry,[status(thm)],[152])).
% 0.15/0.43 tff(154,plain,
% 0.15/0.43 ((~lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3)) <=> (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[153])).
% 0.15/0.43 tff(155,plain,
% 0.15/0.43 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(156,plain,
% 0.15/0.43 (model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[155, 99])).
% 0.15/0.43 tff(157,plain,
% 0.15/0.43 (model_max(max(X!5, Y!4), Y!4, Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[124])).
% 0.15/0.43 tff(158,plain,
% 0.15/0.43 (model_max(X!5, Y!4, Z!3) <=> model_max(max(X!5, Y!4), Y!4, Z!3)),
% 0.15/0.43 inference(symmetry,[status(thm)],[157])).
% 0.15/0.43 tff(159,plain,
% 0.15/0.43 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(max(X!5, Y!4), Y!4, Z!3))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[158])).
% 0.15/0.43 tff(160,assumption,(~model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.15/0.43 tff(161,plain,
% 0.15/0.43 (~model_max(max(X!5, Y!4), Y!4, Z!3)),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.15/0.43 tff(162,plain,
% 0.15/0.43 ((~(model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3))) | model_max(max(X!5, Y!4), Y!4, Z!3) | (~lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(163,plain,
% 0.15/0.43 (~lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[162, 161, 156])).
% 0.15/0.43 tff(164,plain,
% 0.15/0.43 (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[163, 154])).
% 0.15/0.43 tff(165,plain,
% 0.15/0.43 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(166,plain,
% 0.15/0.43 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(167,plain,
% 0.15/0.43 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.15/0.43 tff(168,plain,
% 0.15/0.43 (lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[167, 34])).
% 0.15/0.43 tff(169,plain,
% 0.15/0.43 (lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[168, 164])).
% 0.15/0.43 tff(170,plain,
% 0.15/0.43 (tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[124])).
% 0.15/0.43 tff(171,plain,
% 0.15/0.43 (summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[170])).
% 0.15/0.43 tff(172,plain,
% 0.15/0.43 (sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) = sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[171])).
% 0.15/0.43 tff(173,plain,
% 0.15/0.43 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.15/0.43 inference(monotonicity,[status(thm)],[172])).
% 0.15/0.43 tff(174,plain,
% 0.15/0.43 (((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))))))) | ((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(175,plain,
% 0.15/0.43 ((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[174, 121])).
% 0.15/0.43 tff(176,plain,
% 0.15/0.43 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | model_max(X!5, Y!4, Z!3)),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(177,plain,
% 0.15/0.43 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[176, 160])).
% 0.15/0.43 tff(178,plain,
% 0.15/0.43 (^[X: $i, Y: $i, N: $i] : refl((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(179,plain,
% 0.15/0.43 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[178])).
% 0.15/0.43 tff(180,plain,
% 0.15/0.43 (^[X: $i, Y: $i, N: $i] : rewrite((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(181,plain,
% 0.15/0.43 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[180])).
% 0.15/0.43 tff(182,plain,
% 0.15/0.43 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[181, 179])).
% 0.15/0.43 tff(183,plain,
% 0.15/0.43 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) <=> ((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))), rewrite((minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))) <=> (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))), rewrite((((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(184,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[183])).
% 0.15/0.44 tff(185,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : rewrite((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))) <=> (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(186,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))) <=> ![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[185])).
% 0.15/0.44 tff(187,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(188,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : rewrite((minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z)))) <=> (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(189,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[188])).
% 0.15/0.44 tff(190,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_max')).
% 0.15/0.44 tff(191,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.15/0.44 tff(192,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.15/0.44 tff(193,plain,(
% 0.15/0.44 ![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.15/0.44 inference(skolemize,[status(sab)],[192])).
% 0.15/0.44 tff(194,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.15/0.44 tff(195,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[194, 184])).
% 0.15/0.44 tff(196,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[195, 182])).
% 0.15/0.44 tff(197,plain,
% 0.15/0.44 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(198,plain,
% 0.15/0.44 (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.15/0.44 tff(199,plain,
% 0.15/0.44 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(200,plain,
% 0.15/0.44 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.15/0.44 tff(201,plain,
% 0.15/0.44 ((~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(202,plain,
% 0.15/0.44 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.15/0.44 tff(203,plain,
% 0.15/0.44 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[202, 177])).
% 0.15/0.44 tff(204,plain,
% 0.15/0.44 ((~(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))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(205,plain,
% 0.15/0.44 ((~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))) <=> (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(206,axiom,(~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.15/0.44 tff(207,plain,
% 0.15/0.44 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.15/0.44 tff(208,plain,
% 0.15/0.44 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[207, 205])).
% 0.15/0.44 tff(209,plain,
% 0.15/0.44 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[208, 205])).
% 0.15/0.44 tff(210,plain,
% 0.15/0.44 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.15/0.44 tff(211,plain,
% 0.15/0.44 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[210, 205])).
% 0.15/0.44 tff(212,plain,
% 0.15/0.44 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[211, 205])).
% 0.15/0.44 tff(213,plain,
% 0.15/0.44 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.15/0.44 tff(214,plain,(
% 0.15/0.44 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.15/0.44 inference(skolemize,[status(sab)],[213])).
% 0.15/0.44 tff(215,plain,
% 0.15/0.44 ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[214, 204])).
% 0.15/0.44 tff(216,plain,
% 0.15/0.44 (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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(217,plain,
% 0.15/0.44 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.15/0.44 tff(218,plain,
% 0.15/0.44 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[217, 203])).
% 0.15/0.44 tff(219,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(220,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[219])).
% 0.15/0.44 tff(221,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : refl((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(222,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[221])).
% 0.15/0.44 tff(223,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(224,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[223])).
% 0.15/0.44 tff(225,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[224, 222])).
% 0.15/0.44 tff(226,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) <=> ((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))), rewrite((minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))) <=> (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))), rewrite((((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(227,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[226])).
% 0.15/0.44 tff(228,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : rewrite((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))) <=> (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(229,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))) <=> ![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[228])).
% 0.15/0.44 tff(230,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(231,plain,
% 0.15/0.44 (^[X: $i, Y: $i, N: $i] : rewrite((minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z)))) <=> (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(232,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[231])).
% 0.15/0.44 tff(233,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.15/0.44 tff(234,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.15/0.44 tff(235,plain,
% 0.15/0.44 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.15/0.44 tff(236,plain,(
% 0.15/0.44 ![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))),
% 0.15/0.45 inference(skolemize,[status(sab)],[235])).
% 0.15/0.45 tff(237,plain,
% 0.15/0.45 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.15/0.45 tff(238,plain,
% 0.15/0.45 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[237, 227])).
% 0.15/0.45 tff(239,plain,
% 0.15/0.45 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[238, 225])).
% 0.15/0.45 tff(240,plain,
% 0.15/0.45 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[239, 220])).
% 0.15/0.45 tff(241,plain,
% 0.15/0.45 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.15/0.45 inference(quant_inst,[status(thm)],[])).
% 0.15/0.45 tff(242,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(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.15/0.45 tff(243,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(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(244,plain,
% 0.15/0.45 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.15/0.45 tff(245,plain,
% 0.15/0.45 ((~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))) | (~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(246,plain,
% 0.15/0.45 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.15/0.45 tff(247,plain,
% 0.15/0.45 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[246, 218])).
% 0.15/0.45 tff(248,plain,
% 0.15/0.45 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | model_ub(X!5, Y!4, Z!3)),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(249,plain,
% 0.15/0.45 (model_ub(X!5, Y!4, Z!3)),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.15/0.45 tff(250,plain,
% 0.15/0.45 (model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[249, 126])).
% 0.15/0.45 tff(251,plain,
% 0.15/0.45 ((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))))) | (~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(252,plain,
% 0.15/0.45 (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[251, 250, 175])).
% 0.15/0.45 tff(253,plain,
% 0.15/0.45 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(254,plain,
% 0.15/0.45 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.15/0.45 tff(255,plain,
% 0.15/0.45 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[254, 173])).
% 0.15/0.45 tff(256,plain,
% 0.15/0.45 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(257,plain,
% 0.15/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((lesseq(X, Y) & lesseq(Y, Z)) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Y))))), ((~(lesseq(X, Y) & lesseq(Y, Z))) <=> (~(~((~lesseq(Y, Z)) | (~lesseq(X, Y))))))), rewrite((~(~((~lesseq(Y, Z)) | (~lesseq(X, Y))))) <=> ((~lesseq(Y, Z)) | (~lesseq(X, Y)))), ((~(lesseq(X, Y) & lesseq(Y, Z))) <=> ((~lesseq(Y, Z)) | (~lesseq(X, Y))))), (((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> (((~lesseq(Y, Z)) | (~lesseq(X, Y))) | lesseq(X, Z)))), rewrite((((~lesseq(Y, Z)) | (~lesseq(X, Y))) | lesseq(X, Z)) <=> (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))), (((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(258,plain,
% 0.15/0.45 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[257])).
% 0.15/0.45 tff(259,plain,
% 0.15/0.45 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(260,plain,
% 0.15/0.45 (^[X: $i, Y: $i, Z: $i] : rewrite(((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z)) <=> ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(261,plain,
% 0.15/0.45 (![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.15/0.45 inference(quant_intro,[status(thm)],[260])).
% 0.15/0.45 tff(262,axiom,(![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lesseq_trans')).
% 0.15/0.45 tff(263,plain,
% 0.15/0.45 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.15/0.45 tff(264,plain,
% 0.15/0.45 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.15/0.45 tff(265,plain,(
% 0.15/0.45 ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.15/0.45 inference(skolemize,[status(sab)],[264])).
% 0.15/0.45 tff(266,plain,
% 0.15/0.45 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.15/0.46 tff(267,plain,
% 0.15/0.46 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[266, 256])).
% 0.15/0.46 tff(268,plain,
% 0.15/0.46 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(269,plain,
% 0.15/0.46 ((lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))) <=> ((~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(270,plain,
% 0.15/0.46 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4))))))),
% 0.15/0.46 inference(monotonicity,[status(thm)],[269])).
% 0.15/0.46 tff(271,plain,
% 0.15/0.46 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.46 inference(transitivity,[status(thm)],[270, 268])).
% 0.15/0.46 tff(272,plain,
% 0.15/0.46 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(273,plain,
% 0.15/0.46 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.15/0.46 tff(274,plain,
% 0.15/0.46 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[273, 267, 255, 169])).
% 0.15/0.46 tff(275,plain,
% 0.15/0.46 ((~(lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(276,plain,
% 0.15/0.46 ((~(lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.15/0.46 tff(277,plain,
% 0.15/0.46 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[276, 151])).
% 0.15/0.46 tff(278,assumption,(~(lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))))), introduced(assumption)).
% 0.15/0.46 tff(279,plain,
% 0.15/0.46 (^[X: $i, Y: $i] : refl((lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))))),
% 0.15/0.46 inference(bind,[status(th)],[])).
% 0.15/0.46 tff(280,plain,
% 0.15/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.15/0.46 inference(quant_intro,[status(thm)],[279])).
% 0.15/0.46 tff(281,plain,
% 0.15/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(282,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','summation_monotone')).
% 0.15/0.46 tff(283,plain,
% 0.15/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.15/0.46 tff(284,plain,(
% 0.15/0.46 ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.15/0.46 inference(skolemize,[status(sab)],[283])).
% 0.15/0.46 tff(285,plain,
% 0.15/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.15/0.46 tff(286,plain,
% 0.15/0.46 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(287,plain,
% 0.15/0.46 ($false),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[286, 285, 278])).
% 0.15/0.46 tff(288,plain,(lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.46 tff(289,plain,
% 0.15/0.46 ((~(lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(290,plain,
% 0.15/0.46 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) | (~lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.15/0.46 tff(291,plain,
% 0.15/0.46 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[290, 277])).
% 0.15/0.46 tff(292,plain,
% 0.15/0.46 (^[X: $i, Y: $i, Z: $i] : refl((ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))) <=> (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))))),
% 0.15/0.46 inference(bind,[status(th)],[])).
% 0.15/0.46 tff(293,plain,
% 0.15/0.46 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))) <=> ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.15/0.46 inference(quant_intro,[status(thm)],[292])).
% 0.15/0.46 tff(294,plain,
% 0.15/0.46 (^[X: $i, Y: $i, Z: $i] : rewrite((ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))))),
% 0.15/0.46 inference(bind,[status(th)],[])).
% 0.15/0.46 tff(295,plain,
% 0.15/0.46 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.15/0.46 inference(quant_intro,[status(thm)],[294])).
% 0.15/0.46 tff(296,plain,
% 0.15/0.46 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(297,axiom,(![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ub')).
% 0.15/0.46 tff(298,plain,
% 0.15/0.46 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.15/0.46 tff(299,plain,(
% 0.15/0.46 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.15/0.46 inference(skolemize,[status(sab)],[298])).
% 0.15/0.46 tff(300,plain,
% 0.15/0.46 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[299, 295])).
% 0.15/0.46 tff(301,plain,
% 0.15/0.46 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.15/0.46 tff(302,plain,
% 0.15/0.46 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(303,plain,
% 0.15/0.46 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.15/0.46 tff(304,plain,
% 0.15/0.46 (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))),
% 0.15/0.46 inference(monotonicity,[status(thm)],[124])).
% 0.15/0.46 tff(305,plain,
% 0.15/0.46 (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))),
% 0.15/0.46 inference(symmetry,[status(thm)],[304])).
% 0.15/0.46 tff(306,plain,
% 0.15/0.46 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.46 inference(monotonicity,[status(thm)],[124, 170])).
% 0.15/0.46 tff(307,assumption,(~minsol_model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.15/0.46 tff(308,plain,
% 0.15/0.46 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[217, 307])).
% 0.15/0.46 tff(309,plain,
% 0.15/0.46 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[246, 308])).
% 0.15/0.46 tff(310,plain,
% 0.15/0.46 (model_ub(X!5, Y!4, Z!3)),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[248, 309])).
% 0.15/0.46 tff(311,plain,
% 0.15/0.46 (model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[310, 126])).
% 0.15/0.46 tff(312,plain,
% 0.15/0.46 (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[251, 311, 175])).
% 0.15/0.46 tff(313,plain,
% 0.15/0.46 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3))) | ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(314,plain,
% 0.15/0.46 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.15/0.46 tff(315,plain,
% 0.15/0.46 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[314, 306])).
% 0.15/0.46 tff(316,plain,
% 0.15/0.46 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[315, 305])).
% 0.15/0.46 tff(317,plain,
% 0.15/0.46 ((~(ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(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))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(318,plain,
% 0.15/0.46 (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[317, 316, 303])).
% 0.15/0.46 tff(319,plain,
% 0.15/0.46 (((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(320,plain,
% 0.15/0.46 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.15/0.47 tff(321,plain,
% 0.15/0.47 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(322,plain,
% 0.15/0.47 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.47 inference(quant_inst,[status(thm)],[])).
% 0.15/0.47 tff(323,plain,
% 0.15/0.47 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.15/0.47 tff(324,plain,
% 0.15/0.47 (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[323, 58, 320])).
% 0.15/0.47 tff(325,assumption,(max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4)), introduced(assumption)).
% 0.15/0.47 tff(326,plain,
% 0.15/0.47 (max(X!5, Y!4) = max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.47 inference(symmetry,[status(thm)],[325])).
% 0.15/0.47 tff(327,plain,
% 0.15/0.47 (X!5 = max(X!5, Y!4)),
% 0.15/0.47 inference(symmetry,[status(thm)],[124])).
% 0.15/0.47 tff(328,plain,
% 0.15/0.47 (X!5 = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.47 inference(transitivity,[status(thm)],[327, 326, 324])).
% 0.15/0.47 tff(329,plain,
% 0.15/0.47 (minsol_model_max(X!5, Y!4, Z!3) <=> minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)),
% 0.15/0.47 inference(monotonicity,[status(thm)],[328])).
% 0.15/0.47 tff(330,plain,
% 0.15/0.47 (minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.47 inference(symmetry,[status(thm)],[329])).
% 0.15/0.47 tff(331,plain,
% 0.15/0.47 (((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z))))))))))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(332,plain,
% 0.15/0.47 ((~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z))))))))) <=> (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(333,plain,
% 0.15/0.47 (((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z))))))))))),
% 0.15/0.47 inference(monotonicity,[status(thm)],[332])).
% 0.15/0.47 tff(334,plain,
% 0.15/0.47 (((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z))))))))))),
% 0.15/0.47 inference(transitivity,[status(thm)],[333, 331])).
% 0.15/0.47 tff(335,plain,
% 0.15/0.47 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(336,plain,
% 0.15/0.48 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.15/0.48 tff(337,plain,
% 0.15/0.48 (~((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z))))))))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[336, 196])).
% 0.15/0.48 tff(338,plain,
% 0.15/0.48 (((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | (~![Z: $i] : ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z)) | lesseq(Z!3, Z)))))))) | ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(339,plain,
% 0.15/0.48 ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[338, 337])).
% 0.15/0.48 tff(340,plain,
% 0.15/0.48 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), Z!3))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(341,plain,
% 0.15/0.48 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), Z!3)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[340, 99])).
% 0.15/0.48 tff(342,plain,
% 0.15/0.48 (sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) = sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))))),
% 0.15/0.48 inference(symmetry,[status(thm)],[172])).
% 0.15/0.48 tff(343,plain,
% 0.15/0.48 (((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(344,plain,
% 0.15/0.48 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[343, 318])).
% 0.15/0.48 tff(345,plain,
% 0.15/0.48 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(346,plain,
% 0.15/0.48 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(347,plain,
% 0.15/0.48 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.15/0.48 tff(348,plain,
% 0.15/0.48 (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[347, 12, 344])).
% 0.15/0.48 tff(349,plain,
% 0.15/0.48 (summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[348])).
% 0.15/0.48 tff(350,plain,
% 0.15/0.48 (sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))) = sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[349])).
% 0.15/0.48 tff(351,plain,
% 0.15/0.48 (sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))) = sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))))),
% 0.15/0.48 inference(transitivity,[status(thm)],[350, 342])).
% 0.15/0.48 tff(352,plain,
% 0.15/0.48 (lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), Z!3) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)),
% 0.15/0.48 inference(monotonicity,[status(thm)],[351])).
% 0.15/0.48 tff(353,plain,
% 0.15/0.48 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), Z!3)),
% 0.15/0.48 inference(symmetry,[status(thm)],[352])).
% 0.15/0.48 tff(354,plain,
% 0.15/0.48 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))), Z!3)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[253, 312])).
% 0.15/0.48 tff(355,plain,
% 0.15/0.48 (lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), Z!3)),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.15/0.48 tff(356,plain,
% 0.15/0.48 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), Z!3))) | model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), Z!3))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(357,plain,
% 0.15/0.48 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[356, 355, 341])).
% 0.15/0.48 tff(358,plain,
% 0.15/0.48 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | ![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(359,plain,
% 0.15/0.48 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[358, 309])).
% 0.15/0.48 tff(360,plain,
% 0.15/0.48 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(361,plain,
% 0.15/0.48 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[360, 301])).
% 0.15/0.48 tff(362,assumption,(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.15/0.48 tff(363,plain,
% 0.15/0.48 ((~(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(364,plain,
% 0.15/0.48 ((~(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[363, 362])).
% 0.15/0.48 tff(365,plain,
% 0.15/0.48 (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[364, 361])).
% 0.15/0.48 tff(366,plain,
% 0.15/0.48 (((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(367,plain,
% 0.15/0.48 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[366, 365])).
% 0.15/0.48 tff(368,plain,
% 0.15/0.48 (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[347, 12, 367])).
% 0.15/0.48 tff(369,plain,
% 0.15/0.48 (summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[368])).
% 0.15/0.48 tff(370,plain,
% 0.15/0.48 (sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))) = sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[369])).
% 0.15/0.48 tff(371,plain,
% 0.15/0.48 (sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) = sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)))),
% 0.15/0.48 inference(symmetry,[status(thm)],[370])).
% 0.15/0.48 tff(372,plain,
% 0.15/0.48 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(monotonicity,[status(thm)],[371])).
% 0.15/0.48 tff(373,plain,
% 0.15/0.48 (lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(symmetry,[status(thm)],[372])).
% 0.15/0.48 tff(374,plain,
% 0.15/0.48 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(375,plain,
% 0.15/0.48 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[374, 99])).
% 0.15/0.48 tff(376,assumption,(~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))), introduced(assumption)).
% 0.15/0.48 tff(377,plain,
% 0.15/0.48 (((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(378,plain,
% 0.15/0.48 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[377, 376])).
% 0.15/0.48 tff(379,plain,
% 0.15/0.48 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(380,plain,
% 0.15/0.49 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))) | lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[379, 378])).
% 0.15/0.49 tff(381,plain,
% 0.15/0.49 (lesseq(sum(c, summation(max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[380, 375])).
% 0.15/0.49 tff(382,plain,
% 0.15/0.49 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[381, 373])).
% 0.15/0.49 tff(383,plain,
% 0.15/0.49 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(384,plain,
% 0.15/0.49 (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[383, 114])).
% 0.15/0.49 tff(385,plain,
% 0.15/0.49 (((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)), Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(386,plain,
% 0.15/0.49 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[385, 384])).
% 0.15/0.49 tff(387,plain,
% 0.15/0.49 (((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(388,plain,
% 0.15/0.49 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[387, 376])).
% 0.15/0.49 tff(389,assumption,(![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.15/0.49 tff(390,plain,
% 0.15/0.49 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(391,plain,
% 0.15/0.49 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(392,plain,
% 0.15/0.49 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.15/0.49 tff(393,plain,
% 0.15/0.49 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[392, 389, 388])).
% 0.15/0.49 tff(394,plain,
% 0.15/0.49 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(395,plain,
% 0.15/0.49 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.15/0.49 tff(396,plain,
% 0.15/0.49 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[395, 386])).
% 0.15/0.49 tff(397,plain,
% 0.15/0.49 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, 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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, 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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(398,plain,
% 0.15/0.49 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, 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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(399,plain,
% 0.15/0.49 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.15/0.49 tff(400,plain,
% 0.15/0.49 ($false),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[399, 362, 396, 382])).
% 0.15/0.49 tff(401,plain,(((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, 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))) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.50 tff(402,plain,
% 0.15/0.50 ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[401, 315, 359])).
% 0.15/0.50 tff(403,plain,
% 0.15/0.50 ((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(404,plain,
% 0.15/0.50 ((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[403, 402])).
% 0.15/0.50 tff(405,plain,
% 0.15/0.50 (minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[404, 357, 339])).
% 0.15/0.50 tff(406,plain,
% 0.15/0.50 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[405, 330])).
% 0.15/0.50 tff(407,plain,
% 0.15/0.50 ($false),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[307, 406])).
% 0.15/0.50 tff(408,plain,((~(max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4))) | minsol_model_max(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.50 tff(409,plain,
% 0.15/0.50 (~(max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[408, 203, 124])).
% 0.15/0.50 tff(410,plain,
% 0.15/0.50 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4)))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(411,plain,
% 0.15/0.50 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4)))),
% 0.15/0.50 inference(quant_inst,[status(thm)],[])).
% 0.15/0.50 tff(412,plain,
% 0.15/0.50 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.15/0.50 tff(413,plain,
% 0.15/0.50 ($false),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[412, 12, 409, 291])).
% 0.15/0.50 tff(414,plain,(model_max(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.50 tff(415,plain,
% 0.15/0.50 (model_max(X!5, Y!4, Z!3)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[414, 124])).
% 0.15/0.50 tff(416,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(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(417,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(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[416, 198])).
% 0.15/0.50 tff(418,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(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(419,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(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[418, 417])).
% 0.15/0.50 tff(420,plain,
% 0.15/0.50 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[419, 307, 415])).
% 0.15/0.50 tff(421,plain,
% 0.15/0.50 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) | model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(422,plain,
% 0.15/0.50 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[421, 420])).
% 0.15/0.50 tff(423,plain,
% 0.15/0.50 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[422, 142])).
% 0.15/0.50 tff(424,plain,
% 0.15/0.50 ((~(model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), 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))) | lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(425,plain,
% 0.15/0.50 (lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[424, 423, 140])).
% 0.15/0.50 tff(426,plain,
% 0.15/0.50 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[425, 138])).
% 0.15/0.50 tff(427,plain,
% 0.15/0.50 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))),
% 0.15/0.50 inference(quant_inst,[status(thm)],[])).
% 0.15/0.50 tff(428,plain,
% 0.15/0.50 (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5)))))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[427, 114])).
% 0.15/0.50 tff(429,plain,
% 0.15/0.50 (((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(430,plain,
% 0.15/0.50 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[429, 428])).
% 0.15/0.51 tff(431,plain,
% 0.15/0.51 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(monotonicity,[status(thm)],[124])).
% 0.15/0.51 tff(432,plain,
% 0.15/0.51 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(symmetry,[status(thm)],[431])).
% 0.15/0.51 tff(433,plain,
% 0.15/0.51 ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) <=> (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.15/0.51 inference(monotonicity,[status(thm)],[432])).
% 0.15/0.51 tff(434,plain,
% 0.15/0.51 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(435,plain,
% 0.15/0.51 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[434, 420])).
% 0.15/0.51 tff(436,plain,
% 0.15/0.51 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.15/0.51 inference(rewrite,[status(thm)],[])).
% 0.15/0.51 tff(437,plain,
% 0.15/0.51 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(438,plain,
% 0.15/0.51 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.15/0.51 tff(439,plain,
% 0.15/0.51 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[438, 435, 359])).
% 0.15/0.51 tff(440,plain,
% 0.15/0.51 (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[439, 433])).
% 0.15/0.51 tff(441,plain,
% 0.15/0.51 ((~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(442,plain,
% 0.15/0.51 (![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[441, 440, 430])).
% 0.15/0.51 tff(443,plain,
% 0.15/0.51 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.15/0.51 inference(monotonicity,[status(thm)],[327])).
% 0.15/0.51 tff(444,plain,
% 0.15/0.51 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[83, 443])).
% 0.15/0.51 tff(445,plain,
% 0.15/0.51 ((~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(446,plain,
% 0.15/0.51 ((~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[445, 129])).
% 0.15/0.51 tff(447,plain,
% 0.15/0.51 (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[446, 444])).
% 0.15/0.51 tff(448,assumption,(~(ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))), introduced(assumption)).
% 0.15/0.51 tff(449,plain,
% 0.15/0.51 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(450,plain,
% 0.15/0.51 ($false),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[449, 301, 448])).
% 0.15/0.51 tff(451,plain,(ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.51 tff(452,plain,
% 0.15/0.51 ((~(ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))) | ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(453,plain,
% 0.15/0.51 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[452, 451])).
% 0.15/0.51 tff(454,plain,
% 0.15/0.51 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[453, 447])).
% 0.15/0.51 tff(455,plain,
% 0.15/0.51 (((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.51 inference(rewrite,[status(thm)],[])).
% 0.15/0.51 tff(456,plain,
% 0.15/0.51 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.15/0.51 inference(quant_inst,[status(thm)],[])).
% 0.15/0.51 tff(457,plain,
% 0.15/0.51 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.15/0.51 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.15/0.51 tff(458,plain,
% 0.15/0.51 ($false),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[457, 454, 442, 426])).
% 0.15/0.51 tff(459,plain,(minsol_model_max(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.51 tff(460,plain,
% 0.15/0.51 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[459, 124])).
% 0.15/0.51 tff(461,plain,
% 0.15/0.51 ((~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)))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(462,plain,
% 0.15/0.51 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[461, 215])).
% 0.15/0.51 tff(463,plain,
% 0.15/0.51 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[462, 460])).
% 0.15/0.51 tff(464,plain,
% 0.15/0.51 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[202, 460])).
% 0.15/0.51 tff(465,plain,
% 0.15/0.51 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | ![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(466,plain,
% 0.15/0.51 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[465, 464])).
% 0.15/0.51 tff(467,assumption,(![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.15/0.51 tff(468,assumption,(~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))), introduced(assumption)).
% 0.15/0.51 tff(469,plain,
% 0.15/0.51 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) | model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(470,plain,
% 0.15/0.51 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.51 inference(unit_resolution,[status(thm)],[469, 468])).
% 0.15/0.51 tff(471,plain,
% 0.15/0.51 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.51 inference(tautology,[status(thm)],[])).
% 0.15/0.51 tff(472,plain,
% 0.15/0.51 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[471, 468])).
% 0.15/0.52 tff(473,plain,
% 0.15/0.52 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(474,plain,
% 0.15/0.52 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[473, 99])).
% 0.15/0.52 tff(475,plain,
% 0.15/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(476,plain,
% 0.15/0.52 (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4)))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[475, 285])).
% 0.15/0.52 tff(477,plain,
% 0.15/0.52 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(478,plain,
% 0.15/0.52 (lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[477, 149])).
% 0.15/0.52 tff(479,plain,
% 0.15/0.52 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(480,plain,
% 0.15/0.52 (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[479, 99])).
% 0.15/0.52 tff(481,assumption,(~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.15/0.52 tff(482,plain,
% 0.15/0.52 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.52 inference(rewrite,[status(thm)],[])).
% 0.15/0.52 tff(483,plain,
% 0.15/0.52 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(484,plain,
% 0.15/0.52 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.15/0.52 tff(485,plain,
% 0.15/0.52 (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[484, 467, 481])).
% 0.15/0.52 tff(486,plain,
% 0.15/0.52 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.52 inference(tautology,[status(thm)],[])).
% 0.15/0.52 tff(487,plain,
% 0.15/0.52 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[486, 485])).
% 0.15/0.52 tff(488,plain,
% 0.15/0.52 (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[487, 480])).
% 0.15/0.52 tff(489,plain,
% 0.15/0.52 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.52 inference(rewrite,[status(thm)],[])).
% 0.15/0.52 tff(490,plain,
% 0.15/0.52 ((lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.52 inference(rewrite,[status(thm)],[])).
% 0.15/0.52 tff(491,plain,
% 0.15/0.52 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))))),
% 0.15/0.52 inference(monotonicity,[status(thm)],[490])).
% 0.15/0.52 tff(492,plain,
% 0.15/0.52 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.52 inference(transitivity,[status(thm)],[491, 489])).
% 0.15/0.52 tff(493,plain,
% 0.15/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(494,plain,
% 0.15/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.15/0.52 tff(495,plain,
% 0.15/0.52 (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[494, 34, 488])).
% 0.15/0.52 tff(496,plain,
% 0.15/0.52 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.15/0.52 inference(quant_inst,[status(thm)],[])).
% 0.15/0.52 tff(497,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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))),
% 0.15/0.52 inference(unit_resolution,[status(thm)],[496, 114])).
% 0.15/0.52 tff(498,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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(499,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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[498, 497])).
% 0.15/0.53 tff(500,assumption,(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.15/0.53 tff(501,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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(502,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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[501, 500])).
% 0.15/0.53 tff(503,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(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[502, 499])).
% 0.15/0.53 tff(504,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(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(505,plain,
% 0.15/0.53 (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[504, 503])).
% 0.15/0.53 tff(506,plain,
% 0.15/0.53 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))))),
% 0.15/0.53 inference(rewrite,[status(thm)],[])).
% 0.15/0.53 tff(507,plain,
% 0.15/0.53 ((lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))))),
% 0.15/0.53 inference(rewrite,[status(thm)],[])).
% 0.15/0.53 tff(508,plain,
% 0.15/0.53 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))))))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[507])).
% 0.15/0.53 tff(509,plain,
% 0.15/0.53 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))))),
% 0.15/0.53 inference(transitivity,[status(thm)],[508, 506])).
% 0.15/0.53 tff(510,plain,
% 0.15/0.53 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4))))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.15/0.53 inference(quant_inst,[status(thm)],[])).
% 0.15/0.53 tff(511,plain,
% 0.15/0.53 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.53 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.15/0.53 tff(512,plain,
% 0.15/0.53 (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[511, 267, 505, 495])).
% 0.15/0.53 tff(513,plain,
% 0.15/0.53 ((~(lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))) | lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(514,plain,
% 0.15/0.53 ((~(lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))) | lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4)))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[513, 512])).
% 0.15/0.53 tff(515,plain,
% 0.15/0.53 (lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4)))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[514, 478])).
% 0.15/0.53 tff(516,plain,
% 0.15/0.53 ((~(lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))))),
% 0.15/0.53 inference(tautology,[status(thm)],[])).
% 0.15/0.53 tff(517,plain,
% 0.15/0.53 ((~(lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) <=> lesseq(summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), summation(max(X!5, Y!4))))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[516, 515])).
% 0.15/0.53 tff(518,plain,
% 0.15/0.53 (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[517, 476])).
% 0.15/0.53 tff(519,plain,
% 0.15/0.53 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.15/0.53 inference(rewrite,[status(thm)],[])).
% 0.15/0.53 tff(520,plain,
% 0.15/0.53 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.15/0.53 inference(quant_inst,[status(thm)],[])).
% 0.15/0.53 tff(521,plain,
% 0.15/0.53 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4))),
% 0.15/0.53 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.15/0.53 tff(522,plain,
% 0.15/0.53 (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)),
% 0.15/0.53 inference(unit_resolution,[status(thm)],[521, 58, 518])).
% 0.15/0.53 tff(523,plain,
% 0.15/0.53 (summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) = summation(max(X!5, Y!4))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[522])).
% 0.15/0.53 tff(524,plain,
% 0.15/0.53 (sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))) = sum(c, summation(max(X!5, Y!4)))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[523])).
% 0.15/0.53 tff(525,plain,
% 0.15/0.53 (lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[524])).
% 0.15/0.53 tff(526,plain,
% 0.15/0.53 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.53 inference(symmetry,[status(thm)],[525])).
% 0.15/0.53 tff(527,plain,
% 0.15/0.53 ((~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.53 inference(monotonicity,[status(thm)],[526])).
% 0.15/0.53 tff(528,plain,
% 0.15/0.53 (~lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.53 inference(modus_ponens,[status(thm)],[488, 527])).
% 0.15/0.53 tff(529,plain,
% 0.15/0.53 ((~(model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | (~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(530,plain,
% 0.15/0.54 (~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[529, 528, 474])).
% 0.15/0.54 tff(531,plain,
% 0.15/0.54 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.54 inference(quant_inst,[status(thm)],[])).
% 0.15/0.54 tff(532,plain,
% 0.15/0.54 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[531, 99])).
% 0.15/0.54 tff(533,plain,
% 0.15/0.54 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))),
% 0.15/0.54 inference(quant_inst,[status(thm)],[])).
% 0.15/0.54 tff(534,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)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[533, 301])).
% 0.15/0.54 tff(535,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))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(536,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))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[535, 503])).
% 0.15/0.54 tff(537,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)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(538,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)) <=> (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[537, 536])).
% 0.15/0.54 tff(539,plain,
% 0.15/0.54 (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[538, 534])).
% 0.15/0.54 tff(540,plain,
% 0.15/0.54 (((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(541,plain,
% 0.15/0.54 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[540, 539])).
% 0.15/0.54 tff(542,plain,
% 0.15/0.54 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.15/0.54 inference(rewrite,[status(thm)],[])).
% 0.15/0.54 tff(543,plain,
% 0.15/0.54 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.15/0.54 inference(quant_inst,[status(thm)],[])).
% 0.15/0.54 tff(544,plain,
% 0.15/0.54 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.54 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.15/0.54 tff(545,plain,
% 0.15/0.54 (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[544, 12, 541])).
% 0.15/0.54 tff(546,plain,
% 0.15/0.54 (summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4)) = summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.54 inference(monotonicity,[status(thm)],[545])).
% 0.15/0.54 tff(547,plain,
% 0.15/0.54 (sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))) = sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.15/0.54 inference(monotonicity,[status(thm)],[546])).
% 0.15/0.54 tff(548,plain,
% 0.15/0.54 (lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(monotonicity,[status(thm)],[547])).
% 0.15/0.54 tff(549,plain,
% 0.15/0.54 (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(symmetry,[status(thm)],[548])).
% 0.15/0.54 tff(550,plain,
% 0.15/0.54 (lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(modus_ponens,[status(thm)],[505, 549])).
% 0.15/0.54 tff(551,plain,
% 0.15/0.54 ((~(model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.54 inference(tautology,[status(thm)],[])).
% 0.15/0.54 tff(552,plain,
% 0.15/0.54 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(unit_resolution,[status(thm)],[551, 550, 532])).
% 0.15/0.54 tff(553,assumption,(max(X!5, Y!4) = Y!4), introduced(assumption)).
% 0.15/0.54 tff(554,plain,
% 0.15/0.54 (Y!4 = max(X!5, Y!4)),
% 0.15/0.54 inference(symmetry,[status(thm)],[553])).
% 0.15/0.54 tff(555,plain,
% 0.15/0.54 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(monotonicity,[status(thm)],[554])).
% 0.15/0.54 tff(556,plain,
% 0.15/0.54 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.54 inference(symmetry,[status(thm)],[555])).
% 0.15/0.54 tff(557,plain,
% 0.15/0.54 ((~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.54 inference(monotonicity,[status(thm)],[556])).
% 0.15/0.54 tff(558,assumption,(~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.15/0.54 tff(559,plain,
% 0.15/0.55 (~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.15/0.55 tff(560,assumption,(model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.15/0.55 tff(561,plain,
% 0.15/0.55 ($false),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[560, 559])).
% 0.15/0.55 tff(562,plain,((~(max(X!5, Y!4) = Y!4)) | (~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.55 tff(563,plain,
% 0.15/0.55 (~(max(X!5, Y!4) = Y!4)),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[562, 552, 530])).
% 0.15/0.55 tff(564,plain,
% 0.15/0.55 (~lesseq(X!5, Y!4)),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[62, 563])).
% 0.15/0.55 tff(565,plain,
% 0.15/0.55 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, X!5) | lesseq(X!5, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, X!5) | lesseq(X!5, Y!4))),
% 0.15/0.55 inference(rewrite,[status(thm)],[])).
% 0.15/0.55 tff(566,plain,
% 0.15/0.55 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, X!5) | lesseq(X!5, Y!4))),
% 0.15/0.55 inference(quant_inst,[status(thm)],[])).
% 0.15/0.55 tff(567,plain,
% 0.15/0.55 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, X!5) | lesseq(X!5, Y!4)),
% 0.15/0.55 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.15/0.55 tff(568,plain,
% 0.15/0.55 (lesseq(Y!4, X!5)),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[567, 34, 564])).
% 0.15/0.55 tff(569,plain,
% 0.15/0.55 (max(X!5, Y!4) = X!5),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[16, 568])).
% 0.15/0.55 tff(570,plain,
% 0.15/0.55 (X!5 = max(X!5, Y!4)),
% 0.15/0.55 inference(symmetry,[status(thm)],[569])).
% 0.15/0.55 tff(571,plain,
% 0.15/0.55 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(monotonicity,[status(thm)],[570])).
% 0.15/0.55 tff(572,plain,
% 0.15/0.55 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(symmetry,[status(thm)],[571])).
% 0.15/0.55 tff(573,plain,
% 0.15/0.55 ((~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.55 inference(monotonicity,[status(thm)],[572])).
% 0.15/0.55 tff(574,plain,
% 0.15/0.55 (~model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(modus_ponens,[status(thm)],[530, 573])).
% 0.15/0.55 tff(575,plain,
% 0.15/0.55 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.55 inference(quant_inst,[status(thm)],[])).
% 0.15/0.55 tff(576,plain,
% 0.15/0.55 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[575, 99])).
% 0.15/0.55 tff(577,plain,
% 0.15/0.55 (((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.55 inference(tautology,[status(thm)],[])).
% 0.15/0.55 tff(578,plain,
% 0.15/0.55 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[577, 539])).
% 0.15/0.55 tff(579,plain,
% 0.15/0.55 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.15/0.55 inference(rewrite,[status(thm)],[])).
% 0.15/0.55 tff(580,plain,
% 0.15/0.55 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.15/0.55 inference(quant_inst,[status(thm)],[])).
% 0.15/0.55 tff(581,plain,
% 0.15/0.55 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.55 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.15/0.55 tff(582,plain,
% 0.15/0.55 (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[581, 12, 578])).
% 0.15/0.55 tff(583,plain,
% 0.15/0.55 (summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5)) = summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.15/0.55 inference(monotonicity,[status(thm)],[582])).
% 0.15/0.55 tff(584,plain,
% 0.15/0.55 (sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))) = sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.15/0.55 inference(monotonicity,[status(thm)],[583])).
% 0.15/0.55 tff(585,plain,
% 0.15/0.55 (lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(monotonicity,[status(thm)],[584])).
% 0.15/0.55 tff(586,plain,
% 0.15/0.55 (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(symmetry,[status(thm)],[585])).
% 0.15/0.55 tff(587,plain,
% 0.15/0.55 (lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(modus_ponens,[status(thm)],[505, 586])).
% 0.15/0.55 tff(588,plain,
% 0.15/0.55 ((~(model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.15/0.55 inference(tautology,[status(thm)],[])).
% 0.15/0.55 tff(589,plain,
% 0.15/0.55 (model_max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[588, 587, 576])).
% 0.15/0.55 tff(590,plain,
% 0.15/0.55 ($false),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[589, 574])).
% 0.15/0.55 tff(591,plain,((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.55 tff(592,plain,
% 0.15/0.55 ($false),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[591, 472, 470, 467])).
% 0.15/0.55 tff(593,plain,(((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.55 tff(594,plain,
% 0.15/0.55 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.15/0.55 inference(unit_resolution,[status(thm)],[593, 466])).
% 0.15/0.55 tff(595,plain,
% 0.15/0.55 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.15/0.56 inference(tautology,[status(thm)],[])).
% 0.15/0.56 tff(596,plain,
% 0.15/0.56 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[595, 242])).
% 0.15/0.56 tff(597,plain,
% 0.15/0.56 ((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.15/0.56 inference(tautology,[status(thm)],[])).
% 0.15/0.56 tff(598,plain,
% 0.15/0.56 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[597, 596])).
% 0.15/0.56 tff(599,plain,
% 0.15/0.56 (~model_ub(X!5, Y!4, Z!3)),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[598, 594, 463])).
% 0.15/0.56 tff(600,plain,
% 0.15/0.56 (~model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.15/0.56 inference(modus_ponens,[status(thm)],[599, 127])).
% 0.15/0.56 tff(601,plain,
% 0.15/0.56 ((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.15/0.56 inference(tautology,[status(thm)],[])).
% 0.15/0.56 tff(602,plain,
% 0.15/0.56 (![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[601, 600, 123])).
% 0.15/0.56 tff(603,plain,
% 0.15/0.56 (model_max(max(X!5, Y!4), Y!4, Z!3)),
% 0.15/0.56 inference(modus_ponens,[status(thm)],[415, 158])).
% 0.15/0.56 tff(604,plain,
% 0.15/0.56 ((~(model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3))) | (~model_max(max(X!5, Y!4), Y!4, Z!3)) | lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3)),
% 0.15/0.56 inference(tautology,[status(thm)],[])).
% 0.15/0.56 tff(605,plain,
% 0.15/0.56 (lesseq(sum(c, summation(max(max(X!5, Y!4), Y!4))), Z!3)),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[604, 603, 156])).
% 0.15/0.56 tff(606,plain,
% 0.15/0.56 (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.15/0.56 inference(modus_ponens,[status(thm)],[605, 153])).
% 0.15/0.56 tff(607,plain,
% 0.15/0.56 (((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | ((~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))) <=> ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))),
% 0.15/0.56 inference(rewrite,[status(thm)],[])).
% 0.15/0.56 tff(608,plain,
% 0.15/0.56 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | ((~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))),
% 0.15/0.56 inference(quant_inst,[status(thm)],[])).
% 0.15/0.56 tff(609,plain,
% 0.15/0.56 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.15/0.56 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.15/0.56 tff(610,plain,
% 0.15/0.56 ($false),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[609, 454, 606, 602])).
% 0.15/0.56 tff(611,plain,(~(max(X!5, Y!4) = X!5)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.56 tff(612,plain,
% 0.15/0.56 (~lesseq(Y!4, X!5)),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[16, 611])).
% 0.15/0.56 tff(613,plain,
% 0.15/0.56 (lesseq(X!5, Y!4)),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[47, 34, 612])).
% 0.15/0.56 tff(614,plain,
% 0.15/0.56 (max(X!5, Y!4) = Y!4),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[62, 613])).
% 0.15/0.56 tff(615,plain,
% 0.15/0.56 (model_max(X!5, max(X!5, Y!4), Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.15/0.56 inference(monotonicity,[status(thm)],[614])).
% 0.15/0.56 tff(616,plain,
% 0.15/0.56 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.15/0.56 inference(symmetry,[status(thm)],[615])).
% 0.15/0.56 tff(617,plain,
% 0.15/0.56 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))),
% 0.15/0.56 inference(rewrite,[status(thm)],[])).
% 0.15/0.56 tff(618,plain,
% 0.15/0.56 ((ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, 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)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.15/0.56 inference(rewrite,[status(thm)],[])).
% 0.15/0.56 tff(619,plain,
% 0.15/0.56 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))),
% 0.15/0.56 inference(monotonicity,[status(thm)],[618])).
% 0.15/0.56 tff(620,plain,
% 0.15/0.56 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))))))),
% 0.15/0.56 inference(transitivity,[status(thm)],[619, 617])).
% 0.15/0.56 tff(621,plain,
% 0.15/0.56 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.15/0.56 inference(quant_inst,[status(thm)],[])).
% 0.15/0.56 tff(622,plain,
% 0.15/0.56 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.15/0.56 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.15/0.56 tff(623,plain,
% 0.15/0.56 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.56 inference(unit_resolution,[status(thm)],[622, 301])).
% 0.15/0.56 tff(624,plain,
% 0.15/0.56 (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))),
% 0.15/0.56 inference(monotonicity,[status(thm)],[553])).
% 0.15/0.56 tff(625,plain,
% 0.15/0.56 (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))),
% 0.15/0.56 inference(symmetry,[status(thm)],[624])).
% 0.15/0.56 tff(626,plain,
% 0.15/0.56 (tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.56 inference(monotonicity,[status(thm)],[553])).
% 0.15/0.56 tff(627,plain,
% 0.15/0.56 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.56 inference(monotonicity,[status(thm)],[553, 626])).
% 0.15/0.56 tff(628,plain,
% 0.15/0.56 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))))),
% 0.15/0.57 inference(quant_inst,[status(thm)],[])).
% 0.15/0.57 tff(629,plain,
% 0.15/0.57 (~((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[628, 114])).
% 0.15/0.57 tff(630,plain,
% 0.15/0.57 (((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))) | ((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)))))),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(631,plain,
% 0.15/0.57 ((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3))))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[630, 629])).
% 0.15/0.57 tff(632,plain,
% 0.15/0.57 (model_ub(X!5, max(X!5, Y!4), Z!3) <=> model_ub(X!5, Y!4, Z!3)),
% 0.15/0.57 inference(monotonicity,[status(thm)],[553])).
% 0.15/0.57 tff(633,plain,
% 0.15/0.57 (model_ub(X!5, Y!4, Z!3) <=> model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.15/0.57 inference(symmetry,[status(thm)],[632])).
% 0.15/0.57 tff(634,plain,
% 0.15/0.57 (model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[249, 633])).
% 0.15/0.57 tff(635,plain,
% 0.15/0.57 ((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)))))) | (~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3))))),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(636,plain,
% 0.15/0.57 (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[635, 634, 631])).
% 0.15/0.57 tff(637,plain,
% 0.15/0.57 (((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3))) | ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(638,plain,
% 0.15/0.57 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[637, 636])).
% 0.15/0.57 tff(639,plain,
% 0.15/0.57 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[638, 627])).
% 0.15/0.57 tff(640,plain,
% 0.15/0.57 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[639, 625])).
% 0.15/0.57 tff(641,plain,
% 0.15/0.57 ((~(ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(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))) | (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(642,plain,
% 0.15/0.57 (~((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[641, 640, 623])).
% 0.15/0.57 tff(643,plain,
% 0.15/0.57 (((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(644,plain,
% 0.15/0.57 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[643, 642])).
% 0.15/0.57 tff(645,plain,
% 0.15/0.57 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.57 inference(rewrite,[status(thm)],[])).
% 0.15/0.57 tff(646,plain,
% 0.15/0.57 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.57 inference(quant_inst,[status(thm)],[])).
% 0.15/0.57 tff(647,plain,
% 0.15/0.57 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.15/0.57 tff(648,plain,
% 0.15/0.57 (max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[647, 58, 644])).
% 0.15/0.57 tff(649,plain,
% 0.15/0.57 (summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(monotonicity,[status(thm)],[648])).
% 0.15/0.57 tff(650,plain,
% 0.15/0.57 (sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) = sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.57 inference(monotonicity,[status(thm)],[649])).
% 0.15/0.57 tff(651,plain,
% 0.15/0.57 (lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.15/0.57 inference(monotonicity,[status(thm)],[650])).
% 0.15/0.57 tff(652,plain,
% 0.15/0.57 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3) <=> lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3)),
% 0.15/0.57 inference(symmetry,[status(thm)],[651])).
% 0.15/0.57 tff(653,plain,
% 0.15/0.57 (summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)) = summation(tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(monotonicity,[status(thm)],[626])).
% 0.15/0.57 tff(654,plain,
% 0.15/0.57 (sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) = sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.15/0.57 inference(monotonicity,[status(thm)],[653])).
% 0.15/0.57 tff(655,plain,
% 0.15/0.57 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.15/0.57 inference(monotonicity,[status(thm)],[654])).
% 0.15/0.57 tff(656,plain,
% 0.15/0.57 (((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(657,plain,
% 0.15/0.57 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[656, 636])).
% 0.15/0.57 tff(658,plain,
% 0.15/0.57 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[657, 655])).
% 0.15/0.57 tff(659,plain,
% 0.15/0.57 (lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3)),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[658, 652])).
% 0.15/0.57 tff(660,plain,
% 0.15/0.57 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3))),
% 0.15/0.57 inference(quant_inst,[status(thm)],[])).
% 0.15/0.57 tff(661,plain,
% 0.15/0.57 (model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3)),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[660, 99])).
% 0.15/0.57 tff(662,plain,
% 0.15/0.57 (((~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(663,plain,
% 0.15/0.57 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[662, 642])).
% 0.15/0.57 tff(664,plain,
% 0.15/0.57 (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[323, 58, 663])).
% 0.15/0.57 tff(665,plain,
% 0.15/0.57 ((~lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3)) <=> (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.15/0.57 inference(monotonicity,[status(thm)],[92])).
% 0.15/0.57 tff(666,plain,
% 0.15/0.57 (model_max(X!5, max(X!5, Y!4), Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.15/0.57 inference(monotonicity,[status(thm)],[553])).
% 0.15/0.57 tff(667,plain,
% 0.15/0.57 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.15/0.57 inference(symmetry,[status(thm)],[666])).
% 0.15/0.57 tff(668,plain,
% 0.15/0.57 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(X!5, max(X!5, Y!4), Z!3))),
% 0.15/0.57 inference(monotonicity,[status(thm)],[667])).
% 0.15/0.57 tff(669,plain,
% 0.15/0.57 (~model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[160, 668])).
% 0.15/0.57 tff(670,plain,
% 0.15/0.57 ((~(model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3))) | model_max(X!5, max(X!5, Y!4), Z!3) | (~lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3))),
% 0.15/0.57 inference(tautology,[status(thm)],[])).
% 0.15/0.57 tff(671,plain,
% 0.15/0.57 (~lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3)),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[670, 669, 101])).
% 0.15/0.57 tff(672,plain,
% 0.15/0.57 (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[671, 665])).
% 0.15/0.57 tff(673,plain,
% 0.15/0.57 (lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[168, 672])).
% 0.15/0.57 tff(674,assumption,(lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)), introduced(assumption)).
% 0.15/0.57 tff(675,plain,
% 0.15/0.57 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4))))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[273, 267, 674, 673])).
% 0.15/0.57 tff(676,plain,
% 0.15/0.57 ((~(lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4))) <=> lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), sum(c, summation(max(X!5, Y!4)))))) | lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[275, 675])).
% 0.15/0.57 tff(677,plain,
% 0.15/0.57 (lesseq(summation(tptp_fun_Z_0(Z!3, Y!4, X!5)), summation(max(X!5, Y!4)))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[676, 151])).
% 0.15/0.57 tff(678,plain,
% 0.15/0.57 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[290, 677])).
% 0.15/0.57 tff(679,plain,
% 0.15/0.57 ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4))),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[412, 12])).
% 0.15/0.57 tff(680,plain,
% 0.15/0.57 (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4)),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[679, 678])).
% 0.15/0.57 tff(681,assumption,(max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)), introduced(assumption)).
% 0.15/0.57 tff(682,plain,
% 0.15/0.57 (tptp_fun_Z_0(Z!3, Y!4, X!5) = max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.15/0.57 inference(symmetry,[status(thm)],[681])).
% 0.15/0.57 tff(683,plain,
% 0.15/0.57 (tptp_fun_Z_0(Z!3, Y!4, X!5) = Y!4),
% 0.15/0.57 inference(transitivity,[status(thm)],[682, 680, 553])).
% 0.15/0.57 tff(684,plain,
% 0.15/0.57 (model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.15/0.57 inference(monotonicity,[status(thm)],[683])).
% 0.15/0.57 tff(685,plain,
% 0.15/0.57 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.15/0.57 inference(symmetry,[status(thm)],[684])).
% 0.15/0.57 tff(686,plain,
% 0.15/0.57 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))),
% 0.15/0.57 inference(monotonicity,[status(thm)],[685])).
% 0.15/0.57 tff(687,plain,
% 0.15/0.57 (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.15/0.57 inference(modus_ponens,[status(thm)],[160, 686])).
% 0.15/0.57 tff(688,assumption,(model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)), introduced(assumption)).
% 0.15/0.57 tff(689,plain,
% 0.15/0.57 ($false),
% 0.15/0.57 inference(unit_resolution,[status(thm)],[688, 687])).
% 0.15/0.57 tff(690,plain,(model_max(X!5, Y!4, Z!3) | (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~(max(X!5, Y!4) = Y!4)) | (~(max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.58 tff(691,plain,
% 0.44/0.58 (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[690, 664, 553, 160, 658])).
% 0.44/0.58 tff(692,plain,
% 0.44/0.58 ((~(model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3))) | model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) | (~lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3))),
% 0.44/0.58 inference(tautology,[status(thm)],[])).
% 0.44/0.58 tff(693,plain,
% 0.44/0.58 ((~(model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3))) | (~lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[692, 691])).
% 0.44/0.58 tff(694,plain,
% 0.44/0.58 (~lesseq(sum(c, summation(max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))), Z!3)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[693, 661])).
% 0.44/0.58 tff(695,plain,
% 0.44/0.58 ($false),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[694, 659])).
% 0.44/0.58 tff(696,plain,(model_max(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.58 tff(697,plain,
% 0.44/0.58 (model_max(X!5, Y!4, Z!3)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[696, 614])).
% 0.44/0.58 tff(698,plain,
% 0.44/0.58 (model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[697, 616])).
% 0.44/0.58 tff(699,plain,
% 0.44/0.58 ((~(model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3))) | (~model_max(X!5, max(X!5, Y!4), Z!3)) | lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3)),
% 0.44/0.58 inference(tautology,[status(thm)],[])).
% 0.44/0.58 tff(700,plain,
% 0.44/0.58 (lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), Z!3)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[699, 698, 101])).
% 0.44/0.58 tff(701,plain,
% 0.44/0.58 (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[700, 92])).
% 0.44/0.58 tff(702,plain,
% 0.44/0.58 (((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))) | (model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))),
% 0.44/0.58 inference(tautology,[status(thm)],[])).
% 0.44/0.58 tff(703,plain,
% 0.44/0.58 (model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[702, 629])).
% 0.44/0.58 tff(704,plain,
% 0.44/0.58 (model_ub(X!5, max(X!5, Y!4), Z!3) <=> model_ub(X!5, Y!4, Z!3)),
% 0.44/0.58 inference(monotonicity,[status(thm)],[614])).
% 0.44/0.58 tff(705,plain,
% 0.44/0.58 (model_ub(X!5, Y!4, Z!3) <=> model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.44/0.58 inference(symmetry,[status(thm)],[704])).
% 0.44/0.58 tff(706,plain,
% 0.44/0.58 ((~model_ub(X!5, Y!4, Z!3)) <=> (~model_ub(X!5, max(X!5, Y!4), Z!3))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[705])).
% 0.44/0.58 tff(707,plain,
% 0.44/0.58 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[90])).
% 0.44/0.58 tff(708,plain,
% 0.44/0.58 (lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(symmetry,[status(thm)],[707])).
% 0.44/0.58 tff(709,plain,
% 0.44/0.58 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(710,plain,
% 0.44/0.58 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[709, 99])).
% 0.44/0.58 tff(711,plain,
% 0.44/0.58 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[614])).
% 0.44/0.58 tff(712,plain,
% 0.44/0.58 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(symmetry,[status(thm)],[711])).
% 0.44/0.58 tff(713,plain,
% 0.44/0.58 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[419, 307, 697])).
% 0.44/0.58 tff(714,plain,
% 0.44/0.58 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[421, 713])).
% 0.44/0.58 tff(715,plain,
% 0.44/0.58 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[714, 712])).
% 0.44/0.58 tff(716,plain,
% 0.44/0.58 ((~(model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | (~model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(tautology,[status(thm)],[])).
% 0.44/0.58 tff(717,plain,
% 0.44/0.58 (lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[716, 715, 710])).
% 0.44/0.58 tff(718,plain,
% 0.44/0.58 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[717, 708])).
% 0.44/0.58 tff(719,plain,
% 0.44/0.58 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(720,plain,
% 0.44/0.58 (~((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5)))))))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[719, 114])).
% 0.44/0.58 tff(721,plain,
% 0.44/0.58 (((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))))) | (model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.44/0.58 inference(tautology,[status(thm)],[])).
% 0.44/0.58 tff(722,plain,
% 0.44/0.58 (model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[721, 720])).
% 0.44/0.58 tff(723,plain,
% 0.44/0.58 (model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[614])).
% 0.44/0.58 tff(724,plain,
% 0.44/0.58 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.58 inference(symmetry,[status(thm)],[723])).
% 0.44/0.58 tff(725,plain,
% 0.44/0.58 ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) <=> (~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[724])).
% 0.44/0.59 tff(726,plain,
% 0.44/0.59 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[434, 713])).
% 0.44/0.59 tff(727,plain,
% 0.44/0.59 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[438, 726, 359])).
% 0.44/0.59 tff(728,plain,
% 0.44/0.59 (~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[727, 725])).
% 0.44/0.59 tff(729,plain,
% 0.44/0.59 ((~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(730,plain,
% 0.44/0.59 (![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[729, 728, 722])).
% 0.44/0.59 tff(731,plain,
% 0.44/0.59 (lesseq(max(X!5, Y!4), max(X!5, Y!4)) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[553])).
% 0.44/0.59 tff(732,plain,
% 0.44/0.59 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.44/0.59 inference(symmetry,[status(thm)],[731])).
% 0.44/0.59 tff(733,plain,
% 0.44/0.59 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[129, 732])).
% 0.44/0.59 tff(734,assumption,(~lesseq(max(X!5, Y!4), max(X!5, Y!4))), introduced(assumption)).
% 0.44/0.59 tff(735,plain,
% 0.44/0.59 ($false),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[734, 733])).
% 0.44/0.59 tff(736,plain,(lesseq(max(X!5, Y!4), max(X!5, Y!4)) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.59 tff(737,plain,
% 0.44/0.59 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[736, 614])).
% 0.44/0.59 tff(738,plain,
% 0.44/0.59 ((~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(739,plain,
% 0.44/0.59 ((~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[738, 83])).
% 0.44/0.59 tff(740,plain,
% 0.44/0.59 (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[739, 737])).
% 0.44/0.59 tff(741,assumption,(~(ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))), introduced(assumption)).
% 0.44/0.59 tff(742,plain,
% 0.44/0.59 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(743,plain,
% 0.44/0.59 ((ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))))) <=> (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(744,plain,
% 0.44/0.59 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))))))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[743])).
% 0.44/0.59 tff(745,plain,
% 0.44/0.59 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[744, 742])).
% 0.44/0.59 tff(746,plain,
% 0.44/0.59 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))))),
% 0.44/0.59 inference(quant_inst,[status(thm)],[])).
% 0.44/0.59 tff(747,plain,
% 0.44/0.59 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.44/0.59 tff(748,plain,
% 0.44/0.59 ($false),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[747, 301, 741])).
% 0.44/0.59 tff(749,plain,(ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.59 tff(750,plain,
% 0.44/0.59 ((~(ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))) | ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(751,plain,
% 0.44/0.59 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[750, 749])).
% 0.44/0.59 tff(752,plain,
% 0.44/0.59 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[751, 740])).
% 0.44/0.59 tff(753,plain,
% 0.44/0.59 (((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(754,plain,
% 0.44/0.59 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.44/0.59 inference(quant_inst,[status(thm)],[])).
% 0.44/0.59 tff(755,plain,
% 0.44/0.59 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.44/0.59 tff(756,plain,
% 0.44/0.59 ($false),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[755, 752, 730, 718])).
% 0.44/0.59 tff(757,plain,(minsol_model_max(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.59 tff(758,plain,
% 0.44/0.59 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[462, 757])).
% 0.44/0.59 tff(759,plain,
% 0.44/0.59 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[202, 757])).
% 0.44/0.59 tff(760,plain,
% 0.44/0.59 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[465, 759])).
% 0.44/0.59 tff(761,plain,
% 0.44/0.59 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[593, 760])).
% 0.44/0.59 tff(762,plain,
% 0.44/0.59 (~model_ub(X!5, Y!4, Z!3)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[598, 761, 758])).
% 0.44/0.59 tff(763,plain,
% 0.44/0.59 (~model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[762, 706])).
% 0.44/0.59 tff(764,plain,
% 0.44/0.59 ((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.46/0.60 inference(tautology,[status(thm)],[])).
% 0.46/0.60 tff(765,plain,
% 0.46/0.60 (![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[764, 763, 703])).
% 0.46/0.60 tff(766,plain,
% 0.46/0.60 (((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | ((~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))) <=> ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(767,plain,
% 0.46/0.60 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | ((~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(768,plain,
% 0.46/0.60 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.46/0.60 tff(769,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[768, 752, 765, 701])).
% 0.46/0.60 % SZS output end Proof
%------------------------------------------------------------------------------