TSTP Solution File: ARI692_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI692_1 : TPTP v8.1.0. Released v6.3.0.
% 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 : Tue Sep 6 17:02:37 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 22 unt; 3 typ; 0 def)
% Number of atoms : 40 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 0 ~; 0 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 262 ( 0 atm; 135 fun; 127 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 3 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(z_type,type,
z: $int ).
tff(y_type,type,
y: $int ).
tff(x_type,type,
x: $int ).
tff(1,plain,
( ( $sum($product(-6,z),$product(2,y)) = -5 )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
$sum($product(2,y),$product(-6,z)) = $sum($product(-6,z),$product(2,y)),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( $sum($product(2,y),$product(-6,z)) = -5 )
<=> ( $sum($product(-6,z),$product(2,y)) = -5 ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ( $sum($product(2,y),$product(-6,z)) = -5 )
<=> $false ),
inference(transitivity,[status(thm)],[3,1]) ).
tff(5,plain,
( ( $sum(6,$sum($product(2,y),$product(-6,z))) = 1 )
<=> ( $sum($product(2,y),$product(-6,z)) = -5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
$sum($product(2,y),$sum(6,$product(-6,z))) = $sum(6,$sum($product(2,y),$product(-6,z))),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
$sum($product(3,2),$product(3,$product(-2,z))) = $sum(6,$product(-6,z)),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
$product(3,$sum(2,$product(-2,z))) = $sum($product(3,2),$product(3,$product(-2,z))),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
$sum(2,$product(-1,$product(2,z))) = $sum(2,$product(-2,z)),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
$difference(2,$product(2,z)) = $sum(2,$product(-1,$product(2,z))),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
$difference(2,$product(2,z)) = $sum(2,$product(-2,z)),
inference(transitivity,[status(thm)],[10,9]) ).
tff(12,plain,
( ( $sum($product(2,z),x) = 2 )
<=> ( x = $difference(2,$product(2,z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( $sum($product(2,z),x) = 2 )
<=> ( $sum($product(2,z),x) = 2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
$sum($product(2,z),x) = 2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq1) ).
tff(15,plain,
$sum($product(2,z),x) = 2,
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
$sum($product(2,z),x) = 2,
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
x = $difference(2,$product(2,z)),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
x = $sum(2,$product(-2,z)),
inference(transitivity,[status(thm)],[17,11]) ).
tff(19,plain,
$product(3,x) = $product(3,$sum(2,$product(-2,z))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
$product(3,x) = $sum($product(3,2),$product(3,$product(-2,z))),
inference(transitivity,[status(thm)],[19,8]) ).
tff(21,plain,
$product(3,x) = $sum(6,$product(-6,z)),
inference(transitivity,[status(thm)],[20,7]) ).
tff(22,plain,
$sum($product(2,y),$product(3,x)) = $sum($product(2,y),$sum(6,$product(-6,z))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
$sum($product(2,y),$product(3,x)) = $sum(6,$sum($product(2,y),$product(-6,z))),
inference(transitivity,[status(thm)],[22,6]) ).
tff(24,plain,
( ( $sum($product(2,y),$product(3,x)) = 1 )
<=> ( $sum(6,$sum($product(2,y),$product(-6,z))) = 1 ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( $sum($product(2,y),$product(3,x)) = 1 )
<=> ( $sum($product(2,y),$product(-6,z)) = -5 ) ),
inference(transitivity,[status(thm)],[24,5]) ).
tff(26,plain,
( ( $sum($product(2,y),$product(3,x)) = 1 )
<=> ( $sum($product(2,y),$product(3,x)) = 1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
$sum($product(2,y),$product(3,x)) = 1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq2) ).
tff(28,plain,
$sum($product(2,y),$product(3,x)) = 1,
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$sum($product(2,y),$product(3,x)) = 1,
inference(modus_ponens,[status(thm)],[28,26]) ).
tff(30,plain,
$sum($product(2,y),$product(-6,z)) = -5,
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
$false,
inference(modus_ponens,[status(thm)],[30,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI692_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 01:56:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------