TSTP Solution File: ARI688_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI688_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 17:02:36 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 20 unt; 3 typ; 0 def)
% Number of atoms : 48 ( 41 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 0 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 246 ( 0 atm; 132 fun; 114 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 : 16 ( 3 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $int ).
tff(b_type,type,
b: $int ).
tff(x_type,type,
x: $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(8,x),$sum($product(-28173120816,x),$product(28173120808,x))) = 0,
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
$product(287,$product(98164184,x)) = $product(28173120808,x),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( $product(98164184,x) = a )
<=> ( a = $product(98164184,x) ) ),
inference(commutativity,[status(thm)],]) ).
tff(6,plain,
( ( $product(98164184,x) = a )
<=> ( $product(98164184,x) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
$product(98164184,x) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq1) ).
tff(8,plain,
$product(98164184,x) = a,
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
a = $product(98164184,x),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
$product(287,a) = $product(287,$product(98164184,x)),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
$product(287,a) = $product(28173120808,x),
inference(transitivity,[status(thm)],[10,4]) ).
tff(12,plain,
$product(-4353078,$product(6472,x)) = $product(-28173120816,x),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( $product(6472,x) = b )
<=> ( b = $product(6472,x) ) ),
inference(commutativity,[status(thm)],]) ).
tff(14,plain,
( ( $product(6472,x) = b )
<=> ( $product(6472,x) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
$product(6472,x) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq2) ).
tff(16,plain,
$product(6472,x) = b,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
b = $product(6472,x),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
$product(-4353078,b) = $product(-4353078,$product(6472,x)),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
$product(-4353078,b) = $product(-28173120816,x),
inference(transitivity,[status(thm)],[18,12]) ).
tff(20,plain,
$sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = $sum($product(8,x),$sum($product(-28173120816,x),$product(28173120808,x))),
inference(monotonicity,[status(thm)],[19,11]) ).
tff(21,plain,
$sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0,
inference(transitivity,[status(thm)],[20,3]) ).
tff(22,plain,
( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 )
<=> ( 0 = 0 ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 )
<=> $true ),
inference(transitivity,[status(thm)],[22,2]) ).
tff(24,plain,
( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
<=> $false ),
inference(transitivity,[status(thm)],[24,1]) ).
tff(26,plain,
( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 )
<=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
<=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
<=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( $sum($product(8,x),$product(-1,$difference($product(4353078,b),$product(287,a)))) != 0 )
<=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
$sum($product(8,x),$product(-1,$difference($product(4353078,b),$product(287,a)))) != 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(31,plain,
$sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0,
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
$sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0,
inference(modus_ponens,[status(thm)],[32,27]) ).
tff(34,plain,
$false,
inference(modus_ponens,[status(thm)],[33,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI688_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 01:38:40 EDT 2022
% 0.13/0.33 % 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.
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------