TSTP Solution File: ARI685_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI685_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Tue Sep 6 17:02:35 EDT 2022
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 10 unt; 4 typ; 0 def)
% Number of atoms : 36 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 0 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 20 ( 3 avg)
% Number arithmetic : 1100 ( 0 atm; 872 fun; 228 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 4 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(d_type,type,
d: $int ).
tff(c_type,type,
c: $int ).
tff(b_type,type,
b: $int ).
tff(a_type,type,
a: $int ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( 0 = 0 )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( $sum($product(2,$product(a,a)),$sum($product(2,$product(a,1)),$sum($product(2,$product(b,1)),$sum($product(a,b),$sum($product(a,c),$sum($product(a,$product(a,c)),$sum($product(b,c),$sum($product(a,$product(b,c)),$sum($product(2,$product(a,d)),$sum($product(a,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,d)),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d))))))))))))))))))) = 0 )
<=> ( $sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( $sum($product(a,a),$sum($product($sum(2,a),$product($sum(a,b),$sum(1,$sum(c,d)))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 )
<=> ( $sum($product(2,$product(a,a)),$sum($product(2,$product(a,1)),$sum($product(2,$product(b,1)),$sum($product(a,b),$sum($product(a,c),$sum($product(a,$product(a,c)),$sum($product(b,c),$sum($product(a,$product(b,c)),$sum($product(2,$product(a,d)),$sum($product(a,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,d)),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d))))))))))))))))))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( $sum($product(a,a),$sum($product($sum(2,a),$product($sum(a,b),$sum(1,$sum(c,d)))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 )
<=> ( $sum($product(a,a),$sum($product($sum(2,a),$product($sum(a,b),$sum(1,$sum(c,d)))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( $sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0 )
<=> ( $sum($product(a,a),$sum($product($sum(2,a),$product($sum(a,b),$sum(1,$sum(c,d)))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
$sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(8,plain,
$sum($product(a,a),$sum($product($sum(2,a),$product($sum(a,b),$sum(1,$sum(c,d)))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0,
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
$sum($product(a,a),$sum($product($sum(2,a),$product($sum(a,b),$sum(1,$sum(c,d)))),$sum(b,$product(-1,$product($sum(2,c),$sum(a,$sum(b,$sum(c,d)))))))) = 0,
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
$sum($product(2,$product(a,a)),$sum($product(2,$product(a,1)),$sum($product(2,$product(b,1)),$sum($product(a,b),$sum($product(a,c),$sum($product(a,$product(a,c)),$sum($product(b,c),$sum($product(a,$product(b,c)),$sum($product(2,$product(a,d)),$sum($product(a,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,d)),$sum($product(-1,b),$sum($product(-2,a),$sum($product(-2,c),$sum($product(-1,$product(c,c)),$sum($product(-2,d),$product(-1,$product(c,d))))))))))))))))))) = 0,
inference(modus_ponens,[status(thm)],[9,4]) ).
tff(11,plain,
$sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) = 0,
inference(modus_ponens,[status(thm)],[10,3]) ).
tff(12,plain,
( ( $sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) = 0 )
<=> ( 0 = 0 ) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ( $sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) = 0 )
<=> $true ),
inference(transitivity,[status(thm)],[12,2]) ).
tff(14,plain,
( ( $sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) != 0 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( $sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) != 0 )
<=> $false ),
inference(transitivity,[status(thm)],[14,1]) ).
tff(16,plain,
( ( $sum($product(a,$product(b,d)),$sum($product(2,$product(a,a)),$sum($product(a,c),$sum(b,$sum($product(a,b),$sum($product(-2,c),$sum($product(b,c),$sum($product(-1,$product(c,c)),$sum($product(a,$product(a,c)),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,c)),$sum($product(-1,$product(c,d)),$sum($product(a,$product(a,d)),$product(-2,d))))))))))))))) != 0 )
<=> ( $sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) != 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ( $sum($product(a,$product(b,d)),$sum($product(2,$product(a,a)),$sum($product(a,c),$sum(b,$sum($product(a,b),$sum($product(-2,c),$sum($product(b,c),$sum($product(-1,$product(c,c)),$sum($product(a,$product(a,c)),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,c)),$sum($product(-1,$product(c,d)),$sum($product(a,$product(a,d)),$product(-2,d))))))))))))))) != 0 )
<=> ( $sum($product(a,$product(b,d)),$sum($product(2,$product(a,a)),$sum($product(a,c),$sum(b,$sum($product(a,b),$sum($product(-2,c),$sum($product(b,c),$sum($product(-1,$product(c,c)),$sum($product(a,$product(a,c)),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,c)),$sum($product(-1,$product(c,d)),$sum($product(a,$product(a,d)),$product(-2,d))))))))))))))) != 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),b),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) != 0 )
<=> ( $sum($product(a,$product(b,d)),$sum($product(2,$product(a,a)),$sum($product(a,c),$sum(b,$sum($product(a,b),$sum($product(-2,c),$sum($product(b,c),$sum($product(-1,$product(c,c)),$sum($product(a,$product(a,c)),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,c)),$sum($product(-1,$product(c,d)),$sum($product(a,$product(a,d)),$product(-2,d))))))))))))))) != 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
$sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),b),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) != 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(20,plain,
$sum($product(a,$product(b,d)),$sum($product(2,$product(a,a)),$sum($product(a,c),$sum(b,$sum($product(a,b),$sum($product(-2,c),$sum($product(b,c),$sum($product(-1,$product(c,c)),$sum($product(a,$product(a,c)),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,c)),$sum($product(-1,$product(c,d)),$sum($product(a,$product(a,d)),$product(-2,d))))))))))))))) != 0,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
$sum($product(a,$product(b,d)),$sum($product(2,$product(a,a)),$sum($product(a,c),$sum(b,$sum($product(a,b),$sum($product(-2,c),$sum($product(b,c),$sum($product(-1,$product(c,c)),$sum($product(a,$product(a,c)),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,$product(b,c)),$sum($product(-1,$product(c,d)),$sum($product(a,$product(a,d)),$product(-2,d))))))))))))))) != 0,
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
$sum($product(2,$product(a,a)),$sum(b,$sum($product(-2,c),$sum($product(-2,d),$sum($product(-1,$product(c,c)),$sum($product(a,c),$sum($product(b,c),$sum($product(2,$product(a,d)),$sum($product(2,$product(b,d)),$sum($product(a,b),$sum($product(a,$product(a,c)),$sum($product(a,$product(b,c)),$sum($product(a,$product(a,d)),$sum($product(a,$product(b,d)),$product(-1,$product(c,d)))))))))))))))) != 0,
inference(modus_ponens,[status(thm)],[21,16]) ).
tff(23,plain,
$false,
inference(modus_ponens,[status(thm)],[22,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ARI685_1 : TPTP v8.1.0. Released v6.3.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 30 01:41:30 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------