TSTP Solution File: DAT029_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : DAT029_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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 : Fri Sep 16 14:36:26 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : DAT029_1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n009.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 : Wed Aug 31 01:40:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % SZS output start Proof
% 0.13/0.38  tff(tptp_fun_Z_3_type, type, (
% 0.13/0.38     tptp_fun_Z_3: $int)).
% 0.13/0.38  tff(in_type, type, (
% 0.13/0.38     in: ( $int * collection ) > $o)).
% 0.13/0.38  tff(tptp_fun_U_1_type, type, (
% 0.13/0.38     tptp_fun_U_1: collection)).
% 0.13/0.38  tff(tptp_fun_Y_2_type, type, (
% 0.13/0.38     tptp_fun_Y_2: $int > $int)).
% 0.13/0.38  tff(tptp_fun_V_0_type, type, (
% 0.13/0.38     tptp_fun_V_0: collection)).
% 0.13/0.38  tff(1,plain,
% 0.13/0.38      (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2))))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2)))))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(2,plain,
% 0.13/0.38      ((~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2)))) <=> (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2))))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(3,plain,
% 0.13/0.38      ((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$greatereq($sum($product(5, tptp_fun_Y_2(X)), $product(-2, X)), 0))))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(4,plain,
% 0.13/0.38      (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$greatereq($sum($product(5, tptp_fun_Y_2(X)), $product(-2, X)), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2))))) <=> ((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2)))))),
% 0.13/0.38      inference(monotonicity,[status(thm)],[3, 2])).
% 0.13/0.38  tff(5,plain,
% 0.13/0.38      (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$greatereq($sum($product(5, tptp_fun_Y_2(X)), $product(-2, X)), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2))))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2)))))),
% 0.13/0.38      inference(transitivity,[status(thm)],[4, 1])).
% 0.13/0.38  tff(6,plain,
% 0.13/0.38      ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum($product(5, Y), $product(-2, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum($product(5, Y), $product(-2, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2)))))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(7,plain,
% 0.13/0.38      ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum($product(5, Y), $product(-2, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2)))))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(8,plain,
% 0.13/0.38      ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2)))))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(9,plain,
% 0.13/0.39      ((~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & ![X: $int] : (in(X, U) => ?[Y: $int] : (in(Y, V) & $greater($difference($product(2, X), $product(5, Y)), 0)))) => ![Z: $int] : (in(Z, U) => $greater(Z, 2)))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2)))))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(10,axiom,(~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & ![X: $int] : (in(X, U) => ?[Y: $int] : (in(Y, V) & $greater($difference($product(2, X), $product(5, Y)), 0)))) => ![Z: $int] : (in(Z, U) => $greater(Z, 2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.13/0.39  tff(11,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.39  tff(12,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[11, 8])).
% 0.13/0.39  tff(13,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[12, 8])).
% 0.13/0.39  tff(14,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[13, 8])).
% 0.13/0.39  tff(15,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum($product(2, X), $product(-5, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[14, 8])).
% 0.13/0.39  tff(16,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum($product(5, Y), $product(-2, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[15, 7])).
% 0.13/0.39  tff(17,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum($product(5, Y), $product(-2, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[16, 6])).
% 0.13/0.39  tff(18,plain,
% 0.13/0.39      (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum($product(5, Y), $product(-2, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[17, 6])).
% 0.13/0.39  tff(19,plain,
% 0.13/0.39      (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[18, 5])).
% 0.13/0.39  tff(20,plain,
% 0.13/0.39      (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 2)))),
% 0.13/0.39      inference(and_elim,[status(thm)],[19])).
% 0.13/0.39  tff(21,plain,
% 0.13/0.39      ($lesseq(Z!3, 2)),
% 0.13/0.39      inference(or_elim,[status(thm)],[20])).
% 0.13/0.39  tff(22,plain,
% 0.13/0.39      (in(Z!3, U!1)),
% 0.13/0.39      inference(or_elim,[status(thm)],[20])).
% 0.13/0.39  tff(23,plain,
% 0.13/0.39      (^[X: $int] : refl(((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))) <=> ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))))),
% 0.13/0.39      inference(bind,[status(th)],[])).
% 0.13/0.39  tff(24,plain,
% 0.13/0.39      (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))) <=> ![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))),
% 0.13/0.39      inference(quant_intro,[status(thm)],[23])).
% 0.13/0.39  tff(25,plain,
% 0.13/0.39      (^[X: $int] : rewrite(((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))) <=> ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))))),
% 0.13/0.39      inference(bind,[status(th)],[])).
% 0.13/0.39  tff(26,plain,
% 0.13/0.39      (![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0)))) <=> ![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))),
% 0.13/0.39      inference(quant_intro,[status(thm)],[25])).
% 0.13/0.39  tff(27,plain,
% 0.13/0.39      (![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))),
% 0.13/0.39      inference(and_elim,[status(thm)],[19])).
% 0.13/0.39  tff(28,plain,
% 0.13/0.39      (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.39  tff(29,plain,
% 0.13/0.39      (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.39  tff(30,plain,
% 0.13/0.39      (((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))) | ((~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0))))) <=> ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))) | (~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0))))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(31,plain,
% 0.13/0.39      ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))) | ((~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0))))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(32,plain,
% 0.13/0.39      ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum($product(2, X), $product(-5, tptp_fun_Y_2(X))), 0))))) | (~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0)))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.39  tff(33,plain,
% 0.13/0.39      (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0))),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 0.13/0.39  tff(34,plain,
% 0.13/0.39      (((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0)) | (~$lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0))),
% 0.13/0.39      inference(tautology,[status(thm)],[])).
% 0.13/0.39  tff(35,plain,
% 0.13/0.39      (~$lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0)),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[34, 33])).
% 0.13/0.39  tff(36,plain,
% 0.13/0.39      (((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum($product(2, Z!3), $product(-5, tptp_fun_Y_2(Z!3))), 0)) | in(tptp_fun_Y_2(Z!3), V!0)),
% 0.13/0.39      inference(tautology,[status(thm)],[])).
% 0.13/0.39  tff(37,plain,
% 0.13/0.39      (in(tptp_fun_Y_2(Z!3), V!0)),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[36, 33])).
% 0.13/0.39  tff(38,plain,
% 0.13/0.39      (^[W: $int] : refl(((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ((~$lesseq(W, 0)) | (~in(W, V!0))))),
% 0.13/0.39      inference(bind,[status(th)],[])).
% 0.13/0.39  tff(39,plain,
% 0.13/0.39      (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.13/0.39      inference(quant_intro,[status(thm)],[38])).
% 0.13/0.39  tff(40,plain,
% 0.13/0.39      (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.13/0.39      inference(and_elim,[status(thm)],[19])).
% 0.13/0.39  tff(41,plain,
% 0.13/0.39      (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.39  tff(42,plain,
% 0.13/0.39      (((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(tptp_fun_Y_2(Z!3), 0)) | (~in(tptp_fun_Y_2(Z!3), V!0)))) <=> ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(tptp_fun_Y_2(Z!3), 0)) | (~in(tptp_fun_Y_2(Z!3), V!0)))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(43,plain,
% 0.13/0.39      ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(tptp_fun_Y_2(Z!3), 0)) | (~in(tptp_fun_Y_2(Z!3), V!0)))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(44,plain,
% 0.13/0.39      ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(tptp_fun_Y_2(Z!3), 0)) | (~in(tptp_fun_Y_2(Z!3), V!0))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.39  tff(45,plain,
% 0.13/0.39      (~$lesseq(tptp_fun_Y_2(Z!3), 0)),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[44, 41, 37])).
% 0.13/0.39  tff(46,plain,
% 0.13/0.39      ($false),
% 0.13/0.39      inference(theory_lemma,[status(thm)],[45, 35, 21])).
% 0.13/0.39  % SZS output end Proof
%------------------------------------------------------------------------------