TSTP Solution File: ARI700_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI700_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 17:02:39 EDT 2022
% Result : Theorem 4.54s 2.40s
% Output : Proof 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 44 ( 26 unt; 4 typ; 0 def)
% Number of atoms : 54 ( 47 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 0 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 293 ( 0 atm; 214 fun; 79 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 : 14 ( 4 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(b_type,type,
b: $int ).
tff(x_type,type,
x: $int ).
tff(a_type,type,
a: $int ).
tff(y_type,type,
y: $int ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( $product(63218647815567936,$product(x,$product(x,$product(y,y)))) = $product(63218647815567936,$product(x,$product(x,$product(y,y)))) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
$product(1509274329,$product(41886784,$product(x,$product(x,$product(y,y))))) = $product(63218647815567936,$product(x,$product(x,$product(y,y)))),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
$product(41886784,$product(x,$product(y,$product(x,y)))) = $product(41886784,$product(x,$product(x,$product(y,y)))),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
$product($product(6472,$product(x,y)),$product(6472,$product(x,y))) = $product(41886784,$product(x,$product(y,$product(x,y)))),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( $product(6472,$product(x,y)) = b )
<=> ( b = $product(6472,$product(x,y)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(7,plain,
( ( $product(6472,$product(x,y)) = b )
<=> ( $product(6472,$product(x,y)) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( ( $product($product(6472,x),y) = b )
<=> ( $product(6472,$product(x,y)) = b ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
$product($product(6472,x),y) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq2) ).
tff(10,plain,
$product(6472,$product(x,y)) = b,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
$product(6472,$product(x,y)) = b,
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
b = $product(6472,$product(x,y)),
inference(modus_ponens,[status(thm)],[11,6]) ).
tff(13,plain,
$product(b,b) = $product($product(6472,$product(x,y)),$product(6472,$product(x,y))),
inference(monotonicity,[status(thm)],[12,12]) ).
tff(14,plain,
$product(b,b) = $product(41886784,$product(x,$product(y,$product(x,y)))),
inference(transitivity,[status(thm)],[13,5]) ).
tff(15,plain,
$product(b,b) = $product(41886784,$product(x,$product(x,$product(y,y)))),
inference(transitivity,[status(thm)],[14,4]) ).
tff(16,plain,
$product(1509274329,$product(b,b)) = $product(1509274329,$product(41886784,$product(x,$product(x,$product(y,y))))),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
$product(1509274329,$product(b,b)) = $product(63218647815567936,$product(x,$product(x,$product(y,y)))),
inference(transitivity,[status(thm)],[16,3]) ).
tff(18,plain,
$product(644009304,$product(98164184,$product(x,$product(x,$product(y,y))))) = $product(63218647815567936,$product(x,$product(x,$product(y,y)))),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
$product($product(98164184,$product(y,y)),$product(x,x)) = $product(98164184,$product(x,$product(x,$product(y,y)))),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( $product(98164184,$product(y,y)) = a )
<=> ( a = $product(98164184,$product(y,y)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(21,plain,
( ( $product(98164184,$product(y,y)) = a )
<=> ( $product(98164184,$product(y,y)) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( $product($product(98164184,y),y) = a )
<=> ( $product(98164184,$product(y,y)) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
$product($product(98164184,y),y) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq1) ).
tff(24,plain,
$product(98164184,$product(y,y)) = a,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
$product(98164184,$product(y,y)) = a,
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
a = $product(98164184,$product(y,y)),
inference(modus_ponens,[status(thm)],[25,20]) ).
tff(27,plain,
$product(a,$product(x,x)) = $product($product(98164184,$product(y,y)),$product(x,x)),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
$product(a,$product(x,x)) = $product(98164184,$product(x,$product(x,$product(y,y)))),
inference(transitivity,[status(thm)],[27,19]) ).
tff(29,plain,
$product(644009304,$product(a,$product(x,x))) = $product(644009304,$product(98164184,$product(x,$product(x,$product(y,y))))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
$product(644009304,$product(a,$product(x,x))) = $product(63218647815567936,$product(x,$product(x,$product(y,y)))),
inference(transitivity,[status(thm)],[29,18]) ).
tff(31,plain,
( ( $product(644009304,$product(a,$product(x,x))) = $product(1509274329,$product(b,b)) )
<=> ( $product(63218647815567936,$product(x,$product(x,$product(y,y)))) = $product(63218647815567936,$product(x,$product(x,$product(y,y)))) ) ),
inference(monotonicity,[status(thm)],[30,17]) ).
tff(32,plain,
( ( $product(644009304,$product(a,$product(x,x))) = $product(1509274329,$product(b,b)) )
<=> $true ),
inference(transitivity,[status(thm)],[31,2]) ).
tff(33,plain,
( ( $product(644009304,$product(a,$product(x,x))) != $product(1509274329,$product(b,b)) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( $product(644009304,$product(a,$product(x,x))) != $product(1509274329,$product(b,b)) )
<=> $false ),
inference(transitivity,[status(thm)],[33,1]) ).
tff(35,plain,
( ( $product(644009304,$product(a,$product(x,x))) != $product(1509274329,$product(b,b)) )
<=> ( $product(644009304,$product(a,$product(x,x))) != $product(1509274329,$product(b,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( $product(5235848,$product($product($product(123,x),x),a)) != $product(12270523,$product($product(123,b),b)) )
<=> ( $product(644009304,$product(a,$product(x,x))) != $product(1509274329,$product(b,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
$product(5235848,$product($product($product(123,x),x),a)) != $product(12270523,$product($product(123,b),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(38,plain,
$product(644009304,$product(a,$product(x,x))) != $product(1509274329,$product(b,b)),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$product(644009304,$product(a,$product(x,x))) != $product(1509274329,$product(b,b)),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,plain,
$false,
inference(modus_ponens,[status(thm)],[39,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ARI700_1 : TPTP v8.1.0. Released v6.3.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n007.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 01:31:15 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.
% 4.54/2.40 % SZS status Theorem
% 4.54/2.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------