TSTP Solution File: DAT030_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT030_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : DAT030_1 : TPTP v8.1.0. Released v5.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.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 01:52:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(tptp_fun_X1_4_type, type, (
% 0.20/0.40 tptp_fun_X1_4: $int)).
% 0.20/0.40 tff(in_type, type, (
% 0.20/0.40 in: ( $int * collection ) > $o)).
% 0.20/0.40 tff(tptp_fun_U_1_type, type, (
% 0.20/0.40 tptp_fun_U_1: collection)).
% 0.20/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.40 tptp_fun_Y_3: $int > $int)).
% 0.20/0.40 tff(tptp_fun_Z_2_type, type, (
% 0.20/0.40 tptp_fun_Z_2: $int > $int)).
% 0.20/0.40 tff(tptp_fun_V_0_type, type, (
% 0.20/0.40 tptp_fun_V_0: collection)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))) & (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1))))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))) & (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(tptp_fun_Z_2(X), $sum(tptp_fun_Y_3(X), $product(-1, X))) = 0)))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(tptp_fun_Z_2(X), $sum(tptp_fun_Y_3(X), $product(-1, X))) = 0)))) & (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1))))) <=> ((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))) & (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(tptp_fun_Z_2(X), $sum(tptp_fun_Y_3(X), $product(-1, X))) = 0)))) & (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1))))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))) & (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(Z, $sum(Y, $product(-1, X))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(Z, $sum(Y, $product(-1, X))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(X, $sum($product(-1, Y), $product(-1, Z))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(Z, $sum(Y, $product(-1, X))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(X, $sum($product(-1, Y), $product(-1, Z))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 ((~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & ![X: $int] : (in(X, U) => ?[Y: $int, Z: $int] : ((in(Y, V) & in(Z, V)) & (X = $sum(Y, Z))))) => ![X1: $int] : (in(X1, U) => $greater(X1, 1)))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(10,axiom,(~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & ![X: $int] : (in(X, U) => ?[Y: $int, Z: $int] : ((in(Y, V) & in(Z, V)) & (X = $sum(Y, Z))))) => ![X1: $int] : (in(X1, U) => $greater(X1, 1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & (X = $sum(Y, Z)))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(X, $sum($product(-1, Y), $product(-1, Z))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(Z, $sum(Y, $product(-1, X))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(Z, $sum(Y, $product(-1, X))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & ![X: $int] : ((~in(X, U)) | ?[Y: $int, Z: $int] : (in(Y, V) & in(Z, V) & ($sum(Z, $sum(Y, $product(-1, X))) = 0))))) | ![X1: $int] : ((~$lesseq(X1, 1)) | (~in(X1, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & ![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))) & (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 4])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (~((~$lesseq(X1!4, 1)) | (~in(X1!4, U!1)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ($lesseq(X1!4, 1)),
% 0.20/0.40 inference(or_elim,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (in(X1!4, U!1)),
% 0.20/0.40 inference(or_elim,[status(thm)],[20])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (^[X: $int] : refl(((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))))) <=> ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))))) <=> ![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (^[X: $int] : rewrite(((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))) <=> ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0))) <=> ![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![X: $int] : ((~in(X, U!1)) | (in(tptp_fun_Y_3(X), V!0) & in(tptp_fun_Z_2(X), V!0) & ($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[19])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | ((~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0)))))) <=> ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | (~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (((~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Z_2(X1!4)), $product(-1, tptp_fun_Y_3(X1!4)))) = 0))))) <=> ((~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | ((~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Z_2(X1!4)), $product(-1, tptp_fun_Y_3(X1!4)))) = 0)))))) <=> ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | ((~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | ((~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Z_2(X1!4)), $product(-1, tptp_fun_Y_3(X1!4)))) = 0)))))) <=> ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | (~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | ((~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Z_2(X1!4)), $product(-1, tptp_fun_Y_3(X1!4)))) = 0)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~![X: $int] : ((~in(X, U!1)) | (~((~in(tptp_fun_Y_3(X), V!0)) | (~in(tptp_fun_Z_2(X), V!0)) | (~($sum(X, $sum($product(-1, tptp_fun_Z_2(X)), $product(-1, tptp_fun_Y_3(X)))) = 0)))))) | (~in(X1!4, U!1)) | (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (~((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[35, 29, 22])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0))) | ($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0)) | $greatereq($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ($greatereq($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0))) | in(tptp_fun_Z_2(X1!4), V!0)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (in(tptp_fun_Z_2(X1!4), V!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[41, 36])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (^[W: $int] : refl(((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ((~$lesseq(W, 0)) | (~in(W, V!0))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[19])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(tptp_fun_Z_2(X1!4), 0)) | (~in(tptp_fun_Z_2(X1!4), V!0)))) <=> ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(tptp_fun_Z_2(X1!4), 0)) | (~in(tptp_fun_Z_2(X1!4), V!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(tptp_fun_Z_2(X1!4), 0)) | (~in(tptp_fun_Z_2(X1!4), V!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(tptp_fun_Z_2(X1!4), 0)) | (~in(tptp_fun_Z_2(X1!4), V!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (~$lesseq(tptp_fun_Z_2(X1!4), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[49, 46, 42])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~in(tptp_fun_Y_3(X1!4), V!0)) | (~in(tptp_fun_Z_2(X1!4), V!0)) | (~($sum(X1!4, $sum($product(-1, tptp_fun_Y_3(X1!4)), $product(-1, tptp_fun_Z_2(X1!4)))) = 0))) | in(tptp_fun_Y_3(X1!4), V!0)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (in(tptp_fun_Y_3(X1!4), V!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[51, 36])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(tptp_fun_Y_3(X1!4), 0)) | (~in(tptp_fun_Y_3(X1!4), V!0)))) <=> ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(tptp_fun_Y_3(X1!4), 0)) | (~in(tptp_fun_Y_3(X1!4), V!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(tptp_fun_Y_3(X1!4), 0)) | (~in(tptp_fun_Y_3(X1!4), V!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(tptp_fun_Y_3(X1!4), 0)) | (~in(tptp_fun_Y_3(X1!4), V!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (~$lesseq(tptp_fun_Y_3(X1!4), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 46, 52])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[56, 50, 40, 21])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------