TSTP Solution File: NUM858+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:12:20 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.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 15:35:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(lesseq_type, type, (
% 0.19/0.39 lesseq: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.39 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X_4_type, type, (
% 0.19/0.39 tptp_fun_X_4: $i)).
% 0.19/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.39 tptp_fun_Y_3: $i)).
% 0.19/0.39 tff(tptp_fun_Z_2_type, type, (
% 0.19/0.39 tptp_fun_Z_2: $i)).
% 0.19/0.39 tff(max_type, type, (
% 0.19/0.39 max: ( $i * $i ) > $i)).
% 0.19/0.39 tff(ub_type, type, (
% 0.19/0.39 ub: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(model_ub_type, type, (
% 0.19/0.39 model_ub: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(minsol_model_ub_type, type, (
% 0.19/0.39 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(model_max_type, type, (
% 0.19/0.39 model_max: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(minsol_model_max_type, type, (
% 0.19/0.39 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Z_1_type, type, (
% 0.19/0.39 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,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')).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,plain,(
% 0.19/0.39 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[7])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Z!2) <=> (~((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (ub(X!4, Y!3, Z!2) <=> (~((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (^[X: $i, Y: $i, N: $i] : refl((model_ub(X, Y, N) <=> ub(X, Y, N)) <=> (model_ub(X, Y, N) <=> ub(X, Y, N)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N)) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N)) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_ub_1')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,(
% 0.19/0.39 ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.39 inference(skolemize,[status(sab)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> (N = max(X, Y))) <=> (model_max(X, Y, N) <=> (N = max(X, Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y))) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y))) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_max_1')).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.40 tff(27,plain,(
% 0.19/0.40 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[26])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))) | (model_max(X!4, Y!3, Z!2) <=> (Z!2 = max(X!4, Y!3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (model_max(X!4, Y!3, Z!2) <=> (Z!2 = max(X!4, Y!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.40 tff(31,assumption,(~minsol_model_ub(X!4, Y!3, Z!2)), introduced(assumption)).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~(minsol_model_ub(X!4, Y!3, Z!2) <=> minsol_model_max(X!4, Y!3, Z!2))) <=> ((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,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')).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 33])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.40 tff(42,plain,(
% 0.19/0.40 ~(minsol_model_ub(X!4, Y!3, Z!2) <=> minsol_model_max(X!4, Y!3, Z!2))),
% 0.19/0.40 inference(skolemize,[status(sab)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (minsol_model_ub(X!4, Y!3, Z!2) | minsol_model_max(X!4, Y!3, Z!2) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (minsol_model_ub(X!4, Y!3, Z!2) | minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[45, 31])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (^[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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (^[X: $i, Y: $i, N: $i] : refl((~((~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (^[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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))) <=> (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (^[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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.40 tff(61,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')).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.40 tff(64,plain,(
% 0.19/0.40 ![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[63])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![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_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 53])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 48])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_0(N, Y, X))) | lesseq(N, tptp_fun_Z_0(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!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (~((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))))) | ((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))))))) | (~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 46])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))) | model_max(X!4, Y!3, Z!2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (model_max(X!4, Y!3, Z!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~(model_max(X!4, Y!3, Z!2) <=> (Z!2 = max(X!4, Y!3)))) | (~model_max(X!4, Y!3, Z!2)) | (Z!2 = max(X!4, Y!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((~(model_max(X!4, Y!3, Z!2) <=> (Z!2 = max(X!4, Y!3)))) | (Z!2 = max(X!4, Y!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (Z!2 = max(X!4, Y!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[79, 30])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))) | ![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_max(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2))) <=> ((~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_max(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_max(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_max(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (lesseq(Z!2, Z!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 77, 82])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, max(X!4, Y!3)) <=> (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (ub(X!4, Y!3, max(X!4, Y!3)) <=> (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[87, 10])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, max(X!4, Y!3)) <=> ub(X!4, Y!3, max(X!4, Y!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (model_ub(X!4, Y!3, max(X!4, Y!3)) <=> ub(X!4, Y!3, max(X!4, Y!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[89, 19])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (max(X!4, Y!3) = Z!2),
% 0.19/0.41 inference(symmetry,[status(thm)],[80])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (model_ub(X!4, Y!3, max(X!4, Y!3)) <=> model_ub(X!4, Y!3, Z!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (model_ub(X!4, Y!3, Z!2) <=> model_ub(X!4, Y!3, max(X!4, Y!3))),
% 0.19/0.41 inference(symmetry,[status(thm)],[92])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~model_ub(X!4, Y!3, Z!2)) <=> (~model_ub(X!4, Y!3, max(X!4, Y!3)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4)))))) <=> (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 10])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (model_ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 19])).
% 0.19/0.41 tff(105,assumption,(~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))), introduced(assumption)).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 10])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> ub(max(X!4, Y!3), Y!3, max(X!4, Y!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[108, 19])).
% 0.19/0.41 tff(110,assumption,(lesseq(Y!3, X!4)), introduced(assumption)).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = X) | (~lesseq(Y, X))) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.41 tff(116,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_1')).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.19/0.41 tff(119,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.41 inference(skolemize,[status(sab)],[118])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!3, X!4)) | (max(X!4, Y!3) = X!4))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!3, X!4)) | (max(X!4, Y!3) = X!4))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!3, X!4)) | (max(X!4, Y!3) = X!4))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!3, X!4)) | (max(X!4, Y!3) = X!4)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~lesseq(Y!3, X!4)) | (max(X!4, Y!3) = X!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (max(X!4, Y!3) = X!4),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[124, 110])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> model_ub(X!4, Y!3, Z!2)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[125, 91])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (model_ub(X!4, Y!3, Z!2) <=> model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3))),
% 0.19/0.42 inference(symmetry,[status(thm)],[126])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 ((~model_ub(X!4, Y!3, Z!2)) <=> (~model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[129, 10])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (model_ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[131, 19])).
% 0.19/0.42 tff(133,assumption,(max(X!4, Y!3) = X!4), introduced(assumption)).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (model_ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(symmetry,[status(thm)],[134])).
% 0.19/0.42 tff(136,assumption,(model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))), introduced(assumption)).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (model_ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((~(model_ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)))) | (~model_ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 137, 132])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (((~lesseq(Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))) | lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~lesseq(Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[140, 105])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 ((~(ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))) | (~ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~((~lesseq(Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 ((~(ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))) | (~ub(max(X!4, Y!3), Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[143, 139, 130])).
% 0.19/0.42 tff(145,plain,((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) | (~(max(X!4, Y!3) = X!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[145, 125, 105])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))) | model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (^[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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))) <=> (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (^[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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (^[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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[154, 152])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (^[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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))) <=> (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (^[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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[161])).
% 0.19/0.42 tff(163,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')).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.19/0.42 tff(166,plain,(
% 0.19/0.42 ![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[165])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (![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_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[168, 155])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[169, 150])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(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!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (~((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))))) | (minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 ((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))))) | minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (~model_ub(X!4, Y!3, Z!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[176, 148, 31])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (~model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[177, 128])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 ((~(model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)))) | model_ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) | (~ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (~ub(max(X!4, Y!3), Y!3, max(X!4, Y!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[179, 178, 109])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (lesseq(Y!3, max(X!4, Y!3)) <=> lesseq(Y!3, X!4)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (lesseq(Y!3, X!4) <=> lesseq(Y!3, max(X!4, Y!3))),
% 0.19/0.43 inference(symmetry,[status(thm)],[181])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (lesseq(Y!3, max(X!4, Y!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[110, 182])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (lesseq(max(X!4, Y!3), max(X!4, Y!3)) <=> lesseq(Z!2, Z!2)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[91, 91])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (lesseq(Z!2, Z!2) <=> lesseq(max(X!4, Y!3), max(X!4, Y!3))),
% 0.19/0.43 inference(symmetry,[status(thm)],[184])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (lesseq(max(X!4, Y!3), max(X!4, Y!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[86, 185])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 ((~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))))) | (~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[187, 186, 183])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 ((~(ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))))))) | ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) | ((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 ((~(ub(max(X!4, Y!3), Y!3, max(X!4, Y!3)) <=> (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))))))) | ub(max(X!4, Y!3), Y!3, max(X!4, Y!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[190, 180, 107])).
% 0.19/0.43 tff(192,plain,((~lesseq(Y!3, X!4)) | minsol_model_ub(X!4, Y!3, Z!2) | lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 (~lesseq(Y!3, X!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[192, 105, 31])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[194])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(197,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lesseq_total')).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.43 tff(199,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.43 inference(skolemize,[status(sab)],[198])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!4, Y!3) | lesseq(Y!3, X!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!4, Y!3) | lesseq(Y!3, X!4))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!4, Y!3) | lesseq(Y!3, X!4))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!4, Y!3) | lesseq(Y!3, X!4)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 (lesseq(X!4, Y!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[203, 200, 193])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(208,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[208])).
% 0.19/0.43 tff(210,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_2')).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.19/0.43 tff(213,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.43 inference(skolemize,[status(sab)],[212])).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.19/0.43 tff(215,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!4, Y!3)) | (max(X!4, Y!3) = Y!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!4, Y!3)) | (max(X!4, Y!3) = Y!3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(216,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!4, Y!3)) | (max(X!4, Y!3) = Y!3))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!4, Y!3)) | (max(X!4, Y!3) = Y!3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.43 tff(218,plain,
% 0.19/0.43 ((~lesseq(X!4, Y!3)) | (max(X!4, Y!3) = Y!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[217, 214])).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 (max(X!4, Y!3) = Y!3),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[218, 204])).
% 0.19/0.43 tff(220,plain,
% 0.19/0.43 (model_ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.43 tff(221,plain,
% 0.19/0.43 (model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> model_ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.43 inference(symmetry,[status(thm)],[220])).
% 0.19/0.43 tff(222,plain,
% 0.19/0.43 (lesseq(X!4, max(X!4, Y!3)) <=> lesseq(X!4, Y!3)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.43 tff(223,plain,
% 0.19/0.43 (lesseq(X!4, Y!3) <=> lesseq(X!4, max(X!4, Y!3))),
% 0.19/0.43 inference(symmetry,[status(thm)],[222])).
% 0.19/0.43 tff(224,plain,
% 0.19/0.43 (lesseq(X!4, max(X!4, Y!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[204, 223])).
% 0.19/0.43 tff(225,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> (~((~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(226,plain,
% 0.19/0.43 (ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> (~((~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[225, 10])).
% 0.19/0.43 tff(227,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> ub(X!4, max(X!4, Y!3), max(X!4, Y!3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(228,plain,
% 0.19/0.43 (model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> ub(X!4, max(X!4, Y!3), max(X!4, Y!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[227, 19])).
% 0.19/0.43 tff(229,assumption,(Z!2 = max(X!4, Y!3)), introduced(assumption)).
% 0.19/0.43 tff(230,plain,
% 0.19/0.43 (max(X!4, Y!3) = Z!2),
% 0.19/0.43 inference(symmetry,[status(thm)],[229])).
% 0.19/0.43 tff(231,assumption,(max(X!4, Y!3) = Y!3), introduced(assumption)).
% 0.19/0.43 tff(232,plain,
% 0.19/0.43 (model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> model_ub(X!4, Y!3, Z!2)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[231, 230])).
% 0.19/0.43 tff(233,plain,
% 0.19/0.43 (model_ub(X!4, Y!3, Z!2) <=> model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3))),
% 0.19/0.43 inference(symmetry,[status(thm)],[232])).
% 0.19/0.43 tff(234,plain,
% 0.19/0.43 ((~model_ub(X!4, Y!3, Z!2)) <=> (~model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[233])).
% 0.19/0.43 tff(235,assumption,(~model_ub(X!4, Y!3, Z!2)), introduced(assumption)).
% 0.19/0.43 tff(236,plain,
% 0.19/0.43 (~model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.19/0.43 tff(237,plain,
% 0.19/0.43 ((~(model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> ub(X!4, max(X!4, Y!3), max(X!4, Y!3)))) | model_ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) | (~ub(X!4, max(X!4, Y!3), max(X!4, Y!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(238,plain,
% 0.19/0.43 (~ub(X!4, max(X!4, Y!3), max(X!4, Y!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[237, 236, 228])).
% 0.19/0.43 tff(239,assumption,(lesseq(X!4, max(X!4, Y!3))), introduced(assumption)).
% 0.19/0.43 tff(240,assumption,(lesseq(max(X!4, Y!3), max(X!4, Y!3))), introduced(assumption)).
% 0.19/0.43 tff(241,plain,
% 0.19/0.43 ((~((~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(242,plain,
% 0.19/0.43 (~((~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[241, 240, 239])).
% 0.19/0.43 tff(243,plain,
% 0.19/0.43 ((~(ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> (~((~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))))) | ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) | ((~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(244,plain,
% 0.19/0.44 ((~(ub(X!4, max(X!4, Y!3), max(X!4, Y!3)) <=> (~((~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))))) | ub(X!4, max(X!4, Y!3), max(X!4, Y!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.19/0.44 tff(245,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[244, 238, 226])).
% 0.19/0.44 tff(246,plain,(model_ub(X!4, Y!3, Z!2) | (~lesseq(max(X!4, Y!3), max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))) | (~(Z!2 = max(X!4, Y!3))) | (~(max(X!4, Y!3) = Y!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(247,plain,
% 0.19/0.44 (model_ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[246, 224, 186, 80, 219])).
% 0.19/0.44 tff(248,plain,
% 0.19/0.44 (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[176, 247, 31])).
% 0.19/0.44 tff(249,plain,
% 0.19/0.44 (model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[147, 248])).
% 0.19/0.44 tff(250,plain,
% 0.19/0.44 (model_ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[249, 221])).
% 0.19/0.44 tff(251,plain,
% 0.19/0.44 ((~(model_ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))) | (~model_ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))) | ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(252,plain,
% 0.19/0.44 (ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[251, 250, 104])).
% 0.19/0.44 tff(253,plain,
% 0.19/0.44 (((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))) | lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(254,plain,
% 0.19/0.44 ((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[253, 105])).
% 0.19/0.44 tff(255,plain,
% 0.19/0.44 ((~(ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))) | (~ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(256,plain,
% 0.19/0.44 ((~(ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) <=> (~((~lesseq(X!4, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))))))) | (~ub(X!4, max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.19/0.44 tff(257,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[256, 252, 102])).
% 0.19/0.44 tff(258,plain,(lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4)) | minsol_model_ub(X!4, Y!3, Z!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(259,plain,
% 0.19/0.44 (lesseq(max(X!4, Y!3), tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[258, 31])).
% 0.19/0.44 tff(260,plain,
% 0.19/0.44 (lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[259, 95])).
% 0.19/0.44 tff(261,plain,
% 0.19/0.44 (((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))) | (~lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(262,plain,
% 0.19/0.44 ((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[261, 260])).
% 0.19/0.44 tff(263,plain,
% 0.19/0.44 (~model_ub(X!4, Y!3, Z!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[176, 262, 31])).
% 0.19/0.44 tff(264,plain,
% 0.19/0.44 (~model_ub(X!4, Y!3, max(X!4, Y!3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[263, 94])).
% 0.19/0.44 tff(265,plain,
% 0.19/0.44 ((~(model_ub(X!4, Y!3, max(X!4, Y!3)) <=> ub(X!4, Y!3, max(X!4, Y!3)))) | model_ub(X!4, Y!3, max(X!4, Y!3)) | (~ub(X!4, Y!3, max(X!4, Y!3)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(266,plain,
% 0.19/0.44 (~ub(X!4, Y!3, max(X!4, Y!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[265, 264, 90])).
% 0.19/0.44 tff(267,plain,
% 0.19/0.44 ((~(ub(X!4, Y!3, max(X!4, Y!3)) <=> (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))))) | ub(X!4, Y!3, max(X!4, Y!3)) | ((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(268,plain,
% 0.19/0.44 ((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[267, 266, 88])).
% 0.19/0.44 tff(269,assumption,((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3)))), introduced(assumption)).
% 0.19/0.44 tff(270,plain,
% 0.19/0.44 (X!4 = max(X!4, Y!3)),
% 0.19/0.44 inference(symmetry,[status(thm)],[125])).
% 0.19/0.44 tff(271,plain,
% 0.19/0.44 (lesseq(Y!3, X!4) <=> lesseq(Y!3, max(X!4, Y!3))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[270])).
% 0.19/0.44 tff(272,plain,
% 0.19/0.44 (lesseq(Y!3, max(X!4, Y!3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[110, 271])).
% 0.19/0.44 tff(273,plain,
% 0.19/0.44 (X!4 = Z!2),
% 0.19/0.44 inference(transitivity,[status(thm)],[270, 230])).
% 0.19/0.44 tff(274,plain,
% 0.19/0.44 (lesseq(X!4, max(X!4, Y!3)) <=> lesseq(Z!2, Z!2)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[273, 230])).
% 0.19/0.44 tff(275,plain,
% 0.19/0.44 (lesseq(Z!2, Z!2) <=> lesseq(X!4, max(X!4, Y!3))),
% 0.19/0.44 inference(symmetry,[status(thm)],[274])).
% 0.19/0.44 tff(276,assumption,(lesseq(Z!2, Z!2)), introduced(assumption)).
% 0.19/0.44 tff(277,plain,
% 0.19/0.44 (lesseq(X!4, max(X!4, Y!3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.19/0.44 tff(278,plain,
% 0.19/0.44 ((~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))) | (~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(279,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[278, 277, 272, 269])).
% 0.19/0.44 tff(280,plain,((~lesseq(Y!3, X!4)) | (~((~lesseq(Y!3, max(X!4, Y!3))) | (~lesseq(X!4, max(X!4, Y!3))))) | (~lesseq(Z!2, Z!2)) | (~(Z!2 = max(X!4, Y!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(281,plain,
% 0.19/0.44 (~lesseq(Y!3, X!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[280, 268, 86, 80])).
% 0.19/0.44 tff(282,plain,
% 0.19/0.44 (lesseq(X!4, Y!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[203, 200, 281])).
% 0.19/0.44 tff(283,plain,
% 0.19/0.44 (max(X!4, Y!3) = Y!3),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[218, 282])).
% 0.19/0.44 tff(284,plain,
% 0.19/0.44 (Y!3 = max(X!4, Y!3)),
% 0.19/0.44 inference(symmetry,[status(thm)],[283])).
% 0.19/0.44 tff(285,plain,
% 0.19/0.44 (lesseq(X!4, Y!3) <=> lesseq(X!4, max(X!4, Y!3))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[284])).
% 0.19/0.44 tff(286,plain,
% 0.19/0.44 (lesseq(X!4, max(X!4, Y!3)) <=> lesseq(X!4, Y!3)),
% 0.19/0.44 inference(symmetry,[status(thm)],[285])).
% 0.19/0.44 tff(287,plain,
% 0.19/0.44 ((~lesseq(X!4, max(X!4, Y!3))) <=> (~lesseq(X!4, Y!3))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[286])).
% 0.19/0.44 tff(288,plain,
% 0.19/0.44 (~lesseq(X!4, max(X!4, Y!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[246, 283, 263, 80, 186])).
% 0.19/0.44 tff(289,plain,
% 0.19/0.44 (~lesseq(X!4, Y!3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.19/0.44 tff(290,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[282, 289])).
% 0.19/0.44 tff(291,plain,(minsol_model_ub(X!4, Y!3, Z!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(292,plain,
% 0.19/0.44 (((~(minsol_model_ub(X!4, Y!3, Z!2) | (~model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, tptp_fun_Z_1(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_1(Z!2, Y!3, X!4)))))) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))))) | ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(293,plain,
% 0.19/0.44 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[292, 172])).
% 0.19/0.44 tff(294,plain,
% 0.19/0.44 ((~((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))))))) | (~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(295,plain,
% 0.19/0.45 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.19/0.45 tff(296,plain,
% 0.19/0.45 (~((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[295, 291])).
% 0.19/0.45 tff(297,plain,
% 0.19/0.45 (((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))) | model_ub(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(298,plain,
% 0.19/0.45 (model_ub(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[297, 296])).
% 0.19/0.45 tff(299,plain,
% 0.19/0.45 ((~(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))) | (~model_ub(X!4, Y!3, Z!2)) | ub(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(300,plain,
% 0.19/0.45 ((~(model_ub(X!4, Y!3, Z!2) <=> ub(X!4, Y!3, Z!2))) | ub(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.19/0.45 tff(301,plain,
% 0.19/0.45 (ub(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[300, 21])).
% 0.19/0.45 tff(302,plain,
% 0.19/0.45 ((~(ub(X!4, Y!3, Z!2) <=> (~((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2)))))) | (~ub(X!4, Y!3, Z!2)) | (~((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(303,plain,
% 0.19/0.45 ((~(ub(X!4, Y!3, Z!2) <=> (~((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2)))))) | (~((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.19/0.45 tff(304,plain,
% 0.19/0.45 (~((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[303, 12])).
% 0.19/0.45 tff(305,plain,
% 0.19/0.45 (((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2))) | lesseq(X!4, Z!2)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(306,plain,
% 0.19/0.45 (lesseq(X!4, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[305, 304])).
% 0.19/0.45 tff(307,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!4, Z!2)) | (max(X!4, Z!2) = Z!2))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!4, Z!2)) | (max(X!4, Z!2) = Z!2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(308,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!4, Z!2)) | (max(X!4, Z!2) = Z!2))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(309,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!4, Z!2)) | (max(X!4, Z!2) = Z!2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.19/0.45 tff(310,plain,
% 0.19/0.45 (max(X!4, Z!2) = Z!2),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[309, 214, 306])).
% 0.19/0.45 tff(311,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))) | (model_max(X!4, Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(X!4, Z!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(312,plain,
% 0.19/0.45 (model_max(X!4, Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(X!4, Z!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[311, 28])).
% 0.19/0.45 tff(313,plain,
% 0.19/0.45 (((~lesseq(Y!3, Z!2)) | (~lesseq(X!4, Z!2))) | lesseq(Y!3, Z!2)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(314,plain,
% 0.19/0.45 (lesseq(Y!3, Z!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[313, 304])).
% 0.19/0.45 tff(315,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!3, Z!2)) | (max(Z!2, Y!3) = Z!2))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!3, Z!2)) | (max(Z!2, Y!3) = Z!2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(316,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!3, Z!2)) | (max(Z!2, Y!3) = Z!2))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(317,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!3, Z!2)) | (max(Z!2, Y!3) = Z!2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.19/0.45 tff(318,plain,
% 0.19/0.45 (max(Z!2, Y!3) = Z!2),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[317, 120, 314])).
% 0.19/0.45 tff(319,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))) | (model_max(Z!2, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(Z!2, Y!3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(320,plain,
% 0.19/0.45 (model_max(Z!2, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(Z!2, Y!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[319, 28])).
% 0.19/0.45 tff(321,assumption,(~lesseq(X!4, Y!3)), introduced(assumption)).
% 0.19/0.45 tff(322,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!3, X!4) | lesseq(X!4, Y!3))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!3, X!4) | lesseq(X!4, Y!3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(323,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!3, X!4) | lesseq(X!4, Y!3))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(324,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!3, X!4) | lesseq(X!4, Y!3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.19/0.45 tff(325,plain,
% 0.19/0.45 (lesseq(Y!3, X!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[324, 200, 321])).
% 0.19/0.45 tff(326,plain,
% 0.19/0.45 (max(X!4, Y!3) = X!4),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[124, 325])).
% 0.19/0.45 tff(327,assumption,(~lesseq(X!4, X!4)), introduced(assumption)).
% 0.19/0.45 tff(328,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!4, X!4)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!4, X!4))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(329,plain,
% 0.19/0.45 ((lesseq(X!4, X!4) | lesseq(X!4, X!4)) <=> lesseq(X!4, X!4)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(330,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!4, X!4) | lesseq(X!4, X!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!4, X!4))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[329])).
% 0.19/0.45 tff(331,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!4, X!4) | lesseq(X!4, X!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!4, X!4))),
% 0.19/0.45 inference(transitivity,[status(thm)],[330, 328])).
% 0.19/0.45 tff(332,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!4, X!4) | lesseq(X!4, X!4))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(333,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!4, X!4)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.19/0.45 tff(334,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[333, 200, 327])).
% 0.19/0.45 tff(335,plain,(lesseq(X!4, X!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(336,plain,
% 0.19/0.45 ((~((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))) | (~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(337,plain,
% 0.19/0.45 ((~((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))) | (~lesseq(Y!3, X!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[336, 335])).
% 0.19/0.45 tff(338,plain,
% 0.19/0.45 (~((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[337, 325])).
% 0.19/0.45 tff(339,assumption,(~(ub(X!4, Y!3, X!4) <=> (~((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))))), introduced(assumption)).
% 0.19/0.45 tff(340,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, X!4) <=> (~((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(341,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[340, 10, 339])).
% 0.19/0.45 tff(342,plain,(ub(X!4, Y!3, X!4) <=> (~((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(343,plain,
% 0.19/0.45 ((~(ub(X!4, Y!3, X!4) <=> (~((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))))) | ub(X!4, Y!3, X!4) | ((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(344,plain,
% 0.19/0.45 (ub(X!4, Y!3, X!4) | ((~lesseq(Y!3, X!4)) | (~lesseq(X!4, X!4)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[343, 342])).
% 0.19/0.45 tff(345,plain,
% 0.19/0.45 (ub(X!4, Y!3, X!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[344, 338])).
% 0.19/0.45 tff(346,assumption,(~(model_ub(X!4, Y!3, X!4) <=> ub(X!4, Y!3, X!4))), introduced(assumption)).
% 0.19/0.45 tff(347,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, X!4) <=> ub(X!4, Y!3, X!4))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(348,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[347, 19, 346])).
% 0.19/0.45 tff(349,plain,(model_ub(X!4, Y!3, X!4) <=> ub(X!4, Y!3, X!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(350,plain,
% 0.19/0.45 ((~(model_ub(X!4, Y!3, X!4) <=> ub(X!4, Y!3, X!4))) | model_ub(X!4, Y!3, X!4) | (~ub(X!4, Y!3, X!4))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(351,plain,
% 0.19/0.45 (model_ub(X!4, Y!3, X!4) | (~ub(X!4, Y!3, X!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[350, 349])).
% 0.19/0.45 tff(352,plain,
% 0.19/0.45 (model_ub(X!4, Y!3, X!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[351, 345])).
% 0.19/0.45 tff(353,plain,
% 0.19/0.45 (Z!2 = max(X!4, Z!2)),
% 0.19/0.45 inference(symmetry,[status(thm)],[310])).
% 0.19/0.45 tff(354,plain,
% 0.19/0.45 ((Z!2 = max(X!4, Y!3)) <=> (max(X!4, Z!2) = X!4)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[353, 326])).
% 0.19/0.45 tff(355,plain,
% 0.19/0.45 ((~(Z!2 = max(X!4, Y!3))) <=> (~(max(X!4, Z!2) = X!4))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[354])).
% 0.19/0.45 tff(356,assumption,(~(Z!2 = max(X!4, Y!3))), introduced(assumption)).
% 0.19/0.45 tff(357,plain,
% 0.19/0.45 (~(max(X!4, Z!2) = X!4)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.19/0.45 tff(358,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!2, X!4)) | (max(X!4, Z!2) = X!4))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!2, X!4)) | (max(X!4, Z!2) = X!4))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(359,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!2, X!4)) | (max(X!4, Z!2) = X!4))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(360,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!2, X!4)) | (max(X!4, Z!2) = X!4)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.19/0.45 tff(361,plain,
% 0.19/0.45 ((~lesseq(Z!2, X!4)) | (max(X!4, Z!2) = X!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[360, 120])).
% 0.19/0.45 tff(362,plain,
% 0.19/0.45 (~lesseq(Z!2, X!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[361, 357])).
% 0.19/0.45 tff(363,plain,
% 0.19/0.45 (((~model_ub(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z)))) | ![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(364,plain,
% 0.19/0.45 (![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[363, 296])).
% 0.19/0.45 tff(365,plain,
% 0.19/0.45 (((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_ub(X!4, Y!3, X!4)) | lesseq(Z!2, X!4))) <=> ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_ub(X!4, Y!3, X!4)) | lesseq(Z!2, X!4))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(366,plain,
% 0.19/0.45 ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_ub(X!4, Y!3, X!4)) | lesseq(Z!2, X!4))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(367,plain,
% 0.19/0.45 ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_ub(X!4, Y!3, X!4)) | lesseq(Z!2, X!4)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.19/0.45 tff(368,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[367, 364, 362, 352])).
% 0.19/0.45 tff(369,plain,((Z!2 = max(X!4, Y!3)) | lesseq(X!4, Y!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(370,plain,
% 0.19/0.45 (Z!2 = max(X!4, Y!3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[369, 321])).
% 0.19/0.45 tff(371,plain,
% 0.19/0.45 (Z!2 = X!4),
% 0.19/0.45 inference(transitivity,[status(thm)],[370, 326])).
% 0.19/0.45 tff(372,plain,
% 0.19/0.45 (model_max(Z!2, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[371])).
% 0.19/0.45 tff(373,plain,
% 0.19/0.45 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> model_max(Z!2, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.45 inference(symmetry,[status(thm)],[372])).
% 0.19/0.45 tff(374,plain,
% 0.19/0.45 (Z!2 = X!4),
% 0.19/0.45 inference(transitivity,[status(thm)],[229, 133])).
% 0.19/0.45 tff(375,plain,
% 0.19/0.45 (model_max(Z!2, Y!3, Z!2) <=> model_max(X!4, Y!3, Z!2)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[374])).
% 0.19/0.45 tff(376,plain,
% 0.19/0.46 (model_max(X!4, Y!3, Z!2) <=> model_max(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(symmetry,[status(thm)],[375])).
% 0.19/0.46 tff(377,plain,
% 0.19/0.46 ((~model_max(X!4, Y!3, Z!2)) <=> (~model_max(Z!2, Y!3, Z!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[376])).
% 0.19/0.46 tff(378,assumption,(~model_max(X!4, Y!3, Z!2)), introduced(assumption)).
% 0.19/0.46 tff(379,plain,
% 0.19/0.46 (~model_max(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.19/0.46 tff(380,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))) | (model_max(Z!2, Y!3, Z!2) <=> (Z!2 = max(Z!2, Y!3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(381,plain,
% 0.19/0.46 (model_max(Z!2, Y!3, Z!2) <=> (Z!2 = max(Z!2, Y!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[380, 28])).
% 0.19/0.46 tff(382,plain,
% 0.19/0.46 (Z!2 = max(Z!2, Y!3)),
% 0.19/0.46 inference(symmetry,[status(thm)],[318])).
% 0.19/0.46 tff(383,plain,
% 0.19/0.46 ((~(model_max(Z!2, Y!3, Z!2) <=> (Z!2 = max(Z!2, Y!3)))) | model_max(Z!2, Y!3, Z!2) | (~(Z!2 = max(Z!2, Y!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(384,plain,
% 0.19/0.46 ((~(model_max(Z!2, Y!3, Z!2) <=> (Z!2 = max(Z!2, Y!3)))) | model_max(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[383, 382])).
% 0.19/0.46 tff(385,plain,
% 0.19/0.46 (model_max(Z!2, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[384, 381])).
% 0.19/0.46 tff(386,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[385, 379])).
% 0.19/0.46 tff(387,plain,(model_max(X!4, Y!3, Z!2) | (~(max(X!4, Y!3) = X!4)) | (~(Z!2 = max(X!4, Y!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(388,plain,
% 0.19/0.46 (model_max(X!4, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[387, 326, 370])).
% 0.19/0.46 tff(389,plain,
% 0.19/0.46 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~minsol_model_max(X!4, Y!3, Z!2)) | (~((~minsol_model_ub(X!4, Y!3, Z!2)) <=> minsol_model_max(X!4, Y!3, Z!2)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(390,plain,
% 0.19/0.46 ((~minsol_model_ub(X!4, Y!3, Z!2)) | (~minsol_model_max(X!4, Y!3, Z!2))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[389, 43])).
% 0.19/0.46 tff(391,plain,
% 0.19/0.46 (~minsol_model_max(X!4, Y!3, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[390, 291])).
% 0.19/0.46 tff(392,plain,
% 0.19/0.46 (((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))))) | (~((~minsol_model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, Z!2)) | (~![Z: $i] : ((~model_max(X!4, Y!3, Z)) | lesseq(Z!2, Z)))))))) | (minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(393,plain,
% 0.19/0.46 (minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[392, 70])).
% 0.19/0.46 tff(394,plain,
% 0.19/0.46 ((~(minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))))) | minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(395,plain,
% 0.19/0.46 (minsol_model_max(X!4, Y!3, Z!2) | (~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.19/0.46 tff(396,plain,
% 0.19/0.46 ((~model_max(X!4, Y!3, Z!2)) | (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[395, 391])).
% 0.19/0.46 tff(397,plain,
% 0.19/0.46 (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[396, 388])).
% 0.19/0.46 tff(398,plain,
% 0.19/0.46 (((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))) | model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(399,plain,
% 0.19/0.46 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[398, 397])).
% 0.19/0.46 tff(400,plain,
% 0.19/0.46 (model_max(Z!2, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[399, 373])).
% 0.19/0.46 tff(401,plain,
% 0.19/0.46 ((~(model_max(Z!2, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(Z!2, Y!3)))) | (~model_max(Z!2, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(Z!2, Y!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(402,plain,
% 0.19/0.46 (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(Z!2, Y!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[401, 400, 320])).
% 0.19/0.46 tff(403,plain,
% 0.19/0.46 (tptp_fun_Z_0(Z!2, Y!3, X!4) = Z!2),
% 0.19/0.46 inference(transitivity,[status(thm)],[402, 318])).
% 0.19/0.46 tff(404,plain,
% 0.19/0.46 (lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> lesseq(Z!2, Z!2)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[403])).
% 0.19/0.46 tff(405,plain,
% 0.19/0.46 (lesseq(Z!2, Z!2) <=> lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(symmetry,[status(thm)],[404])).
% 0.19/0.46 tff(406,plain,
% 0.19/0.46 (((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_ub(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2))) <=> ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_ub(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(407,plain,
% 0.19/0.46 ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_ub(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(408,plain,
% 0.19/0.46 ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_ub(X!4, Y!3, Z!2)) | lesseq(Z!2, Z!2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.19/0.46 tff(409,plain,
% 0.19/0.46 (lesseq(Z!2, Z!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[408, 298, 364])).
% 0.19/0.46 tff(410,plain,
% 0.19/0.46 (lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.19/0.46 tff(411,plain,
% 0.19/0.46 (((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))) | (~lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(412,plain,
% 0.19/0.46 (~lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[411, 397])).
% 0.19/0.46 tff(413,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[412, 410])).
% 0.19/0.46 tff(414,plain,(lesseq(X!4, Y!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(415,plain,
% 0.19/0.46 (max(X!4, Y!3) = Y!3),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[217, 214, 414])).
% 0.19/0.46 tff(416,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(Y!3, Z!2)) | (max(Y!3, Z!2) = Z!2))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(Y!3, Z!2)) | (max(Y!3, Z!2) = Z!2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(417,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(Y!3, Z!2)) | (max(Y!3, Z!2) = Z!2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(418,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(Y!3, Z!2)) | (max(Y!3, Z!2) = Z!2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.19/0.46 tff(419,plain,
% 0.19/0.46 (max(Y!3, Z!2) = Z!2),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[418, 214, 314])).
% 0.19/0.46 tff(420,plain,
% 0.19/0.46 (Z!2 = max(Y!3, Z!2)),
% 0.19/0.46 inference(symmetry,[status(thm)],[419])).
% 0.19/0.46 tff(421,plain,
% 0.19/0.46 ((Z!2 = max(X!4, Y!3)) <=> (max(Y!3, Z!2) = Y!3)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[420, 415])).
% 0.19/0.46 tff(422,assumption,(~(model_ub(X!4, Y!3, Y!3) <=> ub(X!4, Y!3, Y!3))), introduced(assumption)).
% 0.19/0.46 tff(423,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ub(X, Y, N))) | (model_ub(X!4, Y!3, Y!3) <=> ub(X!4, Y!3, Y!3))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(424,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[423, 19, 422])).
% 0.19/0.46 tff(425,plain,(model_ub(X!4, Y!3, Y!3) <=> ub(X!4, Y!3, Y!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(426,assumption,(~(ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))))), introduced(assumption)).
% 0.19/0.46 tff(427,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(428,plain,
% 0.19/0.46 ((ub(X!4, Y!3, Y!3) <=> (~((~lesseq(Y!3, Y!3)) | (~lesseq(X!4, Y!3))))) <=> (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(429,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(Y!3, Y!3)) | (~lesseq(X!4, Y!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[428])).
% 0.19/0.46 tff(430,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(Y!3, Y!3)) | (~lesseq(X!4, Y!3)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[429, 427])).
% 0.19/0.46 tff(431,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(Y!3, Y!3)) | (~lesseq(X!4, Y!3)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(432,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z)))))) | (ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.19/0.46 tff(433,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[432, 10, 426])).
% 0.19/0.46 tff(434,plain,(ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(435,assumption,(lesseq(X!4, Y!3)), introduced(assumption)).
% 0.19/0.46 tff(436,assumption,(~lesseq(Y!3, Y!3)), introduced(assumption)).
% 0.19/0.46 tff(437,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!3, Y!3)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!3, Y!3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(438,plain,
% 0.19/0.46 ((lesseq(Y!3, Y!3) | lesseq(Y!3, Y!3)) <=> lesseq(Y!3, Y!3)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(439,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!3, Y!3) | lesseq(Y!3, Y!3))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!3, Y!3))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[438])).
% 0.19/0.46 tff(440,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!3, Y!3) | lesseq(Y!3, Y!3))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!3, Y!3))),
% 0.19/0.46 inference(transitivity,[status(thm)],[439, 437])).
% 0.19/0.46 tff(441,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!3, Y!3) | lesseq(Y!3, Y!3))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(442,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!3, Y!3)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.19/0.46 tff(443,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[442, 200, 436])).
% 0.19/0.46 tff(444,plain,(lesseq(Y!3, Y!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(445,plain,
% 0.19/0.46 ((~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))) | (~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(446,plain,
% 0.19/0.46 ((~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))) | (~lesseq(X!4, Y!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[445, 444])).
% 0.19/0.46 tff(447,plain,
% 0.19/0.46 (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[446, 435])).
% 0.19/0.46 tff(448,plain,
% 0.19/0.46 ((~(ub(X!4, Y!3, Y!3) <=> (~((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))))) | ub(X!4, Y!3, Y!3) | ((~lesseq(X!4, Y!3)) | (~lesseq(Y!3, Y!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(449,plain,
% 0.19/0.47 (ub(X!4, Y!3, Y!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[448, 447, 434])).
% 0.19/0.47 tff(450,plain,
% 0.19/0.47 ((~(model_ub(X!4, Y!3, Y!3) <=> ub(X!4, Y!3, Y!3))) | model_ub(X!4, Y!3, Y!3) | (~ub(X!4, Y!3, Y!3))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(451,plain,
% 0.19/0.47 (model_ub(X!4, Y!3, Y!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[450, 449, 425])).
% 0.19/0.47 tff(452,plain,
% 0.19/0.47 (max(X!4, Y!3) = Y!3),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[218, 435])).
% 0.19/0.47 tff(453,plain,
% 0.19/0.47 ((Z!2 = max(X!4, Y!3)) <=> (max(Y!3, Z!2) = Y!3)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[420, 452])).
% 0.19/0.47 tff(454,plain,
% 0.19/0.47 ((~(Z!2 = max(X!4, Y!3))) <=> (~(max(Y!3, Z!2) = Y!3))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[453])).
% 0.19/0.47 tff(455,plain,
% 0.19/0.47 (~(max(Y!3, Z!2) = Y!3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[356, 454])).
% 0.19/0.47 tff(456,plain,
% 0.19/0.47 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!2, Y!3)) | (max(Y!3, Z!2) = Y!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!2, Y!3)) | (max(Y!3, Z!2) = Y!3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(457,plain,
% 0.19/0.47 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!2, Y!3)) | (max(Y!3, Z!2) = Y!3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(458,plain,
% 0.19/0.47 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!2, Y!3)) | (max(Y!3, Z!2) = Y!3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.19/0.47 tff(459,plain,
% 0.19/0.47 ((~lesseq(Z!2, Y!3)) | (max(Y!3, Z!2) = Y!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[458, 120])).
% 0.19/0.47 tff(460,plain,
% 0.19/0.47 (~lesseq(Z!2, Y!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[459, 455])).
% 0.19/0.47 tff(461,plain,
% 0.19/0.47 (((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_ub(X!4, Y!3, Y!3)) | lesseq(Z!2, Y!3))) <=> ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_ub(X!4, Y!3, Y!3)) | lesseq(Z!2, Y!3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(462,plain,
% 0.19/0.47 ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | ((~model_ub(X!4, Y!3, Y!3)) | lesseq(Z!2, Y!3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(463,plain,
% 0.19/0.47 ((~![Z: $i] : ((~model_ub(X!4, Y!3, Z)) | lesseq(Z!2, Z))) | (~model_ub(X!4, Y!3, Y!3)) | lesseq(Z!2, Y!3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.19/0.47 tff(464,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[463, 364, 460, 451])).
% 0.19/0.47 tff(465,plain,((~lesseq(X!4, Y!3)) | (Z!2 = max(X!4, Y!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(466,plain,
% 0.19/0.47 (Z!2 = max(X!4, Y!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[465, 414])).
% 0.19/0.47 tff(467,plain,
% 0.19/0.47 (max(Y!3, Z!2) = Y!3),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[466, 421])).
% 0.19/0.47 tff(468,plain,
% 0.19/0.47 (Z!2 = Y!3),
% 0.19/0.47 inference(transitivity,[status(thm)],[420, 467])).
% 0.19/0.47 tff(469,plain,
% 0.19/0.47 (model_max(X!4, Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[468])).
% 0.19/0.47 tff(470,plain,
% 0.19/0.47 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> model_max(X!4, Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(symmetry,[status(thm)],[469])).
% 0.19/0.47 tff(471,plain,
% 0.19/0.47 (model_max(X!4, Z!2, Z!2) <=> model_max(X!4, Y!3, Z!2)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[468])).
% 0.19/0.47 tff(472,plain,
% 0.19/0.47 (model_max(X!4, Y!3, Z!2) <=> model_max(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(symmetry,[status(thm)],[471])).
% 0.19/0.47 tff(473,plain,
% 0.19/0.47 ((~model_max(X!4, Y!3, Z!2)) <=> (~model_max(X!4, Z!2, Z!2))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[472])).
% 0.19/0.47 tff(474,plain,
% 0.19/0.47 (~model_max(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[378, 473])).
% 0.19/0.47 tff(475,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> (N = max(X, Y)))) | (model_max(X!4, Z!2, Z!2) <=> (Z!2 = max(X!4, Z!2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(476,plain,
% 0.19/0.47 (model_max(X!4, Z!2, Z!2) <=> (Z!2 = max(X!4, Z!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[475, 28])).
% 0.19/0.47 tff(477,plain,
% 0.19/0.47 ((~(model_max(X!4, Z!2, Z!2) <=> (Z!2 = max(X!4, Z!2)))) | model_max(X!4, Z!2, Z!2) | (~(Z!2 = max(X!4, Z!2)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(478,plain,
% 0.19/0.47 ((~(model_max(X!4, Z!2, Z!2) <=> (Z!2 = max(X!4, Z!2)))) | model_max(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[477, 353])).
% 0.19/0.47 tff(479,plain,
% 0.19/0.47 (model_max(X!4, Z!2, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[478, 476])).
% 0.19/0.47 tff(480,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[479, 474])).
% 0.19/0.47 tff(481,plain,(model_max(X!4, Y!3, Z!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(482,plain,
% 0.19/0.47 (~((~model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))) | lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[396, 481])).
% 0.19/0.47 tff(483,plain,
% 0.19/0.47 (model_max(X!4, Y!3, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[398, 482])).
% 0.19/0.47 tff(484,plain,
% 0.19/0.47 (model_max(X!4, Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[483, 470])).
% 0.19/0.47 tff(485,plain,
% 0.19/0.47 ((~(model_max(X!4, Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(X!4, Z!2)))) | (~model_max(X!4, Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))) | (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(X!4, Z!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(486,plain,
% 0.19/0.47 (tptp_fun_Z_0(Z!2, Y!3, X!4) = max(X!4, Z!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[485, 484, 312])).
% 0.19/0.47 tff(487,plain,
% 0.19/0.47 (tptp_fun_Z_0(Z!2, Y!3, X!4) = Z!2),
% 0.19/0.47 inference(transitivity,[status(thm)],[486, 310])).
% 0.19/0.47 tff(488,plain,
% 0.19/0.47 (lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4)) <=> lesseq(Z!2, Z!2)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[487])).
% 0.19/0.47 tff(489,plain,
% 0.19/0.47 (lesseq(Z!2, Z!2) <=> lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(symmetry,[status(thm)],[488])).
% 0.19/0.47 tff(490,plain,
% 0.19/0.47 (lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[409, 489])).
% 0.19/0.47 tff(491,plain,
% 0.19/0.47 (~lesseq(Z!2, tptp_fun_Z_0(Z!2, Y!3, X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[411, 482])).
% 0.19/0.47 tff(492,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[491, 490])).
% 0.19/0.47 % SZS output end Proof
%------------------------------------------------------------------------------