TSTP Solution File: DAT045_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT045_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : Fri Sep 16 14:36:30 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT045_1 : TPTP v8.1.0. Released v5.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 01:54:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $int * collection ) > $o)).
% 0.21/0.39 tff(tptp_fun_U_1_type, type, (
% 0.21/0.39 tptp_fun_U_1: collection)).
% 0.21/0.39 tff(tptp_fun_V_0_type, type, (
% 0.21/0.39 tptp_fun_V_0: $int)).
% 0.21/0.39 tff(count_type, type, (
% 0.21/0.39 count: collection > $int)).
% 0.21/0.39 tff(add_type, type, (
% 0.21/0.39 add: ( $int * collection ) > collection)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[X8: $int, X9: collection] : refl(((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)) <=> ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (^[X8: $int, X9: collection] : rewrite(((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1)) <=> ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1)) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (^[X8: $int, X9: collection] : rewrite(((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))) <=> ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (^[X8: $int, X9: collection] : rewrite(((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(count(X9), 1))) <=> ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(count(X9), 1))) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.39 tff(10,axiom,(![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(count(X9), 1)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax','ax3')).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.21/0.39 tff(15,plain,(
% 0.21/0.39 ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.21/0.39 inference(skolemize,[status(sab)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 ((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (((~(~$greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0))) & ![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) <=> ($greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0) & ![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 ((~![U: collection, V: $int] : ((~$greatereq($sum(count(U), $product(-1, count(add(V, U)))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$greatereq($sum(W, $product(-1, V)), 0)))))) <=> (~![U: collection, V: $int] : ((~$greatereq($sum(count(U), $product(-1, count(add(V, U)))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$greatereq($sum(W, $product(-1, V)), 0))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 ((~![U: collection, V: $int] : ((~$lesseq($sum(count(add(V, U)), $product(-1, count(U))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$lesseq($sum(V, $product(-1, W)), 0)))))) <=> (~![U: collection, V: $int] : ((~$greatereq($sum(count(U), $product(-1, count(add(V, U)))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$greatereq($sum(W, $product(-1, V)), 0))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 ((~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W)))))) <=> (~![U: collection, V: $int] : ((~$lesseq($sum(count(add(V, U)), $product(-1, count(U))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$lesseq($sum(V, $product(-1, W)), 0))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W)))))) <=> (~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 ((~![U: collection, V: $int] : (![W: $int] : (in(W, U) => $greater(V, W)) => $greater(count(add(V, U)), count(U)))) <=> (~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(25,axiom,(~![U: collection, V: $int] : (![W: $int] : (in(W, U) => $greater(V, W)) => $greater(count(add(V, U)), count(U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$lesseq(count(add(V, U)), count(U))) | (~![W: $int] : ((~in(W, U)) | (~$lesseq(V, W)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$lesseq($sum(count(add(V, U)), $product(-1, count(U))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$lesseq($sum(V, $product(-1, W)), 0)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$greatereq($sum(count(U), $product(-1, count(add(V, U)))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$greatereq($sum(W, $product(-1, V)), 0)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$greatereq($sum(count(U), $product(-1, count(add(V, U)))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$greatereq($sum(W, $product(-1, V)), 0)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (~![U: collection, V: $int] : ((~$greatereq($sum(count(U), $product(-1, count(add(V, U)))), 0)) | (~![W: $int] : ((~in(W, U)) | (~$greatereq($sum(W, $product(-1, V)), 0)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[32, 20])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 ($greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0) & ![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 19])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ($greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0)),
% 0.21/0.40 inference(and_elim,[status(thm)],[34])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 ((~$lesseq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), -1)) | (~$greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0))),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (~$lesseq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)) | $lesseq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (~($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ((~((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1))) | in(V!0, U!1) | ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 ((~((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1))) | in(V!0, U!1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (in(V!0, U!1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[41, 18])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (^[W: $int] : refl(((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0))) <=> ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0))) <=> ![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))),
% 0.21/0.40 inference(and_elim,[status(thm)],[34])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | (~in(V!0, U!1))) <=> ((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | (~in(V!0, U!1)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (((~in(V!0, U!1)) | $false) <=> (~in(V!0, U!1))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 ((~$true) <=> $false),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 ($greatereq(0, 0) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 ($sum(V!0, $product(-1, V!0)) = 0),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 ($greatereq($sum(V!0, $product(-1, V!0)), 0) <=> $greatereq(0, 0)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 ($greatereq($sum(V!0, $product(-1, V!0)), 0) <=> $true),
% 0.21/0.40 inference(transitivity,[status(thm)],[52, 50])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 ((~$greatereq($sum(V!0, $product(-1, V!0)), 0)) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ((~$greatereq($sum(V!0, $product(-1, V!0)), 0)) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[54, 49])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (((~in(V!0, U!1)) | (~$greatereq($sum(V!0, $product(-1, V!0)), 0))) <=> ((~in(V!0, U!1)) | $false)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (((~in(V!0, U!1)) | (~$greatereq($sum(V!0, $product(-1, V!0)), 0))) <=> (~in(V!0, U!1))),
% 0.21/0.40 inference(transitivity,[status(thm)],[56, 48])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | ((~in(V!0, U!1)) | (~$greatereq($sum(V!0, $product(-1, V!0)), 0)))) <=> ((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | (~in(V!0, U!1)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | ((~in(V!0, U!1)) | (~$greatereq($sum(V!0, $product(-1, V!0)), 0)))) <=> ((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | (~in(V!0, U!1)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[58, 47])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 ((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | ((~in(V!0, U!1)) | (~$greatereq($sum(V!0, $product(-1, V!0)), 0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 ((~![W: $int] : ((~in(W, U!1)) | (~$greatereq($sum(W, $product(-1, V!0)), 0)))) | (~in(V!0, U!1))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[61, 46, 42])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------