TSTP Solution File: NUM861+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM861+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM861+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 15:28:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(ub_type, type, (
% 0.21/0.44 ub: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(max_type, type, (
% 0.21/0.44 max: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_Y_4_type, type, (
% 0.21/0.44 tptp_fun_Y_4: $i)).
% 0.21/0.44 tff(tptp_fun_X_5_type, type, (
% 0.21/0.44 tptp_fun_X_5: $i)).
% 0.21/0.44 tff(lesseq_type, type, (
% 0.21/0.44 lesseq: ( $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_Z_3_type, type, (
% 0.21/0.44 tptp_fun_Z_3: $i)).
% 0.21/0.44 tff(sum_type, type, (
% 0.21/0.44 sum: ( $i * $i ) > $i)).
% 0.21/0.44 tff(c_type, type, (
% 0.21/0.44 c: $i)).
% 0.21/0.44 tff(model_ub_type, type, (
% 0.21/0.44 model_ub: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.44 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(model_max_type, type, (
% 0.21/0.44 model_max: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(minsol_model_ub_type, type, (
% 0.21/0.44 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(minsol_model_max_type, type, (
% 0.21/0.44 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_Z_1_type, type, (
% 0.21/0.44 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_Z_2_type, type, (
% 0.21/0.44 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (^[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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (^[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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (^[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, 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, tptp_fun_Z_0(N, Y, X)), N)))))), rewrite((model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N)))) <=> (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N))) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(9,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_ub_4')).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, Z), N)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.44 tff(11,plain,(
% 0.21/0.44 ![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, Z), N)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[10])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 ((~((~((~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, 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, Z), Z!3))))))) <=> (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), Z!3)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 (((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 (model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.46 tff(23,assumption,(max(X!5, Y!4) = X!5), introduced(assumption)).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 ((~((~((~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, 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, 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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, 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, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[26, 24])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), Z!3)))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (~((~((~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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[29, 13])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (((~((~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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))) | (model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 (model_ub(max(X!5, Y!4), Y!4, Z!3) <=> model_ub(X!5, Y!4, Z!3)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (model_ub(X!5, Y!4, Z!3) <=> model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.21/0.46 inference(symmetry,[status(thm)],[33])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 ((~model_ub(X!5, Y!4, Z!3)) <=> (~model_ub(max(X!5, Y!4), Y!4, Z!3))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.46 tff(36,assumption,(model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.21/0.46 tff(37,assumption,((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))), introduced(assumption)).
% 0.21/0.46 tff(38,assumption,(lesseq(Y!4, X!5)), introduced(assumption)).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = X) | (~lesseq(Y, X))) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.46 tff(44,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_1')).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.46 tff(47,plain,(
% 0.21/0.46 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.21/0.46 inference(skolemize,[status(sab)],[46])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 (((~![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))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.21/0.46 tff(53,plain,
% 0.21/0.46 (max(X!5, Y!4) = X!5),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[52, 38])).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (X!5 = max(X!5, Y!4)),
% 0.21/0.46 inference(symmetry,[status(thm)],[53])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (lesseq(X!5, X!5) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[54])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, X!5)),
% 0.21/0.46 inference(symmetry,[status(thm)],[55])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 ((~lesseq(X!5, max(X!5, Y!4))) <=> (~lesseq(X!5, X!5))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, X!5)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 (lesseq(Y!4, X!5) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.21/0.46 inference(symmetry,[status(thm)],[58])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (lesseq(Y!4, max(X!5, Y!4))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[38, 59])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 ((~((~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)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (~lesseq(X!5, max(X!5, Y!4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[61, 60, 37])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (~lesseq(X!5, X!5)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(67,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lesseq_total')).
% 0.21/0.46 tff(68,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.47 tff(69,plain,(
% 0.21/0.47 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.21/0.47 inference(skolemize,[status(sab)],[68])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 ((lesseq(X!5, X!5) | lesseq(X!5, X!5)) <=> lesseq(X!5, X!5)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(transitivity,[status(thm)],[73, 71])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.47 tff(77,plain,
% 0.21/0.47 (lesseq(X!5, X!5)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[77, 63])).
% 0.21/0.47 tff(79,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,[]))).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 (~lesseq(Y!4, X!5)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[79, 37])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 (lesseq(X!5, Y!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[83, 70, 80])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.47 tff(90,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_2')).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.21/0.47 tff(93,plain,(
% 0.21/0.47 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.21/0.47 inference(skolemize,[status(sab)],[92])).
% 0.21/0.47 tff(94,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.47 tff(95,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (max(X!5, Y!4) = Y!4),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[98, 84])).
% 0.21/0.47 tff(100,plain,
% 0.21/0.47 (Y!4 = max(X!5, Y!4)),
% 0.21/0.47 inference(symmetry,[status(thm)],[99])).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 (lesseq(Y!4, Y!4) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.47 tff(102,plain,
% 0.21/0.47 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.21/0.47 inference(symmetry,[status(thm)],[101])).
% 0.21/0.47 tff(103,plain,
% 0.21/0.47 ((~lesseq(Y!4, max(X!5, Y!4))) <=> (~lesseq(Y!4, Y!4))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[102])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, Y!4)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[99])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 (lesseq(X!5, Y!4) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.21/0.47 inference(symmetry,[status(thm)],[104])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 (lesseq(X!5, max(X!5, Y!4))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[84, 105])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 (~lesseq(Y!4, max(X!5, Y!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[61, 106, 37])).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 (~lesseq(Y!4, Y!4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 ((lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(transitivity,[status(thm)],[111, 109])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (lesseq(Y!4, Y!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[114, 70])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[115, 108])).
% 0.21/0.47 tff(117,plain,(~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) | lesseq(Y!4, max(X!5, Y!4))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (lesseq(Y!4, max(X!5, Y!4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (((~![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 ((~![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[122, 48, 119])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (sum(c, max(max(X!5, Y!4), Y!4)) = sum(c, max(X!5, Y!4))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (sum(c, max(X!5, Y!4)) = sum(c, max(max(X!5, Y!4), Y!4))),
% 0.21/0.47 inference(symmetry,[status(thm)],[124])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(max(X!5, Y!4), Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[125])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (lesseq(sum(c, max(max(X!5, Y!4), Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.47 inference(symmetry,[status(thm)],[126])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)) <=> (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(131,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_max_4')).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.47 tff(133,plain,(
% 0.21/0.47 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.21/0.47 inference(skolemize,[status(sab)],[132])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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, max(max(X!5, Y!4), Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(max(X!5, Y!4), Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.47 inference(symmetry,[status(thm)],[137])).
% 0.21/0.47 tff(139,assumption,(~minsol_model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (^[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)) | (~((~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))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (![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)))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[140])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (^[X: $i, Y: $i, N: $i] : refl((~((~((~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)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 (^[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)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[144])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[145, 143])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (^[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)) | (~![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)))))) <=> (~((~((~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))))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 (^[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)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.48 tff(154,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/sandbox/benchmark/theBenchmark.p','minsol_model_max')).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.21/0.48 tff(157,plain,(
% 0.21/0.48 ![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)))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[156])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[159, 146])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 (![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)))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[160, 141])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 ((~![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)))))))))) | (~((~(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)))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(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))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(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)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 ((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(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))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (~((~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)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[167, 139, 36])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (((~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))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[170, 138])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 ((~(model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, 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, max(max(X!5, Y!4), Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (lesseq(sum(c, max(max(X!5, Y!4), Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[172, 171, 136])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[173, 127])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 (~((~((~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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[175, 13])).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 (((~((~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, 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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(178,plain,
% 0.21/0.49 (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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (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))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.49 (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))),
% 0.21/0.49 inference(symmetry,[status(thm)],[179])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 ((~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)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.49 tff(182,plain,
% 0.21/0.49 ((~(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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 ((~![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(184,axiom,(~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.49 tff(186,plain,
% 0.21/0.49 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[185, 183])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[186, 183])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.21/0.49 tff(189,plain,
% 0.21/0.49 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[188, 183])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[189, 183])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.21/0.49 tff(192,plain,(
% 0.21/0.49 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.21/0.49 inference(skolemize,[status(sab)],[191])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[192, 182])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 (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)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[195, 139])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 (^[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))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(198,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[197])).
% 0.21/0.49 tff(199,plain,
% 0.21/0.49 (^[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)))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[199])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 (^[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)))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(202,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[201])).
% 0.21/0.49 tff(203,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[202, 200])).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 (^[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))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(205,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.49 tff(206,plain,
% 0.21/0.49 (^[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)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[206])).
% 0.21/0.49 tff(208,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(209,plain,
% 0.21/0.49 (^[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)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(210,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[209])).
% 0.21/0.49 tff(211,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/sandbox/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.21/0.49 tff(212,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.21/0.49 tff(213,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.21/0.49 tff(214,plain,(
% 0.21/0.49 ![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)))))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[213])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[215, 205])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 (![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))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[216, 203])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 (![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)))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[217, 198])).
% 0.21/0.49 tff(219,plain,
% 0.21/0.49 ((~![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)))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(220,plain,
% 0.21/0.49 (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(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))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.21/0.49 tff(221,plain,
% 0.21/0.49 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(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))))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(222,plain,
% 0.21/0.49 ((~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)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 ((~((~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)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(224,plain,
% 0.21/0.49 ((~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)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.21/0.49 tff(225,plain,
% 0.21/0.49 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[224, 196])).
% 0.21/0.49 tff(226,plain,
% 0.21/0.49 (((~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))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 (((~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)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[228, 168])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 (((~![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, 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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 ((~![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, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 ((~![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, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[232, 229, 227])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[233, 181])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 ((~(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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 (![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[235, 234, 178])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 (X!5 = max(X!5, Y!4)),
% 0.21/0.49 inference(symmetry,[status(thm)],[23])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[237])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 (((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) | lesseq(X!5, max(X!5, Y!4))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 (lesseq(X!5, max(X!5, Y!4))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[239, 117])).
% 0.21/0.50 tff(241,plain,
% 0.21/0.50 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[240, 238])).
% 0.21/0.50 tff(242,plain,
% 0.21/0.50 ((~((~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)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(243,plain,
% 0.21/0.50 ((~((~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)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[242, 119])).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[243, 241])).
% 0.21/0.50 tff(245,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)).
% 0.21/0.50 tff(246,plain,
% 0.21/0.50 (^[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))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (![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)))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[246])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 (^[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))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 (![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)))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[248])).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(251,axiom,(![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ub')).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.21/0.50 tff(253,plain,(
% 0.21/0.50 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[252])).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.21/0.50 tff(255,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.21/0.50 tff(256,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[256, 255, 245])).
% 0.21/0.50 tff(258,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,[]))).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 ((~(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))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 (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))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.21/0.50 tff(261,plain,
% 0.21/0.50 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[260, 244])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 (((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, 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, 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, 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, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(263,plain,
% 0.21/0.50 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, 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, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[264, 261, 236, 174])).
% 0.21/0.50 tff(266,plain,(minsol_model_max(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = X!5)) | (~model_max(X!5, Y!4, Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(267,plain,
% 0.21/0.50 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[266, 36, 23])).
% 0.21/0.50 tff(268,plain,
% 0.21/0.50 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(269,plain,
% 0.21/0.50 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[268, 193])).
% 0.21/0.50 tff(270,plain,
% 0.21/0.50 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[269, 267])).
% 0.21/0.50 tff(271,plain,
% 0.21/0.50 (((~(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)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(272,plain,
% 0.21/0.50 ((~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)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[271, 163])).
% 0.21/0.50 tff(273,plain,
% 0.21/0.50 ((~((~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)))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(274,plain,
% 0.21/0.50 ((~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)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.21/0.50 tff(275,plain,
% 0.21/0.50 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[274, 267])).
% 0.21/0.50 tff(276,plain,
% 0.21/0.50 (((~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))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(277,plain,
% 0.21/0.50 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[276, 275])).
% 0.21/0.50 tff(278,assumption,(![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.21/0.50 tff(279,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)).
% 0.21/0.50 tff(280,plain,
% 0.21/0.50 (((~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))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(281,plain,
% 0.21/0.50 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.21/0.50 tff(282,plain,
% 0.21/0.50 (((~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)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(283,plain,
% 0.21/0.50 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[282, 279])).
% 0.21/0.50 tff(284,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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, 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)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(285,plain,
% 0.21/0.50 (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, 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))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[284, 134])).
% 0.21/0.50 tff(286,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(287,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[286])).
% 0.21/0.50 tff(288,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(289,axiom,(![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sum_monotone_1')).
% 0.21/0.50 tff(290,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.21/0.50 tff(291,plain,(
% 0.21/0.50 ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[290])).
% 0.21/0.50 tff(292,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.21/0.50 tff(293,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, 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(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(294,plain,
% 0.21/0.50 (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(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.21/0.50 tff(295,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(296,plain,
% 0.21/0.50 (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[295, 134])).
% 0.21/0.50 tff(297,assumption,(~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.21/0.50 tff(298,plain,
% 0.21/0.50 (((~![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(299,plain,
% 0.21/0.50 ((~![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)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(300,plain,
% 0.21/0.50 ((~![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))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.21/0.50 tff(301,plain,
% 0.21/0.50 (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[300, 278, 297])).
% 0.21/0.50 tff(302,plain,
% 0.21/0.50 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, 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, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(303,plain,
% 0.21/0.50 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | (~lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.21/0.50 tff(304,plain,
% 0.21/0.50 (~lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[303, 296])).
% 0.21/0.50 tff(305,plain,
% 0.21/0.50 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, 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, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, 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, max(X!5, Y!4))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(306,plain,
% 0.21/0.50 ((lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (lesseq(sum(c, 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, max(X!5, Y!4))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(307,plain,
% 0.21/0.50 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4))) | lesseq(sum(c, 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, 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, max(X!5, Y!4)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[306])).
% 0.21/0.50 tff(308,plain,
% 0.21/0.50 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4))) | lesseq(sum(c, 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, 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, max(X!5, Y!4))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[307, 305])).
% 0.21/0.50 tff(309,plain,
% 0.21/0.50 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(310,plain,
% 0.21/0.50 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, 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, max(X!5, Y!4)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.21/0.50 tff(311,plain,
% 0.21/0.50 (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[310, 70, 304])).
% 0.21/0.50 tff(312,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(313,plain,
% 0.21/0.50 (~((~((~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, 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, Z), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[312, 13])).
% 0.21/0.51 tff(314,plain,
% 0.21/0.51 (((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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, 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, 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))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(315,plain,
% 0.21/0.51 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.21/0.51 tff(316,assumption,(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.21/0.51 tff(317,plain,
% 0.21/0.51 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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, 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)))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(318,plain,
% 0.21/0.51 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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, 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)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[317, 316])).
% 0.21/0.51 tff(319,plain,
% 0.21/0.51 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[318, 315])).
% 0.21/0.51 tff(320,plain,
% 0.21/0.51 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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, 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))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(321,plain,
% 0.21/0.51 (lesseq(sum(c, 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))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[320, 319])).
% 0.21/0.51 tff(322,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(323,plain,
% 0.21/0.51 (^[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)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(324,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[323])).
% 0.21/0.51 tff(325,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(326,plain,
% 0.21/0.51 (^[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)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(327,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[326])).
% 0.21/0.51 tff(328,axiom,(![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lesseq_trans')).
% 0.21/0.51 tff(329,plain,
% 0.21/0.51 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.21/0.51 tff(330,plain,
% 0.21/0.51 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[329, 325])).
% 0.21/0.51 tff(331,plain,(
% 0.21/0.51 ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.21/0.51 inference(skolemize,[status(sab)],[330])).
% 0.21/0.51 tff(332,plain,
% 0.21/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[331, 324])).
% 0.21/0.51 tff(333,plain,
% 0.21/0.51 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[332, 322])).
% 0.21/0.51 tff(334,plain,
% 0.21/0.51 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, 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(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, 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(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(335,plain,
% 0.21/0.51 ((lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, 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, 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(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(336,plain,
% 0.21/0.51 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, 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, 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(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[335])).
% 0.21/0.51 tff(337,plain,
% 0.21/0.51 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, 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, 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(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[336, 334])).
% 0.21/0.51 tff(338,plain,
% 0.21/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, 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))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(339,plain,
% 0.21/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, 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(tptp_fun_Z_2(Z!3, Y!4, X!5), sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.21/0.51 tff(340,plain,
% 0.21/0.51 (lesseq(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[339, 333, 321, 311])).
% 0.21/0.51 tff(341,plain,
% 0.21/0.51 ((~(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(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, 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(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(342,plain,
% 0.21/0.51 ((~(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(sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)), sum(c, 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))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[341, 340])).
% 0.21/0.51 tff(343,plain,
% 0.21/0.51 (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[342, 294])).
% 0.21/0.51 tff(344,plain,
% 0.21/0.51 (((~![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(345,plain,
% 0.21/0.51 ((~![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)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(346,plain,
% 0.21/0.51 ((~![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.21/0.51 tff(347,plain,
% 0.21/0.51 (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)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[346, 94, 343])).
% 0.21/0.51 tff(348,plain,
% 0.21/0.51 (sum(c, 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, max(X!5, Y!4))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[347])).
% 0.21/0.51 tff(349,plain,
% 0.21/0.51 (lesseq(sum(c, 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, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[348])).
% 0.21/0.51 tff(350,plain,
% 0.21/0.51 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, 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))),
% 0.21/0.51 inference(symmetry,[status(thm)],[349])).
% 0.21/0.51 tff(351,plain,
% 0.21/0.51 ((~lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(sum(c, 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)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[350])).
% 0.21/0.51 tff(352,plain,
% 0.21/0.51 (~lesseq(sum(c, 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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[304, 351])).
% 0.21/0.51 tff(353,plain,
% 0.21/0.51 ((~(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, 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, 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))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(354,plain,
% 0.21/0.51 (~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))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[353, 352, 285])).
% 0.21/0.51 tff(355,plain,
% 0.21/0.51 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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, 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)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(356,plain,
% 0.21/0.51 (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, 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))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[355, 134])).
% 0.21/0.51 tff(357,plain,
% 0.21/0.51 ((~![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))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(358,plain,
% 0.21/0.51 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~lesseq(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)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[357, 255])).
% 0.21/0.51 tff(359,plain,
% 0.21/0.51 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(sum(c, 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))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(360,plain,
% 0.21/0.51 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[359, 319])).
% 0.21/0.51 tff(361,plain,
% 0.21/0.51 ((~(ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~lesseq(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)))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(362,plain,
% 0.21/0.51 ((~(ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> (~((~lesseq(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)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[361, 360])).
% 0.21/0.52 tff(363,plain,
% 0.21/0.52 (~((~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))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[362, 358])).
% 0.21/0.52 tff(364,plain,
% 0.21/0.52 (((~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))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(365,plain,
% 0.21/0.52 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[364, 363])).
% 0.21/0.52 tff(366,plain,
% 0.21/0.52 (((~![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)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(367,plain,
% 0.21/0.52 ((~![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)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(368,plain,
% 0.21/0.52 ((~![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))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.21/0.52 tff(369,plain,
% 0.21/0.52 (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)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[368, 48, 365])).
% 0.21/0.52 tff(370,plain,
% 0.21/0.52 (sum(c, max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), Y!4)) = sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[369])).
% 0.21/0.52 tff(371,plain,
% 0.21/0.52 (lesseq(sum(c, 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, 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))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[370])).
% 0.21/0.52 tff(372,plain,
% 0.21/0.52 (lesseq(sum(c, 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, 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))),
% 0.21/0.52 inference(symmetry,[status(thm)],[371])).
% 0.21/0.52 tff(373,plain,
% 0.21/0.52 (lesseq(sum(c, 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))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[321, 372])).
% 0.21/0.52 tff(374,plain,
% 0.21/0.52 ((~(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, 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, 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)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(375,plain,
% 0.21/0.52 (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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[374, 373, 356])).
% 0.21/0.52 tff(376,assumption,(max(X!5, Y!4) = Y!4), introduced(assumption)).
% 0.21/0.52 tff(377,plain,
% 0.21/0.52 (Y!4 = max(X!5, Y!4)),
% 0.21/0.52 inference(symmetry,[status(thm)],[376])).
% 0.21/0.52 tff(378,plain,
% 0.21/0.52 (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))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[377])).
% 0.21/0.52 tff(379,plain,
% 0.21/0.52 (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)) <=> 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))),
% 0.21/0.52 inference(symmetry,[status(thm)],[378])).
% 0.21/0.52 tff(380,plain,
% 0.21/0.52 ((~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))) <=> (~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)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[379])).
% 0.21/0.52 tff(381,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)).
% 0.21/0.52 tff(382,plain,
% 0.21/0.52 (~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))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.21/0.52 tff(383,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)).
% 0.21/0.52 tff(384,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[383, 382])).
% 0.21/0.52 tff(385,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,[]))).
% 0.21/0.52 tff(386,plain,
% 0.21/0.52 (~(max(X!5, Y!4) = Y!4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[385, 375, 354])).
% 0.21/0.52 tff(387,plain,
% 0.21/0.52 (~lesseq(X!5, Y!4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[98, 386])).
% 0.21/0.52 tff(388,plain,
% 0.21/0.52 (((~![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))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(389,plain,
% 0.21/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, X!5) | lesseq(X!5, Y!4))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(390,plain,
% 0.21/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, X!5) | lesseq(X!5, Y!4)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.21/0.52 tff(391,plain,
% 0.21/0.52 (lesseq(Y!4, X!5)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[390, 70, 387])).
% 0.21/0.52 tff(392,plain,
% 0.21/0.52 (max(X!5, Y!4) = X!5),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[52, 391])).
% 0.21/0.52 tff(393,plain,
% 0.21/0.52 (X!5 = max(X!5, Y!4)),
% 0.21/0.52 inference(symmetry,[status(thm)],[392])).
% 0.21/0.52 tff(394,plain,
% 0.21/0.52 (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))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[393])).
% 0.21/0.52 tff(395,plain,
% 0.21/0.52 (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)) <=> 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))),
% 0.21/0.52 inference(symmetry,[status(thm)],[394])).
% 0.21/0.52 tff(396,plain,
% 0.21/0.52 ((~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))) <=> (~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)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[395])).
% 0.21/0.52 tff(397,plain,
% 0.21/0.52 (~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))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[354, 396])).
% 0.21/0.52 tff(398,plain,
% 0.21/0.52 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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, 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)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(399,plain,
% 0.21/0.52 (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, 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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[398, 134])).
% 0.21/0.52 tff(400,plain,
% 0.21/0.52 (((~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))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(401,plain,
% 0.21/0.52 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[400, 363])).
% 0.21/0.52 tff(402,plain,
% 0.21/0.52 (((~![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)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(403,plain,
% 0.21/0.52 ((~![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)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(404,plain,
% 0.21/0.52 ((~![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))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.21/0.52 tff(405,plain,
% 0.21/0.52 (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)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[404, 48, 401])).
% 0.21/0.52 tff(406,plain,
% 0.21/0.52 (sum(c, max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), X!5)) = sum(c, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[405])).
% 0.21/0.52 tff(407,plain,
% 0.21/0.52 (lesseq(sum(c, 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, 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))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[406])).
% 0.21/0.52 tff(408,plain,
% 0.21/0.52 (lesseq(sum(c, 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, 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))),
% 0.21/0.52 inference(symmetry,[status(thm)],[407])).
% 0.21/0.52 tff(409,plain,
% 0.21/0.52 (lesseq(sum(c, 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))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[321, 408])).
% 0.21/0.52 tff(410,plain,
% 0.21/0.52 ((~(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, 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, 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)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(411,plain,
% 0.21/0.52 (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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[410, 409, 399])).
% 0.21/0.52 tff(412,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[411, 397])).
% 0.21/0.52 tff(413,plain,((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(414,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[413, 283, 281, 278])).
% 0.21/0.52 tff(415,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,[]))).
% 0.21/0.53 tff(416,plain,
% 0.21/0.53 ((~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))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[415, 277])).
% 0.21/0.53 tff(417,plain,
% 0.21/0.53 (((~(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)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(418,plain,
% 0.21/0.53 (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))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[417, 220])).
% 0.21/0.53 tff(419,plain,
% 0.21/0.53 ((~(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))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(420,plain,
% 0.21/0.53 (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))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[419, 418])).
% 0.21/0.53 tff(421,plain,
% 0.21/0.53 (~model_ub(X!5, Y!4, Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[420, 416, 270])).
% 0.21/0.53 tff(422,plain,
% 0.21/0.53 (~model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[421, 35])).
% 0.21/0.53 tff(423,plain,
% 0.21/0.53 ((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(424,plain,
% 0.21/0.53 (![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[423, 422, 32])).
% 0.21/0.53 tff(425,plain,
% 0.21/0.53 (lesseq(sum(c, max(X!5, Y!4)), Z!3) <=> lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[125])).
% 0.21/0.53 tff(426,plain,
% 0.21/0.53 (lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.53 inference(symmetry,[status(thm)],[425])).
% 0.21/0.53 tff(427,plain,
% 0.21/0.53 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(428,plain,
% 0.21/0.53 (model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[427, 134])).
% 0.21/0.53 tff(429,plain,
% 0.21/0.53 (model_max(max(X!5, Y!4), Y!4, Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.53 tff(430,plain,
% 0.21/0.53 (model_max(X!5, Y!4, Z!3) <=> model_max(max(X!5, Y!4), Y!4, Z!3)),
% 0.21/0.53 inference(symmetry,[status(thm)],[429])).
% 0.21/0.53 tff(431,plain,
% 0.21/0.53 (model_max(max(X!5, Y!4), Y!4, Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[36, 430])).
% 0.21/0.53 tff(432,plain,
% 0.21/0.53 ((~(model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3))) | (~model_max(max(X!5, Y!4), Y!4, Z!3)) | lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3)),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(433,plain,
% 0.21/0.53 (lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[432, 431, 428])).
% 0.21/0.53 tff(434,plain,
% 0.21/0.53 (lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[433, 426])).
% 0.21/0.53 tff(435,plain,
% 0.21/0.53 (((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | ((~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | (~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(436,plain,
% 0.21/0.53 ((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | ((~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(437,plain,
% 0.21/0.53 ((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | (~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.21/0.53 tff(438,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[437, 261, 434, 424])).
% 0.21/0.53 tff(439,plain,((~model_max(X!5, Y!4, Z!3)) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(440,plain,
% 0.21/0.53 (~model_max(X!5, Y!4, Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[439, 23])).
% 0.21/0.53 tff(441,plain,
% 0.21/0.53 ((~lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3)) <=> (~lesseq(sum(c, max(X!5, Y!4)), Z!3))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[426])).
% 0.21/0.53 tff(442,plain,
% 0.21/0.53 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(max(X!5, Y!4), Y!4, Z!3))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[430])).
% 0.21/0.53 tff(443,assumption,(~model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.21/0.53 tff(444,plain,
% 0.21/0.53 (~model_max(max(X!5, Y!4), Y!4, Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.21/0.53 tff(445,plain,
% 0.21/0.53 ((~(model_max(max(X!5, Y!4), Y!4, Z!3) <=> lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3))) | model_max(max(X!5, Y!4), Y!4, Z!3) | (~lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(446,plain,
% 0.21/0.53 (~lesseq(sum(c, max(max(X!5, Y!4), Y!4)), Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[445, 444, 428])).
% 0.21/0.53 tff(447,plain,
% 0.21/0.53 (~lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[446, 441])).
% 0.21/0.53 tff(448,plain,
% 0.21/0.53 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Z!3, sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), Z!3))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Z!3, sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), Z!3))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(449,plain,
% 0.21/0.53 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Z!3, sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), Z!3))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(450,plain,
% 0.21/0.53 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Z!3, sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.21/0.53 tff(451,plain,
% 0.21/0.53 (lesseq(Z!3, sum(c, max(X!5, Y!4))) | lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[450, 70])).
% 0.21/0.53 tff(452,plain,
% 0.21/0.53 (lesseq(Z!3, sum(c, max(X!5, Y!4)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[451, 447])).
% 0.21/0.53 tff(453,plain,
% 0.21/0.53 (tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.53 tff(454,plain,
% 0.21/0.53 (sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[453])).
% 0.21/0.53 tff(455,plain,
% 0.21/0.53 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[454])).
% 0.21/0.53 tff(456,plain,
% 0.21/0.53 (((~((~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, 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] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))) | ((~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, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(457,plain,
% 0.21/0.53 ((~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, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[456, 30])).
% 0.21/0.53 tff(458,plain,
% 0.21/0.53 (((~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)),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(459,plain,
% 0.21/0.53 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[458, 443])).
% 0.21/0.53 tff(460,plain,
% 0.21/0.53 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[274, 459])).
% 0.21/0.53 tff(461,plain,
% 0.21/0.53 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[195, 460])).
% 0.21/0.53 tff(462,plain,
% 0.21/0.53 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[224, 461])).
% 0.21/0.53 tff(463,plain,
% 0.21/0.53 (((~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)),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(464,plain,
% 0.21/0.53 (model_ub(X!5, Y!4, Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[463, 462])).
% 0.21/0.53 tff(465,plain,
% 0.21/0.53 (model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[464, 34])).
% 0.21/0.53 tff(466,plain,
% 0.21/0.53 ((~((~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, 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, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(467,plain,
% 0.21/0.53 (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[466, 465, 457])).
% 0.21/0.53 tff(468,plain,
% 0.21/0.53 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3)),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(469,plain,
% 0.21/0.53 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[468, 467])).
% 0.21/0.53 tff(470,plain,
% 0.21/0.53 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[469, 455])).
% 0.21/0.53 tff(471,assumption,(~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4)))), introduced(assumption)).
% 0.21/0.53 tff(472,plain,
% 0.21/0.53 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(473,plain,
% 0.21/0.53 ((lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))) <=> ((~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(474,plain,
% 0.21/0.53 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, 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, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4)))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[473])).
% 0.21/0.53 tff(475,plain,
% 0.21/0.53 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, 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, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[474, 472])).
% 0.21/0.53 tff(476,plain,
% 0.21/0.53 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(477,plain,
% 0.21/0.53 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)) | (~lesseq(Z!3, sum(c, max(X!5, Y!4)))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.21/0.53 tff(478,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[477, 333, 471, 470, 452])).
% 0.21/0.53 tff(479,plain,(model_max(X!5, Y!4, Z!3) | lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(480,plain,
% 0.21/0.53 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[479, 440, 23])).
% 0.21/0.53 tff(481,assumption,(~(lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))), introduced(assumption)).
% 0.21/0.53 tff(482,plain,
% 0.21/0.53 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(483,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[482, 292, 481])).
% 0.21/0.53 tff(484,plain,(lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(485,plain,
% 0.21/0.53 ((~(lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(486,plain,
% 0.21/0.53 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4)) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[485, 484])).
% 0.21/0.53 tff(487,plain,
% 0.21/0.53 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[486, 480])).
% 0.21/0.53 tff(488,plain,
% 0.21/0.53 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[458, 440])).
% 0.21/0.53 tff(489,plain,
% 0.21/0.53 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[274, 488])).
% 0.21/0.53 tff(490,plain,
% 0.21/0.53 ((~![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))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(491,plain,
% 0.21/0.53 (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)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[490, 255])).
% 0.21/0.53 tff(492,plain,
% 0.21/0.53 (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))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.53 tff(493,plain,
% 0.21/0.53 (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))),
% 0.21/0.53 inference(symmetry,[status(thm)],[492])).
% 0.21/0.54 tff(494,plain,
% 0.21/0.54 (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))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[23, 453])).
% 0.21/0.54 tff(495,plain,
% 0.21/0.54 (model_ub(X!5, Y!4, Z!3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[463, 225])).
% 0.21/0.54 tff(496,plain,
% 0.21/0.54 (model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[495, 34])).
% 0.21/0.54 tff(497,plain,
% 0.21/0.54 (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[466, 496, 457])).
% 0.21/0.54 tff(498,plain,
% 0.21/0.54 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, 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)))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(499,plain,
% 0.21/0.54 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[498, 497])).
% 0.21/0.54 tff(500,plain,
% 0.21/0.54 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[499, 494])).
% 0.21/0.54 tff(501,plain,
% 0.21/0.54 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[500, 493])).
% 0.21/0.54 tff(502,plain,
% 0.21/0.54 ((~(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)))))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(503,plain,
% 0.21/0.54 (~((~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))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[502, 501, 491])).
% 0.21/0.54 tff(504,plain,
% 0.21/0.54 (((~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))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(505,plain,
% 0.21/0.54 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[504, 503])).
% 0.21/0.54 tff(506,plain,
% 0.21/0.54 (((~![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)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(507,plain,
% 0.21/0.54 ((~![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)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(508,plain,
% 0.21/0.54 ((~![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))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.21/0.54 tff(509,plain,
% 0.21/0.54 (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)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[508, 94, 505])).
% 0.21/0.54 tff(510,assumption,(max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4)), introduced(assumption)).
% 0.21/0.54 tff(511,plain,
% 0.21/0.54 (max(X!5, Y!4) = max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.54 inference(symmetry,[status(thm)],[510])).
% 0.21/0.54 tff(512,plain,
% 0.21/0.54 (X!5 = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.21/0.54 inference(transitivity,[status(thm)],[237, 511, 509])).
% 0.21/0.54 tff(513,plain,
% 0.21/0.54 (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)),
% 0.21/0.54 inference(monotonicity,[status(thm)],[512])).
% 0.21/0.54 tff(514,plain,
% 0.21/0.54 (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)),
% 0.21/0.54 inference(symmetry,[status(thm)],[513])).
% 0.21/0.54 tff(515,plain,
% 0.21/0.54 (((~![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))))))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(516,plain,
% 0.21/0.54 ((~((~(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)))))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(517,plain,
% 0.21/0.54 (((~![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))))))))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[516])).
% 0.21/0.54 tff(518,plain,
% 0.21/0.54 (((~![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))))))))))),
% 0.21/0.54 inference(transitivity,[status(thm)],[517, 515])).
% 0.21/0.54 tff(519,plain,
% 0.21/0.54 ((~![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)))))))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(520,plain,
% 0.21/0.54 ((~![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)))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.21/0.54 tff(521,plain,
% 0.21/0.54 (~((~((~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))))))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[520, 161])).
% 0.21/0.55 tff(522,plain,
% 0.21/0.55 (((~((~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))))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(523,plain,
% 0.21/0.55 ((~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)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[522, 521])).
% 0.21/0.55 tff(524,plain,
% 0.21/0.55 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)), Z!3))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(525,plain,
% 0.21/0.55 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)), Z!3)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[524, 134])).
% 0.21/0.55 tff(526,plain,
% 0.21/0.55 (sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)) = sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))),
% 0.21/0.55 inference(symmetry,[status(thm)],[454])).
% 0.21/0.55 tff(527,plain,
% 0.21/0.55 (((~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))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(528,plain,
% 0.21/0.55 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[527, 503])).
% 0.21/0.55 tff(529,plain,
% 0.21/0.55 (((~![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)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(530,plain,
% 0.21/0.55 ((~![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)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(531,plain,
% 0.21/0.55 ((~![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))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.21/0.55 tff(532,plain,
% 0.21/0.55 (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[531, 48, 528])).
% 0.21/0.55 tff(533,plain,
% 0.21/0.55 (sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[532])).
% 0.21/0.55 tff(534,plain,
% 0.21/0.55 (sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)) = sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[533, 526])).
% 0.21/0.55 tff(535,plain,
% 0.21/0.55 (lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)), Z!3) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[534])).
% 0.21/0.55 tff(536,plain,
% 0.21/0.55 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3) <=> lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)), Z!3)),
% 0.21/0.55 inference(symmetry,[status(thm)],[535])).
% 0.21/0.55 tff(537,plain,
% 0.21/0.55 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))), Z!3)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[468, 497])).
% 0.21/0.55 tff(538,plain,
% 0.21/0.55 (lesseq(sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)), Z!3)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.21/0.55 tff(539,plain,
% 0.21/0.55 ((~(model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) <=> lesseq(sum(c, 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, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)), Z!3))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(540,plain,
% 0.21/0.55 (model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[539, 538, 525])).
% 0.21/0.55 tff(541,plain,
% 0.21/0.55 ((~![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))))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(542,plain,
% 0.21/0.55 (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)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[541, 255])).
% 0.21/0.55 tff(543,assumption,(ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.21/0.55 tff(544,plain,
% 0.21/0.55 ((~(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)))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(545,plain,
% 0.21/0.55 ((~(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)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[544, 543])).
% 0.21/0.55 tff(546,plain,
% 0.21/0.55 (~((~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))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[545, 542])).
% 0.21/0.55 tff(547,plain,
% 0.21/0.55 (((~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))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(548,plain,
% 0.21/0.55 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[547, 546])).
% 0.21/0.55 tff(549,plain,
% 0.21/0.55 (max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[531, 48, 548])).
% 0.21/0.55 tff(550,plain,
% 0.21/0.55 (sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4)) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[549])).
% 0.21/0.55 tff(551,plain,
% 0.21/0.55 (sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)) = sum(c, max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4))),
% 0.21/0.55 inference(symmetry,[status(thm)],[550])).
% 0.21/0.55 tff(552,plain,
% 0.21/0.55 (lesseq(sum(c, 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, 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)))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[551])).
% 0.21/0.55 tff(553,plain,
% 0.21/0.55 (lesseq(sum(c, 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, 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)))),
% 0.21/0.55 inference(symmetry,[status(thm)],[552])).
% 0.21/0.55 tff(554,plain,
% 0.21/0.55 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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, 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))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(555,plain,
% 0.21/0.55 (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, 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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[554, 134])).
% 0.21/0.55 tff(556,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)).
% 0.21/0.55 tff(557,plain,
% 0.21/0.55 (((~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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(558,plain,
% 0.21/0.55 (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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[557, 556])).
% 0.21/0.55 tff(559,plain,
% 0.21/0.55 ((~(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, 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, 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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(560,plain,
% 0.21/0.55 ((~(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, 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, 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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[559, 558])).
% 0.21/0.55 tff(561,plain,
% 0.21/0.55 (lesseq(sum(c, 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)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[560, 555])).
% 0.21/0.55 tff(562,plain,
% 0.21/0.55 (lesseq(sum(c, 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)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[561, 553])).
% 0.21/0.55 tff(563,plain,
% 0.21/0.55 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(564,plain,
% 0.21/0.55 (~((~((~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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[563, 13])).
% 0.21/0.55 tff(565,plain,
% 0.21/0.55 (((~((~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, 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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(566,plain,
% 0.21/0.55 (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, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[565, 564])).
% 0.21/0.55 tff(567,plain,
% 0.21/0.55 (((~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))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(568,plain,
% 0.21/0.55 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[567, 556])).
% 0.21/0.55 tff(569,assumption,(![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.21/0.55 tff(570,plain,
% 0.21/0.55 (((~![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))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(571,plain,
% 0.21/0.55 ((~![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))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(572,plain,
% 0.21/0.55 ((~![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)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.21/0.55 tff(573,plain,
% 0.21/0.55 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[572, 569, 568])).
% 0.21/0.55 tff(574,plain,
% 0.21/0.55 ((~(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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(575,plain,
% 0.21/0.55 ((~(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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[574, 573])).
% 0.21/0.55 tff(576,plain,
% 0.21/0.55 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[575, 566])).
% 0.21/0.55 tff(577,plain,
% 0.21/0.55 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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, 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, 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, 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)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(578,plain,
% 0.21/0.55 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, 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, 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)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(579,plain,
% 0.21/0.56 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.21/0.56 tff(580,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[579, 543, 576, 562])).
% 0.21/0.56 tff(581,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: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.56 tff(582,plain,
% 0.21/0.56 ((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[581, 500, 227])).
% 0.21/0.56 tff(583,plain,
% 0.21/0.56 ((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(584,plain,
% 0.21/0.56 ((~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3) | (~((~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)) | minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[583, 582])).
% 0.21/0.56 tff(585,plain,
% 0.21/0.56 (minsol_model_max(tptp_fun_Z_0(Z!3, Y!4, X!5), Y!4, Z!3)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[584, 540, 523])).
% 0.21/0.56 tff(586,plain,
% 0.21/0.56 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[585, 514])).
% 0.21/0.56 tff(587,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[139, 586])).
% 0.21/0.56 tff(588,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,[]))).
% 0.21/0.56 tff(589,plain,
% 0.21/0.56 (~(max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[588, 489, 23])).
% 0.21/0.56 tff(590,plain,
% 0.21/0.56 (((~![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)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(591,plain,
% 0.21/0.56 ((~![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)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(592,plain,
% 0.21/0.56 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))) | (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.21/0.56 tff(593,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[592, 48, 589, 487])).
% 0.21/0.56 tff(594,plain,(~(max(X!5, Y!4) = X!5)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.56 tff(595,plain,
% 0.21/0.56 (~lesseq(Y!4, X!5)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[52, 594])).
% 0.21/0.56 tff(596,plain,
% 0.21/0.56 (lesseq(X!5, Y!4)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[83, 70, 595])).
% 0.21/0.56 tff(597,plain,
% 0.21/0.56 (max(X!5, Y!4) = Y!4),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[98, 596])).
% 0.21/0.56 tff(598,plain,
% 0.21/0.56 (model_ub(X!5, max(X!5, Y!4), Z!3) <=> model_ub(X!5, Y!4, Z!3)),
% 0.21/0.56 inference(monotonicity,[status(thm)],[597])).
% 0.21/0.56 tff(599,plain,
% 0.21/0.56 (model_ub(X!5, Y!4, Z!3) <=> model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.21/0.56 inference(symmetry,[status(thm)],[598])).
% 0.21/0.56 tff(600,plain,
% 0.21/0.56 ((~model_ub(X!5, Y!4, Z!3)) <=> (~model_ub(X!5, max(X!5, Y!4), Z!3))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[599])).
% 0.21/0.56 tff(601,plain,
% 0.21/0.56 (((~![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)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(602,plain,
% 0.21/0.56 ((~![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)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(603,plain,
% 0.21/0.56 ((~![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))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.21/0.56 tff(604,plain,
% 0.21/0.56 (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[603, 94, 240])).
% 0.21/0.56 tff(605,plain,
% 0.21/0.56 (sum(c, max(X!5, max(X!5, Y!4))) = sum(c, max(X!5, Y!4))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[604])).
% 0.21/0.56 tff(606,plain,
% 0.21/0.56 (sum(c, max(X!5, Y!4)) = sum(c, max(X!5, max(X!5, Y!4)))),
% 0.21/0.56 inference(symmetry,[status(thm)],[605])).
% 0.21/0.56 tff(607,plain,
% 0.21/0.56 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[606])).
% 0.21/0.56 tff(608,plain,
% 0.21/0.56 (lesseq(sum(c, max(X!5, max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.56 inference(symmetry,[status(thm)],[607])).
% 0.21/0.56 tff(609,plain,
% 0.21/0.56 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, 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, max(X!5, max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(610,plain,
% 0.21/0.56 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, max(X!5, max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[609, 134])).
% 0.21/0.56 tff(611,plain,
% 0.21/0.56 (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))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[597])).
% 0.21/0.56 tff(612,plain,
% 0.21/0.56 (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))),
% 0.21/0.56 inference(symmetry,[status(thm)],[611])).
% 0.21/0.56 tff(613,plain,
% 0.21/0.56 (((~![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)))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(614,plain,
% 0.21/0.56 ((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))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(615,plain,
% 0.21/0.56 (((~![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)))))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[614])).
% 0.21/0.56 tff(616,plain,
% 0.21/0.56 (((~![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)))))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[615, 613])).
% 0.21/0.56 tff(617,plain,
% 0.21/0.56 ((~![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))))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(618,plain,
% 0.21/0.56 ((~![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))))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.21/0.56 tff(619,plain,
% 0.21/0.56 (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)))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[618, 255])).
% 0.21/0.56 tff(620,plain,
% 0.21/0.56 (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))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[597])).
% 0.21/0.56 tff(621,plain,
% 0.21/0.56 (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))),
% 0.21/0.56 inference(symmetry,[status(thm)],[620])).
% 0.21/0.56 tff(622,plain,
% 0.21/0.56 (tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.21/0.56 inference(monotonicity,[status(thm)],[597])).
% 0.21/0.56 tff(623,plain,
% 0.21/0.56 (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))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[597, 622])).
% 0.21/0.56 tff(624,plain,
% 0.21/0.56 (((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~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, 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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)))))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(625,plain,
% 0.21/0.56 ((~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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[624, 20])).
% 0.21/0.56 tff(626,plain,
% 0.21/0.56 (model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[464, 599])).
% 0.21/0.56 tff(627,plain,
% 0.21/0.56 ((~((~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, 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, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3))))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(628,plain,
% 0.21/0.56 (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[627, 626, 625])).
% 0.21/0.56 tff(629,plain,
% 0.21/0.56 (((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, 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))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(630,plain,
% 0.21/0.57 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[629, 628])).
% 0.21/0.57 tff(631,plain,
% 0.21/0.57 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[630, 623])).
% 0.21/0.57 tff(632,plain,
% 0.21/0.57 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[631, 621])).
% 0.21/0.57 tff(633,plain,
% 0.21/0.57 ((~(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)))))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(634,plain,
% 0.21/0.57 (~((~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))))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[633, 632, 619])).
% 0.21/0.57 tff(635,plain,
% 0.21/0.57 (((~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))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(636,plain,
% 0.21/0.57 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[635, 634])).
% 0.21/0.57 tff(637,plain,
% 0.21/0.57 (((~![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)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(638,plain,
% 0.21/0.57 ((~![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)))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(639,plain,
% 0.21/0.57 ((~![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))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.21/0.57 tff(640,plain,
% 0.21/0.57 (max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) = tptp_fun_Z_0(Z!3, Y!4, X!5)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[639, 94, 636])).
% 0.21/0.57 tff(641,plain,
% 0.21/0.57 (sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[640])).
% 0.21/0.57 tff(642,plain,
% 0.21/0.57 (lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.21/0.57 inference(monotonicity,[status(thm)],[641])).
% 0.21/0.57 tff(643,plain,
% 0.21/0.57 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3) <=> lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.21/0.57 inference(symmetry,[status(thm)],[642])).
% 0.21/0.57 tff(644,plain,
% 0.21/0.57 (sum(c, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)) = sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[622])).
% 0.21/0.57 tff(645,plain,
% 0.21/0.57 (lesseq(sum(c, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3) <=> lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.21/0.57 inference(monotonicity,[status(thm)],[644])).
% 0.21/0.57 tff(646,plain,
% 0.21/0.57 (((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(sum(c, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3))) | lesseq(sum(c, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(647,plain,
% 0.21/0.57 (lesseq(sum(c, tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5)), Z!3)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[646, 628])).
% 0.21/0.57 tff(648,plain,
% 0.21/0.57 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[647, 645])).
% 0.21/0.57 tff(649,plain,
% 0.21/0.57 (lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[648, 643])).
% 0.21/0.57 tff(650,plain,
% 0.21/0.57 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(651,plain,
% 0.21/0.57 (model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[650, 134])).
% 0.21/0.57 tff(652,plain,
% 0.21/0.57 (((~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))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(653,plain,
% 0.21/0.57 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[652, 634])).
% 0.21/0.57 tff(654,plain,
% 0.21/0.57 (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)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[508, 94, 653])).
% 0.21/0.57 tff(655,plain,
% 0.21/0.57 (lesseq(sum(c, max(X!5, Y!4)), Z!3) <=> lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3)),
% 0.21/0.57 inference(monotonicity,[status(thm)],[606])).
% 0.21/0.57 tff(656,plain,
% 0.21/0.57 (lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3) <=> lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.57 inference(symmetry,[status(thm)],[655])).
% 0.21/0.57 tff(657,plain,
% 0.21/0.57 ((~lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3)) <=> (~lesseq(sum(c, max(X!5, Y!4)), Z!3))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[656])).
% 0.21/0.57 tff(658,plain,
% 0.21/0.57 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, max(X, Y)), N))) | (model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(659,plain,
% 0.21/0.57 (model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[658, 134])).
% 0.21/0.57 tff(660,plain,
% 0.21/0.57 (model_max(X!5, max(X!5, Y!4), Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.21/0.57 inference(monotonicity,[status(thm)],[376])).
% 0.21/0.57 tff(661,plain,
% 0.21/0.57 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.21/0.57 inference(symmetry,[status(thm)],[660])).
% 0.21/0.57 tff(662,plain,
% 0.21/0.57 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(X!5, max(X!5, Y!4), Z!3))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[661])).
% 0.21/0.57 tff(663,plain,
% 0.21/0.57 (~model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[443, 662])).
% 0.21/0.57 tff(664,plain,
% 0.21/0.57 ((~(model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3))) | model_max(X!5, max(X!5, Y!4), Z!3) | (~lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(665,plain,
% 0.21/0.57 (~lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[664, 663, 659])).
% 0.21/0.57 tff(666,plain,
% 0.21/0.57 (~lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[665, 657])).
% 0.21/0.57 tff(667,plain,
% 0.21/0.57 (lesseq(Z!3, sum(c, max(X!5, Y!4)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[451, 666])).
% 0.21/0.57 tff(668,assumption,(lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3)), introduced(assumption)).
% 0.21/0.57 tff(669,plain,
% 0.21/0.57 (lesseq(sum(c, tptp_fun_Z_0(Z!3, Y!4, X!5)), sum(c, max(X!5, Y!4)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[477, 333, 668, 667])).
% 0.21/0.57 tff(670,plain,
% 0.21/0.57 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), max(X!5, Y!4))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[486, 669])).
% 0.21/0.57 tff(671,plain,
% 0.21/0.57 ((~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))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[592, 48])).
% 0.21/0.57 tff(672,plain,
% 0.21/0.57 (max(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) = max(X!5, Y!4)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[671, 670])).
% 0.21/0.57 tff(673,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)).
% 0.21/0.57 tff(674,plain,
% 0.21/0.57 (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))),
% 0.21/0.57 inference(symmetry,[status(thm)],[673])).
% 0.21/0.57 tff(675,plain,
% 0.21/0.57 (tptp_fun_Z_0(Z!3, Y!4, X!5) = Y!4),
% 0.21/0.57 inference(transitivity,[status(thm)],[674, 672, 376])).
% 0.21/0.57 tff(676,plain,
% 0.21/0.57 (model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.21/0.57 inference(monotonicity,[status(thm)],[675])).
% 0.21/0.57 tff(677,plain,
% 0.21/0.57 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.21/0.57 inference(symmetry,[status(thm)],[676])).
% 0.21/0.57 tff(678,plain,
% 0.21/0.57 ((~model_max(X!5, Y!4, Z!3)) <=> (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[677])).
% 0.21/0.57 tff(679,plain,
% 0.21/0.57 (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[443, 678])).
% 0.21/0.57 tff(680,assumption,(model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)), introduced(assumption)).
% 0.21/0.57 tff(681,plain,
% 0.21/0.57 ($false),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[680, 679])).
% 0.21/0.57 tff(682,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, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.57 tff(683,plain,
% 0.21/0.57 (model_max(X!5, Y!4, Z!3) | (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~(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, tptp_fun_Z_0(Z!3, Y!4, X!5)), Z!3))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[682, 597])).
% 0.21/0.57 tff(684,plain,
% 0.21/0.57 (~model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[683, 654, 443, 648])).
% 0.21/0.57 tff(685,plain,
% 0.21/0.57 ((~(model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, 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, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(686,plain,
% 0.21/0.57 ((~(model_max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3) <=> lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))) | (~lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[685, 684])).
% 0.21/0.57 tff(687,plain,
% 0.21/0.57 (~lesseq(sum(c, max(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[686, 651])).
% 0.21/0.57 tff(688,plain,
% 0.21/0.57 ($false),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[687, 649])).
% 0.21/0.57 tff(689,plain,(model_max(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.57 tff(690,plain,
% 0.21/0.57 (~((~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)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[167, 139, 689])).
% 0.21/0.57 tff(691,plain,
% 0.21/0.57 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[169, 690])).
% 0.21/0.57 tff(692,plain,
% 0.21/0.57 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[691, 612])).
% 0.21/0.57 tff(693,plain,
% 0.21/0.57 ((~(model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, 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, max(X!5, max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(694,plain,
% 0.21/0.57 (lesseq(sum(c, max(X!5, max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[693, 692, 610])).
% 0.21/0.57 tff(695,plain,
% 0.21/0.57 (lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[694, 608])).
% 0.21/0.57 tff(696,plain,
% 0.21/0.57 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(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, 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))) | (~((~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, 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)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(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, 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))) | (~((~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, 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))))))))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(697,plain,
% 0.21/0.57 ((~((~((~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, 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, 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, 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))) | (~((~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, 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)))))))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(698,plain,
% 0.21/0.57 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(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, 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))) | (~((~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, 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))))))))))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[697])).
% 0.21/0.57 tff(699,plain,
% 0.21/0.57 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(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, 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))) | (~((~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, 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))))))))))),
% 0.21/0.58 inference(transitivity,[status(thm)],[698, 696])).
% 0.21/0.58 tff(700,plain,
% 0.21/0.58 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, 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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(701,plain,
% 0.21/0.58 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, tptp_fun_Z_0(N, Y, X)), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, Z), N)))))))) | (~((~(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, 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))) | (~((~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, 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)))))))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.21/0.58 tff(702,plain,
% 0.21/0.58 (~((~(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, 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))) | (~((~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, 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))))))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[701, 13])).
% 0.21/0.58 tff(703,plain,
% 0.21/0.58 (((~(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, 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))) | (~((~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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(704,plain,
% 0.21/0.58 (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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[703, 702])).
% 0.21/0.58 tff(705,plain,
% 0.21/0.58 (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))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[597])).
% 0.21/0.58 tff(706,plain,
% 0.21/0.58 (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))),
% 0.21/0.58 inference(symmetry,[status(thm)],[705])).
% 0.21/0.58 tff(707,plain,
% 0.21/0.58 ((~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)))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[706])).
% 0.21/0.58 tff(708,plain,
% 0.21/0.58 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[228, 690])).
% 0.21/0.58 tff(709,plain,
% 0.21/0.58 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[232, 708, 227])).
% 0.21/0.58 tff(710,plain,
% 0.21/0.58 (~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[709, 707])).
% 0.21/0.58 tff(711,plain,
% 0.21/0.58 ((~(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, 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, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(712,plain,
% 0.21/0.58 (![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[711, 710, 704])).
% 0.21/0.58 tff(713,plain,
% 0.21/0.58 (lesseq(max(X!5, Y!4), max(X!5, Y!4)) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[376])).
% 0.21/0.58 tff(714,plain,
% 0.21/0.58 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.21/0.58 inference(symmetry,[status(thm)],[713])).
% 0.21/0.58 tff(715,plain,
% 0.21/0.58 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[119, 714])).
% 0.21/0.58 tff(716,assumption,(~lesseq(max(X!5, Y!4), max(X!5, Y!4))), introduced(assumption)).
% 0.21/0.58 tff(717,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[716, 715])).
% 0.21/0.58 tff(718,plain,(lesseq(max(X!5, Y!4), max(X!5, Y!4)) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(719,plain,
% 0.21/0.58 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[718, 597])).
% 0.21/0.58 tff(720,plain,
% 0.21/0.58 ((~((~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)))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(721,plain,
% 0.21/0.58 ((~((~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)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[720, 240])).
% 0.21/0.58 tff(722,plain,
% 0.21/0.58 (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[721, 719])).
% 0.21/0.58 tff(723,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)).
% 0.21/0.58 tff(724,plain,
% 0.21/0.58 (((~![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)))))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(725,plain,
% 0.21/0.58 ((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))))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(726,plain,
% 0.21/0.58 (((~![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)))))))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[725])).
% 0.21/0.58 tff(727,plain,
% 0.21/0.58 (((~![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)))))))),
% 0.21/0.58 inference(transitivity,[status(thm)],[726, 724])).
% 0.21/0.58 tff(728,plain,
% 0.21/0.58 ((~![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))))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(729,plain,
% 0.21/0.58 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[728, 727])).
% 0.21/0.58 tff(730,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[729, 255, 723])).
% 0.21/0.58 tff(731,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,[]))).
% 0.21/0.58 tff(732,plain,
% 0.21/0.58 ((~(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))))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(733,plain,
% 0.21/0.58 (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))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[732, 731])).
% 0.21/0.58 tff(734,plain,
% 0.21/0.58 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[733, 722])).
% 0.21/0.58 tff(735,plain,
% 0.21/0.58 (((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, 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, 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, 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, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(736,plain,
% 0.21/0.58 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, 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, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(737,plain,
% 0.21/0.58 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, Z), tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, max(X!5, Y!4)), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.21/0.58 tff(738,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[737, 734, 712, 695])).
% 0.21/0.58 tff(739,plain,(minsol_model_max(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(740,plain,
% 0.21/0.58 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[269, 739])).
% 0.21/0.58 tff(741,plain,
% 0.21/0.58 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[274, 739])).
% 0.21/0.58 tff(742,plain,
% 0.21/0.58 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[276, 741])).
% 0.21/0.58 tff(743,plain,
% 0.21/0.58 ((~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))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[415, 742])).
% 0.21/0.58 tff(744,plain,
% 0.21/0.58 (~model_ub(X!5, Y!4, Z!3)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[420, 743, 740])).
% 0.21/0.58 tff(745,plain,
% 0.21/0.58 (~model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[744, 600])).
% 0.21/0.58 tff(746,plain,
% 0.21/0.58 ((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(747,plain,
% 0.21/0.58 (![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[746, 745, 22])).
% 0.21/0.58 tff(748,plain,
% 0.21/0.58 (model_max(X!5, max(X!5, Y!4), Z!3) <=> model_max(X!5, Y!4, Z!3)),
% 0.21/0.58 inference(monotonicity,[status(thm)],[597])).
% 0.21/0.58 tff(749,plain,
% 0.21/0.58 (model_max(X!5, Y!4, Z!3) <=> model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.21/0.59 inference(symmetry,[status(thm)],[748])).
% 0.21/0.59 tff(750,plain,
% 0.21/0.59 (model_max(X!5, max(X!5, Y!4), Z!3)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[689, 749])).
% 0.21/0.59 tff(751,plain,
% 0.21/0.59 ((~(model_max(X!5, max(X!5, Y!4), Z!3) <=> lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3))) | (~model_max(X!5, max(X!5, Y!4), Z!3)) | lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3)),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(752,plain,
% 0.21/0.59 (lesseq(sum(c, max(X!5, max(X!5, Y!4))), Z!3)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[751, 750, 659])).
% 0.21/0.59 tff(753,plain,
% 0.21/0.59 (lesseq(sum(c, max(X!5, Y!4)), Z!3)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[752, 656])).
% 0.21/0.59 tff(754,plain,
% 0.21/0.59 (((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | ((~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | (~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(755,plain,
% 0.21/0.59 ((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | ((~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(756,plain,
% 0.21/0.59 ((~![Z: $i] : ((~lesseq(sum(c, Z), Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | (~lesseq(sum(c, max(X!5, Y!4)), Z!3)) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.21/0.59 tff(757,plain,
% 0.21/0.59 ($false),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[756, 734, 753, 747])).
% 0.21/0.59 % SZS output end Proof
%------------------------------------------------------------------------------