%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM014-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Sat Jun 21 05:18:41 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 0 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 390 ( 170 ~; 195 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 133 ( 121 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
tff(divides_type,type,
divides: ( $i * $i ) > $o ).
tff(square_type,type,
square: $i > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(prime_type,type,
prime: $i > $o ).
tff(1,plain,
( product(a,square(c),square(b))
<=> product(a,square(c),square(b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
product(a,square(c),square(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_squared_by_c_squared) ).
tff(3,plain,
product(a,square(c),square(b)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ product(X,Y,Z)
| divides(X,Z) )
<=> ( ~ product(X,Y,Z)
| divides(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides) ).
tff(8,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) )
| ~ product(a,square(c),square(b))
| divides(a,square(b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) )
| ~ product(a,square(c),square(b))
| divides(a,square(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) )
| ~ product(a,square(c),square(b))
| divides(a,square(b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| divides(X,Z) )
| ~ product(a,square(c),square(b))
| divides(a,square(b)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
divides(a,square(b)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [X: $i] :
refl(( product(X,X,square(X))
<=> product(X,X,square(X)) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] : product(X,X,square(X))
<=> ! [X: $i] : product(X,X,square(X)) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : product(X,X,square(X))
<=> ! [X: $i] : product(X,X,square(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [X: $i] : product(X,X,square(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square) ).
tff(19,plain,
! [X: $i] : product(X,X,square(X)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : product(X,X,square(X)),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X: $i] : product(X,X,square(X)),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [X: $i] : product(X,X,square(X))
| product(b,b,square(b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
product(b,b,square(b)),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ divides(a,b)
<=> ~ divides(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
~ divides(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divides_b) ).
tff(26,plain,
~ divides(a,b),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( prime(a)
<=> prime(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
tff(29,plain,
prime(a),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
<=> ( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U) )
<=> ( ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) )),
( ( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y) )
<=> ( ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X)
| divides(X,Y) ) )),
rewrite(( ( ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X)
| divides(X,Y) )
<=> ( divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) )),
( ( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y) )
<=> ( divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) )),
( ( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y)
| divides(X,Z) )
<=> ( divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X)
| divides(X,Z) ) )),
rewrite(( ( divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X)
| divides(X,Z) )
<=> ( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) )),
( ( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y)
| divides(X,Z) )
<=> ( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] :
( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y)
| divides(X,Z) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [Z: $i,Y: $i,U: $i,X: $i] :
( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y)
| divides(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',remainder) ).
tff(36,plain,
! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) )
<=> ( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( divides(a,b)
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) )
<=> ( divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) )
<=> ( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) )
<=> ( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [Z: $i,Y: $i,U: $i,X: $i] :
( divides(X,Y)
| divides(X,Z)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) )
| divides(a,b)
| ~ divides(a,square(b))
| ~ product(b,b,square(b))
| ~ prime(a) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,39,29,26,23,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM014-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 23:58:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------