TSTP Solution File: ARI690_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI690_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Theorem 0.17s 2.09s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 19 ( 7 unt; 3 typ; 0 def)
% Number of atoms : 25 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 0 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 42 ( 0 atm; 21 fun; 21 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 : 5 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $int ).
tff(a_type,type,
a: $int ).
tff(d_type,type,
d: $int ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( $product(2,d) = $product(2,d) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
$product(2,c) = $product(2,d),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( $product(2,d) = a )
<=> ( a = $product(2,d) ) ),
inference(commutativity,[status(thm)],]) ).
tff(5,plain,
( ( $product(2,d) = a )
<=> ( $product(2,d) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
$product(2,d) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq1) ).
tff(7,plain,
$product(2,d) = a,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
a = $product(2,d),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
( ( a = $product(2,c) )
<=> ( $product(2,d) = $product(2,d) ) ),
inference(monotonicity,[status(thm)],[8,3]) ).
tff(10,plain,
( ( a = $product(2,c) )
<=> $true ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,plain,
( ( a != $product(2,c) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( a != $product(2,c) )
<=> $false ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( a != $product(2,c) )
<=> ( a != $product(2,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
a != $product(2,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(15,plain,
a != $product(2,c),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
$false,
inference(modus_ponens,[status(thm)],[15,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/1.84 % Problem : ARI690_1 : TPTP v8.1.0. Released v6.3.0.
% 0.06/1.85 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/2.05 % Computer : n022.cluster.edu
% 0.11/2.05 % Model : x86_64 x86_64
% 0.11/2.05 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/2.05 % Memory : 8042.1875MB
% 0.11/2.05 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/2.05 % CPULimit : 300
% 0.11/2.05 % WCLimit : 300
% 0.11/2.05 % DateTime : Tue Aug 30 01:42:43 EDT 2022
% 0.11/2.05 % CPUTime :
% 0.11/2.05 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/2.05 Usage: tptp [options] [-file:]file
% 0.11/2.05 -h, -? prints this message.
% 0.11/2.05 -smt2 print SMT-LIB2 benchmark.
% 0.11/2.05 -m, -model generate model.
% 0.11/2.05 -p, -proof generate proof.
% 0.11/2.05 -c, -core generate unsat core of named formulas.
% 0.11/2.05 -st, -statistics display statistics.
% 0.11/2.05 -t:timeout set timeout (in second).
% 0.11/2.05 -smt2status display status in smt2 format instead of SZS.
% 0.11/2.05 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/2.05 -<param>:<value> configuration parameter and value.
% 0.11/2.05 -o:<output-file> file to place output in.
% 0.17/2.09 % SZS status Theorem
% 0.17/2.09 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------