TSTP Solution File: ARI123_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI123_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 47 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 255 ( 228 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 351 ( 147 ~; 107 |; 72 &)
% ( 23 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number arithmetic : 1245 ( 0 atm; 524 fun; 490 num; 231 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 231 ( 84 !; 133 ?; 231 :)
% Comments :
%------------------------------------------------------------------------------
tff(1,plain,
( ( ~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) )
| $false )
<=> ~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( $true
| $false
| $false
| $false
| $false )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( 0 = 0 )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
$sum(0,0) = 0,
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
$product(-1,0) = 0,
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
$product(0,0) = 0,
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
$product(-1,$product(0,0)) = $product(-1,0),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
$product(-1,$product(0,0)) = 0,
inference(transitivity,[status(thm)],[8,6]) ).
tff(10,plain,
$sum(0,$product(-1,$product(0,0))) = $sum(0,0),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
$sum(0,$product(-1,$product(0,0))) = 0,
inference(transitivity,[status(thm)],[10,5]) ).
tff(12,plain,
( ( $sum(0,$product(-1,$product(0,0))) = 0 )
<=> ( 0 = 0 ) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ( $sum(0,$product(-1,$product(0,0))) = 0 )
<=> $true ),
inference(transitivity,[status(thm)],[12,4]) ).
tff(14,plain,
( ( $sum(0,$product(-1,$product(0,0))) != 0 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( $sum(0,$product(-1,$product(0,0))) != 0 )
<=> $false ),
inference(transitivity,[status(thm)],[14,2]) ).
tff(16,plain,
$sum(0,$product(-1,0)) = $sum(0,0),
inference(monotonicity,[status(thm)],[6]) ).
tff(17,plain,
$sum(0,$product(-1,0)) = 0,
inference(transitivity,[status(thm)],[16,5]) ).
tff(18,plain,
( ( $sum(0,$product(-1,0)) = 0 )
<=> ( 0 = 0 ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( $sum(0,$product(-1,0)) = 0 )
<=> $true ),
inference(transitivity,[status(thm)],[18,4]) ).
tff(20,plain,
( ( ( $sum(0,$product(-1,0)) = 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) )
<=> ( $true
| $false
| $false
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[19,15,15,15,15]) ).
tff(21,plain,
( ( ( $sum(0,$product(-1,0)) = 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) )
<=> $true ),
inference(transitivity,[status(thm)],[20,3]) ).
tff(22,plain,
( ~ ( ( $sum(0,$product(-1,0)) = 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ~ ( ( $sum(0,$product(-1,0)) = 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) )
<=> $false ),
inference(transitivity,[status(thm)],[22,2]) ).
tff(24,plain,
( ( ~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) )
| ~ ( ( $sum(0,$product(-1,0)) = 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) ) )
<=> ( ~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) )
| $false ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) )
| ~ ( ( $sum(0,$product(-1,0)) = 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) ) )
<=> ~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) ) ),
inference(transitivity,[status(thm)],[24,1]) ).
tff(26,plain,
( ~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) )
| ~ ( ( $sum(0,$product(-1,0)) = 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 )
| ( $sum(0,$product(-1,$product(0,0))) != 0 ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
~ ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
rewrite(
( ~ ( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) )
<=> ~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) )
<=> ! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) )
<=> ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum($product(Y,X),$product(-1,Z1)) = 0 )
& ( $sum($product(Z1,Z),$product(-1,Z2)) = 0 )
& ( $sum($product(Z,Y),$product(-1,Z3)) = 0 )
& ( $sum($product(Z3,X),$product(-1,Z4)) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) )
<=> ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) )
<=> ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum($product(Y,X),$product(-1,Z1)) = 0 )
& ( $sum($product(Z1,Z),$product(-1,Z2)) = 0 )
& ( $sum($product(Z,Y),$product(-1,Z3)) = 0 )
& ( $sum($product(Z3,X),$product(-1,Z4)) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) )
<=> ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ( ( $product(X,Y) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Y,Z) = Z3 )
& ( $product(X,Z3) = Z4 ) )
=> ( Z2 = Z4 ) )
<=> ~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ( ( $product(X,Y) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Y,Z) = Z3 )
& ( $product(X,Z3) = Z4 ) )
=> ( Z2 = Z4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_product_exists) ).
tff(36,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) ),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $product(Y,X) = Z1 )
& ( $product(Z1,Z) = Z2 )
& ( $product(Z,Y) = Z3 )
& ( $product(Z3,X) = Z4 ) )
| ( Z2 = Z4 ) ),
inference(modus_ponens,[status(thm)],[38,33]) ).
tff(40,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum($product(Y,X),$product(-1,Z1)) = 0 )
& ( $sum($product(Z1,Z),$product(-1,Z2)) = 0 )
& ( $sum($product(Z,Y),$product(-1,Z3)) = 0 )
& ( $sum($product(Z3,X),$product(-1,Z4)) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ),
inference(modus_ponens,[status(thm)],[40,31]) ).
tff(42,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ),
inference(modus_ponens,[status(thm)],[41,30]) ).
tff(43,plain,
~ ? [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ),
inference(modus_ponens,[status(thm)],[42,30]) ).
tff(44,plain,
^ [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
refl(
$oeq(
~ ( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ),
~ ( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ))),
inference(bind,[status(th)],]) ).
tff(45,plain,
! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ~ ( ( $sum(Z1,$product(-1,$product(X,Y))) = 0 )
& ( $sum(Z2,$product(-1,$product(Z,Z1))) = 0 )
& ( $sum(Z3,$product(-1,$product(Y,Z))) = 0 )
& ( $sum(Z4,$product(-1,$product(X,Z3))) = 0 ) )
| ( $sum(Z2,$product(-1,Z4)) = 0 ) ),
inference(nnf-neg,[status(sab)],[43,44]) ).
tff(46,plain,
! [X: $int,Y: $int,Z: $int,Z1: $int,Z2: $int,Z3: $int,Z4: $int] :
~ ( ( $sum(Z2,$product(-1,Z4)) = 0 )
| ( $sum(Z1,$product(-1,$product(X,Y))) != 0 )
| ( $sum(Z2,$product(-1,$product(Z,Z1))) != 0 )
| ( $sum(Z3,$product(-1,$product(Y,Z))) != 0 )
| ( $sum(Z4,$product(-1,$product(X,Z3))) != 0 ) ),
inference(modus_ponens,[status(thm)],[45,29]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI123_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 22:23:15 EDT 2022
% 0.13/0.34 % 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------