TSTP Solution File: ARI119_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI119_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 17:00:43 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 40 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 184 ( 157 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 251 ( 118 ~; 59 |; 48 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number arithmetic : 316 ( 0 atm; 54 fun; 192 num; 70 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 30 !; 34 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
tff(1,plain,
( ( ~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
| $false )
<=> ~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( $false
| $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( 4 = 4 )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( 4 != 4 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ( 4 != 4 )
<=> $false ),
inference(transitivity,[status(thm)],[5,3]) ).
tff(7,plain,
( ( 16 = 16 )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
$product(4,4) = 16,
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( ( $product(4,4) = 16 )
<=> ( 16 = 16 ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( $product(4,4) = 16 )
<=> $true ),
inference(transitivity,[status(thm)],[9,7]) ).
tff(11,plain,
( ( $product(4,4) != 16 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( $product(4,4) != 16 )
<=> $false ),
inference(transitivity,[status(thm)],[11,3]) ).
tff(13,plain,
( ( ( $product(4,4) != 16 )
| ( 4 != 4 )
| ( 4 != 4 ) )
<=> ( $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[12,6,6]) ).
tff(14,plain,
( ( ( $product(4,4) != 16 )
| ( 4 != 4 )
| ( 4 != 4 ) )
<=> $false ),
inference(transitivity,[status(thm)],[13,2]) ).
tff(15,plain,
( ( ~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
| ( $product(4,4) != 16 )
| ( 4 != 4 )
| ( 4 != 4 ) )
<=> ( ~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
| $false ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( ~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
| ( $product(4,4) != 16 )
| ( 4 != 4 )
| ( 4 != 4 ) )
<=> ~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) ),
inference(transitivity,[status(thm)],[15,1]) ).
tff(17,plain,
( ~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
| ( $product(4,4) != 16 )
| ( 4 != 4 )
| ( 4 != 4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
~ ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X: $int,Y: $int] :
refl(
( ( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
<=> ( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
<=> ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [X: $int,Y: $int] :
trans(
monotonicity(
rewrite(
( ( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ~ ( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) )),
( ~ ( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ~ ~ ( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) )),
rewrite(
( ~ ~ ( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) )
<=> ( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) )),
( ~ ( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $int,Y: $int] :
~ ( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) )
<=> ~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_4_4_16) ).
tff(28,plain,
~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[30,25]) ).
tff(32,plain,
~ ? [X: $int,Y: $int] :
( ( $product(Y,X) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[31,25]) ).
tff(33,plain,
~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[32,24]) ).
tff(34,plain,
~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[33,23]) ).
tff(35,plain,
~ ? [X: $int,Y: $int] :
( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(modus_ponens,[status(thm)],[34,23]) ).
tff(36,plain,
^ [X: $int,Y: $int] :
refl(
$oeq(
~ ( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
~ ( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ))),
inference(bind,[status(th)],]) ).
tff(37,plain,
! [X: $int,Y: $int] :
~ ( ( $product(X,Y) = 16 )
& ( X = 4 )
& ( Y = 4 ) ),
inference(nnf-neg,[status(sab)],[35,36]) ).
tff(38,plain,
! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ),
inference(modus_ponens,[status(thm)],[37,22]) ).
tff(39,plain,
! [X: $int,Y: $int] :
( ( $product(X,Y) != 16 )
| ( X != 4 )
| ( Y != 4 ) ),
inference(modus_ponens,[status(thm)],[38,20]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ARI119_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 21:59:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------