TSTP Solution File: DAT028_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT028_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT028_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 01:28:48 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.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(tptp_fun_Z_3_type, type, (
% 0.20/0.39 tptp_fun_Z_3: $int)).
% 0.20/0.39 tff(in_type, type, (
% 0.20/0.39 in: ( $int * collection ) > $o)).
% 0.20/0.39 tff(tptp_fun_U_1_type, type, (
% 0.20/0.39 tptp_fun_U_1: collection)).
% 0.20/0.39 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.39 tptp_fun_Y_2: $int > $int)).
% 0.20/0.39 tff(tptp_fun_V_0_type, type, (
% 0.20/0.39 tptp_fun_V_0: collection)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (((![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(X, $product(-1, tptp_fun_Y_2(X))), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1))))) <=> (![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(X, $product(-1, tptp_fun_Y_2(X))), 0)))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1)))) <=> (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 ((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$greatereq($sum(tptp_fun_Y_2(X), $product(-1, 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(X, $product(-1, tptp_fun_Y_2(X))), 0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$greatereq($sum(tptp_fun_Y_2(X), $product(-1, X)), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1))))) <=> ((![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(X, $product(-1, tptp_fun_Y_2(X))), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[3, 2])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$greatereq($sum(tptp_fun_Y_2(X), $product(-1, X)), 0))))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1))))) <=> (![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(X, $product(-1, tptp_fun_Y_2(X))), 0)))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[4, 1])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum(Y, $product(-1, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum(Y, $product(-1, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum(X, $product(-1, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum(Y, $product(-1, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum(X, $product(-1, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & ![X: $int] : (in(X, U) => ?[Y: $int] : (in(Y, V) & $greater(X, Y)))) => ![Z: $int] : (in(Z, U) => $greater(Z, 1)))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(11,axiom,(~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & ![X: $int] : (in(X, U) => ?[Y: $int] : (in(Y, V) & $greater(X, Y)))) => ![Z: $int] : (in(Z, U) => $greater(Z, 1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq(X, Y)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$lesseq($sum(X, $product(-1, Y)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum(Y, $product(-1, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum(Y, $product(-1, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 6])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int] : (in(Y, V) & (~$greatereq($sum(Y, $product(-1, X)), 0)))))) | ![Z: $int] : ((~in(Z, U)) | (~$lesseq(Z, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 6])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![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(X, $product(-1, tptp_fun_Y_2(X))), 0)))) & (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 5])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (~((~in(Z!3, U!1)) | (~$lesseq(Z!3, 1)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[20])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ($lesseq(Z!3, 1)),
% 0.20/0.39 inference(or_elim,[status(thm)],[21])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (in(Z!3, U!1)),
% 0.20/0.39 inference(or_elim,[status(thm)],[21])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (^[X: $int] : refl(((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0)))) <=> ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0)))) <=> ![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (^[X: $int] : rewrite(((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0)))) <=> ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0)))) <=> ![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_2(X), V!0) & (~$lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[20])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))) | ((~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0))))) <=> ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))) | (~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))) | ((~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_2(X), V!0)) | $lesseq($sum(X, $product(-1, tptp_fun_Y_2(X))), 0))))) | (~in(Z!3, U!1)) | (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (~((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[33, 30, 23])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0)) | (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (~$lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (((~in(tptp_fun_Y_2(Z!3), V!0)) | $lesseq($sum(Z!3, $product(-1, tptp_fun_Y_2(Z!3))), 0)) | in(tptp_fun_Y_2(Z!3), V!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (in(tptp_fun_Y_2(Z!3), V!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (^[W: $int] : refl(((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ((~$lesseq(W, 0)) | (~in(W, V!0))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[20])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (((~![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~![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)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(tptp_fun_Y_2(Z!3), 0)) | (~in(tptp_fun_Y_2(Z!3), V!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (~$lesseq(tptp_fun_Y_2(Z!3), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 42, 38])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[46, 36, 22])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------