TSTP Solution File: NUM859+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM859+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:12:20 EDT 2022
% Result : Theorem 0.77s 0.71s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM859+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 15:30:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.77/0.71 % SZS status Theorem
% 0.77/0.71 % SZS output start Proof
% 0.77/0.71 tff(lesseq_type, type, (
% 0.77/0.71 lesseq: ( $i * $i ) > $o)).
% 0.77/0.71 tff(tptp_fun_Y_4_type, type, (
% 0.77/0.71 tptp_fun_Y_4: $i)).
% 0.77/0.71 tff(max_type, type, (
% 0.77/0.71 max: ( $i * $i ) > $i)).
% 0.77/0.71 tff(tptp_fun_X_5_type, type, (
% 0.77/0.71 tptp_fun_X_5: $i)).
% 0.77/0.71 tff(ub_type, type, (
% 0.77/0.71 ub: ( $i * $i * $i ) > $o)).
% 0.77/0.71 tff(tptp_fun_Z_1_type, type, (
% 0.77/0.71 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.77/0.71 tff(tptp_fun_Z_3_type, type, (
% 0.77/0.71 tptp_fun_Z_3: $i)).
% 0.77/0.71 tff(model_ub_type, type, (
% 0.77/0.71 model_ub: ( $i * $i * $i ) > $o)).
% 0.77/0.71 tff(tptp_fun_Z_0_type, type, (
% 0.77/0.71 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.77/0.71 tff(minsol_model_ub_type, type, (
% 0.77/0.71 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.77/0.71 tff(model_max_type, type, (
% 0.77/0.71 model_max: ( $i * $i * $i ) > $o)).
% 0.77/0.71 tff(minsol_model_max_type, type, (
% 0.77/0.71 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.77/0.71 tff(tptp_fun_Z_2_type, type, (
% 0.77/0.71 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 0.77/0.71 tff(1,assumption,(lesseq(Y!4, X!5)), introduced(assumption)).
% 0.77/0.71 tff(2,plain,
% 0.77/0.71 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.77/0.71 inference(bind,[status(th)],[])).
% 0.77/0.71 tff(3,plain,
% 0.77/0.71 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.77/0.71 inference(quant_intro,[status(thm)],[2])).
% 0.77/0.71 tff(4,plain,
% 0.77/0.71 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.77/0.71 inference(rewrite,[status(thm)],[])).
% 0.77/0.71 tff(5,plain,
% 0.77/0.71 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = X) | (~lesseq(Y, X))) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.77/0.71 inference(bind,[status(th)],[])).
% 0.77/0.71 tff(6,plain,
% 0.77/0.71 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.77/0.71 inference(quant_intro,[status(thm)],[5])).
% 0.77/0.71 tff(7,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_1')).
% 0.77/0.71 tff(8,plain,
% 0.77/0.71 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.77/0.71 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.77/0.71 tff(9,plain,
% 0.77/0.71 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.77/0.71 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.77/0.71 tff(10,plain,(
% 0.77/0.71 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.77/0.71 inference(skolemize,[status(sab)],[9])).
% 0.77/0.71 tff(11,plain,
% 0.77/0.71 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.77/0.71 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.77/0.71 tff(12,plain,
% 0.77/0.71 (((~![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))),
% 0.77/0.71 inference(rewrite,[status(thm)],[])).
% 0.77/0.71 tff(13,plain,
% 0.77/0.71 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.77/0.71 inference(quant_inst,[status(thm)],[])).
% 0.77/0.71 tff(14,plain,
% 0.77/0.71 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.77/0.71 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.77/0.71 tff(15,plain,
% 0.77/0.71 ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.77/0.71 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.77/0.71 tff(16,plain,
% 0.77/0.71 (max(X!5, Y!4) = X!5),
% 0.77/0.71 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.77/0.71 tff(17,plain,
% 0.77/0.71 (X!5 = max(X!5, Y!4)),
% 0.77/0.71 inference(symmetry,[status(thm)],[16])).
% 0.77/0.71 tff(18,plain,
% 0.77/0.71 (lesseq(X!5, X!5) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.77/0.71 inference(monotonicity,[status(thm)],[17])).
% 0.77/0.71 tff(19,plain,
% 0.77/0.71 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, X!5)),
% 0.77/0.71 inference(symmetry,[status(thm)],[18])).
% 0.77/0.71 tff(20,plain,
% 0.77/0.71 ((~lesseq(X!5, max(X!5, Y!4))) <=> (~lesseq(X!5, X!5))),
% 0.77/0.71 inference(monotonicity,[status(thm)],[19])).
% 0.77/0.71 tff(21,plain,
% 0.77/0.71 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, X!5)),
% 0.77/0.71 inference(monotonicity,[status(thm)],[16])).
% 0.77/0.71 tff(22,plain,
% 0.77/0.71 (lesseq(Y!4, X!5) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.77/0.71 inference(symmetry,[status(thm)],[21])).
% 0.77/0.71 tff(23,plain,
% 0.77/0.71 (lesseq(Y!4, max(X!5, Y!4))),
% 0.77/0.71 inference(modus_ponens,[status(thm)],[1, 22])).
% 0.77/0.71 tff(24,plain,
% 0.77/0.71 (^[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))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(25,plain,
% 0.77/0.72 (![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)))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[24])).
% 0.77/0.72 tff(26,plain,
% 0.77/0.72 (^[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))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(27,plain,
% 0.77/0.72 (![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)))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[26])).
% 0.77/0.72 tff(28,plain,
% 0.77/0.72 (![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)))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(29,axiom,(![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ub')).
% 0.77/0.72 tff(30,plain,
% 0.77/0.72 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.77/0.72 tff(31,plain,(
% 0.77/0.72 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.77/0.72 inference(skolemize,[status(sab)],[30])).
% 0.77/0.72 tff(32,plain,
% 0.77/0.72 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.77/0.72 tff(33,plain,
% 0.77/0.72 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.77/0.72 tff(34,plain,
% 0.77/0.72 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(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, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))))))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(35,plain,
% 0.77/0.72 ((ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))))) <=> (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4))))))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(36,plain,
% 0.77/0.72 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(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, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))))))),
% 0.77/0.72 inference(monotonicity,[status(thm)],[35])).
% 0.77/0.72 tff(37,plain,
% 0.77/0.72 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(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, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))))))),
% 0.77/0.72 inference(transitivity,[status(thm)],[36, 34])).
% 0.77/0.72 tff(38,plain,
% 0.77/0.72 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))))),
% 0.77/0.72 inference(quant_inst,[status(thm)],[])).
% 0.77/0.72 tff(39,plain,
% 0.77/0.72 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4))))))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.77/0.72 tff(40,plain,
% 0.77/0.72 (ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))))),
% 0.77/0.72 inference(unit_resolution,[status(thm)],[39, 33])).
% 0.77/0.72 tff(41,plain,
% 0.77/0.72 (^[X: $i, Y: $i, N: $i] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(42,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[41])).
% 0.77/0.72 tff(43,plain,
% 0.77/0.72 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(44,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[43])).
% 0.77/0.72 tff(45,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.77/0.72 inference(transitivity,[status(thm)],[44, 42])).
% 0.77/0.72 tff(46,plain,
% 0.77/0.72 (^[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(tptp_fun_Z_0(N, Y, X), N))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))), rewrite((model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N)))) <=> (model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(47,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[46])).
% 0.77/0.72 tff(48,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N))) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N)))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(49,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_ub_2')).
% 0.77/0.72 tff(50,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N)))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.77/0.72 tff(51,plain,(
% 0.77/0.72 ![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N)))))),
% 0.77/0.72 inference(skolemize,[status(sab)],[50])).
% 0.77/0.72 tff(52,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.77/0.72 tff(53,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.77/0.72 tff(54,plain,
% 0.77/0.72 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), 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(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))))))))))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(55,plain,
% 0.77/0.72 ((~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), 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)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z))))))) <=> (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5)))))))))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(56,plain,
% 0.77/0.72 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), 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)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, 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(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))))))))))),
% 0.77/0.72 inference(monotonicity,[status(thm)],[55])).
% 0.77/0.72 tff(57,plain,
% 0.77/0.72 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), 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)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, 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(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))))))))))),
% 0.77/0.72 inference(transitivity,[status(thm)],[56, 54])).
% 0.77/0.72 tff(58,plain,
% 0.77/0.72 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), 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)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z)))))))),
% 0.77/0.72 inference(quant_inst,[status(thm)],[])).
% 0.77/0.72 tff(59,plain,
% 0.77/0.72 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5)))))))))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.77/0.72 tff(60,plain,
% 0.77/0.72 (~((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5))))))))),
% 0.77/0.72 inference(unit_resolution,[status(thm)],[59, 53])).
% 0.77/0.72 tff(61,plain,
% 0.77/0.72 (((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, X!5), Y!4, X!5)))))))) | (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.77/0.72 inference(tautology,[status(thm)],[])).
% 0.77/0.72 tff(62,plain,
% 0.77/0.72 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.77/0.72 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.77/0.72 tff(63,assumption,(~minsol_model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.77/0.72 tff(64,plain,
% 0.77/0.72 ((~(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))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(65,plain,
% 0.77/0.72 ((~![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)))),
% 0.77/0.72 inference(rewrite,[status(thm)],[])).
% 0.77/0.72 tff(66,axiom,(~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.77/0.72 tff(67,plain,
% 0.77/0.72 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.77/0.72 tff(68,plain,
% 0.77/0.72 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.77/0.72 tff(69,plain,
% 0.77/0.72 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.77/0.72 tff(70,plain,
% 0.77/0.72 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.77/0.72 tff(71,plain,
% 0.77/0.72 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.77/0.72 tff(72,plain,
% 0.77/0.72 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[71, 65])).
% 0.77/0.72 tff(73,plain,
% 0.77/0.72 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.77/0.72 tff(74,plain,(
% 0.77/0.72 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.77/0.72 inference(skolemize,[status(sab)],[73])).
% 0.77/0.72 tff(75,plain,
% 0.77/0.72 ((~minsol_model_ub(X!5, Y!4, Z!3)) <=> minsol_model_max(X!5, Y!4, Z!3)),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.77/0.72 tff(76,plain,
% 0.77/0.72 (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)))),
% 0.77/0.72 inference(tautology,[status(thm)],[])).
% 0.77/0.72 tff(77,plain,
% 0.77/0.72 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.77/0.72 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.77/0.72 tff(78,plain,
% 0.77/0.72 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.77/0.72 inference(unit_resolution,[status(thm)],[77, 63])).
% 0.77/0.72 tff(79,plain,
% 0.77/0.72 (^[X: $i, Y: $i, N: $i] : refl((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(80,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[79])).
% 0.77/0.72 tff(81,plain,
% 0.77/0.72 (^[X: $i, Y: $i, N: $i] : rewrite((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(82,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[81])).
% 0.77/0.72 tff(83,plain,
% 0.77/0.72 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.77/0.72 inference(transitivity,[status(thm)],[82, 80])).
% 0.77/0.72 tff(84,plain,
% 0.77/0.72 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) <=> ((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))), rewrite((minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))) <=> (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))), rewrite((((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(85,plain,
% 0.77/0.73 (![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)))))))))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[84])).
% 0.77/0.73 tff(86,plain,
% 0.77/0.73 (^[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)))))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(87,plain,
% 0.77/0.73 (![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))))))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[86])).
% 0.77/0.73 tff(88,plain,
% 0.77/0.73 (![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))))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(89,plain,
% 0.77/0.73 (^[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)))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(90,plain,
% 0.77/0.73 (![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))))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[89])).
% 0.77/0.73 tff(91,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_max')).
% 0.77/0.73 tff(92,plain,
% 0.77/0.73 (![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))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.77/0.73 tff(93,plain,
% 0.77/0.73 (![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))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.77/0.73 tff(94,plain,(
% 0.77/0.73 ![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)))))))),
% 0.77/0.73 inference(skolemize,[status(sab)],[93])).
% 0.77/0.73 tff(95,plain,
% 0.77/0.73 (![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))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.77/0.73 tff(96,plain,
% 0.77/0.73 (![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)))))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.77/0.73 tff(97,plain,
% 0.77/0.73 (![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)))))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[96, 83])).
% 0.77/0.73 tff(98,plain,
% 0.77/0.73 ((~![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)))))))))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(99,plain,
% 0.77/0.73 (~((~(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))))))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.77/0.73 tff(100,plain,
% 0.77/0.73 (((~(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))))))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(101,plain,
% 0.77/0.73 ((~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)))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.77/0.73 tff(102,plain,
% 0.77/0.73 ((~((~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)))))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(103,plain,
% 0.77/0.73 ((~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)))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.77/0.73 tff(104,plain,
% 0.77/0.73 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[103, 78])).
% 0.77/0.73 tff(105,plain,
% 0.77/0.73 (((~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))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(106,plain,
% 0.77/0.73 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.77/0.73 tff(107,assumption,(~(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))), introduced(assumption)).
% 0.77/0.73 tff(108,plain,
% 0.77/0.73 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> lesseq(max(X, Y), N)) <=> (model_max(X, Y, N) <=> lesseq(max(X, Y), N)))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(109,plain,
% 0.77/0.73 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[108])).
% 0.77/0.73 tff(110,plain,
% 0.77/0.73 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(111,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_max_2')).
% 0.77/0.73 tff(112,plain,
% 0.77/0.73 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.77/0.73 tff(113,plain,(
% 0.77/0.73 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.77/0.73 inference(skolemize,[status(sab)],[112])).
% 0.77/0.73 tff(114,plain,
% 0.77/0.73 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.77/0.73 tff(115,plain,
% 0.77/0.73 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(116,plain,
% 0.77/0.73 ($false),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[115, 114, 107])).
% 0.77/0.73 tff(117,plain,(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.73 tff(118,assumption,(~lesseq(max(X!5, Y!4), Z!3)), introduced(assumption)).
% 0.77/0.73 tff(119,plain,
% 0.77/0.73 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(max(X!5, Y!4), Z!3)),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(120,plain,
% 0.77/0.73 (~model_max(X!5, Y!4, Z!3)),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[119, 118, 117])).
% 0.77/0.73 tff(121,plain,
% 0.77/0.73 (((~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)),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(122,plain,
% 0.77/0.73 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.77/0.73 tff(123,plain,
% 0.77/0.73 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[103, 122])).
% 0.77/0.73 tff(124,plain,
% 0.77/0.73 ((~![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))))))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(125,plain,
% 0.77/0.73 (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)))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[124, 33])).
% 0.77/0.73 tff(126,assumption,(~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))), introduced(assumption)).
% 0.77/0.73 tff(127,plain,
% 0.77/0.73 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))) | ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(128,plain,
% 0.77/0.73 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.77/0.73 tff(129,plain,
% 0.77/0.73 ((~(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)))))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(130,plain,
% 0.77/0.73 ((~(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)))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.77/0.73 tff(131,plain,
% 0.77/0.73 (~((~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))))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[130, 125])).
% 0.77/0.73 tff(132,plain,
% 0.77/0.73 (((~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))),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(133,plain,
% 0.77/0.73 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.77/0.73 tff(134,plain,
% 0.77/0.73 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.77/0.73 inference(tautology,[status(thm)],[])).
% 0.77/0.73 tff(135,plain,
% 0.77/0.73 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[134, 126])).
% 0.77/0.73 tff(136,plain,
% 0.77/0.73 (![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)))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(137,plain,
% 0.77/0.73 (^[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)))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(138,plain,
% 0.77/0.73 (![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)))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[137])).
% 0.77/0.73 tff(139,plain,
% 0.77/0.73 (![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))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(140,plain,
% 0.77/0.73 (^[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)))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(141,plain,
% 0.77/0.73 (![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))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[140])).
% 0.77/0.73 tff(142,axiom,(![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lesseq_trans')).
% 0.77/0.73 tff(143,plain,
% 0.77/0.73 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.77/0.73 tff(144,plain,
% 0.77/0.73 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.77/0.73 tff(145,plain,(
% 0.77/0.73 ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.77/0.73 inference(skolemize,[status(sab)],[144])).
% 0.77/0.73 tff(146,plain,
% 0.77/0.73 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.77/0.73 tff(147,plain,
% 0.77/0.73 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.77/0.73 tff(148,plain,
% 0.77/0.73 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(149,plain,
% 0.77/0.73 ((lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(150,plain,
% 0.77/0.73 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3)))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[149])).
% 0.77/0.73 tff(151,plain,
% 0.77/0.73 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))),
% 0.77/0.73 inference(transitivity,[status(thm)],[150, 148])).
% 0.77/0.73 tff(152,plain,
% 0.77/0.73 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.77/0.73 inference(quant_inst,[status(thm)],[])).
% 0.77/0.73 tff(153,plain,
% 0.77/0.73 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3)),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.77/0.73 tff(154,plain,
% 0.77/0.73 (lesseq(Y!4, Z!3)),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[153, 147, 135, 133])).
% 0.77/0.73 tff(155,assumption,(max(X!5, Y!4) = Y!4), introduced(assumption)).
% 0.77/0.73 tff(156,plain,
% 0.77/0.73 (Y!4 = max(X!5, Y!4)),
% 0.77/0.73 inference(symmetry,[status(thm)],[155])).
% 0.77/0.73 tff(157,plain,
% 0.77/0.73 (lesseq(Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.77/0.73 inference(monotonicity,[status(thm)],[156])).
% 0.77/0.73 tff(158,plain,
% 0.77/0.73 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(Y!4, Z!3)),
% 0.77/0.73 inference(symmetry,[status(thm)],[157])).
% 0.77/0.73 tff(159,plain,
% 0.77/0.73 ((~lesseq(max(X!5, Y!4), Z!3)) <=> (~lesseq(Y!4, Z!3))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[158])).
% 0.77/0.73 tff(160,plain,
% 0.77/0.73 (~lesseq(Y!4, Z!3)),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[118, 159])).
% 0.77/0.73 tff(161,assumption,(lesseq(Y!4, Z!3)), introduced(assumption)).
% 0.77/0.73 tff(162,plain,
% 0.77/0.73 ($false),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.77/0.73 tff(163,plain,((~(max(X!5, Y!4) = Y!4)) | (~lesseq(Y!4, Z!3)) | lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.73 tff(164,plain,
% 0.77/0.73 (~(max(X!5, Y!4) = Y!4)),
% 0.77/0.73 inference(unit_resolution,[status(thm)],[163, 154, 118])).
% 0.77/0.73 tff(165,plain,
% 0.77/0.73 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(166,plain,
% 0.77/0.73 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[165])).
% 0.77/0.73 tff(167,plain,
% 0.77/0.73 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(168,plain,
% 0.77/0.73 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(169,plain,
% 0.77/0.73 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[168])).
% 0.77/0.73 tff(170,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_2')).
% 0.77/0.73 tff(171,plain,
% 0.77/0.73 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.77/0.73 tff(172,plain,
% 0.77/0.73 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.77/0.73 tff(173,plain,(
% 0.77/0.73 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.77/0.73 inference(skolemize,[status(sab)],[172])).
% 0.77/0.74 tff(174,plain,
% 0.77/0.74 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.77/0.74 tff(175,plain,
% 0.77/0.74 (((~![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))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(176,plain,
% 0.77/0.74 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(177,plain,
% 0.77/0.74 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.77/0.74 tff(178,plain,
% 0.77/0.74 ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[177, 174])).
% 0.77/0.74 tff(179,plain,
% 0.77/0.74 (~lesseq(X!5, Y!4)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[178, 164])).
% 0.77/0.74 tff(180,plain,
% 0.77/0.74 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(181,plain,
% 0.77/0.74 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[180])).
% 0.77/0.74 tff(182,plain,
% 0.77/0.74 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(183,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lesseq_total')).
% 0.77/0.74 tff(184,plain,
% 0.77/0.74 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.77/0.74 tff(185,plain,(
% 0.77/0.74 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.77/0.74 inference(skolemize,[status(sab)],[184])).
% 0.77/0.74 tff(186,plain,
% 0.77/0.74 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.77/0.74 tff(187,plain,
% 0.77/0.74 (((~![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))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(188,plain,
% 0.77/0.74 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, X!5) | lesseq(X!5, Y!4))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(189,plain,
% 0.77/0.74 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, X!5) | lesseq(X!5, Y!4)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.77/0.74 tff(190,plain,
% 0.77/0.74 (lesseq(Y!4, X!5)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[189, 186, 179])).
% 0.77/0.74 tff(191,plain,
% 0.77/0.74 (max(X!5, Y!4) = X!5),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[15, 190])).
% 0.77/0.74 tff(192,plain,
% 0.77/0.74 (X!5 = max(X!5, Y!4)),
% 0.77/0.74 inference(symmetry,[status(thm)],[191])).
% 0.77/0.74 tff(193,plain,
% 0.77/0.74 (lesseq(X!5, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.77/0.74 inference(monotonicity,[status(thm)],[192])).
% 0.77/0.74 tff(194,plain,
% 0.77/0.74 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(X!5, Z!3)),
% 0.77/0.74 inference(symmetry,[status(thm)],[193])).
% 0.77/0.74 tff(195,plain,
% 0.77/0.74 ((~lesseq(max(X!5, Y!4), Z!3)) <=> (~lesseq(X!5, Z!3))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[194])).
% 0.77/0.74 tff(196,plain,
% 0.77/0.74 (~lesseq(X!5, Z!3)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[118, 195])).
% 0.77/0.74 tff(197,plain,
% 0.77/0.74 (((~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(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(198,plain,
% 0.77/0.74 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[197, 131])).
% 0.77/0.74 tff(199,plain,
% 0.77/0.74 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(200,plain,
% 0.77/0.74 ((lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(201,plain,
% 0.77/0.74 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3)))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[200])).
% 0.77/0.74 tff(202,plain,
% 0.77/0.74 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))),
% 0.77/0.74 inference(transitivity,[status(thm)],[201, 199])).
% 0.77/0.74 tff(203,plain,
% 0.77/0.74 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(204,plain,
% 0.77/0.74 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.77/0.74 tff(205,plain,
% 0.77/0.74 (lesseq(X!5, Z!3)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[204, 147, 135, 198])).
% 0.77/0.74 tff(206,plain,
% 0.77/0.74 ($false),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[205, 196])).
% 0.77/0.74 tff(207,plain,(((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))) | lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.74 tff(208,plain,
% 0.77/0.74 ((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[207, 118])).
% 0.77/0.74 tff(209,assumption,((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))))), introduced(assumption)).
% 0.77/0.74 tff(210,plain,
% 0.77/0.74 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))))))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(211,plain,
% 0.77/0.74 ($false),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[210, 53, 209])).
% 0.77/0.74 tff(212,plain,(~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.74 tff(213,plain,
% 0.77/0.74 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))))) | ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(214,plain,
% 0.77/0.74 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.77/0.74 tff(215,plain,
% 0.77/0.74 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(216,plain,
% 0.77/0.74 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.77/0.74 tff(217,plain,
% 0.77/0.74 (~model_ub(X!5, Y!4, Z!3)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[216, 208])).
% 0.77/0.74 tff(218,plain,
% 0.77/0.74 (((~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)),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(219,plain,
% 0.77/0.74 ((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.77/0.74 tff(220,plain,
% 0.77/0.74 (^[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))))))))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(221,plain,
% 0.77/0.74 (![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)))))))))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[220])).
% 0.77/0.74 tff(222,plain,
% 0.77/0.74 (^[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)))))))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(223,plain,
% 0.77/0.74 (![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))))))))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[222])).
% 0.77/0.74 tff(224,plain,
% 0.77/0.74 (^[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)))))))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(225,plain,
% 0.77/0.74 (![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))))))))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[224])).
% 0.77/0.74 tff(226,plain,
% 0.77/0.74 (![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))))))))),
% 0.77/0.74 inference(transitivity,[status(thm)],[225, 223])).
% 0.77/0.74 tff(227,plain,
% 0.77/0.74 (^[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))))))))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(228,plain,
% 0.77/0.74 (![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))))))))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[227])).
% 0.77/0.74 tff(229,plain,
% 0.77/0.74 (^[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)))))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(230,plain,
% 0.77/0.74 (![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))))))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[229])).
% 0.77/0.74 tff(231,plain,
% 0.77/0.74 (![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))))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(232,plain,
% 0.77/0.74 (^[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)))))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(233,plain,
% 0.77/0.74 (![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))))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[232])).
% 0.77/0.74 tff(234,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.77/0.74 tff(235,plain,
% 0.77/0.74 (![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))))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.77/0.74 tff(236,plain,
% 0.77/0.74 (![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))))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.77/0.74 tff(237,plain,(
% 0.77/0.74 ![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)))))))),
% 0.77/0.74 inference(skolemize,[status(sab)],[236])).
% 0.77/0.74 tff(238,plain,
% 0.77/0.74 (![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))))))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.77/0.74 tff(239,plain,
% 0.77/0.74 (![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))))))))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[238, 228])).
% 0.77/0.74 tff(240,plain,
% 0.77/0.74 (![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))))))))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[239, 226])).
% 0.77/0.74 tff(241,plain,
% 0.77/0.74 (![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)))))))))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[240, 221])).
% 0.77/0.74 tff(242,plain,
% 0.77/0.74 ((~![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)))))))))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(243,plain,
% 0.77/0.74 (~((~(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))))))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.77/0.74 tff(244,plain,
% 0.77/0.74 (((~(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))))))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(245,plain,
% 0.77/0.74 ((~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)))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.77/0.74 tff(246,plain,
% 0.77/0.74 ((~((~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)))))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(247,plain,
% 0.77/0.74 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.77/0.74 tff(248,plain,
% 0.77/0.74 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[247, 219])).
% 0.77/0.74 tff(249,plain,
% 0.77/0.74 ($false),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[77, 248, 123])).
% 0.77/0.74 tff(250,plain,(lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.74 tff(251,plain,
% 0.77/0.74 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))) | model_max(X!5, Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(252,plain,
% 0.77/0.74 (model_max(X!5, Y!4, Z!3)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[251, 250, 117])).
% 0.77/0.74 tff(253,plain,
% 0.77/0.74 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(254,plain,
% 0.77/0.74 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(255,plain,
% 0.77/0.74 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.77/0.74 tff(256,plain,
% 0.77/0.74 (lesseq(Z!3, Z!3)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[255, 252, 106])).
% 0.77/0.74 tff(257,assumption,(lesseq(Z!3, Z!3)), introduced(assumption)).
% 0.77/0.74 tff(258,assumption,(![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))), introduced(assumption)).
% 0.77/0.75 tff(259,assumption,((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))), introduced(assumption)).
% 0.77/0.75 tff(260,assumption,(lesseq(max(X!5, Y!4), Z!3)), introduced(assumption)).
% 0.77/0.75 tff(261,plain,
% 0.77/0.75 (lesseq(X!5, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.77/0.75 inference(monotonicity,[status(thm)],[17])).
% 0.77/0.75 tff(262,plain,
% 0.77/0.75 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(X!5, Z!3)),
% 0.77/0.75 inference(symmetry,[status(thm)],[261])).
% 0.77/0.75 tff(263,plain,
% 0.77/0.75 (lesseq(X!5, Z!3)),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[260, 262])).
% 0.77/0.75 tff(264,plain,
% 0.77/0.75 (lesseq(Y!4, X!5) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[17])).
% 0.77/0.75 tff(265,plain,
% 0.77/0.75 (lesseq(Y!4, max(X!5, Y!4))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[1, 264])).
% 0.77/0.75 tff(266,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(267,plain,
% 0.77/0.75 ((lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4)))) <=> (lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(268,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[267])).
% 0.77/0.75 tff(269,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.77/0.75 inference(transitivity,[status(thm)],[268, 266])).
% 0.77/0.75 tff(270,plain,
% 0.77/0.75 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4))))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(271,plain,
% 0.77/0.75 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.77/0.75 tff(272,plain,
% 0.77/0.75 (lesseq(Y!4, Z!3)),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[271, 147, 260, 265])).
% 0.77/0.75 tff(273,plain,
% 0.77/0.75 ((~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))) | (~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(274,plain,
% 0.77/0.75 ($false),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[273, 272, 263, 259])).
% 0.77/0.75 tff(275,plain,((~lesseq(Y!4, X!5)) | (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))) | (~lesseq(max(X!5, Y!4), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.75 tff(276,plain,
% 0.77/0.75 (~lesseq(Y!4, X!5)),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[275, 259, 260])).
% 0.77/0.75 tff(277,plain,
% 0.77/0.75 (((~![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))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(278,plain,
% 0.77/0.75 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(279,plain,
% 0.77/0.75 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5)),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.77/0.75 tff(280,plain,
% 0.77/0.75 (lesseq(X!5, Y!4)),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[279, 186, 276])).
% 0.77/0.75 tff(281,plain,
% 0.77/0.75 (max(X!5, Y!4) = Y!4),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[178, 280])).
% 0.77/0.75 tff(282,plain,
% 0.77/0.75 (Y!4 = max(X!5, Y!4)),
% 0.77/0.75 inference(symmetry,[status(thm)],[281])).
% 0.77/0.75 tff(283,plain,
% 0.77/0.75 (lesseq(Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.77/0.75 inference(monotonicity,[status(thm)],[282])).
% 0.77/0.75 tff(284,plain,
% 0.77/0.75 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(Y!4, Z!3)),
% 0.77/0.75 inference(symmetry,[status(thm)],[283])).
% 0.77/0.75 tff(285,plain,
% 0.77/0.75 (lesseq(Y!4, Z!3)),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[260, 284])).
% 0.77/0.75 tff(286,plain,
% 0.77/0.75 (lesseq(X!5, Y!4) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[282])).
% 0.77/0.75 tff(287,plain,
% 0.77/0.75 (lesseq(X!5, max(X!5, Y!4))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[280, 286])).
% 0.77/0.75 tff(288,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(289,plain,
% 0.77/0.75 ((lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4)))) <=> (lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(290,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[289])).
% 0.77/0.75 tff(291,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.77/0.75 inference(transitivity,[status(thm)],[290, 288])).
% 0.77/0.75 tff(292,plain,
% 0.77/0.75 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4))))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(293,plain,
% 0.77/0.75 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.77/0.75 tff(294,plain,
% 0.77/0.75 (lesseq(X!5, Z!3)),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[293, 147, 260, 287])).
% 0.77/0.75 tff(295,plain,
% 0.77/0.75 ($false),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[273, 294, 285, 259])).
% 0.77/0.75 tff(296,plain,((~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))) | (~lesseq(max(X!5, Y!4), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.75 tff(297,plain,
% 0.77/0.75 (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[296, 250])).
% 0.77/0.75 tff(298,assumption,(~(ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))))), introduced(assumption)).
% 0.77/0.75 tff(299,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(300,plain,
% 0.77/0.75 ((ub(X!5, Y!4, Z!3) <=> (~((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3))))) <=> (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(301,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[300])).
% 0.77/0.75 tff(302,plain,
% 0.77/0.75 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))))))),
% 0.77/0.75 inference(transitivity,[status(thm)],[301, 299])).
% 0.77/0.75 tff(303,plain,
% 0.77/0.75 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3)))))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(304,plain,
% 0.77/0.75 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.77/0.75 tff(305,plain,
% 0.77/0.75 ($false),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[304, 33, 298])).
% 0.77/0.75 tff(306,plain,(ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.75 tff(307,plain,
% 0.77/0.75 ((~(ub(X!5, Y!4, Z!3) <=> (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))))) | ub(X!5, Y!4, Z!3) | ((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(308,plain,
% 0.77/0.75 (ub(X!5, Y!4, Z!3) | ((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[307, 306])).
% 0.77/0.75 tff(309,plain,
% 0.77/0.75 (ub(X!5, Y!4, Z!3)),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[308, 297])).
% 0.77/0.75 tff(310,plain,
% 0.77/0.75 (((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | ((~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3)))) <=> ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | (~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(311,plain,
% 0.77/0.75 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | ((~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3)))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(312,plain,
% 0.77/0.75 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | (~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.77/0.75 tff(313,plain,
% 0.77/0.75 ($false),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[312, 309, 258, 257])).
% 0.77/0.75 tff(314,plain,((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | (~lesseq(Z!3, Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.75 tff(315,plain,
% 0.77/0.75 (~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[314, 256])).
% 0.77/0.75 tff(316,plain,
% 0.77/0.75 (((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))))) | (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(317,plain,
% 0.77/0.75 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[316, 212])).
% 0.77/0.75 tff(318,plain,
% 0.77/0.75 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(319,plain,
% 0.77/0.75 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.77/0.75 tff(320,plain,
% 0.77/0.75 (model_ub(X!5, Y!4, Z!3)),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[319, 315])).
% 0.77/0.75 tff(321,plain,
% 0.77/0.75 (((~(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)))))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(322,plain,
% 0.77/0.75 (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))))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[321, 243])).
% 0.77/0.75 tff(323,plain,
% 0.77/0.75 ((~(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))))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(324,plain,
% 0.77/0.75 (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))))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.77/0.75 tff(325,plain,
% 0.77/0.75 (~((~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)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[324, 320, 63])).
% 0.77/0.75 tff(326,plain,
% 0.77/0.75 (((~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))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(327,plain,
% 0.77/0.75 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[326, 325])).
% 0.77/0.75 tff(328,plain,
% 0.77/0.75 (((~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)))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(329,plain,
% 0.77/0.75 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[328, 325])).
% 0.77/0.75 tff(330,plain,
% 0.77/0.75 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(331,plain,
% 0.77/0.75 (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[330, 114])).
% 0.77/0.75 tff(332,assumption,(~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.77/0.75 tff(333,assumption,(![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.77/0.75 tff(334,plain,
% 0.77/0.75 (((~![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)))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(335,plain,
% 0.77/0.75 ((~![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)))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(336,plain,
% 0.77/0.75 ((~![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))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.77/0.75 tff(337,plain,
% 0.77/0.75 (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[336, 333, 332])).
% 0.77/0.75 tff(338,plain,
% 0.77/0.75 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(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(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.77/0.75 inference(tautology,[status(thm)],[])).
% 0.77/0.75 tff(339,plain,
% 0.77/0.75 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[338, 337])).
% 0.77/0.75 tff(340,plain,
% 0.77/0.75 (~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[339, 331])).
% 0.77/0.75 tff(341,plain,
% 0.77/0.75 (((~![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(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))))))) <=> ((~![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(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)))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(342,plain,
% 0.77/0.76 ((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(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))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(343,plain,
% 0.77/0.76 (((~![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))))))) <=> ((~![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(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)))))))),
% 0.77/0.76 inference(monotonicity,[status(thm)],[342])).
% 0.77/0.76 tff(344,plain,
% 0.77/0.76 (((~![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))))))) <=> ((~![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(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)))))))),
% 0.77/0.76 inference(transitivity,[status(thm)],[343, 341])).
% 0.77/0.76 tff(345,plain,
% 0.77/0.76 ((~![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))))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(346,plain,
% 0.77/0.76 ((~![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(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))))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.77/0.76 tff(347,plain,
% 0.77/0.76 (ub(X!5, 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)))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[346, 33])).
% 0.77/0.76 tff(348,plain,
% 0.77/0.76 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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(Z, tptp_fun_Z_2(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(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(349,plain,
% 0.77/0.76 ((~((~((~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(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] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z))))))) <=> (~((~((~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(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(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(350,plain,
% 0.77/0.76 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, 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(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.77/0.76 inference(monotonicity,[status(thm)],[349])).
% 0.77/0.76 tff(351,plain,
% 0.77/0.76 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, 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(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.77/0.76 inference(transitivity,[status(thm)],[350, 348])).
% 0.77/0.76 tff(352,plain,
% 0.77/0.76 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z)))))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(353,plain,
% 0.77/0.76 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~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(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(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.77/0.76 tff(354,plain,
% 0.77/0.76 (~((~((~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(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(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[353, 53])).
% 0.77/0.76 tff(355,plain,
% 0.77/0.76 (((~((~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(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(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(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))))))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(356,plain,
% 0.77/0.76 ((~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(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)))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[355, 354])).
% 0.77/0.76 tff(357,assumption,(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.77/0.76 tff(358,plain,
% 0.77/0.76 ((~((~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(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(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)))))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(359,plain,
% 0.77/0.76 ((~((~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(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(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)))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[358, 357])).
% 0.77/0.76 tff(360,plain,
% 0.77/0.76 (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(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))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[359, 356])).
% 0.77/0.76 tff(361,plain,
% 0.77/0.76 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(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))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(362,plain,
% 0.77/0.76 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[361, 360])).
% 0.77/0.77 tff(363,plain,
% 0.77/0.77 ((~(ub(X!5, 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))))))) | (~ub(X!5, 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)))))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(364,plain,
% 0.77/0.77 ((~(ub(X!5, 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))) | (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[363, 362])).
% 0.77/0.77 tff(365,plain,
% 0.77/0.77 (~((~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))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[364, 347])).
% 0.77/0.77 tff(366,plain,
% 0.77/0.77 (((~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(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(367,plain,
% 0.77/0.77 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[366, 365])).
% 0.77/0.77 tff(368,plain,
% 0.77/0.77 (((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(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_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))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(369,plain,
% 0.77/0.77 (lesseq(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))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[368, 360])).
% 0.77/0.77 tff(370,plain,
% 0.77/0.77 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(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(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_2(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(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(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_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(371,plain,
% 0.77/0.77 ((lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ((~lesseq(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(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_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(372,plain,
% 0.77/0.77 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(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(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_2(Z!3, Y!4, X!5))))),
% 0.77/0.77 inference(monotonicity,[status(thm)],[371])).
% 0.77/0.77 tff(373,plain,
% 0.77/0.77 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(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(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_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(transitivity,[status(thm)],[372, 370])).
% 0.77/0.77 tff(374,plain,
% 0.77/0.77 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.77/0.77 inference(quant_inst,[status(thm)],[])).
% 0.77/0.77 tff(375,plain,
% 0.77/0.77 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.77/0.77 tff(376,plain,
% 0.77/0.77 (lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[375, 147, 369, 367])).
% 0.77/0.77 tff(377,plain,
% 0.77/0.77 (lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(monotonicity,[status(thm)],[156])).
% 0.77/0.77 tff(378,plain,
% 0.77/0.77 (lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(symmetry,[status(thm)],[377])).
% 0.77/0.77 tff(379,plain,
% 0.77/0.77 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(monotonicity,[status(thm)],[378])).
% 0.77/0.77 tff(380,assumption,(~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.77/0.77 tff(381,plain,
% 0.77/0.77 (~lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.77/0.77 tff(382,assumption,(lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.77/0.77 tff(383,plain,
% 0.77/0.77 ($false),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[382, 381])).
% 0.77/0.77 tff(384,plain,((~(max(X!5, Y!4) = Y!4)) | (~lesseq(Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.77 tff(385,plain,
% 0.77/0.77 (~(max(X!5, Y!4) = Y!4)),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[384, 376, 340])).
% 0.77/0.77 tff(386,plain,
% 0.77/0.77 (~lesseq(X!5, Y!4)),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[178, 385])).
% 0.77/0.77 tff(387,plain,
% 0.77/0.77 (lesseq(Y!4, X!5)),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[189, 186, 386])).
% 0.77/0.77 tff(388,plain,
% 0.77/0.77 (max(X!5, Y!4) = X!5),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[15, 387])).
% 0.77/0.77 tff(389,plain,
% 0.77/0.77 (X!5 = max(X!5, Y!4)),
% 0.77/0.77 inference(symmetry,[status(thm)],[388])).
% 0.77/0.77 tff(390,plain,
% 0.77/0.77 (lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(monotonicity,[status(thm)],[389])).
% 0.77/0.77 tff(391,plain,
% 0.77/0.77 (lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(symmetry,[status(thm)],[390])).
% 0.77/0.77 tff(392,plain,
% 0.77/0.77 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(monotonicity,[status(thm)],[391])).
% 0.77/0.77 tff(393,plain,
% 0.77/0.77 (~lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[340, 392])).
% 0.77/0.77 tff(394,plain,
% 0.77/0.77 (((~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))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(395,plain,
% 0.77/0.77 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[394, 365])).
% 0.77/0.77 tff(396,plain,
% 0.77/0.77 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(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(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_2(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(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(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_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(397,plain,
% 0.77/0.77 ((lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ((~lesseq(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(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_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(398,plain,
% 0.77/0.77 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(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(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_2(Z!3, Y!4, X!5))))),
% 0.77/0.77 inference(monotonicity,[status(thm)],[397])).
% 0.77/0.77 tff(399,plain,
% 0.77/0.77 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(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(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_2(Z!3, Y!4, X!5)))),
% 0.77/0.77 inference(transitivity,[status(thm)],[398, 396])).
% 0.77/0.77 tff(400,plain,
% 0.77/0.77 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(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(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.77/0.77 inference(quant_inst,[status(thm)],[])).
% 0.77/0.77 tff(401,plain,
% 0.77/0.77 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.77/0.77 tff(402,plain,
% 0.77/0.77 (lesseq(X!5, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[401, 147, 369, 395])).
% 0.77/0.77 tff(403,plain,
% 0.77/0.77 ($false),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[402, 393])).
% 0.77/0.77 tff(404,plain,((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.77 tff(405,plain,
% 0.77/0.77 ($false),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[404, 329, 327, 106])).
% 0.77/0.77 tff(406,plain,(minsol_model_ub(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.77 tff(407,plain,
% 0.77/0.77 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[247, 406])).
% 0.77/0.77 tff(408,plain,
% 0.77/0.77 (((~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))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(409,plain,
% 0.77/0.77 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[408, 407])).
% 0.77/0.77 tff(410,plain,
% 0.77/0.77 ((~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)))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(411,plain,
% 0.77/0.77 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[410, 75])).
% 0.77/0.77 tff(412,plain,
% 0.77/0.77 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[411, 406])).
% 0.77/0.77 tff(413,plain,
% 0.77/0.77 (((~(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)))))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(414,plain,
% 0.77/0.77 (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))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[413, 99])).
% 0.77/0.77 tff(415,plain,
% 0.77/0.77 ((~(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))))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(416,plain,
% 0.77/0.77 (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))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[415, 414])).
% 0.77/0.77 tff(417,plain,
% 0.77/0.77 (~((~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)))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[416, 412, 252])).
% 0.77/0.77 tff(418,plain,
% 0.77/0.77 (((~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)))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(419,plain,
% 0.77/0.77 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[418, 417])).
% 0.77/0.77 tff(420,plain,
% 0.77/0.77 (((~![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)))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(421,plain,
% 0.77/0.77 ((~![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)))),
% 0.77/0.77 inference(quant_inst,[status(thm)],[])).
% 0.77/0.77 tff(422,plain,
% 0.77/0.77 ((~![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))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.77/0.77 tff(423,plain,
% 0.77/0.77 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[422, 419, 409])).
% 0.77/0.77 tff(424,plain,
% 0.77/0.77 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, 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)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(425,plain,
% 0.77/0.77 ((~(model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[424, 423])).
% 0.77/0.78 tff(426,plain,
% 0.77/0.78 (![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[425, 62])).
% 0.77/0.78 tff(427,plain,
% 0.77/0.78 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.77/0.78 inference(quant_inst,[status(thm)],[])).
% 0.77/0.78 tff(428,plain,
% 0.77/0.78 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[427, 114])).
% 0.77/0.78 tff(429,plain,
% 0.77/0.78 (((~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))),
% 0.77/0.78 inference(tautology,[status(thm)],[])).
% 0.77/0.78 tff(430,plain,
% 0.77/0.78 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[429, 417])).
% 0.77/0.78 tff(431,plain,
% 0.77/0.78 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(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))) | lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.77/0.78 inference(tautology,[status(thm)],[])).
% 0.77/0.78 tff(432,plain,
% 0.77/0.78 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[431, 430])).
% 0.77/0.78 tff(433,plain,
% 0.77/0.78 (lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[432, 428])).
% 0.77/0.78 tff(434,plain,
% 0.77/0.78 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, max(X!5, Y!4))))),
% 0.77/0.78 inference(rewrite,[status(thm)],[])).
% 0.77/0.78 tff(435,plain,
% 0.77/0.78 (((~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5)))) <=> ((~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, max(X!5, Y!4))))),
% 0.77/0.78 inference(rewrite,[status(thm)],[])).
% 0.77/0.78 tff(436,plain,
% 0.77/0.78 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, max(X!5, Y!4)))))),
% 0.77/0.78 inference(monotonicity,[status(thm)],[435])).
% 0.77/0.78 tff(437,plain,
% 0.77/0.78 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, max(X!5, Y!4))))),
% 0.77/0.78 inference(transitivity,[status(thm)],[436, 434])).
% 0.77/0.78 tff(438,plain,
% 0.77/0.78 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.77/0.78 inference(quant_inst,[status(thm)],[])).
% 0.77/0.78 tff(439,plain,
% 0.77/0.78 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_1(Z!3, Y!4, X!5))))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, max(X!5, Y!4)))),
% 0.77/0.78 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.77/0.78 tff(440,plain,
% 0.77/0.78 (~ub(X!5, Y!4, max(X!5, Y!4))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[439, 433, 426])).
% 0.77/0.78 tff(441,plain,
% 0.77/0.78 ((~(ub(X!5, Y!4, max(X!5, Y!4)) <=> (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4))))))) | ub(X!5, Y!4, max(X!5, Y!4)) | ((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4))))),
% 0.77/0.78 inference(tautology,[status(thm)],[])).
% 0.77/0.78 tff(442,plain,
% 0.77/0.78 ((~(ub(X!5, 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))) | (~lesseq(Y!4, max(X!5, Y!4))))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[441, 440])).
% 0.77/0.78 tff(443,plain,
% 0.77/0.78 ((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[442, 40])).
% 0.77/0.78 tff(444,plain,
% 0.77/0.78 ((~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4))))) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))),
% 0.77/0.78 inference(tautology,[status(thm)],[])).
% 0.77/0.78 tff(445,plain,
% 0.77/0.78 ((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[444, 443])).
% 0.77/0.78 tff(446,plain,
% 0.77/0.78 (~lesseq(X!5, max(X!5, Y!4))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[445, 23])).
% 0.77/0.78 tff(447,plain,
% 0.77/0.78 (~lesseq(X!5, X!5)),
% 0.77/0.78 inference(modus_ponens,[status(thm)],[446, 20])).
% 0.77/0.78 tff(448,plain,
% 0.77/0.78 (((~![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))),
% 0.77/0.78 inference(rewrite,[status(thm)],[])).
% 0.77/0.78 tff(449,plain,
% 0.77/0.78 ((lesseq(X!5, X!5) | lesseq(X!5, X!5)) <=> lesseq(X!5, X!5)),
% 0.77/0.78 inference(rewrite,[status(thm)],[])).
% 0.77/0.78 tff(450,plain,
% 0.77/0.78 (((~![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))),
% 0.77/0.78 inference(monotonicity,[status(thm)],[449])).
% 0.77/0.78 tff(451,plain,
% 0.77/0.78 (((~![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))),
% 0.77/0.78 inference(transitivity,[status(thm)],[450, 448])).
% 0.77/0.78 tff(452,plain,
% 0.77/0.78 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))),
% 0.77/0.78 inference(quant_inst,[status(thm)],[])).
% 0.77/0.78 tff(453,plain,
% 0.77/0.78 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)),
% 0.77/0.78 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.77/0.78 tff(454,plain,
% 0.77/0.78 (lesseq(X!5, X!5)),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[453, 186])).
% 0.77/0.78 tff(455,plain,
% 0.77/0.78 ($false),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[454, 447])).
% 0.77/0.78 tff(456,plain,(~lesseq(Y!4, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.78 tff(457,plain,
% 0.77/0.78 (lesseq(X!5, Y!4)),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[279, 186, 456])).
% 0.77/0.78 tff(458,plain,
% 0.77/0.78 (max(X!5, Y!4) = Y!4),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[178, 457])).
% 0.77/0.78 tff(459,plain,
% 0.77/0.78 (Y!4 = max(X!5, Y!4)),
% 0.77/0.78 inference(symmetry,[status(thm)],[458])).
% 0.77/0.78 tff(460,plain,
% 0.77/0.78 (lesseq(Y!4, Y!4) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.77/0.78 inference(monotonicity,[status(thm)],[459])).
% 0.77/0.78 tff(461,plain,
% 0.77/0.78 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.77/0.78 inference(symmetry,[status(thm)],[460])).
% 0.77/0.78 tff(462,plain,
% 0.77/0.78 ((~lesseq(Y!4, max(X!5, Y!4))) <=> (~lesseq(Y!4, Y!4))),
% 0.77/0.78 inference(monotonicity,[status(thm)],[461])).
% 0.77/0.78 tff(463,plain,
% 0.77/0.78 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, Y!4)),
% 0.77/0.78 inference(monotonicity,[status(thm)],[458])).
% 0.77/0.78 tff(464,plain,
% 0.77/0.78 (lesseq(X!5, Y!4) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.77/0.78 inference(symmetry,[status(thm)],[463])).
% 0.77/0.78 tff(465,plain,
% 0.77/0.78 (lesseq(X!5, max(X!5, Y!4))),
% 0.77/0.78 inference(modus_ponens,[status(thm)],[457, 464])).
% 0.77/0.78 tff(466,plain,
% 0.77/0.78 (~lesseq(Y!4, max(X!5, Y!4))),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[445, 465])).
% 0.77/0.78 tff(467,plain,
% 0.77/0.78 (~lesseq(Y!4, Y!4)),
% 0.77/0.78 inference(modus_ponens,[status(thm)],[466, 462])).
% 0.77/0.78 tff(468,plain,
% 0.77/0.78 (((~![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))),
% 0.77/0.78 inference(rewrite,[status(thm)],[])).
% 0.77/0.78 tff(469,plain,
% 0.77/0.78 ((lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.77/0.78 inference(rewrite,[status(thm)],[])).
% 0.77/0.78 tff(470,plain,
% 0.77/0.78 (((~![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))),
% 0.77/0.78 inference(monotonicity,[status(thm)],[469])).
% 0.77/0.78 tff(471,plain,
% 0.77/0.78 (((~![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))),
% 0.77/0.78 inference(transitivity,[status(thm)],[470, 468])).
% 0.77/0.78 tff(472,plain,
% 0.77/0.78 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))),
% 0.77/0.78 inference(quant_inst,[status(thm)],[])).
% 0.77/0.78 tff(473,plain,
% 0.77/0.78 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)),
% 0.77/0.78 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.77/0.78 tff(474,plain,
% 0.77/0.78 (lesseq(Y!4, Y!4)),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[473, 186])).
% 0.77/0.78 tff(475,plain,
% 0.77/0.78 ($false),
% 0.77/0.78 inference(unit_resolution,[status(thm)],[474, 467])).
% 0.77/0.78 % SZS output end Proof
%------------------------------------------------------------------------------